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+

Comparing models and data

+ + + Source: vignettes/data.Rmd + + +
+ + + +

One of our aims with dust was to enable the creation of +fast particle filters. Most of the high level interface for this is +within the package mcstate. +Typically, when using a dust model with +mcstate, you would define a function in R which compares +the model state at some point in time to some data, returning a +likelihood.

+

It is possible to implement this comparison directly in the dust +model, which may slightly speed up the particle filter (because the +compare function will be evaluated in parallel, and because of slightly +reduced data copying), but also allows running the particle filter on a +GPU (see vignette("gpu")).

+

This vignette outlines the steps in implementing the comparison +directly as part of the model. This is not required for basic use of +dust models, and we would typically recommend this only after your model +has stabilised and you are looking to extract potential additional +speed-ups or accelerate the model on a GPU.

+

We start with a simple example, a model of volatility

+
+volatility <- dust::dust_example("volatility")
+

To demonstrate the approach, we simulate some data from the model +itself:

+
+data <- local({
+  mod <- volatility$new(list(alpha = 0.91, sigma = 1), 0, 1L, seed = 1L)
+  mod$update_state(state = matrix(rnorm(1L, 0, 1L), 1))
+  times <- seq(0, 100, by = 1)
+  res <- mod$simulate(times)
+  observed <- res[1, 1, -1] + rnorm(length(times) - 1, 0, 1)
+  data.frame(time = times[-1], observed = observed)
+})
+head(data)
+#>   time   observed
+#> 1    1  1.7541002
+#> 2    2  2.0385557
+#> 3    3 -0.1353818
+#> 4    4  1.0269850
+#> 5    5  4.6196833
+#> 6    6  4.2211451
+plot(observed ~ time, data, type = "o", pch = 19, las = 1)
+

+

As in the mcstate +vignette we need some way of comparing model output to data. The +likelihood function used there is:

+
+volatility_compare <- function(state, observed, pars) {
+  dnorm(observed$observed, pars$gamma * drop(state), pars$tau, log = TRUE)
+}
+

i.e., the probability is normally distributed with mean of the equal +to gamma multiplied by the modelled value, standard +deviation of tau and evaluated at the observed value. Our +aim here is to adapt this so that it is implemented as part of the C++ +model. This requires:

+
    +
  • describing the types of the observed data at each time point in a +C++ struct (here it will be a single floating-point value, but the data +could be arbitrarily complicated)
    • +
  • implementing a method to do the comparison
    • +
  • describe how to marshal the data from R into this C++ structure
    • +
+
class volatility {
+public:
+  using real_type = double;
+  using internal_type = dust::no_internal;
+  using rng_state_type = dust::random::generator<real_type>;
+
+  struct data_type {
+    real_type observed;
+  };
+
+  struct shared_type {
+    real_type alpha;
+    real_type sigma;
+    real_type gamma;
+    real_type tau;
+    real_type x0;
+  };
+
+  volatility(const dust::pars_type<volatility>& pars) : shared(pars.shared) {
+  }
+
+  size_t size() const {
+    return 1;
+  }
+
+  std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+    std::vector<real_type> state(1);
+    state[0] = shared->x0;
+    return state;
+  }
+
+  void update(size_t time, const real_type * state,
+              rng_state_type& rng_state, real_type * state_next) {
+    const real_type x = state[0];
+    state_next[0] = shared->alpha * x +
+      shared->sigma * dust::random::normal<real_type>(rng_state, 0, 1);
+  }
+
+  real_type compare_data(const real_type * state, const data_type& data,
+                         rng_state_type& rng_state) {
+    return dust::density::normal(data.observed, shared->gamma * state[0],
+                                 shared->tau, true);
+  }
+
+private:
+  dust::shared_ptr<volatility> shared;
+};
+
+// Helper function for accepting values with defaults
+inline double with_default(double default_value, cpp11::sexp value) {
+  return value == R_NilValue ? default_value : cpp11::as_cpp<double>(value);
+}
+
+namespace dust {
+
+template <>
+dust::pars_type<volatility> dust_pars<volatility>(cpp11::list pars) {
+  using real_type = volatility::real_type;
+  real_type x0 = 0;
+  real_type alpha = with_default(0.91, pars["alpha"]);
+  real_type sigma = with_default(1, pars["sigma"]);
+  real_type gamma = with_default(1, pars["gamma"]);
+  real_type tau = with_default(1, pars["tau"]);
+
+  volatility::shared_type shared{alpha, sigma, gamma, tau, x0};
+  return dust::pars_type<volatility>(shared);
+}
+
+template <>
+volatility::data_type dust_data<volatility>(cpp11::list data) {
+  return volatility::data_type{cpp11::as_cpp<double>(data["observed"])};
+}
+
+}
+

The first part, the data definition, is the definition

+
  struct data_type {
+    real_type observed;
+  };
+

which replaces the usual

+
  using data_type = dust::no_data;
+

This structure can contain whatever you want, including things like a +std::vector of values. In our use we’ve typically only had +real_type and int though, even for complex +models.

+

The comparison is implemented by the method +compare_data, which has a standard signature for the +function which takes the current state, the data at the current time +point, and the RNG state:

+
  real_type compare_data(const real_type * state, const data_type& data,
+                         rng_state_type& rng_state) {
+    return dust::density::normal(data.observed, shared->gamma * state[0],
+                                 shared->tau, true);
+  }
+

This looks very much like the R version above:

+
    +
  • +dnorm is replaced with the dust function +dust::density::normal (do not use R API functions here, as +this will be evaluated in a multi-threaded context)
    • +
  • the random number generator is available here, if your comparison is +itself stochastic
    • +
  • unlike the R version where the comparison returns a vector across +all particles, the C++ comparison is done for each particle
    • +
+

Finally, the data marshalling is done by the dust_data +template, within the dust namespace

+
namespace dust {
+template <>
+volatility::data_type dust_data<volatility>(cpp11::list data) {
+  return volatility::data_type{cpp11::as_cpp<double>(data["observed"])};
+}
+}
+

Here, you can use any function you could use from cpp11, +much like within the dust_pars template specialisation. The +input will be a list, corresponding to the data at a single time +point. The data.frame above will first be processed with +dust::dust_data, so the first few entries look like:

+
+head(dust::dust_data(data), 3)
+#> [[1]]
+#> [[1]][[1]]
+#> [1] 1
+#> 
+#> [[1]][[2]]
+#> [[1]][[2]]$time
+#> [1] 1
+#> 
+#> [[1]][[2]]$observed
+#> [1] 1.7541
+#> 
+#> 
+#> 
+#> [[2]]
+#> [[2]][[1]]
+#> [1] 2
+#> 
+#> [[2]][[2]]
+#> [[2]][[2]]$time
+#> [1] 2
+#> 
+#> [[2]][[2]]$observed
+#> [1] 2.038556
+#> 
+#> 
+#> 
+#> [[3]]
+#> [[3]][[1]]
+#> [1] 3
+#> 
+#> [[3]][[2]]
+#> [[3]][[2]]$time
+#> [1] 3
+#> 
+#> [[3]][[2]]$observed
+#> [1] -0.1353818
+

This is definitely a bit fiddly! If using odin.dust, +then this would be somewhat simplified as you could provide a single C++ +file containing something like

+
// [[odin.dust::compare_data(observed = real_type)]]
+// [[odin.dust::compare_function]]
+template <typename T>
+typename T::real_type compare(const typename T::real_type * state,
+                              const typename T::data_type& data,
+                              const typename T::internal_type internal,
+                              std::shared_ptr<const typename T::shared_type> shared,
+                              typename T::rng_state_type& rng_state) {
+  return dust::density::normal(data.observed, odin(gamma) * odin(value), 
+                               odin(tau), true);
+}
+

and the correct code would be generated (the annotations above the +function are special to odin.dust and help it build the +interface, along with the odin() calls to locate quantities +within the data structure).

+

For other examples, see the contents of the files +system.file("examples/sir.cpp", package = "dust") and +system.file("examples/sirs.cpp", package = "dust"), which +are the basis of the sir and sirs models in +dust::dust_example.

+

Once set up, the compare function can be used. First, create the +model

+
+mod <- volatility$new(list(alpha = 0.91, sigma = 1), 0, 30L)
+

We can confirm that we can use this model to compare with data:

+
+mod$has_compare()
+#> [1] TRUE
+

Next, set data into the object:

+
+mod$set_data(dust::dust_data(data))
+#> NULL
+

Then, run to any point in the data set:

+
+y <- mod$run(1)
+

We can now compute the likelihood at this point:

+
+mod$compare_data()
+#>  [1] -3.3387008 -5.0208051 -1.0854863 -1.5228963 -1.6353431 -1.3477045
+#>  [7] -2.4356686 -8.4016479 -1.8043510 -1.5870174 -3.0870610 -1.7114648
+#> [13] -3.7423972 -2.7801303 -2.7084931 -2.4693564 -5.6236678 -4.4665969
+#> [19] -2.3971334 -2.3551619 -0.9401557 -1.8258963 -1.9282897 -3.4471755
+#> [25] -5.8213962 -3.2777100 -4.4103122 -1.9954279 -1.2291336 -2.1151434
+

This will line up with the R version:

+
+volatility_compare(y, data[1, ], list(tau = 1, gamma = 1))
+#>  [1] -3.3387008 -5.0208051 -1.0854863 -1.5228963 -1.6353431 -1.3477045
+#>  [7] -2.4356686 -8.4016479 -1.8043510 -1.5870174 -3.0870610 -1.7114648
+#> [13] -3.7423972 -2.7801303 -2.7084931 -2.4693564 -5.6236678 -4.4665969
+#> [19] -2.3971334 -2.3551619 -0.9401557 -1.8258963 -1.9282897 -3.4471755
+#> [25] -5.8213962 -3.2777100 -4.4103122 -1.9954279 -1.2291336 -2.1151434
+

You can also run a basic bootstrap particle filter using this +approach:

+
+mod$update_state(pars = list(alpha = 0.91, sigma = 1), time = 0)
+res <- mod$filter(save_trajectories = TRUE)
+

This gives an overall likelihood:

+
+res$log_likelihood
+#> [1] -174.946
+

and, as we provided save_trajectories = TRUE, filtered +trajectories during the simulation:

+
+matplot(t(drop(res$trajectories)), type = "l", lty = 1, col = "#00000022")
+points(observed ~ time, data, type = "p", pch = 19, col = "blue")
+

+

Typically, you would use the much higher level interface in +mcstate for this, though.

+

Some additional work is required if you want to run the comparison on +a GPU, see vignette("gpu") for more details.

+
+

Coping with missing data +

+

In the real-world, you will have missing data. If this is possible +then the data type for your input data must be +real_type (and not int, even if it is a +count), because you will want to use std::isnan() against +the data and this is only possibly true for floating point +types.

+

We expect that the likelihood will be a sum over components per data +stream. As such, in the case of missing input data, your likelihood for +that component should be exactly zero. This way if no data streams are +present all particles will return a likelihood of exactly zero. In the +case where this happens, the particle filter will not reorder +particles.

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
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+
+ + + + +
+
+
+

Principles and design of dust

+ + + Source: vignettes/design.Rmd + + +
+ + + +

Fundamentally, using a computer to create a realisation from +stochastic Monte Carlo models is extremely simple. Consider a random +walk in one dimension - we might write that in base R functions by +creating a function that takes a current state state and a +list of parameters:

+
+update_walk <- function(state, pars) {
+  rnorm(1, state, pars$sd)
+}
+

and then iterating it for 20 time steps with:

+
+y <- 0
+pars <- list(sd = 2)
+for (i in 1:20) {
+  y <- update_walk(y, pars)
+}
+

At the end of this process, the variable y contains a +new value, corresponding to 20 time steps with our stochastic update +function.

+

So why does dust apparently require thousands of lines +of code to do this?

+
+

Running multiple realisations +

+

It’s very rare that one might want to run a single stochastic +simulation; normally we want to run a group together. There are several +ways that we might want to do that:

+
    +
  • For a single set of parameters and a starting state run a set of +simulations, as they will differ due to the stochasticity in the +model
    • +
  • In addition to the above, perhaps run with different starting +points, representing uncertainty in initial conditions
    • +
  • In addition to the above, run for many parameter sets at once +possibly with one particle per parameter, possibly with many per +parameter
    • +
  • In addition to the above, the parameters themselves are grouped into +blocks
    • +
+

There book-keeping for this can get tedious and error prone if done +by hand. In dust, we try and restrict concern about this to +a few points, and for the simulation itself – the interaction that we +expect to take the longest in any interesting model – we just run a big +loop over time and all particles no matter what type of structure they +might represent from the above.

+

See vignette("multi") for details of interacting with +different ways that you might want to structure your simulations.

+
+
+

Parallelisation +

+

Once we’re running multiple simulations at once, even a simple +simulation might start taking a long time and because they are +independent we might look to parallelism to try and speed up the +simulations.

+

However, one cannot just draw multiple numbers from a single random +number generator at once. That is, given a generator like those built +into R, there is no parallel equivalent to

+
+runif(10)
+

that would draw the 10 numbers in parallel rather than in series. +When drawing a random number there is a “side +effect” of updating the random number state. That is because the +random number stream is also a Markov chain!

+

As such it makes sense (to us at least) to store the state of each +stream’s random number generator separately, so if we have +n particles within a dust object we have +n separate streams, and we might think of the model state +as being the state that is declared by the user as a vector of floating +point numbers alongside the random number state. During each model step, +the model state is updated and so is the random number state.

+

This might seem wasteful, and if we used the popular Mersenne +Twister it would be to some degree as each particle would require +2560 bytes of additional state. In contrast the newer xoshiro generators that we use +require only 32 or 16 bytes of state; the same as 4 double- or +single-precision floating point numbers respectively. So for any +nontrivial simulation it’s not a very large overhead.

+

Setting the seed for these runs is not trivial, particularly as the +number of simultaneous particles increase. If you’ve used random numbers +with the future +package you may have seen it raise a warning if you do not configure it +to use a “L’Ecuyer-CMRG” which adapts R’s native random number seeds to +be safe in parallel.

+

The reason for this is that if different streams start from seeds +that are set via poor heuristics (e.g., system time and thread id) they +might be exactly the same. If they were set randomly, then they might +collide (see John +Cook’s description of the birthday paradox here) and if they are +picked sequentially there’s no guarantee that these streams might not be +correlated.

+

Ideally we want a similar set of properties to R’s +set.seed method; the user provides an arbitrary integer and +we seed all the random number streams using this in a way that +is reproducible and also statistically robust. We also want the streams +to be reproducible even when the number of particles changes, for +particle indices that are shared. The random number generators we use +(the xoshiro family, a.k.a. Blackmann-Vigna generators) support these +properties and are described more fully in +vignette("rng").

+

To initialise our system with a potentially very large number of +particles we take two steps:

+
    +
  • First, we seed the first stream using the splitmix64 +RNG, following the xoshiro docs. This expands a single 64-bit integer +into the 256-bits of RNG state, while ensuring that the resulting full +random number seed does not contain all zeros.
    • +
  • Then, for each subsequent chain we take a “jump” in the sequence. +This is a special move implemented by the RNG that is equivalent to a +very large number of draws from the generator (e.g., about 2^128 for the +default generator used for double-precision models) ensuring that each +particles state occupies a non-overlapping section of the underling +random number stream (see vignette("rng") for +details).
    • +
+

With this setup we are free to parallelise the system as each +realisation is completely independent of each other; the problem has +become “embarrassingly +parallel”. In practice we do this using OpenMP where available as this is +well supported from R and gracefully falls back on serial operation +where not available. See dust::dust_openmp_support for +information on your system’s OpenMP configuration as seen by R:

+
+dust::dust_openmp_support()
+#> $num_procs
+#> [1] 2
+#> 
+#> $max_threads
+#> [1] 2
+#> 
+#> $thread_limit
+#> [1] 2147483647
+#> 
+#> $openmp_version
+#> [1] 201511
+#> 
+#> $has_openmp
+#> [1] TRUE
+#> 
+#> $mc.cores
+#> [1] NA
+#> 
+#> $OMP_THREAD_LIMIT
+#> [1] NA
+#> 
+#> $OMP_NUM_THREADS
+#> [1] NA
+#> 
+#> $MC_CORES
+#> [1] NA
+#> 
+#> $limit_r
+#> [1] 1
+#> 
+#> $limit_openmp
+#> [1] 2
+#> 
+#> $limit
+#> [1] 1
+

As the number of threads changes, the results will not change; the +same calculations will be carried out and the same random numbers drawn. +The number of threads used can even be changed for a model while it is +running if the computational resources available change during a model +run, using the $set_n_threads() method.

+

Sometimes we might parallelise beyond one computer (e.g., when using +a cluster), in which case we cannot use OpenMP. We call this case +“distributed parallelism” and cope by having each process take a “long +jump” (an even larger jump in the random number space), then within the +process proceed as above. This is the approach taken in our mcstate +package for organising running MCMC chains in parallel, each of which +works with a dust model.

+

The properties of the random number generator are discussed further +in vignette("rng").

+
+
+

Efficient running +

+

A general rule-of-thumb is to avoid unneeded memory allocations in +tight loops; with this sort of stochastic iteration everything is a +tight loop! However, we’ve reduced the problem scope to just providing +an update method, and as long as that does not issue memory allocations +then the whole thing runs in fixed space without having to worry.

+
+
+

Efficient state handling +

+

For nontrivial systems, we often want to record a subset of states - +potentially a very small fraction of the total states computed. For +example, in our sircovid model we track +several thousand states (representing populations in various stages of +disease transmission, in different ages, with different vaccination +status etc), but most of the time we only need to report on a few tens +of these in order to fit to data or to examine key outputs.

+

Reducing the number of state variables returned at different points +in the process has several advantages:

+
    +
  • Saving space: if you run a model with 2000 states, 1000 replicates +and record their trajectories over 100 timesteps, that represents 100 +million floating point numbers, or 1.6 GB of memory or disk if using +double-precision numbers. These are not unrealistic numbers, but would +make even a simple sensitivity analysis all-but impossible to work +with.
    • +
  • Saving time: copying data around is surprisingly slow.
    • +
+

To enable this, you can restrict the state returned by most methods; +some by default and others when you call them.

+
    +
  • The $run() and $simulate() methods move +the system forwards in time and returns the state at that point; it uses +an index set into the object with $set_index(). The +intention here is that these would be repeatedly called and so we +validate the index once and use it over and over.
    • +
  • The $state() method returns the model state and accepts +an argument index as the state to return
    • +
+

In both cases, if index was named then the returned +state carries these names as its rownames.

+

The ordering of the state is important; we always have dimensions +that will contain:

+
    +
  1. the model states within a single particle
    2. +
  2. the particles within a time-step (may be several dimensions; see +vignette("multi"))
    3. +
  3. the time dimension if using simulate +
    4. +
+

This is to minimise repeatedly moving around data during writing, and +to help with concatenation. Multiple particles data is stored +consecutively and read and written in order. Each time step is written +at once. And you can append states from different times easily. The +base-R aperm() function will be useful for reshaping this +output to a different dimension order if you require one, but it can be +very slow.

+

In order to pull all of this off, we allocate all our memory up +front, in C++ and pass back to R a “pointer” to this memory, which will +live for as long as your model object. This means that even if your +model requires GBs of memory to run, it is never copied back and forth +into R (where it would be subject to R’s copy-on-write +semantics but instead accessed only when needed, and written to in +place following C++ reference semantics.

+
+
+

Useful verbs +

+

We try and provide verbs that are useful, given that the model +presents a largely opaque pointer to model state. These are driven by +our needs for running a particle filter.

+

Normally we have in the object several things:

+
    +
  • the random number state: this is effectively a matrix of integers +(either uint32_t or uint64_t)
    • +
  • the model state: this is effectively a matrix of floating point +numbers, (typically either float or +double)
    • +
  • the model parameters: this is specific to the model in question (and +these are likely shared across multiple particles). This is presented to +all particles within a group as an immutable pointer, which allows safe +simultaneous access by multiple threads
    • +
  • the model internal state: this is also specific to the +model and dust has no control over this. Because each particle has its +own state they can safely write to it when running parallel (compare +with parameters). Typically this space is allocated at model +construction. For models that come from odin.dust this is used +as “scratch” space that we write to during an update but which does not +conceptually persist between steps. Importantly, this space is assumed +to be unimportant to specifying model state (i.e., we can shuffle or +reset thee model state while leaving the “internal” data behind).
    • +
+

The internal state is the the hardest to understand in this set. +Suppose that we had a model that each time step we wanted to do +something like take the median value found in a set of random number +draws. We might want to write the update function like

+
  struct internal_type {
+    std::vector<real_type> samples;
+  };
+  // ...
+  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    for (size_t i = 0; i < shared->n; ++i) {
+      internal.samples[i] = dust::random::uniform(rng_state, 0, 1)
+    }
+    state_next[0] = median(samples);
+  }
+

with median defined as something like

+
template <typename T, typename U>
+T median(U& v) {
+  const size_t m = v.size() / 2;
+  std::nth_element(u.begin(), u.begin() + m, u.end());
+  return v[m];
+}
+

this takes advantage of some internal space of the correct size in +internal memory. This might be configured with

+
dust::pars_type<model> dust_pars<model>(cpp11::list pars) {
+  using real_type = typename model::real_type;
+  auto shared = std::make_shared<model::shared_type>();
+  shared->n = 10;
+  model::internal_type internal{std::vector<model::real_type>(shared->n)};
+  return dust::pars_type<model>(shared, internal);
+}
+

There is one additional subtlety about internal state: we assume that +the state entirely specifies a model in a Markov process, and so we +don’t guarantee that models with mutable internal state will not be +discarded between each iteration. Above, samples is +configured in the dust_pars method (so allocated there), +and is used in update, but it should not be read from +within the update method before it is written to, because +it might contain some other particle’s scratch space.

+

The reason why this is important is because if we reorder particles +what we really do is reorder the state vector and not this +internal state. This prevents implementing things like models with +“delays” in the current design. We may relax constraint this if it is +needed.

+

Given this, the sorts of verbs that we need include:

+
    +
  • Running the model up to a time point ($run) - runs the +model’s update method as many times as required to reach +the new time point, returning the model state at this time point. This +is useful where you might want to change the system at this time point, +then continue.
    • +
  • Running the model and collecting history ($simulate) - +as for $run but also collects partial state at a number of +times along the way. This always has one more dimension than +$run (being time) and the two functions coexist so that +dimensionality is easy to program against.
    • +
  • Setting model state ($update_state) - leaves RNG state +and parameters untouched but replaces model state for all particles. +This is useful for model initialisation and for performing arbitrary +model state and/or parameter changes.
    • +
+

In addition, we have more specific methods oriented towards particle +filtering:

+
    +
  • Reordering the particles ($reorder) - shuffles particle +state among particles within a parameter set. This is useful for +implementing a resampling algorithms and updates only the state (as for +$update_state, leaving RNG state and internal state +untouched)
    • +
  • Resampling particles according to some weight vector +($resample) which implements a bootstrap sampling algorithm +on top of $reorder +
    • +
  • Run a bootstrap particle filter ($filter) which is +implemented using the above methods, in the case where the model +provides a compare function. This is likely to be a bit low level for +direct use, and is better approached via the interface in mcstate +
    • +
+
+
+

A compilation target +

+

The most esoteric design of dust is to make it convenient to use as a +target for other programs. We use the package primarily as a target for +models written in odin via odin.dust. This allows +the user to write models at a very high level, describing the updates +between steps. The random walk example at the beginning of this document +might be implemented as

+
+sd <- user()              # user-provided standard deviation
+initial(y) <- 0           # starting point of the simulation
+update(y) <- runif(y, sd) # take random step each time step
+

which will compile a dust model:

+
// [[dust::class(odin)]]
+// [[dust::param(sd, has_default = FALSE, default_value = NULL, rank = 0, min = -Inf, max = Inf, integer = FALSE)]]
+class odin {
+public:
+  using real_type = typename model::real_type;
+  using rng_state_type = dust::random::generator<real_type> rng_state_type;
+  using data_type = dust::no_data;
+  struct shared_type {
+    real_type initial_y;
+    real_type sd;
+  };
+  struct internal_type {
+  };
+  odin(const dust::pars_type<odin>& pars) :
+    shared(pars.shared), internal(pars.internal) {
+  }
+  size_t size() {
+    return 1;
+  }
+  std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+    std::vector<real_type> state(1);
+    state[0] = shared->initial_y;
+    return state;
+  }
+  void update(size_t time, const real_type * state, rng_state_type& rng_state, real_type * state_next) {
+    const real_type y = state[0];
+    state_next[0] = dust::random::uniform<real_type>(rng_state, y, shared->sd);
+  }
+private:
+  std::shared_ptr<const shared_type> shared;
+  internal_type internal;
+};
+};
+
+// ...[some utility code excluded]
+dust::pars_type<odin> dust_pars<odin>(cpp11::list user) {
+  using real_type = typename odin::real_type;
+  auto shared = std::make_shared<odin::shared_type>();
+  odin::internal_type internal;
+  shared->initial_y = 0;
+  shared->sd = NA_REAL;
+  shared->sd = user_get_scalar<real_type>(user, "sd", shared->sd, NA_REAL, NA_REAL);
+  return dust::pars_type<odin>(shared, internal);
+}
+

We have designed these two systems to play well together so the user +can write models at a very high level and generate code that then works +well within this framework and efficiently run in parallel. In sircovid this is used in +a model with hundreds of logical compartments each of which may be +structured, but the interface at the R level remains the same as for the +toy models used in the documentation here.

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
+ + + + + + + + diff --git a/articles/dust.html b/articles/dust.html new file mode 100644 index 000000000..2c5758ca7 --- /dev/null +++ b/articles/dust.html @@ -0,0 +1,1612 @@ + + + + + + + +Introduction to dust • dust + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Introduction to dust

+ + + Source: vignettes/dust.Rmd + + +
+ + + +

Stochastic models can be used in statistical inference via methods +such as particle +filtering but in practice doing so requires that the models can be +run over and over again very quickly. While R has excellent support for +sampling from distributions, it is not necessarily well suited for this +sort of problem because R is single threaded, so we are forced to +evaluate realisations of the stochastic process in series (one after +another) rather than in parallel.

+

The dust package provides tools to help write stochastic +models that can be evaluated in parallel. It does not directly provide +statistical methods; see the mcstate package for that. +Instead, it focuses on providing:

+
    +
  • a fast random number generator that can be evaluated in parallel +(see vignette("rng") for details)
    • +
  • a way of wrapping a user-provided model, itself written as a C++ +class
    • +
  • a lightweight interface that drives this model from R
    • +
  • a set of useful primitives for developing sequential Monte Carlo +methods.
    • +
+
+

A simple example - random walk +

+

Consider a unbiased random walk; at each time step we move our +position with a draw from a normal distribution with mean 0 and some +standard deviation. We consider a single individual moving but will +eventually simulate a family of these individuals, each independent. All +simulations have a sense of time - a unitless measure of time “step” +will be used but it’s up to you how it is interpreted (time is a +non-negative integer, implemented using size_t).

+
+

Model code +

+

To implement this model in dust we write out a C++ file that looks +like:

+
class walk {
+public:
+  using real_type = double;
+  using data_type = dust::no_data;
+  using internal_type = dust::no_internal;
+  using rng_state_type = dust::random::generator<real_type>;
+
+  struct shared_type {
+    real_type sd;
+    bool random_initial;
+  };
+
+  walk(const dust::pars_type<walk>& pars) : shared(pars.shared) {
+  }
+
+  size_t size() const {
+    return 1;
+  }
+
+  std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+    std::vector<real_type> ret = {0};
+    if (shared->random_initial) {
+      ret[0] = dust::random::normal<real_type>(rng_state, 0, shared->sd);
+    }
+    return ret;
+  }
+
+  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    state_next[0] = state[0] +
+      dust::random::normal<real_type>(rng_state, 0, shared->sd);
+  }
+
+private:
+  dust::shared_ptr<walk> shared;
+};
+
+namespace dust {
+
+template <>
+dust::pars_type<walk> dust_pars<walk>(cpp11::list pars) {
+  walk::real_type sd = cpp11::as_cpp<walk::real_type>(pars["sd"]);
+  const bool random_initial = pars["random_initial"] == R_NilValue ? false :
+    cpp11::as_cpp<bool>(pars["random_initial"]);
+  return dust::pars_type<walk>(walk::shared_type{sd, random_initial});
+}
+
+}
+

There are two main parts here; the class (walk) and an +interface function (dust::dust_pars).

+

The class is what does most of the work. It is important that this +does not use anything in the R API as it may be called in parallel. +Therefore use only C++ standard library types. It has to provide every +public type or method as the example above. First, the five types:

+
    +
  • the type real_type has to exist and indicate what sort +of numeric type you use for “real numbers”. Typically this will be +double, but if you need a different type (typically +float) you can use it here.
    • +
  • the type data_type describes data that the model may be +compared with as it runs. Here we use dust::no_data as the +model has no such data but see vignette("data") for the +interface here.
    • +
  • the type shared_type is whatever read-only data your +model needs that is shared across particles. Typically these reflect +parameters of the model (see dust::dust_pars +below), and while these will typically be shared across all particles +that is is not always the case (see vignette("multi"))
    • +
  • the type internal_type is whatever internal data or +space your model needs to run. This is read-write and per-particle (in +contrast with shared_type above)
    • +
  • the type rng_state_type is one of the valid RNG types. +Typically +using rng_state_type = dust::random::generator<real_type>; +will select a reasonable choice, but you could also force a specific +generator such as dust::random::xoshiro256starstar here +(see vignette("rng"))
    • +
+

The constructor must take only one argument, being +const dust::pars_type<model>&. You can do what +you want in the constructor - here we just copy shared +(containing parameters) into the object with the pars +argument (we use the private member shared here but this +can be anything you want, though the type is important). The +dust::pars_type<> template is a wrapper that contains +two fields shared (as +dust::shared_ptr<walk>) and internal (as +internal_type).

+

The method size() must return the +“size” of the system - how many state variables it has. Here we’re +considering a single individual moving randomly so the size is always 1. +Many models will have a size that depends on their parameters, though +the size cannot be changed after construction.

+

There are other forms of the dust::pars_type constructor +which would allow specifying the internal data; typically this is used +to create scratch space (allocating vectors as needed) rather than +compute values because the scratch space and model state can become +separated from each other (by direct setting of state, or by shuffling +model state between particles).

+
+
+

Constructing a model +

+

The function dust::dust will “compile” a model for us to +use:

+
+path_walk <- system.file("examples/walk.cpp", package = "dust")
+walk <- dust::dust(path_walk)
+

However, this is also bundled into the package and can be loaded +with:

+
+walk <- dust::dust_example("walk")
+

The object itself is an “R6ClassGenerator” object:

+
+walk
+#> <dust> object generator
+#>   Public:
+#>     initialize: function (pars, time, n_particles, n_threads = 1L, seed = NULL, 
+#>     name: function () 
+#>     param: function () 
+#>     run: function (time_end) 
+#>     simulate: function (time_end) 
+#>     run_adjoint: function () 
+#>     set_index: function (index) 
+#>     index: function () 
+#>     ode_control: function () 
+#>     ode_statistics: function () 
+#>     n_threads: function () 
+#>     n_state: function () 
+#>     n_particles: function () 
+#>     n_particles_each: function () 
+#>     shape: function () 
+#>     update_state: function (pars = NULL, state = NULL, time = NULL, set_initial_state = NULL, 
+#>     state: function (index = NULL) 
+#>     time: function () 
+#>     set_stochastic_schedule: function (time) 
+#>     reorder: function (index) 
+#>     resample: function (weights) 
+#>     info: function () 
+#>     pars: function () 
+#>     rng_state: function (first_only = FALSE, last_only = FALSE) 
+#>     set_rng_state: function (rng_state) 
+#>     has_openmp: function () 
+#>     has_gpu_support: function (fake_gpu = FALSE) 
+#>     has_compare: function () 
+#>     real_size: function () 
+#>     time_type: function () 
+#>     rng_algorithm: function () 
+#>     uses_gpu: function (fake_gpu = FALSE) 
+#>     n_pars: function () 
+#>     set_n_threads: function (n_threads) 
+#>     set_data: function (data, shared = FALSE) 
+#>     compare_data: function () 
+#>     filter: function (time_end = NULL, save_trajectories = FALSE, time_snapshot = NULL, 
+#>     gpu_info: function () 
+#>   Private:
+#>     pars_: NULL
+#>     pars_multi_: NULL
+#>     index_: NULL
+#>     info_: NULL
+#>     n_threads_: NULL
+#>     n_particles_: NULL
+#>     n_particles_each_: NULL
+#>     shape_: NULL
+#>     ptr_: NULL
+#>     gpu_config_: NULL
+#>     ode_control_: NULL
+#>     methods_: NULL
+#>     param_: NULL
+#>     reload_: NULL
+#>   Parent env: <environment: namespace:dust>
+#>   Locked objects: TRUE
+#>   Locked class: FALSE
+#>   Portable: TRUE
+

Create an instance of the model using walk$new. There +are three required arguments:

+
    +
  • +pars: passed to dust_pars to initialise +the model
    • +
  • +time: the initial time (0 seems like a sensible choice +here given our model has no internal sense of time)
    • +
  • +n_particles: the number of particles to create
    • +
+
+model <- walk$new(list(sd = 1), 0, 20)
+model
+#> <dust>
+#>   Public:
+#>     compare_data: function () 
+#>     filter: function (time_end = NULL, save_trajectories = FALSE, time_snapshot = NULL, 
+#>     gpu_info: function () 
+#>     has_compare: function () 
+#>     has_gpu_support: function (fake_gpu = FALSE) 
+#>     has_openmp: function () 
+#>     index: function () 
+#>     info: function () 
+#>     initialize: function (pars, time, n_particles, n_threads = 1L, seed = NULL, 
+#>     n_pars: function () 
+#>     n_particles: function () 
+#>     n_particles_each: function () 
+#>     n_state: function () 
+#>     n_threads: function () 
+#>     name: function () 
+#>     ode_control: function () 
+#>     ode_statistics: function () 
+#>     param: function () 
+#>     pars: function () 
+#>     real_size: function () 
+#>     reorder: function (index) 
+#>     resample: function (weights) 
+#>     rng_algorithm: function () 
+#>     rng_state: function (first_only = FALSE, last_only = FALSE) 
+#>     run: function (time_end) 
+#>     run_adjoint: function () 
+#>     set_data: function (data, shared = FALSE) 
+#>     set_index: function (index) 
+#>     set_n_threads: function (n_threads) 
+#>     set_rng_state: function (rng_state) 
+#>     set_stochastic_schedule: function (time) 
+#>     shape: function () 
+#>     simulate: function (time_end) 
+#>     state: function (index = NULL) 
+#>     time: function () 
+#>     time_type: function () 
+#>     update_state: function (pars = NULL, state = NULL, time = NULL, set_initial_state = NULL, 
+#>     uses_gpu: function (fake_gpu = FALSE) 
+#>   Private:
+#>     gpu_config_: NULL
+#>     index_: NULL
+#>     info_: NULL
+#>     methods_: list
+#>     n_particles_: 20
+#>     n_particles_each_: 20
+#>     n_threads_: 1
+#>     ode_control_: NULL
+#>     param_: NULL
+#>     pars_: list
+#>     pars_multi_: FALSE
+#>     ptr_: externalptr
+#>     reload_: NULL
+#>     shape_: 20
+

This returns an R6 object that can be used to simulate from or +interact with the model. For example, our initial model state is

+
+model$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]     0     0     0     0     0     0
+

Here there is one row per model state variable (there is only one +here) and one column per particle (there are 20)

+

and we can run the model for 100 time steps, which returns the state +at the end of the walk (and not at any intermediate times):

+
+model$run(100)
+#>           [,1]      [,2]     [,3]     [,4]     [,5]      [,6]      [,7]    [,8]
+#> [1,] -1.661511 0.7103945 6.588881 3.614521 4.920547 -3.276745 -9.419317 19.2609
+#>           [,9]     [,10]    [,11]    [,12]     [,13]    [,14]     [,15]
+#> [1,] -15.55738 -1.737116 16.04619 10.00398 -3.945833 3.928595 -1.869359
+#>         [,16]        [,17]     [,18]    [,19]    [,20]
+#> [1,] 11.10058 -0.002119034 -12.97426 4.078743 2.305779
+

We can also directly retrieve the state from our object

+
+model$state()
+#>           [,1]      [,2]     [,3]     [,4]     [,5]      [,6]      [,7]    [,8]
+#> [1,] -1.661511 0.7103945 6.588881 3.614521 4.920547 -3.276745 -9.419317 19.2609
+#>           [,9]     [,10]    [,11]    [,12]     [,13]    [,14]     [,15]
+#> [1,] -15.55738 -1.737116 16.04619 10.00398 -3.945833 3.928595 -1.869359
+#>         [,16]        [,17]     [,18]    [,19]    [,20]
+#> [1,] 11.10058 -0.002119034 -12.97426 4.078743 2.305779
+

At this point our particles have been run for 100 time steps with +standard deviation 1 at each step so they will +be distributed following Normal(0, 10). This is easier to see if we +simulate a lot of particles, here 20,000:

+
+model <- walk$new(list(sd = 1), 0, 20000)
+invisible(model$run(100))
+hist(model$state(), freq = FALSE, las = 1, col = "steelblue2", main = "",
+     ylim = c(0., 0.04), xlab = "State")
+curve(dnorm(x, 0, 10), col = "orange", add = TRUE, lwd = 2)
+

+
+
+

Running a model in parallel +

+

The approach above still runs everything in serial, one particle +after another. We can configure this system to run in parallel by +providing the extra argument n_threads to the +constructor.

+

Provided that your system can compile with openmp the following code +will execute in parallel using 2 threads

+
+model <- walk$new(list(sd = 1), 0, 20, n_threads = 2)
+model$run(100)
+#>           [,1]     [,2]     [,3]      [,4]      [,5]      [,6]    [,7]
+#> [1,] -2.473672 5.281651 11.32362 -15.76064 -7.432826 -5.691623 -6.7665
+#>           [,8]      [,9]     [,10]    [,11]    [,12]     [,13]    [,14]
+#> [1,] -8.920066 -2.574631 -3.387943 7.825335 15.63247 -3.751144 12.07064
+#>          [,15]     [,16]    [,17]    [,18]     [,19]     [,20]
+#> [1,] -2.491567 -8.842425 2.683083 -10.1628 -5.794097 -6.987676
+

Running this same code in series will give the same results:

+
+model <- walk$new(list(sd = 1), 0, 20, n_threads = 1)
+model$run(100)
+#>           [,1]      [,2]      [,3]     [,4]     [,5]      [,6]     [,7]
+#> [1,] -20.65906 -4.919348 -8.372709 -14.5208 20.67429 -12.22382 7.370698
+#>           [,8]      [,9]     [,10]     [,11]    [,12]    [,13]   [,14]    [,15]
+#> [1,] -0.819519 -29.43508 -31.63771 -12.11069 5.620845 11.53523 2.83174 2.926722
+#>          [,16]     [,17]    [,18]    [,19]     [,20]
+#> [1,] -5.073199 -4.723056 11.58975 -4.39617 -11.26888
+

We use as many random number generators as there are particles, so if +you run fewer particles or more, increase the threads or decrease, the +results will be the same (see vignette("design") for more +on this).

+

You should be careful when selecting the number of threads. +dust will never use more than one thread at a time without +it being requested, but avoid using parallel::detectCores() +to work out how many threads you have available as it will often return +an overestimate. This is particularly the case in a shared-use system +such as a cluster or CRAN’s servers. We provide a helper function +dust::dust_openmp_threads which can be used to try and find +a safe number of threads available to you while respecting various +environment variables which seek to control this (MC_CORES, +OMP_THREAD_LIMIT, etc).

+

For example,

+
+dust::dust_openmp_threads(100, "fix")
+#> Requested number of threads '100' exceeds a limit of '1'
+#>  See dust::dust_openmp_threads() for details
+#> [1] 1
+
+
+
+

A more interesting example +

+

Consider now an SIR model (Susceptible - Infected - Recovered). This +sort of model is common in epidemiology, and is often extended to add +additional compartments (e.g., SEIR which adds an Exposed compartment) +or by structuring each compartment based on properties such as age. +Here, we show a simple example with just 3 compartments:

+
class sir {
+public:
+  using real_type = double;
+  using internal_type = dust::no_internal;
+  using rng_state_type = dust::random::generator<real_type>;
+  
+  struct data_type {
+    real_type incidence;
+  };
+
+  struct shared_type {
+    real_type S0;
+    real_type I0;
+    real_type R0;
+    real_type beta;
+    real_type gamma;
+    real_type dt;
+    size_t freq;
+    // Observation parameters
+    real_type exp_noise;
+  };
+
+  sir(const dust::pars_type<sir>& pars) : shared(pars.shared) {
+  }
+
+  size_t size() const {
+    return 5;
+  }
+
+  std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+    std::vector<real_type> ret = {shared->S0, shared->I0, shared->R0, 0, 0};
+    return ret;
+  }
+
+  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    real_type S = state[0];
+    real_type I = state[1];
+    real_type R = state[2];
+    real_type cumulative_incidence = state[3];
+
+    real_type N = S + I + R;
+
+    real_type p_SI = 1 - std::exp(-(shared->beta) * I / N);
+    real_type p_IR = 1 - std::exp(-(shared->gamma));
+    real_type n_IR = dust::random::binomial<real_type>(rng_state, I,
+                                                       p_IR * shared->dt);
+    real_type n_SI = dust::random::binomial<real_type>(rng_state, S,
+                                                       p_SI * shared->dt);
+
+    state_next[0] = S - n_SI;
+    state_next[1] = I + n_SI - n_IR;
+    state_next[2] = R + n_IR;
+    state_next[3] = cumulative_incidence + n_SI;
+    // Little trick here to compute daily incidence by accumulating
+    // incidence from the first day.
+    state_next[4] = (time % shared->freq == 0) ? n_SI : state[4] + n_SI;
+  }
+
+  real_type compare_data(const real_type * state, const data_type& data,
+                         rng_state_type& rng_state) {
+    const real_type incidence_observed = data.incidence;
+    if (std::isnan(data.incidence)) {
+      return 0;
+    }
+    const real_type incidence_modelled = state[4];
+    const real_type lambda = incidence_modelled +
+      dust::random::exponential(rng_state, shared->exp_noise);
+    return dust::density::poisson(incidence_observed, lambda, true);
+  }
+
+private:
+  dust::shared_ptr<sir> shared;
+};
+
+// Helper function for accepting values with defaults
+inline double with_default(double default_value, cpp11::sexp value) {
+  return value == R_NilValue ? default_value : cpp11::as_cpp<double>(value);
+}
+
+namespace dust {
+
+template <>
+dust::pars_type<sir> dust_pars<sir>(cpp11::list pars) {
+  using real_type = sir::real_type;
+  // Initial state values
+  // [[dust::param(I0, required = FALSE)]]
+  real_type I0 = with_default(10, pars["I0"]);
+  real_type S0 = 1000.0;
+  real_type R0 = 0.0;
+
+  // Rates, which can be set based on the provided pars
+  // [[dust::param(beta, required = FALSE)]]
+  real_type beta = with_default(0.2, pars["beta"]);
+  // [[dust::param(gamma, required = FALSE)]]
+  real_type gamma = with_default(0.1, pars["gamma"]);
+
+  // Time scaling
+  size_t freq = 4;
+  real_type dt = 1.0 / static_cast<real_type>(freq);
+
+  // Compare function
+  // [[dust::param(exp_noise, required = FALSE)]]
+  real_type exp_noise = with_default(1e6, pars["exp_noise"]);
+
+  sir::shared_type shared{S0, I0, R0, beta, gamma, dt, freq, exp_noise};
+  return dust::pars_type<sir>(shared);
+}
+
+template <>
+cpp11::sexp dust_info<sir>(const dust::pars_type<sir>& pars) {
+  using namespace cpp11::literals;
+  // Information about state order
+  cpp11::writable::strings vars({"S", "I", "R", "cases_cumul", "cases_inc"});
+  // Information about parameter values
+  cpp11::list p = cpp11::writable::list({"beta"_nm = pars.shared->beta,
+                                         "gamma"_nm = pars.shared->gamma});
+  return cpp11::writable::list({"vars"_nm = vars, "pars"_nm = p});
+}
+
+// The way that this is going to work is we will process a list
+// *outside* of the C that will take (say) a df and convert it
+// row-wise into a list with elements `time` and `data`, we will pass
+// that in here. Then this function will be called once per data
+// element to create the struct that will be used for future work.
+template <>
+sir::data_type dust_data<sir>(cpp11::list data) {
+  return sir::data_type{cpp11::as_cpp<sir::real_type>(data["incidence"])};
+}
+
+}
+

There a few changes here compared to the version that was shown +before for the walk model, but the core parts are only slightly +different:

+
    +
  • the initial method is slightly more complicated as we +initialise a 3-element vector
    • +
  • our shared_type object has significantly more +elements
    • +
  • the dust_pars function is much more complicated
    • +
  • there is a compare_data method and a nontrivial +data_type definition, but ignore these for now (see +vignette("data"))
    • +
+

The other difference is a new template specialisation of +dust_info - this is optional but can be used to report back +to R information about the model based on the input parameters. Here it +returns information about variable order and core parameters.

+

We also have added C++ pseudo-attributes with +[[dust::param]] to describe the parameters that this +function takes. This is optional, but allows use of a coef +method with the class (see below).

+

As before, we’ll use the version bundled with the package

+
+sir <- dust::dust_example("sir")
+

To get information about the parameters, use coef() on +the generator

+
+coef(sir)
+#> $I0
+#> $I0$required
+#> [1] FALSE
+#> 
+#> 
+#> $beta
+#> $beta$required
+#> [1] FALSE
+#> 
+#> 
+#> $gamma
+#> $gamma$required
+#> [1] FALSE
+#> 
+#> 
+#> $exp_noise
+#> $exp_noise$required
+#> [1] FALSE
+

The model is initialised the same way as before:

+
+model <- sir$new(list(), 0, 20)
+

We can use the $info() method to retrieve information +about our model:

+
+model$info()
+#> $vars
+#> [1] "S"           "I"           "R"           "cases_cumul" "cases_inc"  
+#> 
+#> $pars
+#> $pars$beta
+#> [1] 0.2
+#> 
+#> $pars$gamma
+#> [1] 0.1
+

and get its state as before:

+
+model$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,] 1000 1000 1000 1000 1000 1000 1000 1000 1000  1000  1000  1000  1000  1000
+#> [2,]   10   10   10   10   10   10   10   10   10    10    10    10    10    10
+#> [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#> [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#> [5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]  1000  1000  1000  1000  1000  1000
+#> [2,]    10    10    10    10    10    10
+#> [3,]     0     0     0     0     0     0
+#> [4,]     0     0     0     0     0     0
+#> [5,]     0     0     0     0     0     0
+

Because we have 5 states per particle, this is a 5 x 20 matrix.

+

Suppose that as we run the model we mostly want information on the +“I” compartment. So we’ll run the model for a bit and retrieve the +number of infected individuals, then continue, etc. To do this we use +the $set_index() method to indicate which state elements +should be returned after using $run():

+
+model$set_index(2L)
+

(you can pass any integer vector here, of any length, provided all +the indices lie between 1 and the length of your state vector)

+

Now, when using run, the number of infected individuals +is returned

+
+model$run(10)
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,]   17   12   16   11    9   17   12   10   14    12    11    13    12    13
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]    15    16     7    12    20    15
+model$run(20)
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,]   26   20   24   14   10   22   11   13   21    24    12    21     9    16
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]    15    22    13    12    31    20
+

This is useful when you have many compartments or variables that you +are not that interested in during running the model. For a particle +filter you might be fitting to the sum of all infected individuals over +a number of compartments, so rather than returning hundreds of values +back (times hundreds of particles) you can return back much less data +and keep things nice and fast.

+

If the index vector is named, then those names will be used as row +names on the returned object:

+
+model$set_index(c(I = 2L))
+model$run(30)
+#>   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> I   35   16   31   21    9   32   21   16   28    30    12    21     3    14
+#>   [,15] [,16] [,17] [,18] [,19] [,20]
+#> I    14    27    18    12    35    25
+

We can always use $state() to get the whole state +vector:

+
+model$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,]  958  982  965  983  992  966  981  985  974   969   990   975   991   985
+#> [2,]   35   16   31   21    9   32   21   16   28    30    12    21     3    14
+#> [3,]   17   12   14    6    9   12    8    9    8    11     8    14    16    11
+#> [4,]   42   18   35   17    8   34   19   15   26    31    10    25     9    15
+#> [5,]    4    1    4    0    0    1    1    1    1     3     0     2     1     1
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]   982   970   981   985   954   970
+#> [2,]    14    27    18    12    35    25
+#> [3,]    14    13    11    13    21    15
+#> [4,]    18    30    19    15    46    30
+#> [5,]     2     2     2     0     4     2
+

or select only variables of interest:

+
+model$state(c(S = 1L, R = 3L))
+#>   [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> S  958  982  965  983  992  966  981  985  974   969   990   975   991   985
+#> R   17   12   14    6    9   12    8    9    8    11     8    14    16    11
+#>   [,15] [,16] [,17] [,18] [,19] [,20]
+#> S   982   970   981   985   954   970
+#> R    14    13    11    13    21    15
+

Again, this copies names from the index if they are present.

+

In order to run the simulation beginning-to-end, we use the +$simulate method on a dust object, which runs over a set of +time steps and records the state at each.

+
+model <- sir$new(list(), 0, 200)
+model$set_index(2L)
+times <- seq(0, 600, by = 5)
+state <- model$simulate(times)
+

The output here is a 1 x 200 x 121 matrix (n state x n particles x n +times)

+
+dim(state)
+#> [1]   1 200 121
+

we need to drop the first dimension and transpose the others for ease +of plotting:

+
+traces <- t(drop(state))
+

Plotting this over time (with 4 time steps per day - see the sir code +above)

+
+day <- times / 4
+matplot(day, traces, type = "l", lty = 1, col = "#00000022",
+        xlab = "Day", ylab = "Number infected (I)")
+lines(day, rowMeans(traces), col = "red", lwd = 2)
+

+
+
+

Other methods +

+

There are a few other methods on the dust objects that may be +useful.

+
+

Reordering particles +

+

This method exists to support particle filtering, and allows +resampling or reordering of particles.

+
+model <- walk$new(list(sd = 1), 0, 20)
+model$run(1)
+#>           [,1]     [,2]      [,3]      [,4]      [,5]        [,6]       [,7]
+#> [1,] 0.0651394 0.405443 0.1689178 0.1463947 0.7570664 -0.04058825 -0.6361226
+#>           [,8]     [,9]     [,10]     [,11]     [,12]    [,13]      [,14]
+#> [1,] -0.833459 2.277963 -1.274942 -1.369628 0.7714373 1.344327 -0.9520035
+#>           [,15]     [,16]     [,17]      [,18]    [,19]     [,20]
+#> [1,] -0.5826929 -1.491264 0.4071681 -0.3633957 1.476874 0.0262283
+

Suppose that we wanted to reorder these particles so that they were +in decreasing order:

+
+index <- order(model$state())
+index
+#>  [1] 16 11 10 14  8  7 15 18  6 20  1  4  3  2 17  5 12 13 19  9
+

We then pass this index to the reorder method:

+
+model$reorder(index)
+model$state()
+#>           [,1]      [,2]      [,3]       [,4]      [,5]       [,6]       [,7]
+#> [1,] -1.491264 -1.369628 -1.274942 -0.9520035 -0.833459 -0.6361226 -0.5826929
+#>            [,8]        [,9]     [,10]     [,11]     [,12]     [,13]    [,14]
+#> [1,] -0.3633957 -0.04058825 0.0262283 0.0651394 0.1463947 0.1689178 0.405443
+#>          [,15]     [,16]     [,17]    [,18]    [,19]    [,20]
+#> [1,] 0.4071681 0.7570664 0.7714373 1.344327 1.476874 2.277963
+

We can then continue our random walk. There is no need to sample +every particle and particles can appear multiple times in the sample, +but the total number must be conserved. Suppose that we want to to +sample particles based on how close they are to 0:

+
+p <- dnorm(model$state())
+index <- sample(length(p), replace = TRUE , prob = p)
+index
+#>  [1]  5  4  7 18  9 18  9 16  9  1 13  9  7  5 16 13 18 16  7  8
+

We can then apply this sampling:

+
+model$reorder(index)
+model$state()
+#>           [,1]       [,2]       [,3]     [,4]        [,5]     [,6]        [,7]
+#> [1,] -0.833459 -0.9520035 -0.5826929 1.344327 -0.04058825 1.344327 -0.04058825
+#>           [,8]        [,9]     [,10]     [,11]       [,12]      [,13]     [,14]
+#> [1,] 0.7570664 -0.04058825 -1.491264 0.1689178 -0.04058825 -0.5826929 -0.833459
+#>          [,15]     [,16]    [,17]     [,18]      [,19]      [,20]
+#> [1,] 0.7570664 0.1689178 1.344327 0.7570664 -0.5826929 -0.3633957
+

This is not terribly useful on its own but is a key part of a +particle filter.

+

When this reordering happens, only the model state is copied around; +the internal data and random number state are left +behind.

+
+
+

Set particle state +

+

A particle state is determined by three mutable things; +pars, state and time; these can +all be updated for a model after it has been created. We have found +setting one or more of these at a time important;

+
    +
  • Resetting the model with a new set of parameters +(pars), initial conditions (state) and times +(time)
    • +
  • Changing pars at some point in the simulation to +introduce some new aspect of the model
    • +
  • Changing state to manually move around some individuals +within a model
    • +
  • Setting time along with state when +initialising the model from a previously saved state
    • +
+

The update_state method allows setting any or all of +these components.

+

By default every particle starts from the initial condition specified +by your model classes initial() method. However, you can +specify a state directly using the $update_state() method. +Here, we initialise our SIR model with only 1 infected individual rather +than 10:

+
+model <- sir$new(list(), 0, 20)
+model$update_state(state = c(1000, 1, 0, 0, 0))
+model$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,] 1000 1000 1000 1000 1000 1000 1000 1000 1000  1000  1000  1000  1000  1000
+#> [2,]    1    1    1    1    1    1    1    1    1     1     1     1     1     1
+#> [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#> [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#> [5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]  1000  1000  1000  1000  1000  1000
+#> [2,]     1     1     1     1     1     1
+#> [3,]     0     0     0     0     0     0
+#> [4,]     0     0     0     0     0     0
+#> [5,]     0     0     0     0     0     0
+

Now, when we run the model, far more of the epidemics fail to take +off as the infected individual goes disappears before infecting +anyone.

+
+times <- seq(0, 600, by = 5)
+state <- model$simulate(times)
+day <- times / 4
+matplot(day, t(state[2, , ]), type = "l", lty = 1, col = "#00000022",
+        xlab = "Day", ylab = "Number infected (I)")
+

+

You can optionally set the initial time along with the state. This is +useful if your model depends on time (e.g., you use the time step in a +calculation by transforming it into some more meaningful measure of +time).

+

You can also set the initial state to a range of different values. +Suppose we set the initial number of infections to be Poisson +distributed with a mean of 10, we might write:

+
+I0 <- rpois(20, 10)
+state0 <- rbind(1010 - I0, I0, 0, 0, 0, deparse.level = 0)
+model$update_state(state = state0, time = 0L)
+model$time()
+#> [1] 0
+model$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,]  994 1002 1000  993 1000  996 1001 1005 1004   997  1003  1002   998  1000
+#> [2,]   16    8   10   17   10   14    9    5    6    13     7     8    12    10
+#> [3,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#> [4,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#> [5,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#>      [,15] [,16] [,17] [,18] [,19] [,20]
+#> [1,]   999  1003   992  1002   996   997
+#> [2,]    11     7    18     8    14    13
+#> [3,]     0     0     0     0     0     0
+#> [4,]     0     0     0     0     0     0
+#> [5,]     0     0     0     0     0     0
+
+
+

Reset the model +

+

One particularly common case is to “reset” the model in order to run +it again. you should not simply recreate the model from its constructor +as that will re-seed a new set of random state – it would be preferable +continue with the generator state in your old model.

+

Suppose we run our model with sd of 1 for 100 time steps

+
+model <- walk$new(list(sd = 1), 0, 10, seed = 1L)
+y1 <- model$run(100)
+

we then use reset to set new parameters into the model +and set the time back to zero and can run again

+
+model$update_state(pars = list(sd = 2), time = 0)
+y2 <- model$run(100)
+

The state created in y2 will have started from our new +starting point and time zero, but have used the same random number state +through both simulations, which is generally what we want.

+
+
+
+

Use within a package +

+

You should not use dust::dust() within a package, +because that would cause the model to compile each time you use it, +rather than when the package builds. It may also cause issues when +trying to use the model in parallel (e.g., with the +parallel package). Instead you should use +dust::dust_package() which will generate appropriate code +for you.

+

To use dust in a package, put your dust models in +inst/dust and run dust::dust_package() on the +package’s root directory.

+

A skeleton package might contain:

+
#> .
+#> ├── DESCRIPTION
+#> ├── NAMESPACE
+#> └── inst
+#>     └── dust
+#>         └── walk.cpp
+

This is the normal R package skeleton, though missing R and src +directories (for now). The DESCRIPTION file contains

+
Package: example
+Title: Example Dust in a Package
+Version: 0.0.1
+LinkingTo: cpp11, dust
+Authors@R: c(person('A', 'Person', role = c('aut', 'cre')
+                     email = 'person@example.com'))
+License: CC0
+

The important things here are:

+
    +
  • the package name (Package). We’re using +example, and names with a dot may not work as expected
    • +
  • including cpp11 and +dust in LinkingTo, which allows package +compilation to find their respective header files
    • +
  • a useDynLib call to your package in the +NAMESPACE file
    • +
+

Our NAMESPACE file contains:

+
useDynLib('example', .registration = TRUE)
+

The files in inst/dust are the same files as seen above, +with walk.cpp containing

+
class walk {
+public:
+  using real_type = double;
+  using data_type = dust::no_data;
+  using internal_type = dust::no_internal;
+  using rng_state_type = dust::random::generator<real_type>;
+
+  struct shared_type {
+    real_type sd;
+    bool random_initial;
+  };
+
+  walk(const dust::pars_type<walk>& pars) : shared(pars.shared) {
+  }
+
+  size_t size() const {
+    return 1;
+  }
+
+  std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+    std::vector<real_type> ret = {0};
+    if (shared->random_initial) {
+      ret[0] = dust::random::normal<real_type>(rng_state, 0, shared->sd);
+    }
+    return ret;
+  }
+
+  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    state_next[0] = state[0] +
+      dust::random::normal<real_type>(rng_state, 0, shared->sd);
+  }
+
+private:
+  dust::shared_ptr<walk> shared;
+};
+
+namespace dust {
+
+template <>
+dust::pars_type<walk> dust_pars<walk>(cpp11::list pars) {
+  walk::real_type sd = cpp11::as_cpp<walk::real_type>(pars["sd"]);
+  const bool random_initial = pars["random_initial"] == R_NilValue ? false :
+    cpp11::as_cpp<bool>(pars["random_initial"]);
+  return dust::pars_type<walk>(walk::shared_type{sd, random_initial});
+}
+
+}
+

There can be as many of these files as you want within the directory +inst/dust.

+

To prepare the package, run dust::dust_package():

+
+dust::dust_package(path)
+#> ℹ 21 functions decorated with [[cpp11::register]]
+#> ✔ generated file cpp11.R
+#> ✔ generated file cpp11.cpp
+

The directory structure now has more files:

+
#> .
+#> ├── DESCRIPTION
+#> ├── NAMESPACE
+#> ├── R
+#> │   ├── cpp11.R
+#> │   └── dust.R
+#> ├── inst
+#> │   └── dust
+#> │       └── walk.cpp
+#> └── src
+#>     ├── Makevars
+#>     ├── cpp11.cpp
+#>     └── walk.cpp
+

The file src/walk.cpp are generated by dust and should +not be edited. They include your model, but also a bit of helper +code:

+
// Generated by dust (version 0.15.1) - do not edit
+#include <cpp11.hpp>
+
+[[cpp11::register]]
+cpp11::sexp dust_walk_gpu_info();
+[[cpp11::register]]
+SEXP dust_cpu_walk_alloc(cpp11::list r_pars, bool pars_multi, cpp11::sexp r_time,
+                         cpp11::sexp r_n_particles, int n_threads,
+                         cpp11::sexp r_seed, bool deterministic,
+                         cpp11::sexp gpu_config, cpp11::sexp ode_control);
+
+[[cpp11::register]]
+cpp11::sexp dust_cpu_walk_capabilities();
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_run(SEXP ptr, cpp11::sexp r_time_end);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_simulate(SEXP ptr, cpp11::sexp time_end);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_run_adjoint(SEXP ptr);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_set_index(SEXP ptr, cpp11::sexp r_index);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_update_state(SEXP ptr, SEXP r_pars, SEXP r_state,
+                                           SEXP r_time, SEXP r_set_initial_state,
+                                           SEXP index, SEXP reset_step_size);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_state(SEXP ptr, SEXP r_index);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_time(SEXP ptr);
+
+[[cpp11::register]]
+void dust_cpu_walk_reorder(SEXP ptr, cpp11::sexp r_index);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_resample(SEXP ptr, cpp11::doubles r_weights);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_rng_state(SEXP ptr, bool first_only, bool last_only);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_set_rng_state(SEXP ptr, cpp11::raws rng_state);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_set_data(SEXP ptr, cpp11::list data, bool shared);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_compare_data(SEXP ptr);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_filter(SEXP ptr, SEXP time_end,
+                                     bool save_trajectories,
+                                     cpp11::sexp time_snapshot,
+                                     cpp11::sexp min_log_likelihood);
+
+[[cpp11::register]]
+void dust_cpu_walk_set_n_threads(SEXP ptr, int n_threads);
+
+[[cpp11::register]]
+int dust_cpu_walk_n_state(SEXP ptr);
+
+[[cpp11::register]]
+void dust_cpu_walk_set_stochastic_schedule(SEXP ptr, SEXP time);
+
+[[cpp11::register]]
+SEXP dust_cpu_walk_ode_statistics(SEXP ptr);
+#include <dust/r/dust.hpp>
+
+class walk {
+public:
+  using real_type = double;
+  using data_type = dust::no_data;
+  using internal_type = dust::no_internal;
+  using rng_state_type = dust::random::generator<real_type>;
+
+  struct shared_type {
+    real_type sd;
+    bool random_initial;
+  };
+
+  walk(const dust::pars_type<walk>& pars) : shared(pars.shared) {
+  }
+
+  size_t size() const {
+    return 1;
+  }
+
+  std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+    std::vector<real_type> ret = {0};
+    if (shared->random_initial) {
+      ret[0] = dust::random::normal<real_type>(rng_state, 0, shared->sd);
+    }
+    return ret;
+  }
+
+  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    state_next[0] = state[0] +
+      dust::random::normal<real_type>(rng_state, 0, shared->sd);
+  }
+
+private:
+  dust::shared_ptr<walk> shared;
+};
+
+namespace dust {
+
+template <>
+dust::pars_type<walk> dust_pars<walk>(cpp11::list pars) {
+  walk::real_type sd = cpp11::as_cpp<walk::real_type>(pars["sd"]);
+  const bool random_initial = pars["random_initial"] == R_NilValue ? false :
+    cpp11::as_cpp<bool>(pars["random_initial"]);
+  return dust::pars_type<walk>(walk::shared_type{sd, random_initial});
+}
+
+}
+
+cpp11::sexp dust_walk_gpu_info() {
+  return dust::gpu::r::gpu_info();
+}
+using model_cpu = dust::dust_cpu<walk>;
+
+cpp11::sexp dust_cpu_walk_capabilities() {
+  return dust::r::dust_capabilities<model_cpu>();
+}
+
+SEXP dust_cpu_walk_alloc(cpp11::list r_pars, bool pars_multi, cpp11::sexp r_time,
+                             cpp11::sexp r_n_particles, int n_threads,
+                             cpp11::sexp r_seed, bool deterministic,
+                             cpp11::sexp gpu_config, cpp11::sexp ode_control) {
+  return dust::r::dust_cpu_alloc<walk>(r_pars, pars_multi, r_time, r_n_particles,
+                                        n_threads, r_seed, deterministic,
+                                        gpu_config, ode_control);
+}
+
+SEXP dust_cpu_walk_run(SEXP ptr, cpp11::sexp r_time_end) {
+  return dust::r::dust_run<model_cpu>(ptr, r_time_end);
+}
+
+SEXP dust_cpu_walk_simulate(SEXP ptr, cpp11::sexp r_time_end) {
+  return dust::r::dust_simulate<model_cpu>(ptr, r_time_end);
+}
+
+SEXP dust_cpu_walk_run_adjoint(SEXP ptr) {
+  return dust::r::dust_run_adjoint<model_cpu>(ptr);
+}
+
+SEXP dust_cpu_walk_set_index(SEXP ptr, cpp11::sexp r_index) {
+  dust::r::dust_set_index<model_cpu>(ptr, r_index);
+  return R_NilValue;
+}
+
+SEXP dust_cpu_walk_update_state(SEXP ptr, SEXP r_pars, SEXP r_state,
+                                           SEXP r_time, SEXP r_set_initial_state, SEXP index, SEXP reset_step_size) {
+  return dust::r::dust_update_state<model_cpu>(ptr, r_pars, r_state, r_time,
+                                                      r_set_initial_state, index, reset_step_size);
+}
+
+SEXP dust_cpu_walk_state(SEXP ptr, SEXP r_index) {
+  return dust::r::dust_state<model_cpu>(ptr, r_index);
+}
+
+SEXP dust_cpu_walk_time(SEXP ptr) {
+  return dust::r::dust_time<model_cpu>(ptr);
+}
+
+void dust_cpu_walk_reorder(SEXP ptr, cpp11::sexp r_index) {
+  return dust::r::dust_reorder<model_cpu>(ptr, r_index);
+}
+
+SEXP dust_cpu_walk_resample(SEXP ptr, cpp11::doubles r_weights) {
+  return dust::r::dust_resample<model_cpu>(ptr, r_weights);
+}
+
+SEXP dust_cpu_walk_rng_state(SEXP ptr, bool first_only, bool last_only) {
+  return dust::r::dust_rng_state<model_cpu>(ptr, first_only, last_only);
+}
+
+SEXP dust_cpu_walk_set_rng_state(SEXP ptr, cpp11::raws rng_state) {
+  dust::r::dust_set_rng_state<model_cpu>(ptr, rng_state);
+  return R_NilValue;
+}
+
+SEXP dust_cpu_walk_set_data(SEXP ptr, cpp11::list data,
+                                       bool shared) {
+  dust::r::dust_set_data<model_cpu>(ptr, data, shared);
+  return R_NilValue;
+}
+
+SEXP dust_cpu_walk_compare_data(SEXP ptr) {
+  return dust::r::dust_compare_data<model_cpu>(ptr);
+}
+
+SEXP dust_cpu_walk_filter(SEXP ptr, SEXP time_end,
+                                     bool save_trajectories,
+                                     cpp11::sexp time_snapshot,
+                                     cpp11::sexp min_log_likelihood) {
+  return dust::r::dust_filter<model_cpu>(ptr, time_end,
+                                                save_trajectories,
+                                                time_snapshot,
+                                                min_log_likelihood);
+}
+
+void dust_cpu_walk_set_n_threads(SEXP ptr, int n_threads) {
+  return dust::r::dust_set_n_threads<model_cpu>(ptr, n_threads);
+}
+
+int dust_cpu_walk_n_state(SEXP ptr) {
+  return dust::r::dust_n_state<model_cpu>(ptr);
+}
+
+void dust_cpu_walk_set_stochastic_schedule(SEXP ptr, SEXP time) {
+  dust::r::dust_set_stochastic_schedule<model_cpu>(ptr, time);
+}
+
+SEXP dust_cpu_walk_ode_statistics(SEXP ptr) {
+  return dust::r::dust_ode_statistics<model_cpu>(ptr);
+}
+

The file R/dust.R contains the R interface generated by +dust with the constructor objects (all models’ constructors will be +collected into this file, which also should not be edited).

+
+## Generated by dust (version 0.15.1) - do not edit
+walk <- R6::R6Class(
+  "dust",
+  cloneable = FALSE,
+
+  private = list(
+    pars_ = NULL,
+    pars_multi_ = NULL,
+    index_ = NULL,
+    info_ = NULL,
+    n_threads_ = NULL,
+    n_particles_ = NULL,
+    n_particles_each_ = NULL,
+    shape_ = NULL,
+    ptr_ = NULL,
+    gpu_config_ = NULL,
+    ode_control_ = NULL,
+    methods_ = NULL,
+    param_ = NULL,
+    reload_ = NULL
+  ),
+
+  public = list(
+    initialize = function(pars, time, n_particles, n_threads = 1L,
+                          seed = NULL, pars_multi = FALSE,
+                          deterministic = FALSE,
+                          gpu_config = NULL, ode_control = NULL) {
+      if (is.null(gpu_config)) {
+        private$methods_ <- list(
+           alloc = dust_cpu_walk_alloc,
+           run = dust_cpu_walk_run,
+           simulate = dust_cpu_walk_simulate,
+           run_adjoint = dust_cpu_walk_run_adjoint,
+           set_index = dust_cpu_walk_set_index,
+           n_state = dust_cpu_walk_n_state,
+           update_state = dust_cpu_walk_update_state,
+           state = dust_cpu_walk_state,
+           time = dust_cpu_walk_time,
+           reorder = dust_cpu_walk_reorder,
+           resample = dust_cpu_walk_resample,
+           rng_state = dust_cpu_walk_rng_state,
+           set_rng_state = dust_cpu_walk_set_rng_state,
+           set_n_threads = dust_cpu_walk_set_n_threads,
+           set_data = dust_cpu_walk_set_data,
+           compare_data = dust_cpu_walk_compare_data,
+           filter = dust_cpu_walk_filter,
+           set_stochastic_schedule = dust_cpu_walk_set_stochastic_schedule,
+           ode_statistics = dust_cpu_walk_ode_statistics)
+      } else {
+        private$methods_ <- list(alloc = function(...) {
+          stop("GPU support not enabled for this object")
+        })
+      }
+      res <- private$methods_$alloc(pars, pars_multi, time, n_particles,
+                        n_threads, seed, deterministic, gpu_config, ode_control)
+      private$pars_ <- pars
+      private$pars_multi_ <- pars_multi
+      private$n_threads_ <- n_threads
+      private$ptr_ <- res[[1L]]
+      private$info_ <- res[[2L]]
+      private$shape_ <- res[[3L]]
+      private$gpu_config_ <- res[[4L]]
+      private$ode_control_ <- res[[5L]]
+      private$n_particles_ <- prod(private$shape_)
+      if (pars_multi) {
+        private$n_particles_each_ <- private$n_particles_ / length(pars)
+      } else {
+        private$n_particles_each_ <- private$n_particles_
+      }
+    },
+
+    name = function() {
+      "walk"
+    },
+
+    param = function() {
+      private$param_
+    },
+
+    run = function(time_end) {
+      m <- private$methods_$run(private$ptr_, time_end)
+      rownames(m) <- names(private$index_)
+      m
+    },
+
+    simulate = function(time_end) {
+      m <- private$methods_$simulate(private$ptr_, time_end)
+      rownames(m) <- names(private$index_)
+      m
+    },
+
+    run_adjoint = function() {
+      res <- private$methods_$run_adjoint(private$ptr_)
+      ## This approach may want to change, because it won't cope well
+      ## with cases where are gradient is structured with respect to
+      ## some parameters, but perhaps it's still a reasonable thing to
+      ## do? While we have array-free models it's fine though.
+      nms <- private$info_$adjoint
+      if (!is.null(nms) && length(nms) == length(res$gradient)) {
+        names(res$gradient) <- nms
+      }
+      res
+    },
+
+    set_index = function(index) {
+      private$methods_$set_index(private$ptr_, index)
+      private$index_ <- index
+      invisible()
+    },
+
+    index = function() {
+      private$index_
+    },
+
+    ode_control = function() {
+      private$ode_control_
+    },
+
+    ode_statistics = function() {
+      private$methods_$ode_statistics(private$ptr_)
+    },
+
+    n_threads = function() {
+      private$n_threads_
+    },
+
+    n_state = function() {
+      private$methods_$n_state(private$ptr_)
+    },
+
+    n_particles = function() {
+      private$n_particles_
+    },
+
+    n_particles_each = function() {
+      private$n_particles_each_
+    },
+
+    shape = function() {
+      private$shape_
+    },
+
+    update_state = function(pars = NULL, state = NULL, time = NULL,
+                            set_initial_state = NULL, index = NULL,
+                            reset_step_size = NULL) {
+      info <- private$methods_$update_state(private$ptr_, pars, state, time,
+                                          set_initial_state, index,
+                                          reset_step_size)
+      if (!is.null(pars)) {
+        private$info_ <- info
+        private$pars_ <- pars
+      }
+      invisible()
+    },
+
+    state = function(index = NULL) {
+      m <- private$methods_$state(private$ptr_, index)
+      rownames(m) <- names(index)
+      m
+    },
+
+    time = function() {
+      private$methods_$time(private$ptr_)
+    },
+
+    set_stochastic_schedule = function(time) {
+      private$methods_$set_stochastic_schedule(private$ptr_, time)
+      invisible()
+    },
+
+    reorder = function(index) {
+      storage.mode(index) <- "integer"
+      private$methods_$reorder(private$ptr_, index)
+      invisible()
+    },
+
+    resample = function(weights) {
+      invisible(private$methods_$resample(private$ptr_, weights))
+    },
+
+    info = function() {
+      private$info_
+    },
+
+    pars = function() {
+      private$pars_
+    },
+
+    rng_state = function(first_only = FALSE, last_only = FALSE) {
+      private$methods_$rng_state(private$ptr_, first_only, last_only)
+    },
+
+    set_rng_state = function(rng_state) {
+      private$methods_$set_rng_state(private$ptr_, rng_state)
+      invisible()
+    },
+
+    has_openmp = function() {
+      dust_cpu_walk_capabilities()[["openmp"]]
+    },
+
+    has_gpu_support = function(fake_gpu = FALSE) {
+      if (fake_gpu) {
+        FALSE
+      } else {
+        dust_cpu_walk_capabilities()[["gpu"]]
+      }
+    },
+
+    has_compare = function() {
+      dust_cpu_walk_capabilities()[["compare"]]
+    },
+
+    real_size = function() {
+      dust_cpu_walk_capabilities()[["real_size"]]
+    },
+
+    time_type = function() {
+      dust_cpu_walk_capabilities()[["time_type"]]
+    },
+
+    rng_algorithm = function() {
+      dust_cpu_walk_capabilities()[["rng_algorithm"]]
+    },
+
+    uses_gpu = function(fake_gpu = FALSE) {
+      real_gpu <- private$gpu_config_$real_gpu
+      !is.null(real_gpu) && (fake_gpu || real_gpu)
+    },
+
+    n_pars = function() {
+      if (private$pars_multi_) length(private$pars_) else 0L
+    },
+
+    set_n_threads = function(n_threads) {
+      prev <- private$n_threads_
+      private$methods_$set_n_threads(private$ptr_, n_threads)
+      private$n_threads_ <- n_threads
+      invisible(prev)
+    },
+
+    set_data = function(data, shared = FALSE) {
+      private$methods_$set_data(private$ptr_, data, shared)
+    },
+
+    compare_data = function() {
+      private$methods_$compare_data(private$ptr_)
+    },
+
+    filter = function(time_end = NULL, save_trajectories = FALSE,
+                      time_snapshot = NULL, min_log_likelihood = NULL) {
+      private$methods_$filter(private$ptr_, time_end, save_trajectories,
+                              time_snapshot, min_log_likelihood)
+    },
+
+    gpu_info = function() {
+      ret <- dust_walk_gpu_info()
+      ret$devices <- as.data.frame(ret$devices, stringsAsFactors = FALSE)
+      parent <- parent.env(environment())
+      if (ret$has_cuda && exists("private", parent, inherits = FALSE)) {
+        ret$config <- private$gpu_config_
+      }
+      ret
+    }
+  ))
+class(walk) <- c("dust_generator", class(walk))
+

Finally, R/cpp11.R and src/cpp11.cpp are +files created by cpp11 that should not be edited.

+

Your package can include as much R code as you want, and can be +developed like any other R package. But any time you change the code in +inst/dust you should rerun +dust::dust_package().

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
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+Running models on GPUs with CUDA • dust + + + + + + + + + + + + + + + + + + + +

+
+ + + + +
+
+
+

Running models on GPUs with CUDA

+ + + Source: vignettes/gpu.Rmd + + +
+ + + + +

With the core approach in dust, you can run models in parallel +efficiently up to the number of cores your workstation has available. +Getting more than 32 or 64 cores is hard though, and dust +provides no multi-node parallelism (e.g., MPI). +Instead, we have developed a system for running dust models +on GPUs (graphical processing units), specifically NVIDIA GPUs via CUDA +(Compute Unified Device Architecture).

+

This vignette is written in reverse-order, starting with how to run a +model on a GPU, before covering how to write a dust model +that can be run on a GPU. The reason for this is that we do not expect +that people will write these directly; instead we expect that most +people will use the odin.dust +package to generate these interfaces automatically, without having to +write a single line of C++ or CUDA code.

+
+

Principles +

+
    +
  • A GPU model can be run on the CPU, and vice-versa.
    • +
  • The same random number generator sequence will be used in both +cases.
    • +
  • Differences in results, if they exist, come from different +precision/rounding between compute platforms. When using +real_type = double we want to get the same results.
    • +
  • Just the model update can be defined for the GPU, and comparisons +and shuffling could still happen on the CPU. Defining a comparison +function is also possible, allowing a full particle filter run on a +GPU.
    • +
+
+
+

Running a model with GPU support +

+

The sirs model includes GPU support, and will be the +focus of this vignette. However, the installed version cannot be run +directly on the GPU for a couple of reasons:

+
    +
  • this would complicate distribution of binaries as we’d depend on all +systems having a copy of the CUDA runtime
    • +
  • we would have to compile support for many possible GPU architectures +at once
    • +
  • it is very likely that we’d want to run the model in single +precision (float) mode rather than double precision +(double), and changing that requires re-compilation
    • +
+

In addition, you will also need:

+
    +
  • CUDA toolkit v10.2 or higher, v11.1 or higher preferred (compile +time and run time)
    • +
  • CUDA capable GPU (run time)
    • +
  • nvidia drivers (run time)
    • +
+

You can check with the command-line tool nvidia-smi if +you have suitable hardware and drivers and with +dust::dust_cuda_configuration(quiet = FALSE, forget = TRUE) +if you have suitable build tools.

+

So here, rather than using dust::dust_example, we +compile the model and pass in arguments:

+
+path <- system.file("examples/sirs.cpp", package = "dust")
+sirs <- dust::dust(path, gpu = TRUE, real_type = "float")
+#> ℹ 34 functions decorated with [[cpp11::register]]
+#> ✔ generated file 'cpp11.R'
+#> ✔ generated file 'cpp11.cpp'
+#> Re-compiling sirs817bc717gpu
+#>   ─  installing *source* package ‘sirs817bc717gpu’ ...
+#>      ** using staged installation
+#>      ** libs
+#>      make[1]: Entering directory '/tmp/RtmppiOue1/fileb32bb676504e5/src'
+#>      make[1]: Leaving directory '/tmp/RtmppiOue1/fileb32bb676504e5/src'
+#>      make[1]: Entering directory '/tmp/RtmppiOue1/fileb32bb676504e5/src'
+#>    g++ -std=gnu++14 -I"/usr/share/R/include" -DNDEBUG  -I'/home/rfitzjoh/lib/R/library/cpp11/include' -g -Wall -Wextra -pedantic -Wmaybe-uninitialized -Wno-unused-parameter -Wno-cast-function-type -Wno-missing-field-initializers -O2  -I/home/rfitzjoh/lib/R/library/dust/include -DHAVE_INLINE -fopenmp -fpic  -g -O2 -fdebug-prefix-map=/build/r-base-QwogzP/r-base-4.1.1=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -g  -c cpp11.cpp -o cpp11.o
+#>      nvcc -std=c++14 -O2 -I. -I/usr/share/R/include -I/home/rfitzjoh/lib/R/library/dust/include -I/home/rfitzjoh/.local/share/R/dust/cub -I'/home/rfitzjoh/lib/R/library/cpp11/include' -gencode=arch=compute_75,code=sm_75 -Xcompiler -fPIC -Xcompiler -fopenmp -x cu -c dust.cu -o dust.o
+#>      g++ -std=gnu++14 -shared -L/usr/lib/R/lib -Wl,-Bsymbolic-functions -Wl,-z,relro -o sirs817bc717gpu.so cpp11.o dust.o -lcudart -fopenmp -L/usr/lib/R/lib -lR
+#>      make[1]: Leaving directory '/tmp/RtmppiOue1/fileb32bb676504e5/src'
+#>      installing to /tmp/RtmppiOue1/devtools_install_b32bb69aa2d4d/00LOCK-fileb32bb676504e5/00new/sirs817bc717gpu/libs
+#>      ** checking absolute paths in shared objects and dynamic libraries
+#>   ─  DONE (sirs817bc717gpu)
+#>
+#> ℹ Loading sirs817bc717gpu
+

Notice in compilation that nvcc is used to compile the +model, rather than g++ or clang++. The +additional option -gencode=arch=compute_XX,code=sm_XX was +added by dust and will include the CUDA compute version +supported by the graphics cards found on the current system. You can use +dust::dust_cuda_options to set additional options, passing +in the return value for the gpu argument above.

+

Once compiled with GPU support, the static method +has_gpu_support will report TRUE:

+
+sirs$public_methods$has_gpu_support()
+#> [1] TRUE
+

and the static method gpu_info will report on the GPU +devices available:

+
+sirs$public_methods$gpu_info()
+#> $has_cuda
+#> [1] TRUE
+#>
+#> $cuda_version
+#> [1] '10.1.243'
+#>
+#> $devices
+#>   id                name   memory version
+#> 1  0 GeForce RTX 2080 Ti 11016.31      75
+

If you have more than one GPU, the id in the +devices section will be useful for targeting the correct +device.

+

The object is initialised as usual but with slight differences:

+
    +
  • you will probably want a (much) larger number of particles to take +advantage of your GPU. As a rule of thumb we would suggest at least +10,000, but depending on model and card you may still see per-particle +increases in compute speed as you use up to 1,000,000 particles. See +below for more discussion of this.
    • +
  • the gpu_config argument needs to be provided to +indicate which GPU device we are running on. Minimally this is an +integer indicating the device that you want to use (on this machine the +only option is 0), but you can also provide a list with +elements device_id and run_block_size.
    • +
+
+pars <- list()
+n_particles <- 8192
+model_gpu <- sirs$new(pars, 0, n_particles, gpu_config = 0L, seed = 1L)
+

Once initialised, a model can only be run on either the GPU or CPU, +so we’ll create a CPU version here for comparison:

+
+model_cpu <- sirs$new(pars, 0, n_particles, seed = 1L)
+

By leaving gpu_config as NULL we indicate +that the model should run on the CPU.

+

Once created, the uses_gpu method indicates if the model +is set up to run on the GPU (rather than CPU):

+
+model_gpu$uses_gpu()
+#> [1] TRUE
+model_cpu$uses_gpu()
+#> [1] FALSE
+

Running the model on the CPU is fairly slow as this is a lot of +particles and we’re not running in parallel:

+
+(t_cpu <- system.time(model_cpu$run(400)))
+#>    user  system elapsed
+#>   0.451   0.000   0.451
+

Running the model on the GPU however:

+
+(t_gpu <- system.time(model_gpu$run(400)))
+#>    user  system elapsed
+#>   0.008   0.000   0.008
+

This is much faster! However, ~8,000 particles is unlikely to +saturate a modern GPU and (overhead-aside) this will run about as +quickly for potentially a hundred thousand particles. For example +running 2^17 (131,072) particles only takes a little longer

+
+model_large <- sirs$new(list(), 0, 2^17, gpu_config = 0L, seed = 1L)
+(t_large <- system.time(model_large$run(400)))
+#>    user  system elapsed
+#>   0.033   0.000   0.033
+

This is heaps faster, the GPU model ran in 7.3% of +the time as the CPU model but simulated 16 times as many particles +(i.e., 219 times as fast per particle). With the relatively low times +here, much of this time is just moving the data around, and with over a +hundred thousand particles this is nontrivial. Of course, doing +anything quickly with all these particles is its own problem.

+

All methods will automatically run on the GPU; this includes +run, simulate, compare_data and +filter. The last two are typically used from the mcstate +interface.

+
+
+

Writing a GPU-capable model +

+

The sirs model from above:

+
class sirs {
+public:
+  using real_type = double;
+  using internal_type = dust::no_internal;
+  using rng_state_type = dust::random::generator<real_type>;
+
+  // __align__(16) is required before the data_type definition when using NVCC
+  // This is so when loaded into shared memory it is aligned correctly
+  struct __align__(16) data_type {
+    double incidence;
+  };
+
+  struct shared_type {
+    real_type S0;
+    real_type I0;
+    real_type R0;
+    real_type alpha;
+    real_type beta;
+    real_type gamma;
+    real_type dt;
+    size_t freq;
+    real_type exp_noise;
+  };
+
+  sirs(const dust::pars_type<sirs>& pars): shared(pars.shared) {
+  }
+
+  size_t size() {
+    return 4;
+  }
+
+  std::vector<real_type> initial(size_t time) {
+    std::vector<real_type> state(4);
+    state[0] = shared->S0;
+    state[1] = shared->I0;
+    state[2] = shared->R0;
+    state[3] = 0;
+    return state;
+  }
+
+  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    real_type S = state[0];
+    real_type I = state[1];
+    real_type R = state[2];
+    real_type N = S + I + R;
+
+    real_type p_SI = 1 - exp(- shared->beta * I / N);
+    real_type p_IR = 1 - exp(-(shared->gamma));
+    real_type p_RS = 1 - exp(- shared->alpha);
+
+    real_type dt = shared->dt;
+    real_type n_SI = dust::random::binomial<real_type>(rng_state, S, p_SI * dt);
+    real_type n_IR = dust::random::binomial<real_type>(rng_state, I, p_IR * dt);
+    real_type n_RS = dust::random::binomial<real_type>(rng_state, R, p_RS * dt);
+
+    state_next[0] = S - n_SI + n_RS;
+    state_next[1] = I + n_SI - n_IR;
+    state_next[2] = R + n_IR - n_RS;
+    state_next[3] = (time % shared->freq == 0) ? n_SI : state[3] + n_SI;
+  }
+
+  real_type compare_data(const real_type * state, const data_type& data,
+                         rng_state_type& rng_state) {
+    const real_type incidence_modelled = state[3];
+    const real_type incidence_observed = data.incidence;
+    const real_type lambda = incidence_modelled +
+      dust::random::exponential<real_type>(rng_state, shared->exp_noise);
+    return dust::density::poisson(incidence_observed, lambda, true);
+  }
+
+private:
+  dust::shared_ptr<sirs> shared;
+};
+
+// Helper function for accepting values with defaults
+inline double with_default(double default_value, cpp11::sexp value) {
+  return value == R_NilValue ? default_value : cpp11::as_cpp<double>(value);
+}
+
+namespace dust {
+template <>
+dust::pars_type<sirs> dust_pars<sirs>(cpp11::list pars) {
+  // Initial state values
+  sirs::real_type I0 = 10.0;
+  sirs::real_type S0 = 1000.0;
+  sirs::real_type R0 = 0.0;
+
+  // Time scaling
+  // [[dust::param(freq, required = FALSE, default = 1)]]
+  size_t freq = std::max(1.0, with_default(1.0, pars["freq"]));
+  sirs::real_type dt = 1 / static_cast<sirs::real_type>(freq);
+
+  sirs::real_type exp_noise = 1e6;
+
+  // [[dust::param(alpha, required = FALSE, default = 0.1)]]
+  sirs::real_type alpha = with_default(0.1, pars["alpha"]);
+
+  // [[dust::param(beta, required = FALSE, default = 0.2)]]
+  sirs::real_type beta = with_default(0.2, pars["beta"]);
+
+  // [[dust::param(gamma, required = FALSE, default = 0.1)]]
+  sirs::real_type gamma = with_default(0.1, pars["gamma"]);
+
+  sirs::shared_type shared{S0, I0, R0, alpha, beta, gamma, dt, freq, exp_noise};
+  return dust::pars_type<sirs>(shared);
+}
+
+template <>
+sirs::data_type dust_data<sirs>(cpp11::list data) {
+  return sirs::data_type{cpp11::as_cpp<double>(data["incidence"])};
+}
+
+namespace gpu {
+
+template <>
+size_t shared_int_size<sirs>(dust::shared_ptr<sirs> shared) {
+  return 1;
+}
+
+template <>
+size_t shared_real_size<sirs>(dust::shared_ptr<sirs> shared) {
+  return 5;
+}
+
+template <>
+void shared_copy<sirs>(dust::shared_ptr<sirs> shared,
+                       int * shared_int,
+                       sirs::real_type * shared_real) {
+  using real_type = sirs::real_type;
+  using dust::gpu::shared_copy_data;
+  shared_real = shared_copy_data<real_type>(shared_real, shared->alpha);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->beta);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->gamma);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->dt);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->exp_noise);
+  shared_int = shared_copy_data<int>(shared_int, shared->freq);
+}
+
+template <>
+__device__
+void update_gpu<sirs>(size_t time,
+                      const dust::gpu::interleaved<sirs::real_type> state,
+                      dust::gpu::interleaved<int> internal_int,
+                      dust::gpu::interleaved<sirs::real_type> internal_real,
+                      const int * shared_int,
+                      const sirs::real_type * shared_real,
+                      sirs::rng_state_type& rng_state,
+                      dust::gpu::interleaved<sirs::real_type> state_next) {
+  using dust::random::binomial;
+  using real_type = sirs::real_type;
+  const real_type alpha = shared_real[0];
+  const real_type beta = shared_real[1];
+  const real_type gamma = shared_real[2];
+  const real_type dt = shared_real[3];
+  const int freq = shared_int[0];
+  const real_type S = state[0];
+  const real_type I = state[1];
+  const real_type R = state[2];
+  const real_type N = S + I + R;
+  const real_type p_SI = 1 - exp(- beta * I / N);
+  const real_type p_IR = 1 - exp(- gamma);
+  const real_type p_RS = 1 - exp(- alpha);
+  const real_type n_SI = binomial<real_type>(rng_state, S, p_SI * dt);
+  const real_type n_IR = binomial<real_type>(rng_state, I, p_IR * dt);
+  const real_type n_RS = binomial<real_type>(rng_state, R, p_RS * dt);
+  state_next[0] = S - n_SI + n_RS;
+  state_next[1] = I + n_SI - n_IR;
+  state_next[2] = R + n_IR - n_RS;
+  state_next[3] = (time % freq == 0) ? n_SI : state[3] + n_SI;
+}
+
+template <>
+__device__
+sirs::real_type compare_gpu<sirs>(const dust::gpu::interleaved<sirs::real_type> state,
+                                  const sirs::data_type& data,
+                                  dust::gpu::interleaved<int> internal_int,
+                                  dust::gpu::interleaved<sirs::real_type> internal_real,
+                                  const int * shared_int,
+                                  const sirs::real_type * shared_real,
+                                  sirs::rng_state_type& rng_state) {
+  using real_type = sirs::real_type;
+  const real_type exp_noise = shared_real[4];
+  const real_type incidence_modelled = state[3];
+  const real_type incidence_observed = data.incidence;
+  const real_type lambda = incidence_modelled +
+    dust::random::exponential<real_type>(rng_state, exp_noise);
+  return dust::density::poisson(incidence_observed, lambda, true);
+}
+
+}
+}
+

This is somewhat more complicated than the models described in +vignette("dust.Rmd"). There are several important +components required to run on the GPU.

+

Within the dust::gpu namespace, we declare the size of +the shared parameters for the model. These are parameters that +will be the same across all instances of a parameter set, as opposed to +quantities that change between particles.

+
namespace dust {
+namespace gpu {
+template <>
+size_t shared_int_size<sirs>(dust::shared_ptr<sirs> shared) {
+  return 1;
+}
+
+template <>
+size_t shared_real_size<sirs>(dust::shared_ptr<sirs> shared) {
+  return 5;
+}
+}
+}
+

These can be omitted if your model has no such parameters.

+

The next definition makes the above a bit clearer, it defines the +method for copying these parameters

+
namespace dust {
+namespace gpu {
+template <>
+void shared_copy<sirs>(dust::shared_ptr<sirs> shared,
+                       int * shared_int,
+                       sirs::real_type * shared_real) {
+  using real_type = sirs::real_type;
+  using dust::gpu::shared_copy_data;
+  shared_real = shared_copy_data<real_type>(shared_real, shared->alpha);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->beta);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->gamma);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->dt);
+  shared_real = shared_copy_data<real_type>(shared_real, shared->exp_noise);
+  shared_int = shared_copy_data<int>(shared_int, shared->freq);
+}
+}
+}
+

In the CPU version of the model we have a nice smart pointer to a +struct (dust::shared_ptr<sirs>) from which we can +access parameters by name (e.g., shared->alpha). No such +niceties in CUDA where we need access to a single contiguous block of +memory. The dust::shared_copy_data is a small utility to +make the bookkeeping here a bit easier, but this could have been written +out as:

+
namespace dust {
+template <>
+void shared_copy<sirs>(dust::shared_ptr<sirs> shared,
+                       int * shared_int,
+                       sirs::real_type * shared_real) {
+  using real_type = sirs::real_type;
+  shared_real[0] = shared->alpha;
+  shared_real[1] = shared->beta;
+  shared_real[2] = shared->gamma;
+  shared_real[3] = shared->dt;
+  shared_real[4] = shared->exp_noise;
+  shared_int[0] = shared->freq;
+}
+}
+

The dust::shared_copy_data template has specialisations +where the object being copied is a vector.

+

There are two methods that are not used here, but could be included, +to define the size of per-particle internal storage space. This is +required if your model needs to store intermediate calculations during +the update time if those will not fit on the stack.

+
namespace dust {
+namespace gpu {
+template <>
+size_t dust::internal_real_size<sirs>(dust::shared_ptr<sirs> shared) {
+  return 0;
+}
+template <>
+size_t dust::internal_int_size<sirs>(dust::shared_ptr<sirs> shared) {
+  return 0;
+}
+}
+}
+

Most interestingly we have the update_gpu method that +actually does the update on the GPU

+
template <>
+__device__
+void update_gpu<sirs>(size_t time,
+                      const dust::gpu::interleaved<sirs::real_type> state,
+                      dust::gpu::interleaved<int> internal_int,
+                      dust::gpu::interleaved<sirs::real_type> internal_real,
+                      const int * shared_int,
+                      const sirs::real_type * shared_real,
+                      sirs::rng_state_type& rng_state,
+                      dust::gpu::interleaved<sirs::real_type> state_next) {
+  using real_type = sirs::real_type;
+  const real_type alpha = shared_real[0];
+  const real_type beta = shared_real[1];
+  const real_type gamma = shared_real[2];
+  const real_type dt = shared_real[3];
+  const int freq = shared_int[0];
+  const real_type S = state[0];
+  const real_type I = state[1];
+  const real_type R = state[2];
+  const real_type N = S + I + R;
+  const real_type p_SI = 1 - exp(- beta * I / N);
+  const real_type p_IR = 1 - exp(- gamma);
+  const real_type p_RS = 1 - exp(- alpha);
+  const real_type n_SI = dust::random::binomial<real_type>(rng_state, S, p_SI * dt);
+  const real_type n_IR = dust::random::binomial<real_type>(rng_state, I, p_IR * dt);
+  const real_type n_RS = dust::random::binomial<real_type>(rng_state, R, p_RS * dt);
+  state_next[0] = S - n_SI + n_RS;
+  state_next[1] = I + n_SI - n_IR;
+  state_next[2] = R + n_IR - n_RS;
+  state_next[3] = (time % freq == 0) ? n_SI : state[3] + n_SI;
+}
+

Note that this totally duplicates the logic from the CPU version +(which was a method of the sirs object)

+
  void update(size_t time, const real_type * state, rng_state_type& rng_state,
+              real_type * state_next) {
+    real_type S = state[0];
+    real_type I = state[1];
+    real_type R = state[2];
+    real_type N = S + I + R;
+
+    real_type p_SI = 1 - exp(- shared->beta * I / N);
+    real_type p_IR = 1 - exp(-(shared->gamma));
+    real_type p_RS = 1 - exp(- shared->alpha);
+
+    real_type dt = shared->dt;
+    real_type n_SI = dust::random::binomial<real_type>(rng_state, S, p_SI * dt);
+    real_type n_IR = dust::random::binomial<real_type>(rng_state, I, p_IR * dt);
+    real_type n_RS = dust::random::binomial<real_type>(rng_state, R, p_RS * dt);
+
+    state_next[0] = S - n_SI + n_RS;
+    state_next[1] = I + n_SI - n_IR;
+    state_next[2] = R + n_IR - n_RS;
+    state_next[3] = (time % shared->freq == 0) ? n_SI : state[3] + n_SI;
+  }
+

Differences include:

+
    +
  • the presence of the four auxiliary data elements +(internal_int, internal_real, +shared_int and shared_real)
    • +
  • the data types that vary across particles are a special +dust::gpu::interleaved<> type, which prevents slow +uncoalesced reads from global memory on the GPU
    • +
  • All accesses into the shared_int and +shared_real elements are now by position in the array, +rather than the previous pointer/name based access
    • +
  • The __device__ annotation, which compiles the function +for use on the GPU
    • +
+
+
+

Data comparison functions +

+

Finally, if running a particle filter on the GPU, a version of the +compare_data function is required that can run on the +GPU:

+
template <>
+__device__
+sirs::real_type compare_gpu<sirs>(const dust::gpu::interleaved<sirs::real_type> state,
+                                  const sirs::data_type& data,
+                                  dust::gpu::interleaved<int> internal_int,
+                                  dust::gpu::interleaved<sirs::real_type> internal_real,
+                                  const int * shared_int,
+                                  const sirs::real_type * shared_real,
+                                  sirs::rng_state_type& rng_state) {
+  using real_type = sirs::real_type;
+  const real_type exp_noise = shared_real[4];
+  const real_type incidence_modelled = state[3];
+  const real_type incidence_observed = data.incidence;
+  const real_type lambda = incidence_modelled +
+    dust::random::exponential<real_type>(rng_state, exp_noise);
+  return dust::density::poisson(incidence_observed, lambda, true);
+}
+

This is very similar to the CPU version

+
  real_type compare_data(const real_type * state, const data_type& data,
+                         rng_state_type& rng_state) {
+    const real_type incidence_modelled = state[3];
+    const real_type incidence_observed = data.incidence;
+    const real_type lambda = incidence_modelled +
+      dust::random::exponential<real_type>(rng_state, shared->exp_noise);
+    return dust::density::poisson(incidence_observed, lambda, true);
+  }
+

with similar differences to the update function:

+
    +
  • argument types are different (interleaved types, internals and +shared data passed explicitly)
    • +
  • Accessing of shared parameters is by position, not name
    • +
  • The __device__ annotation
    • +
+
+
+

Developing a GPU model +

+

Debugging on a GPU is a pain, especially because there are typically +many particles, and error recovery is not straightforward. In addition, +most continuous integration systems do not provide GPUs, so testing your +GPU code becomes difficult. To make this easier, dust +allows running GPU code on the CPU - this will be typically slower than +the CPU code, but allows easier debugging and verification that the +model is behaving. We use this extensively in dust’s tests +and also in models built using dust that will run on the +GPU.

+

To do this, compile the model with your preferred real type, but set +the gpu argument to FALSE

+
+sirs_cpu <- dust::dust(path, gpu = FALSE, real_type = "float")
+#> ℹ 34 functions decorated with [[cpp11::register]]
+#> ✔ generated file 'cpp11.R'
+#> ✔ generated file 'cpp11.cpp'
+#> Re-compiling sirs817bc717
+#>   ─  installing *source* package ‘sirs817bc717’ ...
+#>      ** using staged installation
+#>      ** libs
+#>      make[1]: Entering directory '/tmp/RtmppiOue1/fileb32bb452d008e/src'
+#>      make[1]: Leaving directory '/tmp/RtmppiOue1/fileb32bb452d008e/src'
+#>      make[1]: Entering directory '/tmp/RtmppiOue1/fileb32bb452d008e/src'
+#>    g++ -std=gnu++11 -I"/usr/share/R/include" -DNDEBUG  -I'/home/rfitzjoh/lib/R/library/cpp11/include' -g -Wall -Wextra -pedantic -Wmaybe-uninitialized -Wno-unused-parameter -Wno-cast-function-type -Wno-missing-field-initializers -O2  -I/home/rfitzjoh/lib/R/library/dust/include -DHAVE_INLINE -fopenmp -fpic  -g -O2 -fdebug-prefix-map=/build/r-base-QwogzP/r-base-4.1.1=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -g  -c cpp11.cpp -o cpp11.o
+#>      g++ -std=gnu++11 -I"/usr/share/R/include" -DNDEBUG  -I'/home/rfitzjoh/lib/R/library/cpp11/include' -g -Wall -Wextra -pedantic -Wmaybe-uninitialized -Wno-unused-parameter -Wno-cast-function-type -Wno-missing-field-initializers -O2  -I/home/rfitzjoh/lib/R/library/dust/include -DHAVE_INLINE -fopenmp -fpic  -g -O2 -fdebug-prefix-map=/build/r-base-QwogzP/r-base-4.1.1=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -g  -c dust.cpp -o dust.o
+#>      g++ -std=gnu++11 -shared -L/usr/lib/R/lib -Wl,-Bsymbolic-functions -Wl,-z,relro -o sirs817bc717.so cpp11.o dust.o -fopenmp -L/usr/lib/R/lib -lR
+#>      make[1]: Leaving directory '/tmp/RtmppiOue1/fileb32bb452d008e/src'
+#>      installing to /tmp/RtmppiOue1/devtools_install_b32bb3d78d7ef/00LOCK-fileb32bb452d008e/00new/sirs817bc717/libs
+#>      ** checking absolute paths in shared objects and dynamic libraries
+#>   ─  DONE (sirs817bc717)
+#>
+#> ℹ Loading sirs817bc717
+

Note that above the model is compiled with g++, not +nvcc. However, the “GPU” code is still compiled into the +model. We can then initialise this with and without a +gpu_config argument

+
+model1 <- sirs_cpu$new(pars, 0, 10, seed = 1L)
+model2 <- sirs_cpu$new(pars, 0, 10, gpu_config = 0L, seed = 1L)
+

And run the models using the “GPU” code and the normal CPU code, but +this time both on the CPU

+
+model1$run(10)
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
+#> [1,]  981  987  977  986  994  948  958  961  976   968
+#> [2,]   23   16   26   10    7   48   37   31   21    28
+#> [3,]    6    7    7   14    9   14   15   18   13    14
+#> [4,]    5    5    5    2    0   11    6    5    3     6
+model2$run(10)
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
+#> [1,]  981  987  977  986  994  948  958  961  976   968
+#> [2,]   23   16   26   10    7   48   37   31   21    28
+#> [3,]    6    7    7   14    9   14   15   18   13    14
+#> [4,]    5    5    5    2    0   11    6    5    3     6
+

These should be exactly the same, and this can form the basis of +tests. Note that using float rather than +double can throw up a few issues with algorithms, so it’s +worth checking with single-precision in your tests.

+

If you hit problems, then R -d cuda-gdb can work in +place of the usual R -d gdb to work with a debugger, though +because of the huge numbers of particles you will typically work with, +debugging remains a challenge. Our usual strategy has been to try and +recreate any issue purely in CPU code and debug as normal (see this +blog post for hints on doing this effectively).

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
+ + + + + + + + diff --git a/articles/index.html b/articles/index.html new file mode 100644 index 000000000..ba717d2e1 --- /dev/null +++ b/articles/index.html @@ -0,0 +1,140 @@ + +Articles • dust + + +
+
+ + + +
+
+
+

Articles

+
+ +
+

Introduction

+

+ +
Introduction to dust
+
+
Principles and design of dust
+
+
+
+

Random numbers

+

+ +
Random number generation
+
+
Algorithms used to compute random numbers
+
+
Using RNGs from packages
+
+
Distributed parallel random numbers
+
+
+
+

Dive deeper

+

+ +
Comparing models and data
+
+
Running models on GPUs with CUDA
+
+
Multiple parameter sets
+
+
+
+
+ + +
+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

Site built with pkgdown 2.0.7.

+
+ +
+ + + + + + + + diff --git a/articles/multi.html b/articles/multi.html new file mode 100644 index 000000000..044137da5 --- /dev/null +++ b/articles/multi.html @@ -0,0 +1,379 @@ + + + + + + + +Multiple parameter sets • dust + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Multiple parameter sets

+ + + Source: vignettes/multi.Rmd + + +
+ + + +

dust provides support for simulating lots of particles at once. +Sometimes that will be with a single parameter set and many traces to +capture stochastic variability, but other times different particles will +need different parameter sets too.

+

To allow this, dust supports creating a model and indicating that the +parameters represents some group of parameter sets. Consider our SIR +example from vignette("dust"):

+
+sir <- dust::dust_example("sir")
+

For one parameter set with 8 particles we might do:

+
+pars <- list(beta = 0.1)
+mod <- sir$new(pars, 0, 8)
+

The “shape” of this model is most easily seen in the state:

+
+mod$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
+#> [1,] 1000 1000 1000 1000 1000 1000 1000 1000
+#> [2,]   10   10   10   10   10   10   10   10
+#> [3,]    0    0    0    0    0    0    0    0
+#> [4,]    0    0    0    0    0    0    0    0
+#> [5,]    0    0    0    0    0    0    0    0
+

So here we have 5 state variables and 8 particles. The number of +state variables is a property of the model, while the number of +particles is a property of how you have configured the model, and we +will call that the “shape”

+
+mod$shape()
+#> [1] 8
+

There are also two helper methods which report the number of +particles and number of particles per parameter set, here these will +both report 8:

+
+mod$n_particles()
+#> [1] 8
+mod$n_particles_each()
+#> [1] 8
+

So far so easy.

+

Suppose we have 2 regions (or other grouping) that we want to +simulate at once and these have different parameter sets. We create an +unnamed list containing the parameter sets

+
+pars <- list(list(beta = 0.1, I0 = 10), list(beta = 0.2, I0 = 12))
+

and then when creating the model we indicate that we want 4 particles +each for our 2 parameter sets. The total number of particles will be 4 * +2 = 8

+
+mod <- sir$new(pars, 0, 4, pars_multi = TRUE)
+

The state has a different shape now:

+
+mod$state()
+#> , , 1
+#> 
+#>      [,1] [,2] [,3] [,4]
+#> [1,] 1000 1000 1000 1000
+#> [2,]   10   10   10   10
+#> [3,]    0    0    0    0
+#> [4,]    0    0    0    0
+#> [5,]    0    0    0    0
+#> 
+#> , , 2
+#> 
+#>      [,1] [,2] [,3] [,4]
+#> [1,] 1000 1000 1000 1000
+#> [2,]   12   12   12   12
+#> [3,]    0    0    0    0
+#> [4,]    0    0    0    0
+#> [5,]    0    0    0    0
+

It’s a 3-dimensional array with dimensions 5, 4, 2 corresponding to +the number of state elements, number of replicates per parameter set and +the number of parameter sets. Note that the second parameter set’s state +is different because the I0 parameter specifies the number +of infected individuals in the initial conditions.

+

The “shape” of the data here is c(4, 2)

+
+mod$shape()
+#> [1] 4 2
+

We still have 8 particles, but 4 per parameter set:

+
+mod$n_particles()
+#> [1] 8
+mod$n_particles_each()
+#> [1] 4
+

This sort of shape is useful where we want to fit multiple particle +filters to the data, or simulate replicates blocked across a common set +of parameters; that is we’re interested in exploring the stochastic +variation that occurs given a particular parameter set.

+

But there are other way of shaping the state that are useful.

+

Suppose that you have many parameter sets, each representing (say) an +estimate based on some inference process

+
+pars <- lapply(runif(8, 0.05, 0.3), function(x) list(beta = x))
+

For this we might write:

+
+mod <- sir$new(pars, 0, 1, pars_multi = TRUE)
+

to indicate 1 particle per parameter. However, that’s not ideal:

+
+dim(mod$state())
+#> [1] 5 1 8
+mod$shape()
+#> [1] 1 8
+

By doing this we end up with a weird dimension in the middle of our +state. This would make sense if we were going to also replicate within +the parameter set but does not make any sense this way.

+

To indicate that we don’t want this, pass NULL in for +the number of particles:

+
+mod <- sir$new(pars, 0, NULL, pars_multi = TRUE)
+mod$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
+#> [1,] 1000 1000 1000 1000 1000 1000 1000 1000
+#> [2,]   10   10   10   10   10   10   10   10
+#> [3,]    0    0    0    0    0    0    0    0
+#> [4,]    0    0    0    0    0    0    0    0
+#> [5,]    0    0    0    0    0    0    0    0
+mod$shape()
+#> [1] 8
+

(why NULL? because if you tried c(5, 1, 8) +and c(5, NULL, 8) you would see the same values as the two +state vectors above).

+

Further options are useful! Suppose in our previous case, the 8 +parameter sets were themselves structured in some block, representing +two groups of four parameter sets. To indicate this we create a list +with dimensions:

+
+dim(pars) <- c(4, 2)
+pars
+#>      [,1]   [,2]  
+#> [1,] list,1 list,1
+#> [2,] list,1 list,1
+#> [3,] list,1 list,1
+#> [4,] list,1 list,1
+

Then, when creating the object these dimensions will be applied to +the data

+
+mod <- sir$new(pars, 0, NULL, pars_multi = TRUE)
+mod$state()
+#> , , 1
+#> 
+#>      [,1] [,2] [,3] [,4]
+#> [1,] 1000 1000 1000 1000
+#> [2,]   10   10   10   10
+#> [3,]    0    0    0    0
+#> [4,]    0    0    0    0
+#> [5,]    0    0    0    0
+#> 
+#> , , 2
+#> 
+#>      [,1] [,2] [,3] [,4]
+#> [1,] 1000 1000 1000 1000
+#> [2,]   10   10   10   10
+#> [3,]    0    0    0    0
+#> [4,]    0    0    0    0
+#> [5,]    0    0    0    0
+mod$shape()
+#> [1] 4 2
+

These options have implications for a number of methods, and for the +basic running of the simulation. For example, when we run our model with +structured parameters:

+
+res <- mod$simulate(0:10)
+dim(res)
+#> [1]  5  4  2 11
+

Here the simulation output has dimensions:

+
    +
  • 5 - the number of state variables
    • +
  • 4 - the first value of mod$shape(), as the first +dimension of the parameters
    • +
  • 2 - the second value of mod$shape(), as the second +dimension of the parameters
    • +
  • 11 - the number of timesteps recorded in the simulation
    • +
+

Conversely if we’d also replicated parameters with this set +of parameters we might see

+
+mod <- sir$new(pars, 0, 3, pars_multi = TRUE)
+mod$shape()
+#> [1] 3 4 2
+dim(mod$simulate(0:10))
+#> [1]  5  3  4  2 11
+

Again here note that mod$shape() is sandwiched between +the number of state variables and number of timesteps.

+
+

Considerations +

+

There are a few helpful things on single parameter objects that +become ambiguous or awkward with multi-parameter objects. Starting with +a single parameter object:

+
+pars <- list(beta = 0.1)
+mod <- sir$new(pars, 0, 8)
+

We might set all particles to have the same initial state:

+
+mod$update_state(state = c(1000, 10, 0, 0, 0))
+mod$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
+#> [1,] 1000 1000 1000 1000 1000 1000 1000 1000
+#> [2,]   10   10   10   10   10   10   10   10
+#> [3,]    0    0    0    0    0    0    0    0
+#> [4,]    0    0    0    0    0    0    0    0
+#> [5,]    0    0    0    0    0    0    0    0
+

or we might set each particle to a different state, perhaps +representing some stochasticity in starting values

+
+n <- rpois(8, 10)
+mod$update_state(state = rbind(1010 - n, n, 0, 0, 0))
+mod$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
+#> [1,] 1001  993  998 1003 1002 1008 1002 1000
+#> [2,]    9   17   12    7    8    2    8   10
+#> [3,]    0    0    0    0    0    0    0    0
+#> [4,]    0    0    0    0    0    0    0    0
+#> [5,]    0    0    0    0    0    0    0    0
+

The difference here is the dimension of the new state. Recall that +the state will always be in the form

+
n_state, shape[1], ..., shape[n]
+

If the dimension lacks the first element of shape, and if +there is more than one particle per parameter set, then we replicate +state across all particles that share that parameter set.

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
+ + + + + + + + diff --git a/articles/rng.html b/articles/rng.html new file mode 100644 index 000000000..01a89b104 --- /dev/null +++ b/articles/rng.html @@ -0,0 +1,760 @@ + + + + + + + +Random number generation • dust + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Random number generation

+ + + Source: vignettes/rng.Rmd + + +
+ + + +

The core of dust is a very fast parallel random number +generation system. This vignette describes the details of the system and +why it is needed.

+

We provide an interface to the “Xoshiro” / Blackman-Vigna family +of generators (Xoshiro is derived from XOR/shift/rotate). These are +designed to allow use in parallel by “jumping ahead” in the sequence and +we use this below to interleave generators. The stream is unrelated to +and unaffected by R’s random number generation. set.seed +has no effect, for example. The random numbers are not +cryptographically secure; for that see the excellent sodium package.

+

Ordinarily this is used from C++; the model as discussed in +vignette("dust") uses rng_state_type and a +function from dust::random to interact with the generator. +However, an R interface is provided for debugging and testing +purposes.

+
+rng <- dust::dust_rng$new(seed = 1)
+rng
+#> <dust_rng>
+#>   Public:
+#>     binomial: function (n, size, prob, n_threads = 1L) 
+#>     cauchy: function (n, location, scale, n_threads = 1L) 
+#>     exponential: function (n, rate, n_threads = 1L) 
+#>     gamma: function (n, shape, scale, n_threads = 1L) 
+#>     hypergeometric: function (n, n1, n2, k, n_threads = 1L) 
+#>     info: list
+#>     initialize: function (seed = NULL, n_streams = 1L, real_type = "double", 
+#>     jump: function () 
+#>     long_jump: function () 
+#>     multinomial: function (n, size, prob, n_threads = 1L) 
+#>     nbinomial: function (n, size, prob, n_threads = 1L) 
+#>     normal: function (n, mean, sd, n_threads = 1L, algorithm = "box_muller") 
+#>     poisson: function (n, lambda, n_threads = 1L) 
+#>     random_normal: function (n, n_threads = 1L, algorithm = "box_muller") 
+#>     random_real: function (n, n_threads = 1L) 
+#>     size: function () 
+#>     state: function () 
+#>     uniform: function (n, min, max, n_threads = 1L) 
+#>   Private:
+#>     float: FALSE
+#>     n_streams: 1
+#>     ptr: externalptr
+

Currently only a few distributions are supported, with an interface +that somewhat mimics R’s interface (we avoid abbreviations so that +rnorm becomes normal and there are no default +arguments). For example, with the generator above we can generate 100 +standard normal samples:

+
+rng$normal(100, 0, 1)
+#>   [1]  1.12910079  0.53780677 -1.26698746  0.95829321  3.21195234  0.09921154
+#>   [7] -0.18600342 -0.29222356  2.08163389 -0.05121175  0.27770699  0.53856861
+#>  [13]  0.03225818 -0.32777772  0.18042116  0.46339742 -0.38466512 -1.13577238
+#>  [19]  0.91316208  0.03922728 -1.49714784  0.73104348 -0.83564659 -1.11930919
+#>  [25]  0.02762058 -0.99778204  0.85397997  0.93862789  0.27005717 -0.22477757
+#>  [31] -0.44778373  0.14367032 -0.06827267  0.68396692 -1.16518273 -0.89172407
+#>  [37] -0.29950034  0.72347846 -1.14585657  0.34617660 -0.03401702  0.04667183
+#>  [43]  0.09952394 -1.94032159  1.35699294 -0.34150243 -0.62118413  0.06133529
+#>  [49]  1.18840972  0.56786089 -1.70569039  0.37351828  0.78885706  0.52182712
+#>  [55] -0.82799139 -0.04261288  0.61557195  0.83137281 -1.21370978 -0.94812792
+#>  [61] -0.12333629  0.52869359 -0.88974620 -0.17544455  1.80250618  1.12137595
+#>  [67]  0.30129136 -0.07441952  1.03229412 -0.47172538 -0.97177969  0.82461084
+#>  [73] -0.64920225 -0.00744135 -0.90106996  0.03281943 -1.57134280  0.46664117
+#>  [79]  0.16352787  0.21926382  0.20193191 -1.84076636 -0.74116728 -0.99895652
+#>  [85] -0.06497241  0.76942936 -0.67097495 -0.10362127  0.47417215 -0.77659258
+#>  [91] -0.28248620 -1.09359110  0.61960546 -0.20527080  0.79773008  0.31563408
+#>  [97]  0.53182428 -0.41118602  0.05391659  1.16452122
+

One feature that we use here is to allow multiple streams of random +numbers within a rng object. If running in parallel (either via a dust +model or by passing n_threads) these different random +number streams can be given to different threads.

+
+rng1 <- dust::dust_rng$new(seed = 1, n_streams = 1)
+rng2 <- dust::dust_rng$new(seed = 1, n_streams = 2)
+rng1$random_real(5)
+#> [1] 0.45135139 0.07353466 0.21812941 0.20013953 0.01717274
+rng2$random_real(5)
+#>            [,1]      [,2]
+#> [1,] 0.45135139 0.8989717
+#> [2,] 0.07353466 0.3624481
+#> [3,] 0.21812941 0.4729296
+#> [4,] 0.20013953 0.3462430
+#> [5,] 0.01717274 0.4180079
+

Notice here how in the output from rng2, the first +column matches the series of numbers out of rng1.

+

This is achieved by “jumping” the random number streams forward. Here +are the second column of numbers from the output of +rng2:

+
+rng3 <- dust::dust_rng$new(seed = 1)$jump()
+rng3$random_real(5)
+#> [1] 0.8989717 0.3624481 0.4729296 0.3462430 0.4180079
+

With the default generator (xoshoro256+, see below), a +jump is equivalent to 2^128 draws from the random number generator +(about 10^38). There are 2^128 of these non-overlapping subsequences in +the generator, which is quite a lot. If this feels too close together, +then the $long_jump() method jumps even further (2^192 +draws, or about 10^57). There are 2^64 (10^20) of these sequences.

+
+

Supported distributions +

+

We do not yet support the full set of distributions provided by R, +and the distributions that we do support represent our immediate needs. +Contributions of further distributions is welcome. Note that in the R +version the first argument represents the number of draws requested, but +in the C++ interface we always return a single number.

+

Uniform distribution between min and +max:

+
+rng$uniform(10, 3, 6)
+#>  [1] 4.773239 5.654481 3.977174 4.026823 4.115612 3.788596 3.917003 5.702068
+#>  [9] 5.720697 5.547363
+

Normal distribution with parameters +mean and sd

+
+rng$normal(10, 3, 6)
+#>  [1] 12.2139218  4.3761453  0.9866168  4.5615065 -6.0847775  7.4186531
+#>  [7] -4.9939206  5.0829829 -2.7531772  6.3068671
+

This function supports using the ziggurat algorithm, which will +generally be faster:

+
+rng$normal(10, 3, 6, algorithm = "ziggurat")
+#>  [1] 12.679238  3.933790  8.843829  6.480052 -6.475361  5.767795 12.462605
+#>  [8] 10.099802  7.808174 10.040571
+

Poisson distribution with mean +lambda

+
+rng$poisson(10, 4.5)
+#>  [1] 3 6 2 4 7 9 2 4 3 4
+

Binomial distribution with mean size +and prob

+
+rng$binomial(10L, 10, 0.3)
+#>  [1] 6 6 0 1 3 4 4 5 1 1
+

Negative binomial distribution with mean +size and prob

+
+rng$nbinomial(10L, 10, 0.3)
+#>  [1] 14 16 16  8 10 27 42 18 14 23
+

Hypergeometric distribution with parameters +n1 (number of white balls), n2 (number of +black balls) and k (number of samples)

+
+rng$hypergeometric(10L, 3, 10, 4)
+#>  [1] 0 1 1 2 2 1 2 0 1 2
+

Exponential distribution with rate +rate

+
+rng$exponential(10L, 4)
+#>  [1] 0.07361117 0.39088773 0.08186782 0.61963654 0.34793074 0.13892083
+#>  [7] 0.46349529 0.49744941 1.39014645 0.26500585
+

Multinomial distribution with parameters +size and prob

+
+rng$multinomial(10L, 20, c(0.3, 0.5, 0.2))
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
+#> [1,]    8    8    8    6    7    2    7    6    6     8
+#> [2,]    7    9    8   11   11   14   10    9   11     9
+#> [3,]    5    3    4    3    2    4    3    5    3     3
+

There are also two special case distributions, the Standard +uniform distribution (between 0 and 1) - faster than using +$uniform(n, 0, 1):

+
+rng$random_real(10)
+#>  [1] 0.242903786 0.049219283 0.916447682 0.008016532 0.056566402 0.123235690
+#>  [7] 0.967806313 0.406906615 0.586602176 0.539672238
+
real_type u = dust::random::random_real<real_type>(state);
+

the Standard normal distribution (between mean 0 and +sd 1) - faster than using $normal(n, 0, 1):

+
+rng$random_normal(10)
+#>  [1]  0.609695640  0.146842292 -0.131451864 -0.005175636  0.120022427
+#>  [6] -0.464251232  0.054394819 -0.174200970 -0.019314869  1.315462849
+
real_type u = dust::random::random_normal<real_type>(state);
+

Gamma distribution parameterized by +shape and scale

+
+rng$gamma(10L, 2, 5)
+#>  [1] 10.135325 11.303813  4.016615 27.730667  6.175187 15.813924  8.100044
+#>  [8]  2.681611 11.177406  2.162054
+

All of these distributions are available in C++, and this is +documented in +the C++ reference documentation

+
+
+

Performance +

+

Performance should be on par or better with R’s random number +generator, though here the timings are likely to be mostly due to +allocations and copies of memory:

+
+bench::mark(
+  rng1$random_real(1000),
+  rng1$uniform(1000, 0, 1),
+  runif(1000),
+  time_unit = "us",
+  check = FALSE)
+#> # A tibble: 3 × 6
+#>   expression                 min median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr>               <dbl>  <dbl>     <dbl> <bch:byt>    <dbl>
+#> 1 rng1$random_real(1000)    6.20   10.4   103078.    7.86KB     20.6
+#> 2 rng1$uniform(1000, 0, 1)  8.80   13.0    82684.    7.86KB     16.5
+#> 3 runif(1000)              13.9    15.1    60778.   12.77KB     12.2
+

For normally distributed random numbers, the different algorithms +will perform differently:

+
+bench::mark(
+  rng1$random_normal(1000),
+  rng1$random_normal(1000, algorithm = "ziggurat"),
+  rng1$normal(1000, 0, 1),
+  rnorm(1000),
+  time_unit = "us",
+  check = FALSE)
+#> # A tibble: 4 × 6
+#>   expression                             min median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr>                           <dbl>  <dbl>     <dbl> <bch:byt>    <dbl>
+#> 1 "rng1$random_normal(1000)"            44.2   46.0    21634.    7.86KB     2.16
+#> 2 "rng1$random_normal(1000, algorithm…  11.6   12.7    76643.    7.86KB    15.3 
+#> 3 "rng1$normal(1000, 0, 1)"             46.7   48.3    20622.    7.86KB     4.13
+#> 4 "rnorm(1000)"                         46.8   49.0    20343.   12.77KB     4.19
+

On reasonable hardware (10-core i9 at 2.8 GHz) we see throughput of +~1 billion U(0, 1) draws per second (1ns/draw) scaling linearly to 10 +cores if the numbers are immediately discarded. Doing anything with the +numbers or trying to store them comes with a non-trivial overhead.

+

The difference between random_real and +uniform here is the cost of recycling the parameters, not +the actual generation!

+

Binomial distribution, small n * p, which uses an +inversion algorithm

+
+rng1 <- dust::dust_rng$new(seed = 1)
+n <- as.numeric(rep(9:10, length.out = 1000))
+p <- rep(c(0.1, 0.11), length.out = 1000)
+bench::mark(
+  rng1$binomial(1000, n, p),
+  rbinom(1000, n, p),
+  time_unit = "us",
+  check = FALSE)
+#> # A tibble: 2 × 6
+#>   expression                  min median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr>                <dbl>  <dbl>     <dbl> <bch:byt>    <dbl>
+#> 1 rng1$binomial(1000, n, p)  35.2   37.6    26471.    7.86KB     2.65
+#> 2 rbinom(1000, n, p)         47.3   49.6    20106.    8.83KB     4.07
+

(note we vary n and p here as we’ve +optimised things for random parameter access).

+

Large n * p uses a rejection sampling algorithm

+
+n <- as.numeric(rep(9999:10000, length.out = 1000))
+p <- rep(c(0.3, 0.31), length.out = 1000)
+bench::mark(
+  rng1$binomial(1000, n, p),
+  rbinom(1000, n, p),
+  time_unit = "us",
+  check = FALSE)
+#> # A tibble: 2 × 6
+#>   expression                  min median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr>                <dbl>  <dbl>     <dbl> <bch:byt>    <dbl>
+#> 1 rng1$binomial(1000, n, p)  52.9   58.0    17203.    7.86KB     2.02
+#> 2 rbinom(1000, n, p)         78.3   85.7    11651.    6.45KB     2.02
+

Practically, performance will vary based on the parameters of the +distributions and the underlying algorithms, and the principle +performance gain we hope to get here is driven by the ability to +parallelise safely rather than the speed of the draws themselves.

+
+
+

Underlying random number engine +

+

Under the hood, the random number generators work by first creating a +random integer, which we then convert to a floating point number, then +for the distributions above we apply algorithms that convert one or more +uniformly distributed (i.e., U(0, 1)) floating point numbers to a given +distribution through techniques such as inversion (for a random +exponential) or rejection sampling (for a random binomial).

+
[random integer] -> [random real] -> [random draw from a distribution]
+

We include 12 different algorithms for creating the underlying random +integer, from the same family of +generators. These provide different underlying storage types (either +32 bit or 64 bit integers) and different state types.

+

Normally you do not need to worry about these details and +declaring

+
using rng_state_type = dust::random::generator<real_type>;
+

in your model will select a reasonable generator.

+

If for some reason you want to try a different generator you can +directly specify one of the types, for example

+
using rng_state_type = dust::random::xoshiro256starstar;
+

which means that whatever real type you use, you want to use the +Xoshiro256** generator.

+

The supported types are:

+
    +
  • +xoshiro256starstar, xoshiro256plusplus, +xoshiro256plus (4 x 64 bit state)
    • +
  • +xoroshiro128starstar, +xoroshiro128plusplus, xoroshiro128plus (2 x 64 +bit state)
    • +
  • +xoshiro128starstar, xoshiro128plusplus, +xoshiro128plus (4 x 32 bit state)
    • +
  • +xoshiro512starstar, xoshiro512plusplus, +xoshiro512plus (8 x 64 bit state; this is far more state +space than typically needed)
    • +
+

The “starstar”, “plusplus” or “plus” refers to the final scrambling +operation (two multiplications, two additions or one addition, +respectively); the speeds of these might vary depending on your +platform. The “plus” version will be the fastest but produces slightly +less randomness in the the lower bits of the underlying integers, which +theoretically is not a problem when converting to a real number.

+

If you are generating single precision float numbers for +a GPU, then you may want to use the xoshiro128 family as +these will be faster than the 64 bit generators on that platform. On a +CPU you will likely not see a difference

+
+rng_f <- dust::dust_rng$new(seed = 1, real_type = "float")
+rng_d <- dust::dust_rng$new(seed = 1, real_type = "double")
+bench::mark(
+  rng_f$random_real(1000),
+  rng_d$random_real(1000),
+  time_unit = "us",
+  check = FALSE)
+#> # A tibble: 2 × 6
+#>   expression                min median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr>              <dbl>  <dbl>     <dbl> <bch:byt>    <dbl>
+#> 1 rng_f$random_real(1000)  6.40   7.00   138202.    7.86KB     13.8
+#> 2 rng_d$random_real(1000)  6.20   6.70   145091.    7.86KB     29.0
+

If you do not need to run many parallel realisations, then the +xoroshiro256 (note the extra ro) generators +may be preferable as they carry half the state and may be slightly +faster. The xoshiro512 generators are included for +completeness and offer an excessive state space).

+

The table below summarises the properties of the underlying +generators (each of these exists with three different scrambling +options).

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
NameSizeStatePeriodJumpLong jump
xoshiro12832 bits2 uint322^1282^642^96
xoroshiro12864 bits2 uint642^1282^642^96
xoshiro25664 bits4 uint642^2562^1282^192
xoshiro51264 bits4 uint642^5122^5122^384
+

Size is the size of the returned random integer (32 or 64 bits, +though with the + scrambler not all bits will be of high +quality). The State is the number and size of the internal state of the +generator. Period refers to the number of states that the generator will +move through, Jump and Long jump are the number of steps (equivalent) +that a jump operation will take through this sequence.

+

Note that the period is the two size of number of bits in the model +state (e.g., xoshiro256 uses 4 x 64 bit integers, for a total of 256 +bits of state, 2^256 possible combinations, each of which will be +visited once in the cycle). The Jump coefficients have been computed to +have size sqrt(Period).

+
+
+

Reusing the random random number generator in other projects +

+

Our random number library can be reused in other projects without +using anything else from dust; either in an R package or in a standalone +project.

+
+

In a package +

+

A minimal package looks like

+
#> .
+#> ├── DESCRIPTION
+#> ├── NAMESPACE
+#> └── src
+#>     └── rnguse.cpp
+

with the core of the C++ file containing a small program that uses +the dust random number generator to draw a series of normally +distributed random number with a single mean and standard deviation.

+
#include <cpp11.hpp>
+#include <dust/random/random.hpp>
+
+[[cpp11::register]]
+cpp11::doubles random_normal(int n, double mu, double sd, int seed) {
+  using rng_state_type = dust::random::generator<double>;
+  auto state = dust::random::seed<rng_state_type>(seed);
+
+  cpp11::writable::doubles ret(n);
+  for (int i = 0; i < n; ++i) {
+    ret[i] = dust::random::normal<double>(state, mu, sd);
+  }
+
+  return ret;
+}
+

To complete the package, the DESCRIPTION includes +dust and cpp11 in the LinkingTo +section:

+
Package: rnguse
+Title: Use 'dust' RNG From Elsewhere
+Version: 0.1.0
+Authors@R: c(person("Rich", "FitzJohn", role = c("aut", "cre"),
+                    email = "rich.fitzjohn@gmail.com"))
+Description: Simple example package showing how to use dust's random
+    number library from your R package's C++ code.
+License: CC0
+Encoding: UTF-8
+LinkingTo: cpp11, dust
+

You must remember to update your NAMESPACE to include +useDynLib (either directly or via roxygen)

+
useDynLib(rnguse, .registration = TRUE)
+

Finally, run cpp11::cpp_register() before compiling your +package so that the relevant interfaces are created +(R/cpp11.R and cpp11/cpp11.cpp). A similar +process would likely work with Rcpp without any dependency on cpp11.

+

The issue with this example is that every call to +random_normal must provide its own seed +argument, so the random number streams are not continued with each call +to the function. This is is not very useful in practice and we describe +more fully how to do this properly in +vignette("rng_package.Rmd").

+
+
+

Standalone, parallel with OpenMP +

+

This is somewhat more experimental, so let us know if you have +success using the library this way.

+

It is possible to include the dust random library in a standalone C++ +program (or one embedded from another language) without using any R +support. The library is a header only library and +<dust/random/random.hpp> is the main file to +include.

+

The simplest way to get started is to copy the contents of +inst/include/dust/random into your project. You can do this +by downloading and unpacking the +latest release of dust-random. Then after including +<dust/random/random.hpp> you can use the contents of +the random number library.

+

For example, below is a small program that computes the sum of a +series of random numbers, in parallel using OpenMP to parallelise across +a set of generators.

+
#include <iostream>
+#include <iomanip>
+#include <vector>
+
+#ifndef NO_OPENMP
+#include <omp.h>
+#endif
+
+#include <dust/random/random.hpp>
+
+template <typename real_type>
+std::vector<real_type> random_sum(int n_streams, int n_draws,
+                                  int seed, int n_threads) {
+  using rng_state_type = dust::random::generator<real_type>;
+  dust::random::prng<rng_state_type> rng(n_streams, seed, false);
+
+  std::vector<real_type> ret(n_streams, 0.0);
+
+  #pragma omp parallel for schedule(static) num_threads(n_threads)
+  for (int i = 0; i < n_streams; ++i) {
+    for (size_t j = 0; j < n_draws; ++j) {
+      ret[i] += dust::random::random_real<real_type>(rng.state(i));
+    }
+  }
+
+  return ret;
+}
+
+int main(int argc, char* argv[]) {
+  // Extremely simple but non-robust arg handling:
+  if (argc < 2) {
+    std::cout <<
+      "Usage: rnguse <n_draws> [<n_streams> [<seed> [<n_threads>]]]" <<
+      std::endl;
+    return 1;
+  }
+  int n_draws   = atoi(argv[1]);
+  int n_streams = argc < 3 ?  10 : atoi(argv[2]);
+  int seed      = argc < 4 ?  42 : atoi(argv[3]);
+  int n_threads = argc < 5 ?   1 : atoi(argv[4]);
+
+  auto ans = random_sum<double>(n_streams, n_draws, seed, n_threads);
+
+  std::cout << std::setprecision(10);
+  for (int i = 0; i < n_streams; ++i) {
+    std::cout << i << ": " << ans[i] << std::endl;
+  }
+
+  return 0;
+}
+

This program can be compiled with

+
g++ -I$(PATH_DUST_INCLUDE) -O2 -std=c++11 -fopenmp -o rnguse rnguse.cpp
+

where $PATH_DUST_INCLUDE is the path to the header only +library.

+
+
+

Standalone, parallel on a GPU +

+

This is considerably more complicated and will depend on your aims +with your GPU-accelerated program.

+

We include examples +in a repository showing dust::random vs curand +benchmarks. This covers setting up the RNG state so that it can be +set from the host and retrieved, interleaving as appropriate, plus +samples from the uniform, normal, exponential Poisson and binomial +distributions. We overlap with curand only for uniform, +normal, and Poisson. See the repository +for more details.

+
+
+
+

Other packages with similar functionality +

+

There are many packages offering similar functionality to +dust:

+
    +
  • +sitmo +offers several modern RNGs (sitmo, threefry, vandercorput) for +generating standard uniform numbers (U(0, 1)), designed to be usable +from an Rcpp-using package.
    • +
  • +dqrng +offers an overlapping set and generators for normal and exponential +random numbers, also designed to be used with Rcpp and BH.
    • +
  • +rTRNG +exposes “Tina’s Random Number Generator”, among others, and support for +several distributions. It can be used from other packages but requires +linking (i.e., not header only) which does not work on macOS. Generator +jumps typically require a known number of draws per thread.
    • +
  • +miranda +includes support for several underlying generators (including +xoshiro256+) but with a single global state and no support +for use from other packages’ compiled code.
    • +
+

Why does this package exist? We had a set of needs that meant using +the a

+
    +
  • generation of single precision float numbers with the +same interface
    • +
  • absolutely no global state
    • +
  • nice interface for reproducible parallel random number generation +where the generated number does not depend on the number of threads +used
    • +
  • possible to use on GPUs; this exposes some exotic issues around what +types of structures can be used
    • +
  • minimal dependencies and impact on the C++ code (e.g., no boost/BH) +and header-only in order to satisfy the above
    • +
  • support for additional distributions, especially binomial, in a +thread-safe way, optimised for rapidly changing parameters
    • +
+

On this last point; we noticed that many distribution packages, +including Boost.Random (and to a degree R’s random functions) assume +that you want to sample many random numbers from a distribution with +fixed parameters. This is probably reasonable in many cases, but in the +use case we had (stochastic simulation models) we expected that all +parameters were likely to change at every iteration. These different +approaches have important tradeoffs - if you will take many samples from +a single distribution you might compute tables of coefficients once and +use them many times which will make the sampling faster, but this will +be wasteful if only a single sample is taken before the parameters +change.

+

The situation is slightly more complex on a GPU where we need to make +sure that different threads within a block do not get needlessly onto +different branches of conditional logic. Things like early exits need to +be avoided and we have carefully profiled to make sure that threads +within a warp end up re-synchronised at the optimal spot (see for +example this +blog post on __syncwarp).

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
+ + + + + + + + diff --git a/articles/rng_algorithms.html b/articles/rng_algorithms.html new file mode 100644 index 000000000..ec0ad7c7b --- /dev/null +++ b/articles/rng_algorithms.html @@ -0,0 +1,525 @@ + + + + + + + +Algorithms used to compute random numbers • dust + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Algorithms used to compute random numbers

+ + + Source: vignettes/rng_algorithms.Rmd + + +
+ + + +

The dust package includes three algorithms for computing +normally distributed random numbers, all of which should be faster than +R’s rnorm when called from R on a single thread:

+
+rng <- dust::dust_rng$new(NULL)
+n <- 1e6
+bench::mark(
+  r = rnorm(n),
+  box_muller = rng$random_normal(n, algorithm = "box_muller"),
+  polar = rng$random_normal(n, algorithm = "polar"),
+  ziggurat = rng$random_normal(n, algorithm = "ziggurat"),
+  check = FALSE, time_unit = "ms")
+#> # A tibble: 4 × 6
+#>   expression   min median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr> <dbl>  <dbl>     <dbl> <bch:byt>    <dbl>
+#> 1 r          48.4   48.6       20.6    7.63MB     4.58
+#> 2 box_muller 41.8   41.9       23.8    7.63MB     7.95
+#> 3 polar      27.7   27.7       36.0    7.63MB     7.20
+#> 4 ziggurat    8.39   8.73     115.     7.63MB    26.1
+

(This is not their intended purpose of course - that is to be called +from C++ in parallel.) This document collects some notes on the +algorithms that underlie the code used.

+
+

Box-Muller +

+
+n <- 1e5
+theta <- 2 * pi * runif(n)
+r <- sqrt(-2 * log(runif(n)))
+r1 <- r * cos(theta)
+r2 <- r * sin(theta)
+

Here are density plots from these samples against the expectation

+
+plot(dnorm, -4, 4)
+lines(density(r1), col = "red")
+lines(density(r2), col = "blue")
+

+

and the covariance between the two draws is statistically zero:

+
+cov(r1, r2)
+#> [1] -0.003025577
+

Because we’re interested in running these algorithms in parallel we +have opted to discard the second draw (not running sin as +above). The simplest way to implement using both draws involves keeping +a record of your previous spare draw, but doing that in parallel +requires that each thread must be able to do that. We may change this in +future, or expose some system to enable doing this in a thread-safe +way.

+
+
+

Polar +

+

The polar method improves on the Box-Muller method by avoiding the +trigonometric functions at the expense of doing more random number +draws.

+

We first generate points on the unit circle (i.e., a pair +(x, y) such that +x^2 + y^2 < 1). Then, letting s be the +distance between x and y, we can generate two values +x * sqrt(-2 * log(s) / s) and +y * sqrt(-2 * log(s) / s)

+
+n <- 1e5
+x <- runif(n, -1, 1)
+y <- runif(n, -1, 1)
+s <- x * x + y * y
+i <- s < 1 # accept
+r1 <- x[i] * sqrt(-2 * log(s[i]) / s[i])
+r2 <- y[i] * sqrt(-2 * log(s[i]) / s[i])
+plot(dnorm, -4, 4)
+lines(density(r1), col = "red")
+lines(density(r2), col = "blue")
+

+

Again the covariance is essentially zero

+
+cov(r1, r2)
+#> [1] 0.0003916808
+

Here it’s a bit more painful to discard the second draw as it’s +almost free; we already have the second term which cost us one call to +log and we need only do one multiply to get the second. +This would be worse if ziggurat wasn’t much faster.

+
+
+

Ziggurat +

+

The “Ziggurat method” draws random numbers from some distribution by +a rejection sampling scheme. Unfortunately most implementations are +opaque, both because they were written in C and because they have been +milked for every bit of performance possible. We wanted a version that +was fast, but also easy to understand and to relate to the original +papers.

+

The principal reference we will follow is Doornik 2005. +As with that paper, we consider an non-normalised right hand side of the +normal distribution:

+
+f <- function(x) {
+  exp(-x^2 / 2)
+}
+curve(f, 0, 4, las = 1)
+

+

It will be useful to also have functions f_inv (the +inverse of f) and f_int (the integral of +f from x to infinity)

+
+f_inv <- function(y) {
+  sqrt(-2 * log(y))
+}
+f_int <- function(r) {
+  pnorm(r, lower.tail = FALSE) / dnorm(0)
+}
+

To work with the algorithm we need to cover this curve with +n evenly sized rectangles, with the lowest one having +infinite width. We’ll use these rectangles for the sampling scheme, +described below

+

+

Finding these rectangles turns out to be nontrivial.

+

Suppose we want to cover f with 6 rectangles; to do this +we need to find the area of each of the rectangles (will be slightly +larger area under f divided by n due to the +overhangs) and a series of x points (x1, +x2, …, xn) with the last one being 0

+
    +
  1. First we make a starting guess as to the x location of +the final rectangle, say r +
    2. +
  2. We then compute the volume of the lowest rectangle as +f(r) * r + f_int(r) +
    3. +
  3. We can then compute the size of the 2nd rectangle as +f_inv(f(r) + v / r) +
    4. +
  4. Continue this until all ‘x’ values have been computed, replacing +r above with the x value from the previous +iteration
    5. +
+

From the diagram above it looks like x1 might be a bit +bigger than 2. Starting with a guess of 2.2:

+
+n <- 6
+r <- 2.2
+v <- r * f(r) + f_int(r)
+x <- numeric(6)
+x[1] <- r
+for (i in 2:(n - 1)) {
+  x[i] <- f_inv(f(x[i - 1]) + v / x[i - 1])
+}
+

We now have a series of x values

+
+x
+#> [1] 2.2000000 1.8119187 1.5077600 1.2223596 0.9077862 0.0000000
+

The area of the final rectangle must be

+
+x[n - 1] * (f(0) - f(x[n - 1]))
+#> [1] 0.3065602
+

which is bigger than all the others, which have area +v. If we’d made our original guess too small (say 2.1) then +we’d have too small a final area. We can capture this in a +small nonlinear equation to solve:

+
+target <- function(r, n = 6) {
+  v <- r * f(r) + f_int(r)
+  x <- r
+  for (i in 2:(n - 1)) {
+    x <- f_inv(f(x) + v / x)
+  }
+  x * (f(0) - f(x)) - v
+}
+target(2.2)
+#> [1] 0.07608185
+target(2.1)
+#> [1] -0.2233091
+

This is easily solved by uniroot:

+
+ans <- uniroot(target, c(2.1, 2.2))
+ans
+#> $root
+#> [1] 2.176047
+#> 
+#> $f.root
+#> [1] -3.954086e-05
+#> 
+#> $iter
+#> [1] 3
+#> 
+#> $init.it
+#> [1] NA
+#> 
+#> $estim.prec
+#> [1] 6.103516e-05
+

This approach works for any n, though in practice some +care is needed to select good bounds.

+

Once we have found this value, we can compute our series of +x values as above:

+
+r <- ans$root
+v <- r * f(r) + f_int(r)
+x <- numeric(n)
+x[1] <- r
+for (i in 2:(n - 1)) {
+  x[i] <- f_inv(f(x[i - 1]) + v / x[i - 1])
+}
+x
+#> [1] 2.1760469 1.7818609 1.4695742 1.1712803 0.8287847 0.0000000
+
+
+

Sampling +

+

To sample from the distribution using these rectangles we do:

+
    +
  1. select a rectangle to sample from (an integer between 1 and +n)
    2. +
  2. select a random number u (between 0 and 1); scale this +by x[i] to get z +
    3. +
  3. if i == 0 (the base layer) +
      +
    1. if z < r then the point lies in the rectangle and +can be accepted
      2. +
    2. otherwise draw from the tail and accept that point (see +below)
      3. +
    +
    4. +
  4. if i > 1 (any other layer): +
      +
    • if z < x[i - 1] then the point lies entirely within +the distribution and can be accepted
      • +
    • otherwise test the edges once and accept that point or return to +the first step of the algorithm +
      • +
    +
    5. +
+

Note the slightly different alternative conditions for the base layer +and others; for the base layer we will find a sample from the +tail even if it takes a few goes, but for the regions with overlaps we +only try once and if that does not succeed we start again by selecting a +new layer.

+
+

Sampling from the tail +

+

For sampling from the tail we use the algorithm of Marsaglia (1963); +given U(0, 1) random numbers u1 and u2 and +using the value of r from above (i.e., +x[1]):

+
    +
  1. Let x = -log(u1) / r +
    2. +
  2. Let y = -log(u2) +
    3. +
  3. If 2 y > x^2 accept x + r, otherwise +try again
    4. +
+

To see this in action, first, let’s generate a set of normal draws +from the tail (beyond x[1])

+
+z <- abs(rnorm(1e7))
+z <- z[z >= r]
+hist(z - r, nclass = 30, freq = FALSE)
+curve(dnorm(x + r) / pnorm(r, lower.tail = FALSE), add = TRUE, col = "red")
+

+

The curve is the analytical density function, shifted by +r along the x-axis and scaled so that the area under the +tail is 1.

+

Generating a reasonably large number of samples (here 10 thousand) +shows a good agreement between the samples and the expectation:

+
+sx <- -log(runif(1e5)) / r
+sy <- -log(runif(1e5))
+accept <- 2 * sy > sx^2
+hist(sx[accept], nclass = 30, freq = FALSE, xlim = c(0, 3))
+curve(dnorm(x + r) / pnorm(r, lower.tail = FALSE), add = TRUE, col = "red")
+

+

With the relatively low r here, our acceptance +probability is not bad (~86 %) but as r increases it will +improve:

+
+sx <- -log(runif(1e5)) / 3.9
+sy <- -log(runif(1e5))
+mean(2 * sy > sx^2)
+#> [1] 0.94554
+
+
+

The edges +

+

If our point in layer i (i > 1) lies +outside of the safe zone we need to do a full rejection sample. We start +by illustrating this graphically; given two U(0, 1) numbers scaled to +(x[3], x[2]) and f(x[3]), f(x[2]) we would +accept the blue points below but not the red ones:

+
+plot(f, x[3] - 0.05, x[2] + 0.05)
+abline(v = x[2:3], lty = 3)
+abline(h = f(x[2:3]))
+
+f0 <- f(x[3])
+f1 <- f(x[2])
+u1 <- runif(100, x[3], x[2]) # these ones are filtered already
+u2 <- runif(100)
+y <- f0 + u2 * (f1 - f0)
+accept <- y < f(u1)
+points(u1, y, col = ifelse(accept, "blue", "red"), pch = 19, cex = 0.25)
+

+

The above calculation computes three values of f; for +x[2], x[3] and u1, each of these +involves a calculation of exp() which is fairly costly. +Adding in tables of fx = f(x) actually slows things down +slightly as well as increasing the number of constants rattling around +the program.

+

Alternatively if we take the acceptance equation:

+
f(x[3]) + u2 * (f(x[2]) - f(x[3])) < f(u1)
+

and divide both sides by f(u1) we get

+
f(x[3]) / f(u1) + u2 * (f(x[2]) / f(u1) - f(x[3]) / f(u1)) < 1
+

then we can rearrange slightly using the fact that +f(a) / f(b) = exp(-0.5 * (a^2 - b^2) to write

+
f2_u1 <- exp(-0.5 * (x[2]^2 - u1^2))
+f3_u1 <- exp(-0.5 * (x[3]^2 - u1^2))
+

which we can use to get the same acceptance as above:

+
table(f3_u1 + u2 * (f2_u1 - f3_u1) < 1.0, accept)
+

This is the approach we use in the implementation.

+
+
+
+

Optimisations +

+

In the naive version we draw a random number on [0, 1) +and compare that with the bounds x.

+

Suppose we are sampling in the 3rd layer; we draw a random number +u and scale it by x[2], then accept if that +scaled value is less than x[3], otherwise check to see if +we are in the tail

+
+u <- runif(50)
+z <- u * x[2]
+z < x[3]
+#>  [1] FALSE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE FALSE  TRUE
+#> [13]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE
+#> [25] FALSE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE  TRUE FALSE  TRUE  TRUE  TRUE
+#> [37]  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE  TRUE FALSE  TRUE FALSE  TRUE
+#> [49]  TRUE  TRUE
+

Most of the numbers are accepted (this is the point of the algorithm +and that acceptance probability increases as n does).

+

There are two tricks that can be done here to make this more +efficient. First we can notice that the above calculation is equivalent +to u < x[3] / x[2]:

+
+all((u < x[3] / x[2]) == (u * x[2] < x[3]))
+#> [1] TRUE
+

and by saving the values of x[i] / x[i - 1] in our +tables we can avoid many multiplications.

+

In the description above, we take two random draws at first - one for +the layer and one for the x position. Some implementation +do that with a single draw but this is not safe if your random number +generator works in terms of 32 bit integers (see Doornik 2005) +as all bits are needed to convert to a double and this creates a +correlation between the layer and the position.

+

However, most of our random number generators work with 64 bit +integers and we only use the top 53 bits to make a double-precision +number. So we take bits 4 to 11 to create the integer between 0 and 255 +for the layer. If using a 32 bit generator (one of the +xoshiro128 generators) then a second number will be used; +this decision will be made at compile time so should come with no +runtime cost. With the + scramblers the lower bits are not +of the same quality (See this +paper) but for xoshiro256+ by the 4th bit the +randomness should be of sufficient quality.

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
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zTQljX`&D&<*S=u~%vF0;7{l0QfWLv1SWNMOdb`4k^>~r?GIz!_{-O7Cng3TmZQ7Uu j&|yc*e+2x# + + + + + + +Distributed parallel random numbers • dust + + + + + + + + + + + + + + + + + + + +

+ + + + + + + + diff --git a/articles/rng_package.html b/articles/rng_package.html new file mode 100644 index 000000000..46da9b7de --- /dev/null +++ b/articles/rng_package.html @@ -0,0 +1,501 @@ + + + + + + + +Using RNGs from packages • dust + + + + + + + + + + + + + + + + + + + +
+
+ + + + +
+
+
+

Using RNGs from packages

+ + + Source: vignettes/rng_package.Rmd + + +
+ + + + +

The dust random number generators are suitable for use from other +packages and we provide a few helpers in both R and C++ to make this +easier.

+

For illustration purposes we will assume that you want to estimate pi +using rejection sampling. The basic idea of this algorithm is simple; +sample two U(0, 1) points x and y and test if +they lie in the unit circle (i.e. sqrt(x^2 + x^2) < 1) +giving the ratio of the area of a unit circle to a square. Multiplying +the fraction of the points that we accept by 4 yields our estimate of +pi.

+
+

Background using R’s random number generator +

+

First, an example that uses R’s API for example (note that while the +R API is C, we’re using the cpp11 package interface here so that the +following examples are similar):

+
#include <cpp11.hpp>
+#include <R_ext/Random.h>
+
+[[cpp11::register]]
+double pi_r(int n) {
+  int tot = 0;
+  GetRNGstate();
+  for (int i = 0; i < n; ++i) {
+    const double u1 = unif_rand();
+    const double u2 = unif_rand();
+    if (u1 * u1 + u2 * u2 < 1) {
+      tot++;
+    }
+  }
+  PutRNGstate();
+  return tot / static_cast<double>(n) * 4.0;
+}
+

With cpp11 we can load this with cpp11::cpp_source

+
+cpp11::cpp_source("rng_pi_r.cpp")
+

and then run it with

+
+pi_r(1e6)
+#> [1] 3.139504
+

The key bits within the code above are that we:

+
    +
  • included random number support from R via the +R_ext/Random.h header
    • +
  • initialised the state of the global random number stream within our +C++ context with GetRNGstate before drawing any random +numbers
    • +
  • drew some possible large number of numbers using +unif_rand +
    • +
  • restored the random number state back to R.
    • +
+

Failure to run the GetRNGstate / +PutRNGstate will result in the stream not behaving +properly. This is explained in detail in the “Writing R Extensions” +manual.

+
+
+

Basic implementation using dust +

+

The implementation in dust will look very similar to above, but the +way that we cope with the random number stream will look quite +different. With the R version above we are looking after R’s global +stream (stored in the variable .Random.seed) and making +sure that it is fetched and set on entry and exit to the function.

+

One of the design ideas in dust is that there is no single global +source of random numbers, so we need to create a source that our +function can use. If we were to use the simulation function multiple +times we would want the stream to pick up where it left off last time, +so the act of calling the function should update the seed as a “side +effect”.

+

The way we expose this for use within other packages is that the user +(either package developer or user of the package) creates a “pointer” to +some random number state. Passing that state into a C++ function will +allow use of the random functions within dust, and will update the state +correctly (see the following section for details).

+

First we create a pointer object:

+
+rng <- dust:::dust_rng_pointer$new()
+rng
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 2f d6 21 97 9b 4f 43 00 59 87 46 42 d6 ff e5 e4 e8 de d7 ...
+

Unlike the dust::dust_rng object there are no real +useful methods on this object and from the R side we’ll treat it as a +black box. Importantly the rng object knows which algorithm +it has been created to use

+
+rng$algorithm
+#> [1] "xoshiro256plus"
+

The default will be suitable for most purposes.

+

We can rewrite the pi approximation function as:

+
#include <cpp11.hpp>
+#include <dust/r/random.hpp>
+
+[[cpp11::linking_to(dust)]]
+[[cpp11::register]]
+double pi_dust(int n, cpp11::sexp ptr) {
+  auto rng =
+    dust::random::r::rng_pointer_get<dust::random::xoshiro256plus>(ptr);
+  auto& state = rng->state(0);
+  int tot = 0;
+  for (int i = 0; i < n; ++i) {
+    const double u1 = dust::random::random_real<double>(state);
+    const double u2 = dust::random::random_real<double>(state);
+    if (u1 * u1 + u2 * u2 < 1) {
+      tot++;
+    }
+  }
+  return tot / static_cast<double>(n) * 4.0;
+}
+

This snippet looks much the same as above:

+
    +
  • We’ve added [[cpp::linking_to(dust)]] and included the +dust random interface (dust/r/random.hpp)
    • +
  • The first line of the function safely creates a pointer to the +random state data. The template argument here +(<dust::random::xoshiro256plus>) refers to the rng +algorithm and matches rng$algorithm +
    • +
  • The second line extracts a reference to the first (C++ indexing +starting at 0) random number stream - this pair of lines is roughly +equivalent to GetRNGstate() except that that the random +numbers do not come from some global source
    • +
  • After that the listing proceeds as before proceeds as before, except +there is no equivalent to PutRNGstate() because the pointer +object takes care of this automatically.
    • +
+
+cpp11::cpp_source("rng_pi_dust.cpp")
+

and then run it with

+
+pi_dust(1e6, rng)
+#> [1] 3.14206
+

The C++ interface is described in more detail in the online +documentation

+
+
+

Parallel implementation with dust and OpenMP +

+

Part of the point of dust’s random number generators is that they +create independent streams of random numbers that can be safely used in +parallel.

+
#include <cpp11.hpp>
+#include <dust/r/random.hpp>
+
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+
+[[cpp11::linking_to(dust)]]
+[[cpp11::register]]
+double pi_dust_parallel(int n, cpp11::sexp ptr, int n_threads) {
+  auto rng =
+    dust::random::r::rng_pointer_get<dust::random::xoshiro256plus>(ptr);
+  const auto n_streams = rng->size();
+  int tot = 0;
+#ifdef _OPENMP
+#pragma omp parallel for schedule(static)  num_threads(n_threads) \
+  reduction(+:tot)
+#endif
+  for (size_t i = 0; i < n_streams; ++i) {
+    auto& state = rng->state(0);
+    int tot_i = 0;
+    for (int i = 0; i < n; ++i) {
+      const double u1 = dust::random::random_real<double>(state);
+      const double u2 = dust::random::random_real<double>(state);
+      if (u1 * u1 + u2 * u2 < 1) {
+        tot_i++;
+      }
+    }
+    tot += tot_i;
+  }
+  return tot / static_cast<double>(n * n_streams) * 4.0;
+}
+
+cpp11::cpp_source("rng_pi_parallel.cpp")
+

Here we’ve made a number of decisions about how to split the problem +up subject to a few constraints about using OpenMP together with R:

+
    +
  • Generally speaking we want the answer to be independent of the +number of threads used to run it, as this will vary in different +sessions. As such avoid the temptation to do a loop over the threads; +here we instead iterate over streams with the idea that there +will be one or more streams used per threads. If we ran a single thread +we’d get the same answer as if we ran one thread per stream.
    • +
  • Each thread is going to do it’s own loop of length n so +we need to divide by n * n_streams at the end as that’s +many attempts we have made.
    • +
  • We use OpenMP’s reduction clause to safely accumulate +the different subtotals (the tot_i values) into one +tot value.
    • +
  • In order to compile gracefully on machines that do not have OpenMP +support both the #include <omp.h> line and the +#pragma omp line are wrapped in guards that test for +_OPENMP (see “Writing R Extensions”).
    • +
  • We let the generator tell us how many streams it has +(n_streams = rng->size()) but we could as easily specify +an ideal number of streams as an argument here and then test that the +generator has at least that many by adding an argument to the +call to rng_pointer_get (e.g., if we wanted m +streams the call would be +rng_pointer_get<type>(ptr, m))
    • +
+
+rng <- dust:::dust_rng_pointer$new(n_streams = 20)
+pi_dust_parallel(1e6, rng, 4)
+#> [1] 3.140963
+

Unfortunately cpp11::cpp_source +does not support using OpenMP so in the example above the code will +run in serial and we can’t see if parallelisation will help.

+

In order to compile with support, we need to build a little package +and set up an appropriate Makevars file

+

The package is fairly minimal:

+
#> .
+#> ├── DESCRIPTION
+#> ├── NAMESPACE
+#> └── src
+#>     ├── Makevars
+#>     └── code.cpp
+

We have an extremely minimal DESCRIPTION, which contains +line LinkingTo: cpp11, dust from which R will arrange +compiler flags to find both packages’ headers:

+
Package: piparallel
+LinkingTo: cpp11, dust
+Version: 0.0.1
+

The NAMESPACE loads the dynamic library

+
useDynLib("piparallel", .registration = TRUE)
+exportPattern("^[[:alpha:]]+")
+

The src/Makevars file contains important flags to pick +up OpenMP support:

+
PKG_CXXFLAGS=-DHAVE_INLINE $(SHLIB_OPENMP_CXXFLAGS)
+PKG_LIBS=$(SHLIB_OPENMP_CXXFLAGS)
+

And src/code.cpp contains the file above but without the +[[cpp11::linking_to(dust)]] line:

+
#include <cpp11.hpp>
+#include <dust/r/random.hpp>
+
+#ifdef _OPENMP
+#include <omp.h>
+#endif
+
+[[cpp11::register]]
+double pi_dust_parallel(int n, cpp11::sexp ptr, int n_threads) {
+  auto rng =
+    dust::random::r::rng_pointer_get<dust::random::xoshiro256plus>(ptr);
+  const auto n_streams = rng->size();
+  int tot = 0;
+#ifdef _OPENMP
+#pragma omp parallel for schedule(static)  num_threads(n_threads) \
+  reduction(+:tot)
+#endif
+  for (size_t i = 0; i < n_streams; ++i) {
+    auto& state = rng->state(0);
+    int tot_i = 0;
+    for (int i = 0; i < n; ++i) {
+      const double u1 = dust::random::random_real<double>(state);
+      const double u2 = dust::random::random_real<double>(state);
+      if (u1 * u1 + u2 * u2 < 1) {
+        tot_i++;
+      }
+    }
+    tot += tot_i;
+  }
+  return tot / static_cast<double>(n * n_streams) * 4.0;
+}
+

After compiling and installing the package, +pi_dust_parallel will be available

+

Now we have a parallel version we can see a speed-up as we add +threads:

+
+rng <- dust:::dust_rng_pointer$new(n_streams = 20)
+bench::mark(
+  pi_dust_parallel(1e6, rng, 1),
+  pi_dust_parallel(1e6, rng, 2),
+  pi_dust_parallel(1e6, rng, 3),
+  pi_dust_parallel(1e6, rng, 4),
+  check = FALSE)
+#> # A tibble: 4 x 6
+#>   expression                           min   median `itr/sec` mem_alloc `gc/sec`
+#>   <bch:expr>                      <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
+#> 1 pi_dust_parallel(1e+06, rng, 1)   46.4ms   47.2ms      21.2        0B        0
+#> 2 pi_dust_parallel(1e+06, rng, 2)   23.1ms   23.8ms      42.1        0B        0
+#> 3 pi_dust_parallel(1e+06, rng, 3)   16.1ms   16.2ms      60.6        0B        0
+#> 4 pi_dust_parallel(1e+06, rng, 4)   11.6ms   12.5ms      73.6        0B        0
+
+
+

More on the pointer object +

+

This section aims to de-mystify the pointer objects a little. The +dust random number state is a series of integers (by default 64-bit +unsigned integers) that are updated each time a state is drawn (see +vignette("rng.Rmd")). We expose this state to R as a vector +of “raw” values (literally a series of bytes of data).

+
+rng <- dust::dust_rng$new(seed = 1)
+rng$state()
+#>  [1] c1 5c 02 89 ec 2d 0a 91 1e 61 39 74 08 ab 41 5e c3 86 8d 6d f4 02 8a b1 56
+#> [26] 49 ee d9 dd 95 81 e2
+

When numbers are drawn from the stream, the state is modified as a +side-effect:

+
+rng$random_real(20)
+#>  [1] 0.451351392 0.073534657 0.218129406 0.200139527 0.017172743 0.323288520
+#>  [7] 0.338823899 0.862898581 0.005702738 0.006453255 0.844823829 0.222676329
+#> [13] 0.665130023 0.283016916 0.502155564 0.290045309 0.055841255 0.083163285
+#> [19] 0.391729373 0.744045249
+rng$state()
+#>  [1] 2c ed 49 d0 8f 7e 97 2c 2a 5e 9e a1 78 85 47 80 06 d5 05 38 a3 5b 08 12 59
+#> [26] 12 03 5c b3 ea 87 c8
+

The same happens with our dust_rng_pointer objects used +above:

+
+ptr <- dust::dust_rng_pointer$new(seed = 1)
+ptr$state()
+#>  [1] c1 5c 02 89 ec 2d 0a 91 1e 61 39 74 08 ab 41 5e c3 86 8d 6d f4 02 8a b1 56
+#> [26] 49 ee d9 dd 95 81 e2
+

Note that ptr starts with the same state here as +rng did because we started from the same seed. When we draw +20 numbers from the stream (by drawing 10 pairs of numbers with our +pi-estimation algorithm), we will advance the state

+
+pi_dust(10, ptr)
+#> [1] 4
+ptr$state()
+#>  [1] 2c ed 49 d0 8f 7e 97 2c 2a 5e 9e a1 78 85 47 80 06 d5 05 38 a3 5b 08 12 59
+#> [26] 12 03 5c b3 ea 87 c8
+

Note that the state here now matches the value returned by +rng.

+

Normally nobody needs to know this - treat the pointer as an object +that you pass to functions and ignore the details.

+
+
+ + + +
+ + + +
+

+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

+

Site built with pkgdown 2.0.7.

+
+ +
+
+ + + + + + + + diff --git a/authors.html b/authors.html new file mode 100644 index 000000000..b3860fd0b --- /dev/null +++ b/authors.html @@ -0,0 +1,147 @@ + +Authors and Citation • dust + + +
+
+ + + +
+
+
+
+

Authors

+
+ + +
  • +

    Rich FitzJohn. Author, maintainer. +

    +
    • +
  • +

    Alex Hill. Author. +

    +
    • +
  • +

    John Lees. Author. +

    +
    • +
  • +

    Imperial College of Science, Technology and Medicine. Copyright holder. +

    +
    • +
+
+
+

Citation

+ Source: inst/CITATION +
+
+ + +

FitzJohn et al. 2021 Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate. Wellcome Open Research 5, 288 <doi:10.12688/wellcomeopenres.16466.2>

+ 
@Article{,
+  title = {Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate},
+  author = {Richard G. FitzJohn and Edward S. Knock and Lilith K. Whittles and Pablo N. Perez-Guzman and Sangeeta Bhatia and Fernando Guntoro and Oliver J. Watson and Charles Whittaker and Neil M. Ferguson and Anne Cori and Marc Baguelin and John A. Lees},
+  journal = {Wellcome Open Research},
+  year = {2021},
+  volume = {5},
+  pages = {288},
+  doi = {10.12688/wellcomeopenres.16466.2},
+}
+ +
+ +
+ + + +
+

Developed by Rich FitzJohn, Alex Hill, John Lees.

+
+ +
+

Site built with pkgdown 2.0.7.

+
+ +
+ + + + + + + + diff --git a/bootstrap-toc.css b/bootstrap-toc.css new file mode 100644 index 000000000..5a859415c --- /dev/null +++ b/bootstrap-toc.css @@ -0,0 +1,60 @@ +/*! + * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/) + * Copyright 2015 Aidan Feldman + * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */ + +/* modified from https://github.com/twbs/bootstrap/blob/94b4076dd2efba9af71f0b18d4ee4b163aa9e0dd/docs/assets/css/src/docs.css#L548-L601 */ + +/* All levels of nav */ +nav[data-toggle='toc'] .nav > li > a { + display: block; + padding: 4px 20px; + font-size: 13px; + font-weight: 500; + color: #767676; +} +nav[data-toggle='toc'] .nav > li > a:hover, +nav[data-toggle='toc'] .nav > li > a:focus { + padding-left: 19px; + color: #563d7c; + text-decoration: none; + background-color: transparent; + border-left: 1px solid #563d7c; +} +nav[data-toggle='toc'] .nav > .active > a, +nav[data-toggle='toc'] .nav > .active:hover > a, +nav[data-toggle='toc'] .nav > .active:focus > a { + padding-left: 18px; + font-weight: bold; + color: #563d7c; + background-color: transparent; + border-left: 2px solid #563d7c; +} + +/* Nav: second level (shown on .active) */ +nav[data-toggle='toc'] .nav .nav { + display: none; /* Hide by default, but at >768px, show it */ + padding-bottom: 10px; +} +nav[data-toggle='toc'] .nav .nav > li > a { + padding-top: 1px; + padding-bottom: 1px; + padding-left: 30px; + font-size: 12px; + font-weight: normal; +} +nav[data-toggle='toc'] .nav .nav > li > a:hover, +nav[data-toggle='toc'] .nav .nav > li > a:focus { + padding-left: 29px; +} +nav[data-toggle='toc'] .nav .nav > .active > a, +nav[data-toggle='toc'] .nav .nav > .active:hover > a, +nav[data-toggle='toc'] .nav .nav > .active:focus > a { + padding-left: 28px; + font-weight: 500; +} + +/* from https://github.com/twbs/bootstrap/blob/e38f066d8c203c3e032da0ff23cd2d6098ee2dd6/docs/assets/css/src/docs.css#L631-L634 */ +nav[data-toggle='toc'] .nav > .active > ul { + display: block; +} diff --git a/bootstrap-toc.js b/bootstrap-toc.js new file mode 100644 index 000000000..1cdd573b2 --- /dev/null +++ b/bootstrap-toc.js @@ -0,0 +1,159 @@ +/*! + * Bootstrap Table of Contents v0.4.1 (http://afeld.github.io/bootstrap-toc/) + * Copyright 2015 Aidan Feldman + * Licensed under MIT (https://github.com/afeld/bootstrap-toc/blob/gh-pages/LICENSE.md) */ +(function() { + 'use strict'; + + window.Toc = { + helpers: { + // return all matching elements in the set, or their descendants + findOrFilter: function($el, selector) { + // http://danielnouri.org/notes/2011/03/14/a-jquery-find-that-also-finds-the-root-element/ + // http://stackoverflow.com/a/12731439/358804 + var $descendants = $el.find(selector); + return $el.filter(selector).add($descendants).filter(':not([data-toc-skip])'); + }, + + generateUniqueIdBase: function(el) { + var text = $(el).text(); + var anchor = text.trim().toLowerCase().replace(/[^A-Za-z0-9]+/g, '-'); + return anchor || el.tagName.toLowerCase(); + }, + + generateUniqueId: function(el) { + var anchorBase = this.generateUniqueIdBase(el); + for (var i = 0; ; i++) { + var anchor = anchorBase; + if (i > 0) { + // add suffix + anchor += '-' + i; + } + // check if ID already exists + if (!document.getElementById(anchor)) { + return anchor; + } + } + }, + + generateAnchor: function(el) { + if (el.id) { + return el.id; + } else { + var anchor = this.generateUniqueId(el); + el.id = anchor; + return anchor; + } + }, + + createNavList: function() { + return $('
    '); + }, + + createChildNavList: function($parent) { + var $childList = this.createNavList(); + $parent.append($childList); + return $childList; + }, + + generateNavEl: function(anchor, text) { + var $a = $(''); + $a.attr('href', '#' + anchor); + $a.text(text); + var $li = $('
  • '); + $li.append($a); + return $li; + }, + + generateNavItem: function(headingEl) { + var anchor = this.generateAnchor(headingEl); + var $heading = $(headingEl); + var text = $heading.data('toc-text') || $heading.text(); + return this.generateNavEl(anchor, text); + }, + + // Find the first heading level (`

    `, then `

    `, etc.) that has more than one element. Defaults to 1 (for `

    `). + getTopLevel: function($scope) { + for (var i = 1; i <= 6; i++) { + var $headings = this.findOrFilter($scope, 'h' + i); + if ($headings.length > 1) { + return i; + } + } + + return 1; + }, + + // returns the elements for the top level, and the next below it + getHeadings: function($scope, topLevel) { + var topSelector = 'h' + topLevel; + + var secondaryLevel = topLevel + 1; + var secondarySelector = 'h' + secondaryLevel; + + return this.findOrFilter($scope, topSelector + ',' + secondarySelector); + }, + + getNavLevel: function(el) { + return parseInt(el.tagName.charAt(1), 10); + }, + + populateNav: function($topContext, topLevel, $headings) { + var $context = $topContext; + var $prevNav; + + var helpers = this; + $headings.each(function(i, el) { + var $newNav = helpers.generateNavItem(el); + var navLevel = helpers.getNavLevel(el); + + // determine the proper $context + if (navLevel === topLevel) { + // use top level + $context = $topContext; + } else if ($prevNav && $context === $topContext) { + // create a new level of the tree and switch to it + $context = helpers.createChildNavList($prevNav); + } // else use the current $context + + $context.append($newNav); + + $prevNav = $newNav; + }); + }, + + parseOps: function(arg) { + var opts; + if (arg.jquery) { + opts = { + $nav: arg + }; + } else { + opts = arg; + } + opts.$scope = opts.$scope || $(document.body); + return opts; + } + }, + + // accepts a jQuery object, or an options object + init: function(opts) { + opts = this.helpers.parseOps(opts); + + // ensure that the data attribute is in place for styling + opts.$nav.attr('data-toggle', 'toc'); + + var $topContext = this.helpers.createChildNavList(opts.$nav); + var topLevel = this.helpers.getTopLevel(opts.$scope); + var $headings = this.helpers.getHeadings(opts.$scope, topLevel); + this.helpers.populateNav($topContext, topLevel, $headings); + } + }; + + $(function() { + $('nav[data-toggle="toc"]').each(function(i, el) { + var $nav = $(el); + Toc.init($nav); + }); + }); +})(); diff --git a/cpp/.buildinfo b/cpp/.buildinfo new file mode 100644 index 000000000..bf387f3ce --- /dev/null +++ b/cpp/.buildinfo @@ -0,0 +1,4 @@ +# Sphinx build info version 1 +# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done. +config: 15f7815782eb6c4c234eed8799a76bca +tags: 645f666f9bcd5a90fca523b33c5a78b7 diff --git a/cpp/_sources/index.rst.txt b/cpp/_sources/index.rst.txt new file mode 100644 index 000000000..1ea923602 --- /dev/null +++ b/cpp/_sources/index.rst.txt @@ -0,0 +1,10 @@ +dust C++ documentation +====================== + +.. toctree:: + :maxdepth: 2 + :caption: Contents: + + random + +This set of pages describes the ``dust`` C++ API in more detail than that discussed in the main ``dust`` documentation. Principally it covers the random number library. diff --git a/cpp/_sources/random-distributions.rst.txt b/cpp/_sources/random-distributions.rst.txt new file mode 100644 index 000000000..d06034360 --- /dev/null +++ b/cpp/_sources/random-distributions.rst.txt @@ -0,0 +1,52 @@ +Distributions +============= + +Our distribution support will grow over time. If you need a distribution that is not yet supported please `post an issue `. + + +Uniform +------- + +.. doxygenfunction:: dust::random::uniform + +Normal +------ + +.. doxygenfunction:: dust::random::normal + +The enum ``dust::random::algorithm::normal`` controls the normal algorithm used for a given draw + +.. doxygenenum:: dust::random::algorithm::normal + +Binomial +-------- + +.. doxygenfunction:: dust::random::binomial + +Hypergeometric +-------------- + +.. doxygenfunction:: dust::random::hypergeometric + +Exponential +----------- + +.. doxygenfunction:: dust::random::exponential + +Poisson +------- + +.. doxygenfunction:: dust::random::poisson + +Multinomial +----------- + +.. doxygenfunction:: dust::random::multinomial(rng_state_type&, int, const T&, int, U&) + +Example +------- + +.. literalinclude:: examples/random-univariate.cpp + +.. literalinclude:: examples/random-univariate.out + :language: text diff --git a/cpp/_sources/random-jump.rst.txt b/cpp/_sources/random-jump.rst.txt new file mode 100644 index 000000000..e866ab329 --- /dev/null +++ b/cpp/_sources/random-jump.rst.txt @@ -0,0 +1,16 @@ +Advancing the random number state via jumps +=========================================== + +There are two functions for jumping the random number state: + +.. doxygenfunction:: jump(T&) + +.. doxygenfunction:: long_jump(T&) + +Example +------- + +.. literalinclude:: examples/random-jump.cpp + +.. literalinclude:: examples/random-jump.out + :language: text diff --git a/cpp/_sources/random-parallel.rst.txt b/cpp/_sources/random-parallel.rst.txt new file mode 100644 index 000000000..73202f84e --- /dev/null +++ b/cpp/_sources/random-parallel.rst.txt @@ -0,0 +1,13 @@ +Parallel random number object +============================= + +.. doxygenclass:: dust::random::prng + :members: + +Example +------- + +.. literalinclude:: examples/random-prng.cpp + +.. literalinclude:: examples/random-prng.out + :language: text diff --git a/cpp/_sources/random-primitive.rst.txt b/cpp/_sources/random-primitive.rst.txt new file mode 100644 index 000000000..f244132a0 --- /dev/null +++ b/cpp/_sources/random-primitive.rst.txt @@ -0,0 +1,33 @@ +Primitive random number generation functions +============================================ + +Uniform +------- + +The workhorse random number generating function is `random_real`: + +.. doxygenfunction:: random_real + +Integer +-------- + +There is also a low-level function for generating integers of a given width: + +.. doxygenfunction:: random_int + +Note that this **does not** generate an arbitrary integer within some specified range; you are limited to C++ integer types. + +Normal +------ + +The standard normal distribution also gets special treatment. + +.. doxygenfunction:: random_normal + +Example +------- + +.. literalinclude:: examples/random-primitive.cpp + +.. literalinclude:: examples/random-primitive.out + :language: text diff --git a/cpp/_sources/random-r.rst.txt b/cpp/_sources/random-r.rst.txt new file mode 100644 index 000000000..ea14fe7fb --- /dev/null +++ b/cpp/_sources/random-r.rst.txt @@ -0,0 +1,22 @@ +Random number interface from R +============================== + +We provide several functions for use from within R packages, all of which are in the namespace ``dust::random::r``. These are further described in `the package vignette `__ + +To access these functions you must have the ``cpp11`` package available and include ````. + +Seeding the generator +--------------------- + +As a slightly more convienient interace for seeding generators + +.. doxygenfunction:: as_rng_seed + +Once you have a seed, there's no direct interaction with the dust R API any further - you have a seed and can draw numbers as described elsewhere in this manual. + +Persistent streams +------------------ + +To provide access to `persistent streams `__ (see also `the reference documentation `__) + +.. doxygenfunction:: rng_pointer_get diff --git a/cpp/_sources/random-seed.rst.txt b/cpp/_sources/random-seed.rst.txt new file mode 100644 index 000000000..b3ca59ca5 --- /dev/null +++ b/cpp/_sources/random-seed.rst.txt @@ -0,0 +1,20 @@ +Seeding +========== + +We can initialise the random number state with any state that is not zero everywhere. Do do this, we take an integer and pass it through the ``splitmix64`` algorithm until we have enough random state; this depends on the generator involved; a xoshiro512 generator requires more starting seed than a xoshiro128 generator. + +These seedings functions are designed so that any single integer may be passed into them. The first form returns an initialised state: + +.. doxygenfunction:: seed(uint64_t) + +The second initialises a state in-place: + +.. doxygenfunction:: seed(T&, uint64_t) + +Example +------- + +.. literalinclude:: examples/random-seed.cpp + +.. literalinclude:: examples/random-seed.out + :language: text diff --git a/cpp/_sources/random-state.rst.txt b/cpp/_sources/random-state.rst.txt new file mode 100644 index 000000000..b3587accd --- /dev/null +++ b/cpp/_sources/random-state.rst.txt @@ -0,0 +1,63 @@ +Random number state +=================== + +Typically, you don't need to think much about the state used; in the simple example we do + +.. literalinclude:: examples/random-simple.cpp + +This pattern will typically be sufficient - use `dust::random::generator` to select an appropriate algorithm for your floating point type, and use `auto` to save it. This will select `dust::random::xoshiro256plus` for `double` and `dust::random::xoshiro128plus` for `float` + +Core state class +---------------- + +Every random number state is built on the same core class + +.. doxygenclass:: dust::random::xoshiro_state + :members: + +.. note this formats incorrectly, see + https://github.com/michaeljones/breathe/issues/761 + +Every random number state uses one of the three scrambler options, described based on the mathematical operations they perform when creating the final integer from the generator + +.. doxygenenum:: dust::random::scrambler + + +Random number generation algorithms +----------------------------------- + +We then define 12 user-usable types, each representing a different algorithm: + +**32-bit generators**, suitable for generating `float` values + +.. doxygentypedef:: xoshiro128starstar +.. doxygentypedef:: xoshiro128plusplus +.. doxygentypedef:: xoshiro128plus + +**64 bit generators**, suitable for generating either `double` or `float` values, but differing in the size of the internal state: + +*128 bits*: + +.. doxygentypedef:: xoroshiro128starstar +.. doxygentypedef:: xoroshiro128plusplus +.. doxygentypedef:: xoroshiro128plus + +*256 bits*: + +.. doxygentypedef:: xoshiro256starstar +.. doxygentypedef:: xoshiro256plusplus +.. doxygentypedef:: xoshiro256plus + +*512 bits*: + +.. doxygentypedef:: xoshiro512starstar +.. doxygentypedef:: xoshiro512plusplus +.. doxygentypedef:: xoshiro512plus + +Example +------- + +.. literalinclude:: examples/random-state.cpp + +.. literalinclude:: examples/random-state.out + :language: text diff --git a/cpp/_sources/random-version.rst.txt b/cpp/_sources/random-version.rst.txt new file mode 100644 index 000000000..8e0f41e01 --- /dev/null +++ b/cpp/_sources/random-version.rst.txt @@ -0,0 +1,21 @@ +Query version information +========================= + +We define several constants that can be used for feature testing and reporting: + +.. doxygendefine:: DUST_VERSION_MAJOR +.. doxygendefine:: DUST_VERSION_MINOR +.. doxygendefine:: DUST_VERSION_PATCH +.. doxygendefine:: DUST_VERSION_STRING + +The most useful for testing is ``DUST_VERSION_CODE`` which is built from the major, minor and patch numbers (10000 * major + 100 + minor + patch), so version ``1.23.45`` would be ``12345`` and ``0.4.8`` would be ``408`` + +.. doxygendefine:: DUST_VERSION_CODE + +Example +------- + +.. literalinclude:: examples/random-version.cpp + +.. literalinclude:: examples/random-version.out + :language: text diff --git a/cpp/_sources/random.rst.txt b/cpp/_sources/random.rst.txt new file mode 100644 index 000000000..ad73dee4c --- /dev/null +++ b/cpp/_sources/random.rst.txt @@ -0,0 +1,31 @@ +Random number generation +======================== + +To generate random numbers we need to + +1. include ```` +2. decide on the generator algorithm to use +3. seed a random number state +4. draw numbers using some distribution function + +A simple complete example looks like + +.. literalinclude:: examples/random-simple.cpp + +which produces output: + +.. literalinclude:: examples/random-simple.out + :language: text + +.. toctree:: + :maxdepth: 1 + :caption: Contents: + + random-state + random-seed + random-primitive + random-distributions + random-jump + random-parallel + random-version + random-r diff --git a/cpp/_static/_sphinx_javascript_frameworks_compat.js b/cpp/_static/_sphinx_javascript_frameworks_compat.js new file mode 100644 index 000000000..8549469dc --- /dev/null +++ b/cpp/_static/_sphinx_javascript_frameworks_compat.js @@ -0,0 +1,134 @@ +/* + * _sphinx_javascript_frameworks_compat.js + * ~~~~~~~~~~ + * + * Compatability shim for jQuery and underscores.js. + * + * WILL BE REMOVED IN Sphinx 6.0 + * xref RemovedInSphinx60Warning + * + */ + +/** + * select a different prefix for underscore + */ +$u = _.noConflict(); + + +/** + * small helper function to urldecode strings + * + * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL + */ +jQuery.urldecode = function(x) { + if (!x) { + return x + } + return decodeURIComponent(x.replace(/\+/g, ' ')); +}; + +/** + * small helper function to urlencode strings + */ +jQuery.urlencode = encodeURIComponent; + +/** + * This function returns the parsed url parameters of the + * current request. 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+ margin: 1em 0 1em 0; + padding: 0.4em; +} + +/* -- domain module index --------------------------------------------------- */ + +table.modindextable td { + padding: 2px; + border-collapse: collapse; +} + +/* -- general body styles --------------------------------------------------- */ + +div.body { + min-width: 360px; + max-width: 800px; +} + +div.body p, div.body dd, div.body li, div.body blockquote { + -moz-hyphens: auto; + -ms-hyphens: auto; + -webkit-hyphens: auto; + hyphens: auto; +} + +a.headerlink { + visibility: hidden; +} + +a:visited { + color: #551A8B; +} + +h1:hover > a.headerlink, +h2:hover > a.headerlink, +h3:hover > a.headerlink, +h4:hover > a.headerlink, +h5:hover > a.headerlink, +h6:hover > a.headerlink, +dt:hover > a.headerlink, +caption:hover > a.headerlink, +p.caption:hover > a.headerlink, +div.code-block-caption:hover > a.headerlink { + visibility: visible; +} + +div.body p.caption { + text-align: inherit; +} + +div.body td { + text-align: left; +} + +.first { + margin-top: 0 !important; +} + +p.rubric { + margin-top: 30px; + font-weight: bold; +} + +img.align-left, figure.align-left, .figure.align-left, object.align-left { + clear: left; + float: left; + margin-right: 1em; +} + +img.align-right, figure.align-right, .figure.align-right, object.align-right { + clear: right; + float: right; + margin-left: 1em; +} + +img.align-center, figure.align-center, .figure.align-center, object.align-center { + display: block; + margin-left: auto; + margin-right: auto; +} + +img.align-default, figure.align-default, .figure.align-default { + display: block; + margin-left: auto; + margin-right: auto; +} + +.align-left { + text-align: left; +} + +.align-center { + text-align: center; +} + +.align-default { + text-align: center; +} + +.align-right { + text-align: right; +} + +/* -- sidebars -------------------------------------------------------------- */ + +div.sidebar, +aside.sidebar { + margin: 0 0 0.5em 1em; + border: 1px solid #ddb; + padding: 7px; + background-color: #ffe; + width: 40%; + float: right; + clear: right; + overflow-x: auto; +} + +p.sidebar-title { + font-weight: bold; +} + +nav.contents, +aside.topic, +div.admonition, div.topic, blockquote { + clear: left; +} + +/* -- topics ---------------------------------------------------------------- */ + +nav.contents, +aside.topic, +div.topic { + border: 1px solid #ccc; + padding: 7px; + margin: 10px 0 10px 0; +} + +p.topic-title { + font-size: 1.1em; + font-weight: bold; + margin-top: 10px; +} + +/* -- admonitions ----------------------------------------------------------- */ + +div.admonition { + margin-top: 10px; + margin-bottom: 10px; + padding: 7px; +} + +div.admonition dt { + font-weight: bold; +} + +p.admonition-title { + margin: 0px 10px 5px 0px; + font-weight: bold; +} + +div.body p.centered { + text-align: center; + margin-top: 25px; +} + +/* -- content of sidebars/topics/admonitions -------------------------------- */ + +div.sidebar > :last-child, +aside.sidebar > :last-child, +nav.contents > :last-child, +aside.topic > :last-child, +div.topic > :last-child, +div.admonition > :last-child { + margin-bottom: 0; +} + +div.sidebar::after, +aside.sidebar::after, +nav.contents::after, +aside.topic::after, +div.topic::after, +div.admonition::after, +blockquote::after { + display: block; + content: ''; + clear: both; +} + +/* -- tables ---------------------------------------------------------------- */ + +table.docutils { + margin-top: 10px; + margin-bottom: 10px; + border: 0; + border-collapse: collapse; +} + +table.align-center { + margin-left: auto; + margin-right: auto; +} + +table.align-default { + margin-left: auto; + margin-right: auto; +} + +table caption span.caption-number { + font-style: italic; +} + +table caption span.caption-text { +} + +table.docutils td, table.docutils th { + padding: 1px 8px 1px 5px; + border-top: 0; + border-left: 0; + border-right: 0; + border-bottom: 1px solid #aaa; +} + +th { + text-align: left; + padding-right: 5px; +} + +table.citation { + border-left: solid 1px gray; + margin-left: 1px; +} + +table.citation td { + border-bottom: none; +} + +th > :first-child, +td > :first-child { + margin-top: 0px; +} + +th > :last-child, +td > :last-child { + margin-bottom: 0px; +} + +/* -- figures --------------------------------------------------------------- */ + +div.figure, figure { + margin: 0.5em; + padding: 0.5em; +} + +div.figure p.caption, figcaption { + padding: 0.3em; +} + +div.figure p.caption span.caption-number, +figcaption span.caption-number { + font-style: italic; +} + +div.figure p.caption span.caption-text, +figcaption span.caption-text { +} + +/* -- field list styles ----------------------------------------------------- */ + +table.field-list td, table.field-list th { + border: 0 !important; +} + +.field-list ul { + margin: 0; + padding-left: 1em; +} + +.field-list p { + margin: 0; +} + +.field-name { + -moz-hyphens: manual; + -ms-hyphens: manual; + -webkit-hyphens: manual; + hyphens: manual; +} + +/* -- hlist styles ---------------------------------------------------------- */ + +table.hlist { + margin: 1em 0; +} + +table.hlist td { + vertical-align: top; +} + +/* -- object description styles --------------------------------------------- */ + +.sig { + font-family: 'Consolas', 'Menlo', 'DejaVu Sans Mono', 'Bitstream Vera Sans Mono', monospace; +} + +.sig-name, code.descname { + background-color: transparent; + font-weight: bold; +} + +.sig-name { + font-size: 1.1em; +} + +code.descname { + font-size: 1.2em; +} + +.sig-prename, code.descclassname { + background-color: transparent; +} + +.optional { + font-size: 1.3em; +} + +.sig-paren { + font-size: larger; +} + +.sig-param.n { + font-style: italic; +} + +/* C++ specific styling */ + +.sig-inline.c-texpr, +.sig-inline.cpp-texpr { + font-family: unset; +} + +.sig.c .k, .sig.c .kt, +.sig.cpp .k, .sig.cpp .kt { + color: #0033B3; +} + +.sig.c .m, +.sig.cpp .m { + color: #1750EB; +} + +.sig.c .s, .sig.c .sc, +.sig.cpp .s, .sig.cpp .sc { + color: #067D17; +} + + +/* -- other body styles ----------------------------------------------------- */ + +ol.arabic { + list-style: decimal; +} + +ol.loweralpha { + list-style: lower-alpha; +} + +ol.upperalpha { + list-style: upper-alpha; +} + +ol.lowerroman { + list-style: lower-roman; +} + +ol.upperroman { + list-style: upper-roman; +} + +:not(li) > ol > li:first-child > :first-child, +:not(li) > ul > li:first-child > :first-child { + margin-top: 0px; +} + +:not(li) > ol > li:last-child > :last-child, +:not(li) > ul > li:last-child > :last-child { + margin-bottom: 0px; +} + +ol.simple ol p, +ol.simple ul p, +ul.simple ol p, +ul.simple ul p { + margin-top: 0; +} + +ol.simple > li:not(:first-child) > p, +ul.simple > li:not(:first-child) > p { + margin-top: 0; +} + +ol.simple p, +ul.simple p { + margin-bottom: 0; +} + +aside.footnote > span, +div.citation > span { + float: left; +} +aside.footnote > span:last-of-type, +div.citation > span:last-of-type { + padding-right: 0.5em; +} +aside.footnote > p { + margin-left: 2em; +} +div.citation > p { + margin-left: 4em; +} +aside.footnote > p:last-of-type, +div.citation > p:last-of-type { + margin-bottom: 0em; +} +aside.footnote > p:last-of-type:after, +div.citation > p:last-of-type:after { + content: ""; + clear: both; +} + +dl.field-list { + display: grid; + grid-template-columns: fit-content(30%) auto; +} + +dl.field-list > dt { + font-weight: bold; + word-break: break-word; + padding-left: 0.5em; + padding-right: 5px; +} + +dl.field-list > dd { + padding-left: 0.5em; + margin-top: 0em; + margin-left: 0em; + margin-bottom: 0em; +} + +dl { + margin-bottom: 15px; +} + +dd > :first-child { + margin-top: 0px; +} + +dd ul, dd table { + margin-bottom: 10px; +} + +dd { + margin-top: 3px; + margin-bottom: 10px; + margin-left: 30px; +} + +.sig dd { + margin-top: 0px; + margin-bottom: 0px; +} + +.sig dl { + margin-top: 0px; + margin-bottom: 0px; +} + +dl > dd:last-child, +dl > dd:last-child > :last-child { + margin-bottom: 0; +} + +dt:target, span.highlighted { + background-color: #fbe54e; +} + +rect.highlighted { + fill: #fbe54e; +} + +dl.glossary dt { + font-weight: bold; + font-size: 1.1em; +} + +.versionmodified { + font-style: italic; +} + +.system-message { + background-color: #fda; + padding: 5px; + border: 3px solid red; +} + +.footnote:target { + background-color: #ffa; +} + +.line-block { + display: block; + margin-top: 1em; + margin-bottom: 1em; +} + +.line-block .line-block { + margin-top: 0; + margin-bottom: 0; + margin-left: 1.5em; +} + +.guilabel, .menuselection { + font-family: sans-serif; +} + +.accelerator { + text-decoration: underline; +} + +.classifier { + font-style: oblique; +} + +.classifier:before { + font-style: normal; + margin: 0 0.5em; + content: ":"; + display: inline-block; +} + +abbr, acronym { + border-bottom: dotted 1px; + cursor: help; +} + +.translated { + background-color: rgba(207, 255, 207, 0.2) +} + +.untranslated { + background-color: rgba(255, 207, 207, 0.2) +} + +/* -- code displays --------------------------------------------------------- */ + +pre { + overflow: auto; + overflow-y: hidden; /* fixes display issues on Chrome browsers */ +} + +pre, div[class*="highlight-"] { + clear: both; +} + +span.pre { + -moz-hyphens: none; + -ms-hyphens: none; + -webkit-hyphens: none; + hyphens: none; + white-space: nowrap; +} + +div[class*="highlight-"] { + margin: 1em 0; +} + +td.linenos pre { + border: 0; + background-color: transparent; + color: #aaa; +} + +table.highlighttable { + display: block; +} + +table.highlighttable tbody { + display: block; +} + +table.highlighttable tr { + display: flex; +} + +table.highlighttable td { + margin: 0; + padding: 0; +} + +table.highlighttable td.linenos { + padding-right: 0.5em; +} + +table.highlighttable td.code { + flex: 1; + overflow: hidden; +} + +.highlight .hll { + display: block; +} + +div.highlight pre, +table.highlighttable pre { + margin: 0; +} + +div.code-block-caption + div { + margin-top: 0; +} + +div.code-block-caption { + margin-top: 1em; + padding: 2px 5px; + font-size: small; +} + +div.code-block-caption code { + background-color: transparent; +} + +table.highlighttable td.linenos, +span.linenos, +div.highlight span.gp { /* gp: Generic.Prompt */ + user-select: none; + -webkit-user-select: text; /* Safari fallback only */ + -webkit-user-select: none; /* Chrome/Safari */ + -moz-user-select: none; /* Firefox */ + -ms-user-select: none; /* IE10+ */ +} + +div.code-block-caption span.caption-number { + padding: 0.1em 0.3em; + font-style: italic; +} + +div.code-block-caption span.caption-text { +} + +div.literal-block-wrapper { + margin: 1em 0; +} + +code.xref, a code { + background-color: transparent; + font-weight: bold; +} + +h1 code, h2 code, h3 code, h4 code, h5 code, h6 code { + background-color: transparent; +} + +.viewcode-link { + float: right; +} + +.viewcode-back { + float: right; + font-family: sans-serif; +} + +div.viewcode-block:target { + margin: -1px -10px; + padding: 0 10px; +} + +/* -- math display ---------------------------------------------------------- */ + +img.math { + vertical-align: middle; +} + +div.body div.math p { + text-align: center; +} + +span.eqno { + float: right; +} + +span.eqno a.headerlink { + position: absolute; + z-index: 1; +} + +div.math:hover a.headerlink { + visibility: visible; +} + +/* -- printout stylesheet --------------------------------------------------- */ + +@media print { + div.document, + div.documentwrapper, + div.bodywrapper { + margin: 0 !important; + width: 100%; + } + + div.sphinxsidebar, + div.related, + div.footer, + #top-link { + display: none; + } +} \ No newline at end of file diff --git a/cpp/_static/debug.css b/cpp/_static/debug.css new file mode 100644 index 000000000..74d4aec33 --- /dev/null +++ b/cpp/_static/debug.css @@ -0,0 +1,69 @@ +/* + This CSS file should be overridden by the theme authors. It's + meant for debugging and developing the skeleton that this theme provides. +*/ +body { + font-family: -apple-system, "Segoe UI", Roboto, Helvetica, Arial, sans-serif, + "Apple Color Emoji", "Segoe UI Emoji"; + background: lavender; +} +.sb-announcement { + background: rgb(131, 131, 131); +} +.sb-announcement__inner { + background: black; + color: white; +} +.sb-header { + background: lightskyblue; +} +.sb-header__inner { + background: royalblue; + color: white; +} +.sb-header-secondary { + background: lightcyan; +} +.sb-header-secondary__inner { + background: cornflowerblue; + color: white; +} +.sb-sidebar-primary { + background: lightgreen; +} +.sb-main { + background: blanchedalmond; +} +.sb-main__inner { + background: antiquewhite; +} +.sb-header-article { + background: lightsteelblue; +} +.sb-article-container { + background: snow; +} +.sb-article-main { + background: white; +} +.sb-footer-article { + background: lightpink; +} +.sb-sidebar-secondary { + background: lightgoldenrodyellow; +} +.sb-footer-content { + background: plum; +} +.sb-footer-content__inner { + background: palevioletred; +} +.sb-footer { + background: pink; +} +.sb-footer__inner { + background: salmon; +} +.sb-article { + background: white; +} diff --git a/cpp/_static/doctools.js b/cpp/_static/doctools.js new file mode 100644 index 000000000..d06a71d75 --- /dev/null +++ b/cpp/_static/doctools.js @@ -0,0 +1,156 @@ +/* + * doctools.js + * ~~~~~~~~~~~ + * + * Base JavaScript utilities for all Sphinx HTML documentation. + * + * :copyright: Copyright 2007-2023 by the Sphinx team, see AUTHORS. + * :license: BSD, see LICENSE for details. + * + */ +"use strict"; + +const BLACKLISTED_KEY_CONTROL_ELEMENTS = new Set([ + "TEXTAREA", + "INPUT", + "SELECT", + "BUTTON", +]); + +const _ready = (callback) => { + if (document.readyState !== "loading") { + callback(); + } else { + document.addEventListener("DOMContentLoaded", callback); + } +}; + +/** + * Small JavaScript module for the documentation. + */ +const Documentation = { + init: () => { + Documentation.initDomainIndexTable(); + Documentation.initOnKeyListeners(); + }, + + /** + * i18n support + */ + TRANSLATIONS: {}, + PLURAL_EXPR: (n) => (n === 1 ? 0 : 1), + LOCALE: "unknown", + + // gettext and ngettext don't access this so that the functions + // can safely bound to a different name (_ = Documentation.gettext) + gettext: (string) => { + const translated = Documentation.TRANSLATIONS[string]; + switch (typeof translated) { + case "undefined": + return string; // no translation + case "string": + return translated; // translation exists + default: + return translated[0]; // (singular, plural) translation tuple exists + } + }, + + ngettext: (singular, plural, n) => { + const translated = Documentation.TRANSLATIONS[singular]; + if (typeof translated !== "undefined") + return translated[Documentation.PLURAL_EXPR(n)]; + return n === 1 ? singular : plural; + }, + + addTranslations: (catalog) => { + Object.assign(Documentation.TRANSLATIONS, catalog.messages); + Documentation.PLURAL_EXPR = new Function( + "n", + `return (${catalog.plural_expr})` + ); + Documentation.LOCALE = catalog.locale; + }, + + /** + * helper function to focus on search bar + */ + focusSearchBar: () => { + document.querySelectorAll("input[name=q]")[0]?.focus(); + }, + + /** + * Initialise the domain index toggle buttons + */ + initDomainIndexTable: () => { + const toggler = (el) => { + const idNumber = el.id.substr(7); + const toggledRows = document.querySelectorAll(`tr.cg-${idNumber}`); + if (el.src.substr(-9) === "minus.png") { + el.src = `${el.src.substr(0, el.src.length - 9)}plus.png`; + toggledRows.forEach((el) => (el.style.display = "none")); + } else { + el.src = `${el.src.substr(0, el.src.length - 8)}minus.png`; + toggledRows.forEach((el) => (el.style.display = "")); + } + }; + + const togglerElements = document.querySelectorAll("img.toggler"); + togglerElements.forEach((el) => + el.addEventListener("click", (event) => toggler(event.currentTarget)) + ); + togglerElements.forEach((el) => (el.style.display = "")); + if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) togglerElements.forEach(toggler); + }, + + initOnKeyListeners: () => { + // only install a listener if it is really needed + if ( + !DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS && + !DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS + ) + return; + + document.addEventListener("keydown", (event) => { + // bail for input elements + if (BLACKLISTED_KEY_CONTROL_ELEMENTS.has(document.activeElement.tagName)) return; + // bail with special keys + if (event.altKey || event.ctrlKey || event.metaKey) return; + + if (!event.shiftKey) { + switch (event.key) { + case "ArrowLeft": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const prevLink = document.querySelector('link[rel="prev"]'); + if (prevLink && prevLink.href) { + window.location.href = prevLink.href; + event.preventDefault(); + } + break; + case "ArrowRight": + if (!DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) break; + + const nextLink = document.querySelector('link[rel="next"]'); + if (nextLink && nextLink.href) { + window.location.href = nextLink.href; + event.preventDefault(); + } + break; + } + } + + // some keyboard layouts may need Shift to get / + switch (event.key) { + case "/": + if (!DOCUMENTATION_OPTIONS.ENABLE_SEARCH_SHORTCUTS) break; + Documentation.focusSearchBar(); + event.preventDefault(); + } + }); + }, +}; + +// quick alias for translations +const _ = Documentation.gettext; + +_ready(Documentation.init); diff --git a/cpp/_static/documentation_options.js b/cpp/_static/documentation_options.js new file mode 100644 index 000000000..0e79c8c28 --- /dev/null +++ b/cpp/_static/documentation_options.js @@ -0,0 +1,13 @@ +const DOCUMENTATION_OPTIONS = { + VERSION: '0.15.1', + LANGUAGE: 'en', + COLLAPSE_INDEX: false, + BUILDER: 'html', + FILE_SUFFIX: '.html', + LINK_SUFFIX: '.html', + HAS_SOURCE: true, + SOURCELINK_SUFFIX: '.txt', + NAVIGATION_WITH_KEYS: false, + SHOW_SEARCH_SUMMARY: true, + ENABLE_SEARCH_SHORTCUTS: true, +}; \ No newline at end of file diff --git a/cpp/_static/file.png b/cpp/_static/file.png new file mode 100644 index 0000000000000000000000000000000000000000..a858a410e4faa62ce324d814e4b816fff83a6fb3 GIT binary patch literal 286 zcmV+(0pb3MP)s`hMrGg#P~ix$^RISR_I47Y|r1 z_CyJOe}D1){SET-^Amu_i71Lt6eYfZjRyw@I6OQAIXXHDfiX^GbOlHe=Ae4>0m)d(f|Me07*qoM6N<$f}vM^LjV8( literal 0 HcmV?d00001 diff --git a/cpp/_static/jquery-3.6.0.js b/cpp/_static/jquery-3.6.0.js new file mode 100644 index 000000000..fc6c299b7 --- /dev/null +++ b/cpp/_static/jquery-3.6.0.js @@ -0,0 +1,10881 @@ +/*! + * jQuery JavaScript Library v3.6.0 + * https://jquery.com/ + * + * Includes Sizzle.js + * https://sizzlejs.com/ + * + * Copyright OpenJS Foundation and other contributors + * Released under the MIT license + * https://jquery.org/license + * + * Date: 2021-03-02T17:08Z + */ +( function( global, factory ) { + + "use strict"; + + if ( typeof module === "object" && typeof module.exports === "object" ) { + + // For CommonJS and CommonJS-like environments where a proper `window` + // is present, execute the factory and get jQuery. + // For environments that do not have a `window` with a `document` + // (such as Node.js), expose a factory as module.exports. + // This accentuates the need for the creation of a real `window`. + // e.g. var jQuery = require("jquery")(window); + // See ticket #14549 for more info. + module.exports = global.document ? + factory( global, true ) : + function( w ) { + if ( !w.document ) { + throw new Error( "jQuery requires a window with a document" ); + } + return factory( w ); + }; + } else { + factory( global ); + } + +// Pass this if window is not defined yet +} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) { + +// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1 +// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode +// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common +// enough that all such attempts are guarded in a try block. +"use strict"; + +var arr = []; + +var getProto = Object.getPrototypeOf; + +var slice = arr.slice; + +var flat = arr.flat ? function( array ) { + return arr.flat.call( array ); +} : function( array ) { + return arr.concat.apply( [], array ); +}; + + +var push = arr.push; + +var indexOf = arr.indexOf; + +var class2type = {}; + +var toString = class2type.toString; + +var hasOwn = class2type.hasOwnProperty; + +var fnToString = hasOwn.toString; + +var ObjectFunctionString = fnToString.call( Object ); + +var support = {}; + +var isFunction = function isFunction( obj ) { + + // Support: Chrome <=57, Firefox <=52 + // In some browsers, typeof returns "function" for HTML elements + // (i.e., `typeof document.createElement( "object" ) === "function"`). + // We don't want to classify *any* DOM node as a function. + // Support: QtWeb <=3.8.5, WebKit <=534.34, wkhtmltopdf tool <=0.12.5 + // Plus for old WebKit, typeof returns "function" for HTML collections + // (e.g., `typeof document.getElementsByTagName("div") === "function"`). (gh-4756) + return typeof obj === "function" && typeof obj.nodeType !== "number" && + typeof obj.item !== "function"; + }; + + +var isWindow = function isWindow( obj ) { + return obj != null && obj === obj.window; + }; + + +var document = window.document; + + + + var preservedScriptAttributes = { + type: true, + src: true, + nonce: true, + noModule: true + }; + + function DOMEval( code, node, doc ) { + doc = doc || document; + + var i, val, + script = doc.createElement( "script" ); + + script.text = code; + if ( node ) { + for ( i in preservedScriptAttributes ) { + + // Support: Firefox 64+, Edge 18+ + // Some browsers don't support the "nonce" property on scripts. + // On the other hand, just using `getAttribute` is not enough as + // the `nonce` attribute is reset to an empty string whenever it + // becomes browsing-context connected. + // See https://github.com/whatwg/html/issues/2369 + // See https://html.spec.whatwg.org/#nonce-attributes + // The `node.getAttribute` check was added for the sake of + // `jQuery.globalEval` so that it can fake a nonce-containing node + // via an object. + val = node[ i ] || node.getAttribute && node.getAttribute( i ); + if ( val ) { + script.setAttribute( i, val ); + } + } + } + doc.head.appendChild( script ).parentNode.removeChild( script ); + } + + +function toType( obj ) { + if ( obj == null ) { + return obj + ""; + } + + // Support: Android <=2.3 only (functionish RegExp) + return typeof obj === "object" || typeof obj === "function" ? + class2type[ toString.call( obj ) ] || "object" : + typeof obj; +} +/* global Symbol */ +// Defining this global in .eslintrc.json would create a danger of using the global +// unguarded in another place, it seems safer to define global only for this module + + + +var + version = "3.6.0", + + // Define a local copy of jQuery + jQuery = function( selector, context ) { + + // The jQuery object is actually just the init constructor 'enhanced' + // Need init if jQuery is called (just allow error to be thrown if not included) + return new jQuery.fn.init( selector, context ); + }; + +jQuery.fn = jQuery.prototype = { + + // The current version of jQuery being used + jquery: version, + + constructor: jQuery, + + // The default length of a jQuery object is 0 + length: 0, + + toArray: function() { + return slice.call( this ); + }, + + // Get the Nth element in the matched element set OR + // Get the whole matched element set as a clean array + get: function( num ) { + + // Return all the elements in a clean array + if ( num == null ) { + return slice.call( this ); + } + + // Return just the one element from the set + return num < 0 ? this[ num + this.length ] : this[ num ]; + }, + + // Take an array of elements and push it onto the stack + // (returning the new matched element set) + pushStack: function( elems ) { + + // Build a new jQuery matched element set + var ret = jQuery.merge( this.constructor(), elems ); + + // Add the old object onto the stack (as a reference) + ret.prevObject = this; + + // Return the newly-formed element set + return ret; + }, + + // Execute a callback for every element in the matched set. + each: function( callback ) { + return jQuery.each( this, callback ); + }, + + map: function( callback ) { + return this.pushStack( jQuery.map( this, function( elem, i ) { + return callback.call( elem, i, elem ); + } ) ); + }, + + slice: function() { + return this.pushStack( slice.apply( this, arguments ) ); + }, + + first: function() { + return this.eq( 0 ); + }, + + last: function() { + return this.eq( -1 ); + }, + + even: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return ( i + 1 ) % 2; + } ) ); + }, + + odd: function() { + return this.pushStack( jQuery.grep( this, function( _elem, i ) { + return i % 2; + } ) ); + }, + + eq: function( i ) { + var len = this.length, + j = +i + ( i < 0 ? len : 0 ); + return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] ); + }, + + end: function() { + return this.prevObject || this.constructor(); + }, + + // For internal use only. + // Behaves like an Array's method, not like a jQuery method. + push: push, + sort: arr.sort, + splice: arr.splice +}; + +jQuery.extend = jQuery.fn.extend = function() { + var options, name, src, copy, copyIsArray, clone, + target = arguments[ 0 ] || {}, + i = 1, + length = arguments.length, + deep = false; + + // Handle a deep copy situation + if ( typeof target === "boolean" ) { + deep = target; + + // Skip the boolean and the target + target = arguments[ i ] || {}; + i++; + } + + // Handle case when target is a string or something (possible in deep copy) + if ( typeof target !== "object" && !isFunction( target ) ) { + target = {}; + } + + // Extend jQuery itself if only one argument is passed + if ( i === length ) { + target = this; + i--; + } + + for ( ; i < length; i++ ) { + + // Only deal with non-null/undefined values + if ( ( options = arguments[ i ] ) != null ) { + + // Extend the base object + for ( name in options ) { + copy = options[ name ]; + + // Prevent Object.prototype pollution + // Prevent never-ending loop + if ( name === "__proto__" || target === copy ) { + continue; + } + + // Recurse if we're merging plain objects or arrays + if ( deep && copy && ( jQuery.isPlainObject( copy ) || + ( copyIsArray = Array.isArray( copy ) ) ) ) { + src = target[ name ]; + + // Ensure proper type for the source value + if ( copyIsArray && !Array.isArray( src ) ) { + clone = []; + } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) { + clone = {}; + } else { + clone = src; + } + copyIsArray = false; + + // Never move original objects, clone them + target[ name ] = jQuery.extend( deep, clone, copy ); + + // Don't bring in undefined values + } else if ( copy !== undefined ) { + target[ name ] = copy; + } + } + } + } + + // Return the modified object + return target; +}; + +jQuery.extend( { + + // Unique for each copy of jQuery on the page + expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ), + + // Assume jQuery is ready without the ready module + isReady: true, + + error: function( msg ) { + throw new Error( msg ); + }, + + noop: function() {}, + + isPlainObject: function( obj ) { + var proto, Ctor; + + // Detect obvious negatives + // Use toString instead of jQuery.type to catch host objects + if ( !obj || toString.call( obj ) !== "[object Object]" ) { + return false; + } + + proto = getProto( obj ); + + // Objects with no prototype (e.g., `Object.create( null )`) are plain + if ( !proto ) { + return true; + } + + // Objects with prototype are plain iff they were constructed by a global Object function + Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor; + return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString; + }, + + isEmptyObject: function( obj ) { + var name; + + for ( name in obj ) { + return false; + } + return true; + }, + + // Evaluates a script in a provided context; falls back to the global one + // if not specified. + globalEval: function( code, options, doc ) { + DOMEval( code, { nonce: options && options.nonce }, doc ); + }, + + each: function( obj, callback ) { + var length, i = 0; + + if ( isArrayLike( obj ) ) { + length = obj.length; + for ( ; i < length; i++ ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } else { + for ( i in obj ) { + if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) { + break; + } + } + } + + return obj; + }, + + // results is for internal usage only + makeArray: function( arr, results ) { + var ret = results || []; + + if ( arr != null ) { + if ( isArrayLike( Object( arr ) ) ) { + jQuery.merge( ret, + typeof arr === "string" ? + [ arr ] : arr + ); + } else { + push.call( ret, arr ); + } + } + + return ret; + }, + + inArray: function( elem, arr, i ) { + return arr == null ? -1 : indexOf.call( arr, elem, i ); + }, + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + merge: function( first, second ) { + var len = +second.length, + j = 0, + i = first.length; + + for ( ; j < len; j++ ) { + first[ i++ ] = second[ j ]; + } + + first.length = i; + + return first; + }, + + grep: function( elems, callback, invert ) { + var callbackInverse, + matches = [], + i = 0, + length = elems.length, + callbackExpect = !invert; + + // Go through the array, only saving the items + // that pass the validator function + for ( ; i < length; i++ ) { + callbackInverse = !callback( elems[ i ], i ); + if ( callbackInverse !== callbackExpect ) { + matches.push( elems[ i ] ); + } + } + + return matches; + }, + + // arg is for internal usage only + map: function( elems, callback, arg ) { + var length, value, + i = 0, + ret = []; + + // Go through the array, translating each of the items to their new values + if ( isArrayLike( elems ) ) { + length = elems.length; + for ( ; i < length; i++ ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + + // Go through every key on the object, + } else { + for ( i in elems ) { + value = callback( elems[ i ], i, arg ); + + if ( value != null ) { + ret.push( value ); + } + } + } + + // Flatten any nested arrays + return flat( ret ); + }, + + // A global GUID counter for objects + guid: 1, + + // jQuery.support is not used in Core but other projects attach their + // properties to it so it needs to exist. + support: support +} ); + +if ( typeof Symbol === "function" ) { + jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ]; +} + +// Populate the class2type map +jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ), + function( _i, name ) { + class2type[ "[object " + name + "]" ] = name.toLowerCase(); + } ); + +function isArrayLike( obj ) { + + // Support: real iOS 8.2 only (not reproducible in simulator) + // `in` check used to prevent JIT error (gh-2145) + // hasOwn isn't used here due to false negatives + // regarding Nodelist length in IE + var length = !!obj && "length" in obj && obj.length, + type = toType( obj ); + + if ( isFunction( obj ) || isWindow( obj ) ) { + return false; + } + + return type === "array" || length === 0 || + typeof length === "number" && length > 0 && ( length - 1 ) in obj; +} +var Sizzle = +/*! + * Sizzle CSS Selector Engine v2.3.6 + * https://sizzlejs.com/ + * + * Copyright JS Foundation and other contributors + * Released under the MIT license + * https://js.foundation/ + * + * Date: 2021-02-16 + */ +( function( window ) { +var i, + support, + Expr, + getText, + isXML, + tokenize, + compile, + select, + outermostContext, + sortInput, + hasDuplicate, + + // Local document vars + setDocument, + document, + docElem, + documentIsHTML, + rbuggyQSA, + rbuggyMatches, + matches, + contains, + + // Instance-specific data + expando = "sizzle" + 1 * new Date(), + preferredDoc = window.document, + dirruns = 0, + done = 0, + classCache = createCache(), + tokenCache = createCache(), + compilerCache = createCache(), + nonnativeSelectorCache = createCache(), + sortOrder = function( a, b ) { + if ( a === b ) { + hasDuplicate = true; + } + return 0; + }, + + // Instance methods + hasOwn = ( {} ).hasOwnProperty, + arr = [], + pop = arr.pop, + pushNative = arr.push, + push = arr.push, + slice = arr.slice, + + // Use a stripped-down indexOf as it's faster than native + // https://jsperf.com/thor-indexof-vs-for/5 + indexOf = function( list, elem ) { + var i = 0, + len = list.length; + for ( ; i < len; i++ ) { + if ( list[ i ] === elem ) { + return i; + } + } + return -1; + }, + + booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" + + "ismap|loop|multiple|open|readonly|required|scoped", + + // Regular expressions + + // http://www.w3.org/TR/css3-selectors/#whitespace + whitespace = "[\\x20\\t\\r\\n\\f]", + + // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram + identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace + + "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+", + + // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors + attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace + + + // Operator (capture 2) + "*([*^$|!~]?=)" + whitespace + + + // "Attribute values must be CSS identifiers [capture 5] + // or strings [capture 3 or capture 4]" + "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" + + whitespace + "*\\]", + + pseudos = ":(" + identifier + ")(?:\\((" + + + // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments: + // 1. quoted (capture 3; capture 4 or capture 5) + "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" + + + // 2. simple (capture 6) + "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" + + + // 3. anything else (capture 2) + ".*" + + ")\\)|)", + + // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter + rwhitespace = new RegExp( whitespace + "+", "g" ), + rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" + + whitespace + "+$", "g" ), + + rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ), + rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace + + "*" ), + rdescend = new RegExp( whitespace + "|>" ), + + rpseudo = new RegExp( pseudos ), + ridentifier = new RegExp( "^" + identifier + "$" ), + + matchExpr = { + "ID": new RegExp( "^#(" + identifier + ")" ), + "CLASS": new RegExp( "^\\.(" + identifier + ")" ), + "TAG": new RegExp( "^(" + identifier + "|[*])" ), + "ATTR": new RegExp( "^" + attributes ), + "PSEUDO": new RegExp( "^" + pseudos ), + "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" + + whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" + + whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ), + "bool": new RegExp( "^(?:" + booleans + ")$", "i" ), + + // For use in libraries implementing .is() + // We use this for POS matching in `select` + "needsContext": new RegExp( "^" + whitespace + + "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace + + "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" ) + }, + + rhtml = /HTML$/i, + rinputs = /^(?:input|select|textarea|button)$/i, + rheader = /^h\d$/i, + + rnative = /^[^{]+\{\s*\[native \w/, + + // Easily-parseable/retrievable ID or TAG or CLASS selectors + rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/, + + rsibling = /[+~]/, + + // CSS escapes + // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters + runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ), + funescape = function( escape, nonHex ) { + var high = "0x" + escape.slice( 1 ) - 0x10000; + + return nonHex ? + + // Strip the backslash prefix from a non-hex escape sequence + nonHex : + + // Replace a hexadecimal escape sequence with the encoded Unicode code point + // Support: IE <=11+ + // For values outside the Basic Multilingual Plane (BMP), manually construct a + // surrogate pair + high < 0 ? + String.fromCharCode( high + 0x10000 ) : + String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 ); + }, + + // CSS string/identifier serialization + // https://drafts.csswg.org/cssom/#common-serializing-idioms + rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g, + fcssescape = function( ch, asCodePoint ) { + if ( asCodePoint ) { + + // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER + if ( ch === "\0" ) { + return "\uFFFD"; + } + + // Control characters and (dependent upon position) numbers get escaped as code points + return ch.slice( 0, -1 ) + "\\" + + ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " "; + } + + // Other potentially-special ASCII characters get backslash-escaped + return "\\" + ch; + }, + + // Used for iframes + // See setDocument() + // Removing the function wrapper causes a "Permission Denied" + // error in IE + unloadHandler = function() { + setDocument(); + }, + + inDisabledFieldset = addCombinator( + function( elem ) { + return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset"; + }, + { dir: "parentNode", next: "legend" } + ); + +// Optimize for push.apply( _, NodeList ) +try { + push.apply( + ( arr = slice.call( preferredDoc.childNodes ) ), + preferredDoc.childNodes + ); + + // Support: Android<4.0 + // Detect silently failing push.apply + // eslint-disable-next-line no-unused-expressions + arr[ preferredDoc.childNodes.length ].nodeType; +} catch ( e ) { + push = { apply: arr.length ? + + // Leverage slice if possible + function( target, els ) { + pushNative.apply( target, slice.call( els ) ); + } : + + // Support: IE<9 + // Otherwise append directly + function( target, els ) { + var j = target.length, + i = 0; + + // Can't trust NodeList.length + while ( ( target[ j++ ] = els[ i++ ] ) ) {} + target.length = j - 1; + } + }; +} + +function Sizzle( selector, context, results, seed ) { + var m, i, elem, nid, match, groups, newSelector, + newContext = context && context.ownerDocument, + + // nodeType defaults to 9, since context defaults to document + nodeType = context ? context.nodeType : 9; + + results = results || []; + + // Return early from calls with invalid selector or context + if ( typeof selector !== "string" || !selector || + nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) { + + return results; + } + + // Try to shortcut find operations (as opposed to filters) in HTML documents + if ( !seed ) { + setDocument( context ); + context = context || document; + + if ( documentIsHTML ) { + + // If the selector is sufficiently simple, try using a "get*By*" DOM method + // (excepting DocumentFragment context, where the methods don't exist) + if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) { + + // ID selector + if ( ( m = match[ 1 ] ) ) { + + // Document context + if ( nodeType === 9 ) { + if ( ( elem = context.getElementById( m ) ) ) { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( elem.id === m ) { + results.push( elem ); + return results; + } + } else { + return results; + } + + // Element context + } else { + + // Support: IE, Opera, Webkit + // TODO: identify versions + // getElementById can match elements by name instead of ID + if ( newContext && ( elem = newContext.getElementById( m ) ) && + contains( context, elem ) && + elem.id === m ) { + + results.push( elem ); + return results; + } + } + + // Type selector + } else if ( match[ 2 ] ) { + push.apply( results, context.getElementsByTagName( selector ) ); + return results; + + // Class selector + } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName && + context.getElementsByClassName ) { + + push.apply( results, context.getElementsByClassName( m ) ); + return results; + } + } + + // Take advantage of querySelectorAll + if ( support.qsa && + !nonnativeSelectorCache[ selector + " " ] && + ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) && + + // Support: IE 8 only + // Exclude object elements + ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) { + + newSelector = selector; + newContext = context; + + // qSA considers elements outside a scoping root when evaluating child or + // descendant combinators, which is not what we want. + // In such cases, we work around the behavior by prefixing every selector in the + // list with an ID selector referencing the scope context. + // The technique has to be used as well when a leading combinator is used + // as such selectors are not recognized by querySelectorAll. + // Thanks to Andrew Dupont for this technique. + if ( nodeType === 1 && + ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) { + + // Expand context for sibling selectors + newContext = rsibling.test( selector ) && testContext( context.parentNode ) || + context; + + // We can use :scope instead of the ID hack if the browser + // supports it & if we're not changing the context. + if ( newContext !== context || !support.scope ) { + + // Capture the context ID, setting it first if necessary + if ( ( nid = context.getAttribute( "id" ) ) ) { + nid = nid.replace( rcssescape, fcssescape ); + } else { + context.setAttribute( "id", ( nid = expando ) ); + } + } + + // Prefix every selector in the list + groups = tokenize( selector ); + i = groups.length; + while ( i-- ) { + groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " + + toSelector( groups[ i ] ); + } + newSelector = groups.join( "," ); + } + + try { + push.apply( results, + newContext.querySelectorAll( newSelector ) + ); + return results; + } catch ( qsaError ) { + nonnativeSelectorCache( selector, true ); + } finally { + if ( nid === expando ) { + context.removeAttribute( "id" ); + } + } + } + } + } + + // All others + return select( selector.replace( rtrim, "$1" ), context, results, seed ); +} + +/** + * Create key-value caches of limited size + * @returns {function(string, object)} Returns the Object data after storing it on itself with + * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength) + * deleting the oldest entry + */ +function createCache() { + var keys = []; + + function cache( key, value ) { + + // Use (key + " ") to avoid collision with native prototype properties (see Issue #157) + if ( keys.push( key + " " ) > Expr.cacheLength ) { + + // Only keep the most recent entries + delete cache[ keys.shift() ]; + } + return ( cache[ key + " " ] = value ); + } + return cache; +} + +/** + * Mark a function for special use by Sizzle + * @param {Function} fn The function to mark + */ +function markFunction( fn ) { + fn[ expando ] = true; + return fn; +} + +/** + * Support testing using an element + * @param {Function} fn Passed the created element and returns a boolean result + */ +function assert( fn ) { + var el = document.createElement( "fieldset" ); + + try { + return !!fn( el ); + } catch ( e ) { + return false; + } finally { + + // Remove from its parent by default + if ( el.parentNode ) { + el.parentNode.removeChild( el ); + } + + // release memory in IE + el = null; + } +} + +/** + * Adds the same handler for all of the specified attrs + * @param {String} attrs Pipe-separated list of attributes + * @param {Function} handler The method that will be applied + */ +function addHandle( attrs, handler ) { + var arr = attrs.split( "|" ), + i = arr.length; + + while ( i-- ) { + Expr.attrHandle[ arr[ i ] ] = handler; + } +} + +/** + * Checks document order of two siblings + * @param {Element} a + * @param {Element} b + * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b + */ +function siblingCheck( a, b ) { + var cur = b && a, + diff = cur && a.nodeType === 1 && b.nodeType === 1 && + a.sourceIndex - b.sourceIndex; + + // Use IE sourceIndex if available on both nodes + if ( diff ) { + return diff; + } + + // Check if b follows a + if ( cur ) { + while ( ( cur = cur.nextSibling ) ) { + if ( cur === b ) { + return -1; + } + } + } + + return a ? 1 : -1; +} + +/** + * Returns a function to use in pseudos for input types + * @param {String} type + */ +function createInputPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for buttons + * @param {String} type + */ +function createButtonPseudo( type ) { + return function( elem ) { + var name = elem.nodeName.toLowerCase(); + return ( name === "input" || name === "button" ) && elem.type === type; + }; +} + +/** + * Returns a function to use in pseudos for :enabled/:disabled + * @param {Boolean} disabled true for :disabled; false for :enabled + */ +function createDisabledPseudo( disabled ) { + + // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable + return function( elem ) { + + // Only certain elements can match :enabled or :disabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled + // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled + if ( "form" in elem ) { + + // Check for inherited disabledness on relevant non-disabled elements: + // * listed form-associated elements in a disabled fieldset + // https://html.spec.whatwg.org/multipage/forms.html#category-listed + // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled + // * option elements in a disabled optgroup + // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled + // All such elements have a "form" property. + if ( elem.parentNode && elem.disabled === false ) { + + // Option elements defer to a parent optgroup if present + if ( "label" in elem ) { + if ( "label" in elem.parentNode ) { + return elem.parentNode.disabled === disabled; + } else { + return elem.disabled === disabled; + } + } + + // Support: IE 6 - 11 + // Use the isDisabled shortcut property to check for disabled fieldset ancestors + return elem.isDisabled === disabled || + + // Where there is no isDisabled, check manually + /* jshint -W018 */ + elem.isDisabled !== !disabled && + inDisabledFieldset( elem ) === disabled; + } + + return elem.disabled === disabled; + + // Try to winnow out elements that can't be disabled before trusting the disabled property. + // Some victims get caught in our net (label, legend, menu, track), but it shouldn't + // even exist on them, let alone have a boolean value. + } else if ( "label" in elem ) { + return elem.disabled === disabled; + } + + // Remaining elements are neither :enabled nor :disabled + return false; + }; +} + +/** + * Returns a function to use in pseudos for positionals + * @param {Function} fn + */ +function createPositionalPseudo( fn ) { + return markFunction( function( argument ) { + argument = +argument; + return markFunction( function( seed, matches ) { + var j, + matchIndexes = fn( [], seed.length, argument ), + i = matchIndexes.length; + + // Match elements found at the specified indexes + while ( i-- ) { + if ( seed[ ( j = matchIndexes[ i ] ) ] ) { + seed[ j ] = !( matches[ j ] = seed[ j ] ); + } + } + } ); + } ); +} + +/** + * Checks a node for validity as a Sizzle context + * @param {Element|Object=} context + * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value + */ +function testContext( context ) { + return context && typeof context.getElementsByTagName !== "undefined" && context; +} + +// Expose support vars for convenience +support = Sizzle.support = {}; + +/** + * Detects XML nodes + * @param {Element|Object} elem An element or a document + * @returns {Boolean} True iff elem is a non-HTML XML node + */ +isXML = Sizzle.isXML = function( elem ) { + var namespace = elem && elem.namespaceURI, + docElem = elem && ( elem.ownerDocument || elem ).documentElement; + + // Support: IE <=8 + // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes + // https://bugs.jquery.com/ticket/4833 + return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" ); +}; + +/** + * Sets document-related variables once based on the current document + * @param {Element|Object} [doc] An element or document object to use to set the document + * @returns {Object} Returns the current document + */ +setDocument = Sizzle.setDocument = function( node ) { + var hasCompare, subWindow, + doc = node ? node.ownerDocument || node : preferredDoc; + + // Return early if doc is invalid or already selected + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) { + return document; + } + + // Update global variables + document = doc; + docElem = document.documentElement; + documentIsHTML = !isXML( document ); + + // Support: IE 9 - 11+, Edge 12 - 18+ + // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936) + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( preferredDoc != document && + ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) { + + // Support: IE 11, Edge + if ( subWindow.addEventListener ) { + subWindow.addEventListener( "unload", unloadHandler, false ); + + // Support: IE 9 - 10 only + } else if ( subWindow.attachEvent ) { + subWindow.attachEvent( "onunload", unloadHandler ); + } + } + + // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only, + // Safari 4 - 5 only, Opera <=11.6 - 12.x only + // IE/Edge & older browsers don't support the :scope pseudo-class. + // Support: Safari 6.0 only + // Safari 6.0 supports :scope but it's an alias of :root there. + support.scope = assert( function( el ) { + docElem.appendChild( el ).appendChild( document.createElement( "div" ) ); + return typeof el.querySelectorAll !== "undefined" && + !el.querySelectorAll( ":scope fieldset div" ).length; + } ); + + /* Attributes + ---------------------------------------------------------------------- */ + + // Support: IE<8 + // Verify that getAttribute really returns attributes and not properties + // (excepting IE8 booleans) + support.attributes = assert( function( el ) { + el.className = "i"; + return !el.getAttribute( "className" ); + } ); + + /* getElement(s)By* + ---------------------------------------------------------------------- */ + + // Check if getElementsByTagName("*") returns only elements + support.getElementsByTagName = assert( function( el ) { + el.appendChild( document.createComment( "" ) ); + return !el.getElementsByTagName( "*" ).length; + } ); + + // Support: IE<9 + support.getElementsByClassName = rnative.test( document.getElementsByClassName ); + + // Support: IE<10 + // Check if getElementById returns elements by name + // The broken getElementById methods don't pick up programmatically-set names, + // so use a roundabout getElementsByName test + support.getById = assert( function( el ) { + docElem.appendChild( el ).id = expando; + return !document.getElementsByName || !document.getElementsByName( expando ).length; + } ); + + // ID filter and find + if ( support.getById ) { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + return elem.getAttribute( "id" ) === attrId; + }; + }; + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var elem = context.getElementById( id ); + return elem ? [ elem ] : []; + } + }; + } else { + Expr.filter[ "ID" ] = function( id ) { + var attrId = id.replace( runescape, funescape ); + return function( elem ) { + var node = typeof elem.getAttributeNode !== "undefined" && + elem.getAttributeNode( "id" ); + return node && node.value === attrId; + }; + }; + + // Support: IE 6 - 7 only + // getElementById is not reliable as a find shortcut + Expr.find[ "ID" ] = function( id, context ) { + if ( typeof context.getElementById !== "undefined" && documentIsHTML ) { + var node, i, elems, + elem = context.getElementById( id ); + + if ( elem ) { + + // Verify the id attribute + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + + // Fall back on getElementsByName + elems = context.getElementsByName( id ); + i = 0; + while ( ( elem = elems[ i++ ] ) ) { + node = elem.getAttributeNode( "id" ); + if ( node && node.value === id ) { + return [ elem ]; + } + } + } + + return []; + } + }; + } + + // Tag + Expr.find[ "TAG" ] = support.getElementsByTagName ? + function( tag, context ) { + if ( typeof context.getElementsByTagName !== "undefined" ) { + return context.getElementsByTagName( tag ); + + // DocumentFragment nodes don't have gEBTN + } else if ( support.qsa ) { + return context.querySelectorAll( tag ); + } + } : + + function( tag, context ) { + var elem, + tmp = [], + i = 0, + + // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too + results = context.getElementsByTagName( tag ); + + // Filter out possible comments + if ( tag === "*" ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem.nodeType === 1 ) { + tmp.push( elem ); + } + } + + return tmp; + } + return results; + }; + + // Class + Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) { + if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) { + return context.getElementsByClassName( className ); + } + }; + + /* QSA/matchesSelector + ---------------------------------------------------------------------- */ + + // QSA and matchesSelector support + + // matchesSelector(:active) reports false when true (IE9/Opera 11.5) + rbuggyMatches = []; + + // qSa(:focus) reports false when true (Chrome 21) + // We allow this because of a bug in IE8/9 that throws an error + // whenever `document.activeElement` is accessed on an iframe + // So, we allow :focus to pass through QSA all the time to avoid the IE error + // See https://bugs.jquery.com/ticket/13378 + rbuggyQSA = []; + + if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) { + + // Build QSA regex + // Regex strategy adopted from Diego Perini + assert( function( el ) { + + var input; + + // Select is set to empty string on purpose + // This is to test IE's treatment of not explicitly + // setting a boolean content attribute, + // since its presence should be enough + // https://bugs.jquery.com/ticket/12359 + docElem.appendChild( el ).innerHTML = "" + + ""; + + // Support: IE8, Opera 11-12.16 + // Nothing should be selected when empty strings follow ^= or $= or *= + // The test attribute must be unknown in Opera but "safe" for WinRT + // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section + if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) { + rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" ); + } + + // Support: IE8 + // Boolean attributes and "value" are not treated correctly + if ( !el.querySelectorAll( "[selected]" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" ); + } + + // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+ + if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) { + rbuggyQSA.push( "~=" ); + } + + // Support: IE 11+, Edge 15 - 18+ + // IE 11/Edge don't find elements on a `[name='']` query in some cases. + // Adding a temporary attribute to the document before the selection works + // around the issue. + // Interestingly, IE 10 & older don't seem to have the issue. + input = document.createElement( "input" ); + input.setAttribute( "name", "" ); + el.appendChild( input ); + if ( !el.querySelectorAll( "[name='']" ).length ) { + rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" + + whitespace + "*(?:''|\"\")" ); + } + + // Webkit/Opera - :checked should return selected option elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + // IE8 throws error here and will not see later tests + if ( !el.querySelectorAll( ":checked" ).length ) { + rbuggyQSA.push( ":checked" ); + } + + // Support: Safari 8+, iOS 8+ + // https://bugs.webkit.org/show_bug.cgi?id=136851 + // In-page `selector#id sibling-combinator selector` fails + if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) { + rbuggyQSA.push( ".#.+[+~]" ); + } + + // Support: Firefox <=3.6 - 5 only + // Old Firefox doesn't throw on a badly-escaped identifier. + el.querySelectorAll( "\\\f" ); + rbuggyQSA.push( "[\\r\\n\\f]" ); + } ); + + assert( function( el ) { + el.innerHTML = "" + + ""; + + // Support: Windows 8 Native Apps + // The type and name attributes are restricted during .innerHTML assignment + var input = document.createElement( "input" ); + input.setAttribute( "type", "hidden" ); + el.appendChild( input ).setAttribute( "name", "D" ); + + // Support: IE8 + // Enforce case-sensitivity of name attribute + if ( el.querySelectorAll( "[name=d]" ).length ) { + rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" ); + } + + // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled) + // IE8 throws error here and will not see later tests + if ( el.querySelectorAll( ":enabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: IE9-11+ + // IE's :disabled selector does not pick up the children of disabled fieldsets + docElem.appendChild( el ).disabled = true; + if ( el.querySelectorAll( ":disabled" ).length !== 2 ) { + rbuggyQSA.push( ":enabled", ":disabled" ); + } + + // Support: Opera 10 - 11 only + // Opera 10-11 does not throw on post-comma invalid pseudos + el.querySelectorAll( "*,:x" ); + rbuggyQSA.push( ",.*:" ); + } ); + } + + if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches || + docElem.webkitMatchesSelector || + docElem.mozMatchesSelector || + docElem.oMatchesSelector || + docElem.msMatchesSelector ) ) ) ) { + + assert( function( el ) { + + // Check to see if it's possible to do matchesSelector + // on a disconnected node (IE 9) + support.disconnectedMatch = matches.call( el, "*" ); + + // This should fail with an exception + // Gecko does not error, returns false instead + matches.call( el, "[s!='']:x" ); + rbuggyMatches.push( "!=", pseudos ); + } ); + } + + rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) ); + rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) ); + + /* Contains + ---------------------------------------------------------------------- */ + hasCompare = rnative.test( docElem.compareDocumentPosition ); + + // Element contains another + // Purposefully self-exclusive + // As in, an element does not contain itself + contains = hasCompare || rnative.test( docElem.contains ) ? + function( a, b ) { + var adown = a.nodeType === 9 ? a.documentElement : a, + bup = b && b.parentNode; + return a === bup || !!( bup && bup.nodeType === 1 && ( + adown.contains ? + adown.contains( bup ) : + a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16 + ) ); + } : + function( a, b ) { + if ( b ) { + while ( ( b = b.parentNode ) ) { + if ( b === a ) { + return true; + } + } + } + return false; + }; + + /* Sorting + ---------------------------------------------------------------------- */ + + // Document order sorting + sortOrder = hasCompare ? + function( a, b ) { + + // Flag for duplicate removal + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + // Sort on method existence if only one input has compareDocumentPosition + var compare = !a.compareDocumentPosition - !b.compareDocumentPosition; + if ( compare ) { + return compare; + } + + // Calculate position if both inputs belong to the same document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ? + a.compareDocumentPosition( b ) : + + // Otherwise we know they are disconnected + 1; + + // Disconnected nodes + if ( compare & 1 || + ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) { + + // Choose the first element that is related to our preferred document + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( a == document || a.ownerDocument == preferredDoc && + contains( preferredDoc, a ) ) { + return -1; + } + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( b == document || b.ownerDocument == preferredDoc && + contains( preferredDoc, b ) ) { + return 1; + } + + // Maintain original order + return sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + } + + return compare & 4 ? -1 : 1; + } : + function( a, b ) { + + // Exit early if the nodes are identical + if ( a === b ) { + hasDuplicate = true; + return 0; + } + + var cur, + i = 0, + aup = a.parentNode, + bup = b.parentNode, + ap = [ a ], + bp = [ b ]; + + // Parentless nodes are either documents or disconnected + if ( !aup || !bup ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + return a == document ? -1 : + b == document ? 1 : + /* eslint-enable eqeqeq */ + aup ? -1 : + bup ? 1 : + sortInput ? + ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) : + 0; + + // If the nodes are siblings, we can do a quick check + } else if ( aup === bup ) { + return siblingCheck( a, b ); + } + + // Otherwise we need full lists of their ancestors for comparison + cur = a; + while ( ( cur = cur.parentNode ) ) { + ap.unshift( cur ); + } + cur = b; + while ( ( cur = cur.parentNode ) ) { + bp.unshift( cur ); + } + + // Walk down the tree looking for a discrepancy + while ( ap[ i ] === bp[ i ] ) { + i++; + } + + return i ? + + // Do a sibling check if the nodes have a common ancestor + siblingCheck( ap[ i ], bp[ i ] ) : + + // Otherwise nodes in our document sort first + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + /* eslint-disable eqeqeq */ + ap[ i ] == preferredDoc ? -1 : + bp[ i ] == preferredDoc ? 1 : + /* eslint-enable eqeqeq */ + 0; + }; + + return document; +}; + +Sizzle.matches = function( expr, elements ) { + return Sizzle( expr, null, null, elements ); +}; + +Sizzle.matchesSelector = function( elem, expr ) { + setDocument( elem ); + + if ( support.matchesSelector && documentIsHTML && + !nonnativeSelectorCache[ expr + " " ] && + ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) && + ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) { + + try { + var ret = matches.call( elem, expr ); + + // IE 9's matchesSelector returns false on disconnected nodes + if ( ret || support.disconnectedMatch || + + // As well, disconnected nodes are said to be in a document + // fragment in IE 9 + elem.document && elem.document.nodeType !== 11 ) { + return ret; + } + } catch ( e ) { + nonnativeSelectorCache( expr, true ); + } + } + + return Sizzle( expr, document, null, [ elem ] ).length > 0; +}; + +Sizzle.contains = function( context, elem ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( context.ownerDocument || context ) != document ) { + setDocument( context ); + } + return contains( context, elem ); +}; + +Sizzle.attr = function( elem, name ) { + + // Set document vars if needed + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( ( elem.ownerDocument || elem ) != document ) { + setDocument( elem ); + } + + var fn = Expr.attrHandle[ name.toLowerCase() ], + + // Don't get fooled by Object.prototype properties (jQuery #13807) + val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ? + fn( elem, name, !documentIsHTML ) : + undefined; + + return val !== undefined ? + val : + support.attributes || !documentIsHTML ? + elem.getAttribute( name ) : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; +}; + +Sizzle.escape = function( sel ) { + return ( sel + "" ).replace( rcssescape, fcssescape ); +}; + +Sizzle.error = function( msg ) { + throw new Error( "Syntax error, unrecognized expression: " + msg ); +}; + +/** + * Document sorting and removing duplicates + * @param {ArrayLike} results + */ +Sizzle.uniqueSort = function( results ) { + var elem, + duplicates = [], + j = 0, + i = 0; + + // Unless we *know* we can detect duplicates, assume their presence + hasDuplicate = !support.detectDuplicates; + sortInput = !support.sortStable && results.slice( 0 ); + results.sort( sortOrder ); + + if ( hasDuplicate ) { + while ( ( elem = results[ i++ ] ) ) { + if ( elem === results[ i ] ) { + j = duplicates.push( i ); + } + } + while ( j-- ) { + results.splice( duplicates[ j ], 1 ); + } + } + + // Clear input after sorting to release objects + // See https://github.com/jquery/sizzle/pull/225 + sortInput = null; + + return results; +}; + +/** + * Utility function for retrieving the text value of an array of DOM nodes + * @param {Array|Element} elem + */ +getText = Sizzle.getText = function( elem ) { + var node, + ret = "", + i = 0, + nodeType = elem.nodeType; + + if ( !nodeType ) { + + // If no nodeType, this is expected to be an array + while ( ( node = elem[ i++ ] ) ) { + + // Do not traverse comment nodes + ret += getText( node ); + } + } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) { + + // Use textContent for elements + // innerText usage removed for consistency of new lines (jQuery #11153) + if ( typeof elem.textContent === "string" ) { + return elem.textContent; + } else { + + // Traverse its children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + ret += getText( elem ); + } + } + } else if ( nodeType === 3 || nodeType === 4 ) { + return elem.nodeValue; + } + + // Do not include comment or processing instruction nodes + + return ret; +}; + +Expr = Sizzle.selectors = { + + // Can be adjusted by the user + cacheLength: 50, + + createPseudo: markFunction, + + match: matchExpr, + + attrHandle: {}, + + find: {}, + + relative: { + ">": { dir: "parentNode", first: true }, + " ": { dir: "parentNode" }, + "+": { dir: "previousSibling", first: true }, + "~": { dir: "previousSibling" } + }, + + preFilter: { + "ATTR": function( match ) { + match[ 1 ] = match[ 1 ].replace( runescape, funescape ); + + // Move the given value to match[3] whether quoted or unquoted + match[ 3 ] = ( match[ 3 ] || match[ 4 ] || + match[ 5 ] || "" ).replace( runescape, funescape ); + + if ( match[ 2 ] === "~=" ) { + match[ 3 ] = " " + match[ 3 ] + " "; + } + + return match.slice( 0, 4 ); + }, + + "CHILD": function( match ) { + + /* matches from matchExpr["CHILD"] + 1 type (only|nth|...) + 2 what (child|of-type) + 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...) + 4 xn-component of xn+y argument ([+-]?\d*n|) + 5 sign of xn-component + 6 x of xn-component + 7 sign of y-component + 8 y of y-component + */ + match[ 1 ] = match[ 1 ].toLowerCase(); + + if ( match[ 1 ].slice( 0, 3 ) === "nth" ) { + + // nth-* requires argument + if ( !match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + // numeric x and y parameters for Expr.filter.CHILD + // remember that false/true cast respectively to 0/1 + match[ 4 ] = +( match[ 4 ] ? + match[ 5 ] + ( match[ 6 ] || 1 ) : + 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) ); + match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" ); + + // other types prohibit arguments + } else if ( match[ 3 ] ) { + Sizzle.error( match[ 0 ] ); + } + + return match; + }, + + "PSEUDO": function( match ) { + var excess, + unquoted = !match[ 6 ] && match[ 2 ]; + + if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) { + return null; + } + + // Accept quoted arguments as-is + if ( match[ 3 ] ) { + match[ 2 ] = match[ 4 ] || match[ 5 ] || ""; + + // Strip excess characters from unquoted arguments + } else if ( unquoted && rpseudo.test( unquoted ) && + + // Get excess from tokenize (recursively) + ( excess = tokenize( unquoted, true ) ) && + + // advance to the next closing parenthesis + ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) { + + // excess is a negative index + match[ 0 ] = match[ 0 ].slice( 0, excess ); + match[ 2 ] = unquoted.slice( 0, excess ); + } + + // Return only captures needed by the pseudo filter method (type and argument) + return match.slice( 0, 3 ); + } + }, + + filter: { + + "TAG": function( nodeNameSelector ) { + var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase(); + return nodeNameSelector === "*" ? + function() { + return true; + } : + function( elem ) { + return elem.nodeName && elem.nodeName.toLowerCase() === nodeName; + }; + }, + + "CLASS": function( className ) { + var pattern = classCache[ className + " " ]; + + return pattern || + ( pattern = new RegExp( "(^|" + whitespace + + ")" + className + "(" + whitespace + "|$)" ) ) && classCache( + className, function( elem ) { + return pattern.test( + typeof elem.className === "string" && elem.className || + typeof elem.getAttribute !== "undefined" && + elem.getAttribute( "class" ) || + "" + ); + } ); + }, + + "ATTR": function( name, operator, check ) { + return function( elem ) { + var result = Sizzle.attr( elem, name ); + + if ( result == null ) { + return operator === "!="; + } + if ( !operator ) { + return true; + } + + result += ""; + + /* eslint-disable max-len */ + + return operator === "=" ? result === check : + operator === "!=" ? result !== check : + operator === "^=" ? check && result.indexOf( check ) === 0 : + operator === "*=" ? check && result.indexOf( check ) > -1 : + operator === "$=" ? check && result.slice( -check.length ) === check : + operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 : + operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" : + false; + /* eslint-enable max-len */ + + }; + }, + + "CHILD": function( type, what, _argument, first, last ) { + var simple = type.slice( 0, 3 ) !== "nth", + forward = type.slice( -4 ) !== "last", + ofType = what === "of-type"; + + return first === 1 && last === 0 ? + + // Shortcut for :nth-*(n) + function( elem ) { + return !!elem.parentNode; + } : + + function( elem, _context, xml ) { + var cache, uniqueCache, outerCache, node, nodeIndex, start, + dir = simple !== forward ? "nextSibling" : "previousSibling", + parent = elem.parentNode, + name = ofType && elem.nodeName.toLowerCase(), + useCache = !xml && !ofType, + diff = false; + + if ( parent ) { + + // :(first|last|only)-(child|of-type) + if ( simple ) { + while ( dir ) { + node = elem; + while ( ( node = node[ dir ] ) ) { + if ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) { + + return false; + } + } + + // Reverse direction for :only-* (if we haven't yet done so) + start = dir = type === "only" && !start && "nextSibling"; + } + return true; + } + + start = [ forward ? parent.firstChild : parent.lastChild ]; + + // non-xml :nth-child(...) stores cache data on `parent` + if ( forward && useCache ) { + + // Seek `elem` from a previously-cached index + + // ...in a gzip-friendly way + node = parent; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex && cache[ 2 ]; + node = nodeIndex && parent.childNodes[ nodeIndex ]; + + while ( ( node = ++nodeIndex && node && node[ dir ] || + + // Fallback to seeking `elem` from the start + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + // When found, cache indexes on `parent` and break + if ( node.nodeType === 1 && ++diff && node === elem ) { + uniqueCache[ type ] = [ dirruns, nodeIndex, diff ]; + break; + } + } + + } else { + + // Use previously-cached element index if available + if ( useCache ) { + + // ...in a gzip-friendly way + node = elem; + outerCache = node[ expando ] || ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + cache = uniqueCache[ type ] || []; + nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ]; + diff = nodeIndex; + } + + // xml :nth-child(...) + // or :nth-last-child(...) or :nth(-last)?-of-type(...) + if ( diff === false ) { + + // Use the same loop as above to seek `elem` from the start + while ( ( node = ++nodeIndex && node && node[ dir ] || + ( diff = nodeIndex = 0 ) || start.pop() ) ) { + + if ( ( ofType ? + node.nodeName.toLowerCase() === name : + node.nodeType === 1 ) && + ++diff ) { + + // Cache the index of each encountered element + if ( useCache ) { + outerCache = node[ expando ] || + ( node[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ node.uniqueID ] || + ( outerCache[ node.uniqueID ] = {} ); + + uniqueCache[ type ] = [ dirruns, diff ]; + } + + if ( node === elem ) { + break; + } + } + } + } + } + + // Incorporate the offset, then check against cycle size + diff -= last; + return diff === first || ( diff % first === 0 && diff / first >= 0 ); + } + }; + }, + + "PSEUDO": function( pseudo, argument ) { + + // pseudo-class names are case-insensitive + // http://www.w3.org/TR/selectors/#pseudo-classes + // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters + // Remember that setFilters inherits from pseudos + var args, + fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] || + Sizzle.error( "unsupported pseudo: " + pseudo ); + + // The user may use createPseudo to indicate that + // arguments are needed to create the filter function + // just as Sizzle does + if ( fn[ expando ] ) { + return fn( argument ); + } + + // But maintain support for old signatures + if ( fn.length > 1 ) { + args = [ pseudo, pseudo, "", argument ]; + return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ? + markFunction( function( seed, matches ) { + var idx, + matched = fn( seed, argument ), + i = matched.length; + while ( i-- ) { + idx = indexOf( seed, matched[ i ] ); + seed[ idx ] = !( matches[ idx ] = matched[ i ] ); + } + } ) : + function( elem ) { + return fn( elem, 0, args ); + }; + } + + return fn; + } + }, + + pseudos: { + + // Potentially complex pseudos + "not": markFunction( function( selector ) { + + // Trim the selector passed to compile + // to avoid treating leading and trailing + // spaces as combinators + var input = [], + results = [], + matcher = compile( selector.replace( rtrim, "$1" ) ); + + return matcher[ expando ] ? + markFunction( function( seed, matches, _context, xml ) { + var elem, + unmatched = matcher( seed, null, xml, [] ), + i = seed.length; + + // Match elements unmatched by `matcher` + while ( i-- ) { + if ( ( elem = unmatched[ i ] ) ) { + seed[ i ] = !( matches[ i ] = elem ); + } + } + } ) : + function( elem, _context, xml ) { + input[ 0 ] = elem; + matcher( input, null, xml, results ); + + // Don't keep the element (issue #299) + input[ 0 ] = null; + return !results.pop(); + }; + } ), + + "has": markFunction( function( selector ) { + return function( elem ) { + return Sizzle( selector, elem ).length > 0; + }; + } ), + + "contains": markFunction( function( text ) { + text = text.replace( runescape, funescape ); + return function( elem ) { + return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1; + }; + } ), + + // "Whether an element is represented by a :lang() selector + // is based solely on the element's language value + // being equal to the identifier C, + // or beginning with the identifier C immediately followed by "-". + // The matching of C against the element's language value is performed case-insensitively. + // The identifier C does not have to be a valid language name." + // http://www.w3.org/TR/selectors/#lang-pseudo + "lang": markFunction( function( lang ) { + + // lang value must be a valid identifier + if ( !ridentifier.test( lang || "" ) ) { + Sizzle.error( "unsupported lang: " + lang ); + } + lang = lang.replace( runescape, funescape ).toLowerCase(); + return function( elem ) { + var elemLang; + do { + if ( ( elemLang = documentIsHTML ? + elem.lang : + elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) { + + elemLang = elemLang.toLowerCase(); + return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0; + } + } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 ); + return false; + }; + } ), + + // Miscellaneous + "target": function( elem ) { + var hash = window.location && window.location.hash; + return hash && hash.slice( 1 ) === elem.id; + }, + + "root": function( elem ) { + return elem === docElem; + }, + + "focus": function( elem ) { + return elem === document.activeElement && + ( !document.hasFocus || document.hasFocus() ) && + !!( elem.type || elem.href || ~elem.tabIndex ); + }, + + // Boolean properties + "enabled": createDisabledPseudo( false ), + "disabled": createDisabledPseudo( true ), + + "checked": function( elem ) { + + // In CSS3, :checked should return both checked and selected elements + // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked + var nodeName = elem.nodeName.toLowerCase(); + return ( nodeName === "input" && !!elem.checked ) || + ( nodeName === "option" && !!elem.selected ); + }, + + "selected": function( elem ) { + + // Accessing this property makes selected-by-default + // options in Safari work properly + if ( elem.parentNode ) { + // eslint-disable-next-line no-unused-expressions + elem.parentNode.selectedIndex; + } + + return elem.selected === true; + }, + + // Contents + "empty": function( elem ) { + + // http://www.w3.org/TR/selectors/#empty-pseudo + // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5), + // but not by others (comment: 8; processing instruction: 7; etc.) + // nodeType < 6 works because attributes (2) do not appear as children + for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) { + if ( elem.nodeType < 6 ) { + return false; + } + } + return true; + }, + + "parent": function( elem ) { + return !Expr.pseudos[ "empty" ]( elem ); + }, + + // Element/input types + "header": function( elem ) { + return rheader.test( elem.nodeName ); + }, + + "input": function( elem ) { + return rinputs.test( elem.nodeName ); + }, + + "button": function( elem ) { + var name = elem.nodeName.toLowerCase(); + return name === "input" && elem.type === "button" || name === "button"; + }, + + "text": function( elem ) { + var attr; + return elem.nodeName.toLowerCase() === "input" && + elem.type === "text" && + + // Support: IE<8 + // New HTML5 attribute values (e.g., "search") appear with elem.type === "text" + ( ( attr = elem.getAttribute( "type" ) ) == null || + attr.toLowerCase() === "text" ); + }, + + // Position-in-collection + "first": createPositionalPseudo( function() { + return [ 0 ]; + } ), + + "last": createPositionalPseudo( function( _matchIndexes, length ) { + return [ length - 1 ]; + } ), + + "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) { + return [ argument < 0 ? argument + length : argument ]; + } ), + + "even": createPositionalPseudo( function( matchIndexes, length ) { + var i = 0; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "odd": createPositionalPseudo( function( matchIndexes, length ) { + var i = 1; + for ( ; i < length; i += 2 ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "lt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? + argument + length : + argument > length ? + length : + argument; + for ( ; --i >= 0; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ), + + "gt": createPositionalPseudo( function( matchIndexes, length, argument ) { + var i = argument < 0 ? argument + length : argument; + for ( ; ++i < length; ) { + matchIndexes.push( i ); + } + return matchIndexes; + } ) + } +}; + +Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ]; + +// Add button/input type pseudos +for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) { + Expr.pseudos[ i ] = createInputPseudo( i ); +} +for ( i in { submit: true, reset: true } ) { + Expr.pseudos[ i ] = createButtonPseudo( i ); +} + +// Easy API for creating new setFilters +function setFilters() {} +setFilters.prototype = Expr.filters = Expr.pseudos; +Expr.setFilters = new setFilters(); + +tokenize = Sizzle.tokenize = function( selector, parseOnly ) { + var matched, match, tokens, type, + soFar, groups, preFilters, + cached = tokenCache[ selector + " " ]; + + if ( cached ) { + return parseOnly ? 0 : cached.slice( 0 ); + } + + soFar = selector; + groups = []; + preFilters = Expr.preFilter; + + while ( soFar ) { + + // Comma and first run + if ( !matched || ( match = rcomma.exec( soFar ) ) ) { + if ( match ) { + + // Don't consume trailing commas as valid + soFar = soFar.slice( match[ 0 ].length ) || soFar; + } + groups.push( ( tokens = [] ) ); + } + + matched = false; + + // Combinators + if ( ( match = rcombinators.exec( soFar ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + + // Cast descendant combinators to space + type: match[ 0 ].replace( rtrim, " " ) + } ); + soFar = soFar.slice( matched.length ); + } + + // Filters + for ( type in Expr.filter ) { + if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] || + ( match = preFilters[ type ]( match ) ) ) ) { + matched = match.shift(); + tokens.push( { + value: matched, + type: type, + matches: match + } ); + soFar = soFar.slice( matched.length ); + } + } + + if ( !matched ) { + break; + } + } + + // Return the length of the invalid excess + // if we're just parsing + // Otherwise, throw an error or return tokens + return parseOnly ? + soFar.length : + soFar ? + Sizzle.error( selector ) : + + // Cache the tokens + tokenCache( selector, groups ).slice( 0 ); +}; + +function toSelector( tokens ) { + var i = 0, + len = tokens.length, + selector = ""; + for ( ; i < len; i++ ) { + selector += tokens[ i ].value; + } + return selector; +} + +function addCombinator( matcher, combinator, base ) { + var dir = combinator.dir, + skip = combinator.next, + key = skip || dir, + checkNonElements = base && key === "parentNode", + doneName = done++; + + return combinator.first ? + + // Check against closest ancestor/preceding element + function( elem, context, xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + return matcher( elem, context, xml ); + } + } + return false; + } : + + // Check against all ancestor/preceding elements + function( elem, context, xml ) { + var oldCache, uniqueCache, outerCache, + newCache = [ dirruns, doneName ]; + + // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching + if ( xml ) { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + if ( matcher( elem, context, xml ) ) { + return true; + } + } + } + } else { + while ( ( elem = elem[ dir ] ) ) { + if ( elem.nodeType === 1 || checkNonElements ) { + outerCache = elem[ expando ] || ( elem[ expando ] = {} ); + + // Support: IE <9 only + // Defend against cloned attroperties (jQuery gh-1709) + uniqueCache = outerCache[ elem.uniqueID ] || + ( outerCache[ elem.uniqueID ] = {} ); + + if ( skip && skip === elem.nodeName.toLowerCase() ) { + elem = elem[ dir ] || elem; + } else if ( ( oldCache = uniqueCache[ key ] ) && + oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) { + + // Assign to newCache so results back-propagate to previous elements + return ( newCache[ 2 ] = oldCache[ 2 ] ); + } else { + + // Reuse newcache so results back-propagate to previous elements + uniqueCache[ key ] = newCache; + + // A match means we're done; a fail means we have to keep checking + if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) { + return true; + } + } + } + } + } + return false; + }; +} + +function elementMatcher( matchers ) { + return matchers.length > 1 ? + function( elem, context, xml ) { + var i = matchers.length; + while ( i-- ) { + if ( !matchers[ i ]( elem, context, xml ) ) { + return false; + } + } + return true; + } : + matchers[ 0 ]; +} + +function multipleContexts( selector, contexts, results ) { + var i = 0, + len = contexts.length; + for ( ; i < len; i++ ) { + Sizzle( selector, contexts[ i ], results ); + } + return results; +} + +function condense( unmatched, map, filter, context, xml ) { + var elem, + newUnmatched = [], + i = 0, + len = unmatched.length, + mapped = map != null; + + for ( ; i < len; i++ ) { + if ( ( elem = unmatched[ i ] ) ) { + if ( !filter || filter( elem, context, xml ) ) { + newUnmatched.push( elem ); + if ( mapped ) { + map.push( i ); + } + } + } + } + + return newUnmatched; +} + +function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) { + if ( postFilter && !postFilter[ expando ] ) { + postFilter = setMatcher( postFilter ); + } + if ( postFinder && !postFinder[ expando ] ) { + postFinder = setMatcher( postFinder, postSelector ); + } + return markFunction( function( seed, results, context, xml ) { + var temp, i, elem, + preMap = [], + postMap = [], + preexisting = results.length, + + // Get initial elements from seed or context + elems = seed || multipleContexts( + selector || "*", + context.nodeType ? [ context ] : context, + [] + ), + + // Prefilter to get matcher input, preserving a map for seed-results synchronization + matcherIn = preFilter && ( seed || !selector ) ? + condense( elems, preMap, preFilter, context, xml ) : + elems, + + matcherOut = matcher ? + + // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results, + postFinder || ( seed ? preFilter : preexisting || postFilter ) ? + + // ...intermediate processing is necessary + [] : + + // ...otherwise use results directly + results : + matcherIn; + + // Find primary matches + if ( matcher ) { + matcher( matcherIn, matcherOut, context, xml ); + } + + // Apply postFilter + if ( postFilter ) { + temp = condense( matcherOut, postMap ); + postFilter( temp, [], context, xml ); + + // Un-match failing elements by moving them back to matcherIn + i = temp.length; + while ( i-- ) { + if ( ( elem = temp[ i ] ) ) { + matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem ); + } + } + } + + if ( seed ) { + if ( postFinder || preFilter ) { + if ( postFinder ) { + + // Get the final matcherOut by condensing this intermediate into postFinder contexts + temp = []; + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) ) { + + // Restore matcherIn since elem is not yet a final match + temp.push( ( matcherIn[ i ] = elem ) ); + } + } + postFinder( null, ( matcherOut = [] ), temp, xml ); + } + + // Move matched elements from seed to results to keep them synchronized + i = matcherOut.length; + while ( i-- ) { + if ( ( elem = matcherOut[ i ] ) && + ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) { + + seed[ temp ] = !( results[ temp ] = elem ); + } + } + } + + // Add elements to results, through postFinder if defined + } else { + matcherOut = condense( + matcherOut === results ? + matcherOut.splice( preexisting, matcherOut.length ) : + matcherOut + ); + if ( postFinder ) { + postFinder( null, results, matcherOut, xml ); + } else { + push.apply( results, matcherOut ); + } + } + } ); +} + +function matcherFromTokens( tokens ) { + var checkContext, matcher, j, + len = tokens.length, + leadingRelative = Expr.relative[ tokens[ 0 ].type ], + implicitRelative = leadingRelative || Expr.relative[ " " ], + i = leadingRelative ? 1 : 0, + + // The foundational matcher ensures that elements are reachable from top-level context(s) + matchContext = addCombinator( function( elem ) { + return elem === checkContext; + }, implicitRelative, true ), + matchAnyContext = addCombinator( function( elem ) { + return indexOf( checkContext, elem ) > -1; + }, implicitRelative, true ), + matchers = [ function( elem, context, xml ) { + var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || ( + ( checkContext = context ).nodeType ? + matchContext( elem, context, xml ) : + matchAnyContext( elem, context, xml ) ); + + // Avoid hanging onto element (issue #299) + checkContext = null; + return ret; + } ]; + + for ( ; i < len; i++ ) { + if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) { + matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ]; + } else { + matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches ); + + // Return special upon seeing a positional matcher + if ( matcher[ expando ] ) { + + // Find the next relative operator (if any) for proper handling + j = ++i; + for ( ; j < len; j++ ) { + if ( Expr.relative[ tokens[ j ].type ] ) { + break; + } + } + return setMatcher( + i > 1 && elementMatcher( matchers ), + i > 1 && toSelector( + + // If the preceding token was a descendant combinator, insert an implicit any-element `*` + tokens + .slice( 0, i - 1 ) + .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } ) + ).replace( rtrim, "$1" ), + matcher, + i < j && matcherFromTokens( tokens.slice( i, j ) ), + j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ), + j < len && toSelector( tokens ) + ); + } + matchers.push( matcher ); + } + } + + return elementMatcher( matchers ); +} + +function matcherFromGroupMatchers( elementMatchers, setMatchers ) { + var bySet = setMatchers.length > 0, + byElement = elementMatchers.length > 0, + superMatcher = function( seed, context, xml, results, outermost ) { + var elem, j, matcher, + matchedCount = 0, + i = "0", + unmatched = seed && [], + setMatched = [], + contextBackup = outermostContext, + + // We must always have either seed elements or outermost context + elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ), + + // Use integer dirruns iff this is the outermost matcher + dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ), + len = elems.length; + + if ( outermost ) { + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + outermostContext = context == document || context || outermost; + } + + // Add elements passing elementMatchers directly to results + // Support: IE<9, Safari + // Tolerate NodeList properties (IE: "length"; Safari: ) matching elements by id + for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) { + if ( byElement && elem ) { + j = 0; + + // Support: IE 11+, Edge 17 - 18+ + // IE/Edge sometimes throw a "Permission denied" error when strict-comparing + // two documents; shallow comparisons work. + // eslint-disable-next-line eqeqeq + if ( !context && elem.ownerDocument != document ) { + setDocument( elem ); + xml = !documentIsHTML; + } + while ( ( matcher = elementMatchers[ j++ ] ) ) { + if ( matcher( elem, context || document, xml ) ) { + results.push( elem ); + break; + } + } + if ( outermost ) { + dirruns = dirrunsUnique; + } + } + + // Track unmatched elements for set filters + if ( bySet ) { + + // They will have gone through all possible matchers + if ( ( elem = !matcher && elem ) ) { + matchedCount--; + } + + // Lengthen the array for every element, matched or not + if ( seed ) { + unmatched.push( elem ); + } + } + } + + // `i` is now the count of elements visited above, and adding it to `matchedCount` + // makes the latter nonnegative. + matchedCount += i; + + // Apply set filters to unmatched elements + // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount` + // equals `i`), unless we didn't visit _any_ elements in the above loop because we have + // no element matchers and no seed. + // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that + // case, which will result in a "00" `matchedCount` that differs from `i` but is also + // numerically zero. + if ( bySet && i !== matchedCount ) { + j = 0; + while ( ( matcher = setMatchers[ j++ ] ) ) { + matcher( unmatched, setMatched, context, xml ); + } + + if ( seed ) { + + // Reintegrate element matches to eliminate the need for sorting + if ( matchedCount > 0 ) { + while ( i-- ) { + if ( !( unmatched[ i ] || setMatched[ i ] ) ) { + setMatched[ i ] = pop.call( results ); + } + } + } + + // Discard index placeholder values to get only actual matches + setMatched = condense( setMatched ); + } + + // Add matches to results + push.apply( results, setMatched ); + + // Seedless set matches succeeding multiple successful matchers stipulate sorting + if ( outermost && !seed && setMatched.length > 0 && + ( matchedCount + setMatchers.length ) > 1 ) { + + Sizzle.uniqueSort( results ); + } + } + + // Override manipulation of globals by nested matchers + if ( outermost ) { + dirruns = dirrunsUnique; + outermostContext = contextBackup; + } + + return unmatched; + }; + + return bySet ? + markFunction( superMatcher ) : + superMatcher; +} + +compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) { + var i, + setMatchers = [], + elementMatchers = [], + cached = compilerCache[ selector + " " ]; + + if ( !cached ) { + + // Generate a function of recursive functions that can be used to check each element + if ( !match ) { + match = tokenize( selector ); + } + i = match.length; + while ( i-- ) { + cached = matcherFromTokens( match[ i ] ); + if ( cached[ expando ] ) { + setMatchers.push( cached ); + } else { + elementMatchers.push( cached ); + } + } + + // Cache the compiled function + cached = compilerCache( + selector, + matcherFromGroupMatchers( elementMatchers, setMatchers ) + ); + + // Save selector and tokenization + cached.selector = selector; + } + return cached; +}; + +/** + * A low-level selection function that works with Sizzle's compiled + * selector functions + * @param {String|Function} selector A selector or a pre-compiled + * selector function built with Sizzle.compile + * @param {Element} context + * @param {Array} [results] + * @param {Array} [seed] A set of elements to match against + */ +select = Sizzle.select = function( selector, context, results, seed ) { + var i, tokens, token, type, find, + compiled = typeof selector === "function" && selector, + match = !seed && tokenize( ( selector = compiled.selector || selector ) ); + + results = results || []; + + // Try to minimize operations if there is only one selector in the list and no seed + // (the latter of which guarantees us context) + if ( match.length === 1 ) { + + // Reduce context if the leading compound selector is an ID + tokens = match[ 0 ] = match[ 0 ].slice( 0 ); + if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" && + context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) { + + context = ( Expr.find[ "ID" ]( token.matches[ 0 ] + .replace( runescape, funescape ), context ) || [] )[ 0 ]; + if ( !context ) { + return results; + + // Precompiled matchers will still verify ancestry, so step up a level + } else if ( compiled ) { + context = context.parentNode; + } + + selector = selector.slice( tokens.shift().value.length ); + } + + // Fetch a seed set for right-to-left matching + i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length; + while ( i-- ) { + token = tokens[ i ]; + + // Abort if we hit a combinator + if ( Expr.relative[ ( type = token.type ) ] ) { + break; + } + if ( ( find = Expr.find[ type ] ) ) { + + // Search, expanding context for leading sibling combinators + if ( ( seed = find( + token.matches[ 0 ].replace( runescape, funescape ), + rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) || + context + ) ) ) { + + // If seed is empty or no tokens remain, we can return early + tokens.splice( i, 1 ); + selector = seed.length && toSelector( tokens ); + if ( !selector ) { + push.apply( results, seed ); + return results; + } + + break; + } + } + } + } + + // Compile and execute a filtering function if one is not provided + // Provide `match` to avoid retokenization if we modified the selector above + ( compiled || compile( selector, match ) )( + seed, + context, + !documentIsHTML, + results, + !context || rsibling.test( selector ) && testContext( context.parentNode ) || context + ); + return results; +}; + +// One-time assignments + +// Sort stability +support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando; + +// Support: Chrome 14-35+ +// Always assume duplicates if they aren't passed to the comparison function +support.detectDuplicates = !!hasDuplicate; + +// Initialize against the default document +setDocument(); + +// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27) +// Detached nodes confoundingly follow *each other* +support.sortDetached = assert( function( el ) { + + // Should return 1, but returns 4 (following) + return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1; +} ); + +// Support: IE<8 +// Prevent attribute/property "interpolation" +// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx +if ( !assert( function( el ) { + el.innerHTML = ""; + return el.firstChild.getAttribute( "href" ) === "#"; +} ) ) { + addHandle( "type|href|height|width", function( elem, name, isXML ) { + if ( !isXML ) { + return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 ); + } + } ); +} + +// Support: IE<9 +// Use defaultValue in place of getAttribute("value") +if ( !support.attributes || !assert( function( el ) { + el.innerHTML = ""; + el.firstChild.setAttribute( "value", "" ); + return el.firstChild.getAttribute( "value" ) === ""; +} ) ) { + addHandle( "value", function( elem, _name, isXML ) { + if ( !isXML && elem.nodeName.toLowerCase() === "input" ) { + return elem.defaultValue; + } + } ); +} + +// Support: IE<9 +// Use getAttributeNode to fetch booleans when getAttribute lies +if ( !assert( function( el ) { + return el.getAttribute( "disabled" ) == null; +} ) ) { + addHandle( booleans, function( elem, name, isXML ) { + var val; + if ( !isXML ) { + return elem[ name ] === true ? name.toLowerCase() : + ( val = elem.getAttributeNode( name ) ) && val.specified ? + val.value : + null; + } + } ); +} + +return Sizzle; + +} )( window ); + + + +jQuery.find = Sizzle; +jQuery.expr = Sizzle.selectors; + +// Deprecated +jQuery.expr[ ":" ] = jQuery.expr.pseudos; +jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort; +jQuery.text = Sizzle.getText; +jQuery.isXMLDoc = Sizzle.isXML; +jQuery.contains = Sizzle.contains; +jQuery.escapeSelector = Sizzle.escape; + + + + +var dir = function( elem, dir, until ) { + var matched = [], + truncate = until !== undefined; + + while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) { + if ( elem.nodeType === 1 ) { + if ( truncate && jQuery( elem ).is( until ) ) { + break; + } + matched.push( elem ); + } + } + return matched; +}; + + +var siblings = function( n, elem ) { + var matched = []; + + for ( ; n; n = n.nextSibling ) { + if ( n.nodeType === 1 && n !== elem ) { + matched.push( n ); + } + } + + return matched; +}; + + +var rneedsContext = jQuery.expr.match.needsContext; + + + +function nodeName( elem, name ) { + + return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase(); + +} +var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i ); + + + +// Implement the identical functionality for filter and not +function winnow( elements, qualifier, not ) { + if ( isFunction( qualifier ) ) { + return jQuery.grep( elements, function( elem, i ) { + return !!qualifier.call( elem, i, elem ) !== not; + } ); + } + + // Single element + if ( qualifier.nodeType ) { + return jQuery.grep( elements, function( elem ) { + return ( elem === qualifier ) !== not; + } ); + } + + // Arraylike of elements (jQuery, arguments, Array) + if ( typeof qualifier !== "string" ) { + return jQuery.grep( elements, function( elem ) { + return ( indexOf.call( qualifier, elem ) > -1 ) !== not; + } ); + } + + // Filtered directly for both simple and complex selectors + return jQuery.filter( qualifier, elements, not ); +} + +jQuery.filter = function( expr, elems, not ) { + var elem = elems[ 0 ]; + + if ( not ) { + expr = ":not(" + expr + ")"; + } + + if ( elems.length === 1 && elem.nodeType === 1 ) { + return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : []; + } + + return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) { + return elem.nodeType === 1; + } ) ); +}; + +jQuery.fn.extend( { + find: function( selector ) { + var i, ret, + len = this.length, + self = this; + + if ( typeof selector !== "string" ) { + return this.pushStack( jQuery( selector ).filter( function() { + for ( i = 0; i < len; i++ ) { + if ( jQuery.contains( self[ i ], this ) ) { + return true; + } + } + } ) ); + } + + ret = this.pushStack( [] ); + + for ( i = 0; i < len; i++ ) { + jQuery.find( selector, self[ i ], ret ); + } + + return len > 1 ? jQuery.uniqueSort( ret ) : ret; + }, + filter: function( selector ) { + return this.pushStack( winnow( this, selector || [], false ) ); + }, + not: function( selector ) { + return this.pushStack( winnow( this, selector || [], true ) ); + }, + is: function( selector ) { + return !!winnow( + this, + + // If this is a positional/relative selector, check membership in the returned set + // so $("p:first").is("p:last") won't return true for a doc with two "p". + typeof selector === "string" && rneedsContext.test( selector ) ? + jQuery( selector ) : + selector || [], + false + ).length; + } +} ); + + +// Initialize a jQuery object + + +// A central reference to the root jQuery(document) +var rootjQuery, + + // A simple way to check for HTML strings + // Prioritize #id over to avoid XSS via location.hash (#9521) + // Strict HTML recognition (#11290: must start with <) + // Shortcut simple #id case for speed + rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/, + + init = jQuery.fn.init = function( selector, context, root ) { + var match, elem; + + // HANDLE: $(""), $(null), $(undefined), $(false) + if ( !selector ) { + return this; + } + + // Method init() accepts an alternate rootjQuery + // so migrate can support jQuery.sub (gh-2101) + root = root || rootjQuery; + + // Handle HTML strings + if ( typeof selector === "string" ) { + if ( selector[ 0 ] === "<" && + selector[ selector.length - 1 ] === ">" && + selector.length >= 3 ) { + + // Assume that strings that start and end with <> are HTML and skip the regex check + match = [ null, selector, null ]; + + } else { + match = rquickExpr.exec( selector ); + } + + // Match html or make sure no context is specified for #id + if ( match && ( match[ 1 ] || !context ) ) { + + // HANDLE: $(html) -> $(array) + if ( match[ 1 ] ) { + context = context instanceof jQuery ? context[ 0 ] : context; + + // Option to run scripts is true for back-compat + // Intentionally let the error be thrown if parseHTML is not present + jQuery.merge( this, jQuery.parseHTML( + match[ 1 ], + context && context.nodeType ? context.ownerDocument || context : document, + true + ) ); + + // HANDLE: $(html, props) + if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) { + for ( match in context ) { + + // Properties of context are called as methods if possible + if ( isFunction( this[ match ] ) ) { + this[ match ]( context[ match ] ); + + // ...and otherwise set as attributes + } else { + this.attr( match, context[ match ] ); + } + } + } + + return this; + + // HANDLE: $(#id) + } else { + elem = document.getElementById( match[ 2 ] ); + + if ( elem ) { + + // Inject the element directly into the jQuery object + this[ 0 ] = elem; + this.length = 1; + } + return this; + } + + // HANDLE: $(expr, $(...)) + } else if ( !context || context.jquery ) { + return ( context || root ).find( selector ); + + // HANDLE: $(expr, context) + // (which is just equivalent to: $(context).find(expr) + } else { + return this.constructor( context ).find( selector ); + } + + // HANDLE: $(DOMElement) + } else if ( selector.nodeType ) { + this[ 0 ] = selector; + this.length = 1; + return this; + + // HANDLE: $(function) + // Shortcut for document ready + } else if ( isFunction( selector ) ) { + return root.ready !== undefined ? + root.ready( selector ) : + + // Execute immediately if ready is not present + selector( jQuery ); + } + + return jQuery.makeArray( selector, this ); + }; + +// Give the init function the jQuery prototype for later instantiation +init.prototype = jQuery.fn; + +// Initialize central reference +rootjQuery = jQuery( document ); + + +var rparentsprev = /^(?:parents|prev(?:Until|All))/, + + // Methods guaranteed to produce a unique set when starting from a unique set + guaranteedUnique = { + children: true, + contents: true, + next: true, + prev: true + }; + +jQuery.fn.extend( { + has: function( target ) { + var targets = jQuery( target, this ), + l = targets.length; + + return this.filter( function() { + var i = 0; + for ( ; i < l; i++ ) { + if ( jQuery.contains( this, targets[ i ] ) ) { + return true; + } + } + } ); + }, + + closest: function( selectors, context ) { + var cur, + i = 0, + l = this.length, + matched = [], + targets = typeof selectors !== "string" && jQuery( selectors ); + + // Positional selectors never match, since there's no _selection_ context + if ( !rneedsContext.test( selectors ) ) { + for ( ; i < l; i++ ) { + for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) { + + // Always skip document fragments + if ( cur.nodeType < 11 && ( targets ? + targets.index( cur ) > -1 : + + // Don't pass non-elements to Sizzle + cur.nodeType === 1 && + jQuery.find.matchesSelector( cur, selectors ) ) ) { + + matched.push( cur ); + break; + } + } + } + } + + return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched ); + }, + + // Determine the position of an element within the set + index: function( elem ) { + + // No argument, return index in parent + if ( !elem ) { + return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1; + } + + // Index in selector + if ( typeof elem === "string" ) { + return indexOf.call( jQuery( elem ), this[ 0 ] ); + } + + // Locate the position of the desired element + return indexOf.call( this, + + // If it receives a jQuery object, the first element is used + elem.jquery ? elem[ 0 ] : elem + ); + }, + + add: function( selector, context ) { + return this.pushStack( + jQuery.uniqueSort( + jQuery.merge( this.get(), jQuery( selector, context ) ) + ) + ); + }, + + addBack: function( selector ) { + return this.add( selector == null ? + this.prevObject : this.prevObject.filter( selector ) + ); + } +} ); + +function sibling( cur, dir ) { + while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {} + return cur; +} + +jQuery.each( { + parent: function( elem ) { + var parent = elem.parentNode; + return parent && parent.nodeType !== 11 ? parent : null; + }, + parents: function( elem ) { + return dir( elem, "parentNode" ); + }, + parentsUntil: function( elem, _i, until ) { + return dir( elem, "parentNode", until ); + }, + next: function( elem ) { + return sibling( elem, "nextSibling" ); + }, + prev: function( elem ) { + return sibling( elem, "previousSibling" ); + }, + nextAll: function( elem ) { + return dir( elem, "nextSibling" ); + }, + prevAll: function( elem ) { + return dir( elem, "previousSibling" ); + }, + nextUntil: function( elem, _i, until ) { + return dir( elem, "nextSibling", until ); + }, + prevUntil: function( elem, _i, until ) { + return dir( elem, "previousSibling", until ); + }, + siblings: function( elem ) { + return siblings( ( elem.parentNode || {} ).firstChild, elem ); + }, + children: function( elem ) { + return siblings( elem.firstChild ); + }, + contents: function( elem ) { + if ( elem.contentDocument != null && + + // Support: IE 11+ + // elements with no `data` attribute has an object + // `contentDocument` with a `null` prototype. + getProto( elem.contentDocument ) ) { + + return elem.contentDocument; + } + + // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only + // Treat the template element as a regular one in browsers that + // don't support it. + if ( nodeName( elem, "template" ) ) { + elem = elem.content || elem; + } + + return jQuery.merge( [], elem.childNodes ); + } +}, function( name, fn ) { + jQuery.fn[ name ] = function( until, selector ) { + var matched = jQuery.map( this, fn, until ); + + if ( name.slice( -5 ) !== "Until" ) { + selector = until; + } + + if ( selector && typeof selector === "string" ) { + matched = jQuery.filter( selector, matched ); + } + + if ( this.length > 1 ) { + + // Remove duplicates + if ( !guaranteedUnique[ name ] ) { + jQuery.uniqueSort( matched ); + } + + // Reverse order for parents* and prev-derivatives + if ( rparentsprev.test( name ) ) { + matched.reverse(); + } + } + + return this.pushStack( matched ); + }; +} ); +var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g ); + + + +// Convert String-formatted options into Object-formatted ones +function createOptions( options ) { + var object = {}; + jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) { + object[ flag ] = true; + } ); + return object; +} + +/* + * Create a callback list using the following parameters: + * + * options: an optional list of space-separated options that will change how + * the callback list behaves or a more traditional option object + * + * By default a callback list will act like an event callback list and can be + * "fired" multiple times. + * + * Possible options: + * + * once: will ensure the callback list can only be fired once (like a Deferred) + * + * memory: will keep track of previous values and will call any callback added + * after the list has been fired right away with the latest "memorized" + * values (like a Deferred) + * + * unique: will ensure a callback can only be added once (no duplicate in the list) + * + * stopOnFalse: interrupt callings when a callback returns false + * + */ +jQuery.Callbacks = function( options ) { + + // Convert options from String-formatted to Object-formatted if needed + // (we check in cache first) + options = typeof options === "string" ? + createOptions( options ) : + jQuery.extend( {}, options ); + + var // Flag to know if list is currently firing + firing, + + // Last fire value for non-forgettable lists + memory, + + // Flag to know if list was already fired + fired, + + // Flag to prevent firing + locked, + + // Actual callback list + list = [], + + // Queue of execution data for repeatable lists + queue = [], + + // Index of currently firing callback (modified by add/remove as needed) + firingIndex = -1, + + // Fire callbacks + fire = function() { + + // Enforce single-firing + locked = locked || options.once; + + // Execute callbacks for all pending executions, + // respecting firingIndex overrides and runtime changes + fired = firing = true; + for ( ; queue.length; firingIndex = -1 ) { + memory = queue.shift(); + while ( ++firingIndex < list.length ) { + + // Run callback and check for early termination + if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false && + options.stopOnFalse ) { + + // Jump to end and forget the data so .add doesn't re-fire + firingIndex = list.length; + memory = false; + } + } + } + + // Forget the data if we're done with it + if ( !options.memory ) { + memory = false; + } + + firing = false; + + // Clean up if we're done firing for good + if ( locked ) { + + // Keep an empty list if we have data for future add calls + if ( memory ) { + list = []; + + // Otherwise, this object is spent + } else { + list = ""; + } + } + }, + + // Actual Callbacks object + self = { + + // Add a callback or a collection of callbacks to the list + add: function() { + if ( list ) { + + // If we have memory from a past run, we should fire after adding + if ( memory && !firing ) { + firingIndex = list.length - 1; + queue.push( memory ); + } + + ( function add( args ) { + jQuery.each( args, function( _, arg ) { + if ( isFunction( arg ) ) { + if ( !options.unique || !self.has( arg ) ) { + list.push( arg ); + } + } else if ( arg && arg.length && toType( arg ) !== "string" ) { + + // Inspect recursively + add( arg ); + } + } ); + } )( arguments ); + + if ( memory && !firing ) { + fire(); + } + } + return this; + }, + + // Remove a callback from the list + remove: function() { + jQuery.each( arguments, function( _, arg ) { + var index; + while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) { + list.splice( index, 1 ); + + // Handle firing indexes + if ( index <= firingIndex ) { + firingIndex--; + } + } + } ); + return this; + }, + + // Check if a given callback is in the list. + // If no argument is given, return whether or not list has callbacks attached. + has: function( fn ) { + return fn ? + jQuery.inArray( fn, list ) > -1 : + list.length > 0; + }, + + // Remove all callbacks from the list + empty: function() { + if ( list ) { + list = []; + } + return this; + }, + + // Disable .fire and .add + // Abort any current/pending executions + // Clear all callbacks and values + disable: function() { + locked = queue = []; + list = memory = ""; + return this; + }, + disabled: function() { + return !list; + }, + + // Disable .fire + // Also disable .add unless we have memory (since it would have no effect) + // Abort any pending executions + lock: function() { + locked = queue = []; + if ( !memory && !firing ) { + list = memory = ""; + } + return this; + }, + locked: function() { + return !!locked; + }, + + // Call all callbacks with the given context and arguments + fireWith: function( context, args ) { + if ( !locked ) { + args = args || []; + args = [ context, args.slice ? args.slice() : args ]; + queue.push( args ); + if ( !firing ) { + fire(); + } + } + return this; + }, + + // Call all the callbacks with the given arguments + fire: function() { + self.fireWith( this, arguments ); + return this; + }, + + // To know if the callbacks have already been called at least once + fired: function() { + return !!fired; + } + }; + + return self; +}; + + +function Identity( v ) { + return v; +} +function Thrower( ex ) { + throw ex; +} + +function adoptValue( value, resolve, reject, noValue ) { + var method; + + try { + + // Check for promise aspect first to privilege synchronous behavior + if ( value && isFunction( ( method = value.promise ) ) ) { + method.call( value ).done( resolve ).fail( reject ); + + // Other thenables + } else if ( value && isFunction( ( method = value.then ) ) ) { + method.call( value, resolve, reject ); + + // Other non-thenables + } else { + + // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer: + // * false: [ value ].slice( 0 ) => resolve( value ) + // * true: [ value ].slice( 1 ) => resolve() + resolve.apply( undefined, [ value ].slice( noValue ) ); + } + + // For Promises/A+, convert exceptions into rejections + // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in + // Deferred#then to conditionally suppress rejection. + } catch ( value ) { + + // Support: Android 4.0 only + // Strict mode functions invoked without .call/.apply get global-object context + reject.apply( undefined, [ value ] ); + } +} + +jQuery.extend( { + + Deferred: function( func ) { + var tuples = [ + + // action, add listener, callbacks, + // ... .then handlers, argument index, [final state] + [ "notify", "progress", jQuery.Callbacks( "memory" ), + jQuery.Callbacks( "memory" ), 2 ], + [ "resolve", "done", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 0, "resolved" ], + [ "reject", "fail", jQuery.Callbacks( "once memory" ), + jQuery.Callbacks( "once memory" ), 1, "rejected" ] + ], + state = "pending", + promise = { + state: function() { + return state; + }, + always: function() { + deferred.done( arguments ).fail( arguments ); + return this; + }, + "catch": function( fn ) { + return promise.then( null, fn ); + }, + + // Keep pipe for back-compat + pipe: function( /* fnDone, fnFail, fnProgress */ ) { + var fns = arguments; + + return jQuery.Deferred( function( newDefer ) { + jQuery.each( tuples, function( _i, tuple ) { + + // Map tuples (progress, done, fail) to arguments (done, fail, progress) + var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ]; + + // deferred.progress(function() { bind to newDefer or newDefer.notify }) + // deferred.done(function() { bind to newDefer or newDefer.resolve }) + // deferred.fail(function() { bind to newDefer or newDefer.reject }) + deferred[ tuple[ 1 ] ]( function() { + var returned = fn && fn.apply( this, arguments ); + if ( returned && isFunction( returned.promise ) ) { + returned.promise() + .progress( newDefer.notify ) + .done( newDefer.resolve ) + .fail( newDefer.reject ); + } else { + newDefer[ tuple[ 0 ] + "With" ]( + this, + fn ? [ returned ] : arguments + ); + } + } ); + } ); + fns = null; + } ).promise(); + }, + then: function( onFulfilled, onRejected, onProgress ) { + var maxDepth = 0; + function resolve( depth, deferred, handler, special ) { + return function() { + var that = this, + args = arguments, + mightThrow = function() { + var returned, then; + + // Support: Promises/A+ section 2.3.3.3.3 + // https://promisesaplus.com/#point-59 + // Ignore double-resolution attempts + if ( depth < maxDepth ) { + return; + } + + returned = handler.apply( that, args ); + + // Support: Promises/A+ section 2.3.1 + // https://promisesaplus.com/#point-48 + if ( returned === deferred.promise() ) { + throw new TypeError( "Thenable self-resolution" ); + } + + // Support: Promises/A+ sections 2.3.3.1, 3.5 + // https://promisesaplus.com/#point-54 + // https://promisesaplus.com/#point-75 + // Retrieve `then` only once + then = returned && + + // Support: Promises/A+ section 2.3.4 + // https://promisesaplus.com/#point-64 + // Only check objects and functions for thenability + ( typeof returned === "object" || + typeof returned === "function" ) && + returned.then; + + // Handle a returned thenable + if ( isFunction( then ) ) { + + // Special processors (notify) just wait for resolution + if ( special ) { + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ) + ); + + // Normal processors (resolve) also hook into progress + } else { + + // ...and disregard older resolution values + maxDepth++; + + then.call( + returned, + resolve( maxDepth, deferred, Identity, special ), + resolve( maxDepth, deferred, Thrower, special ), + resolve( maxDepth, deferred, Identity, + deferred.notifyWith ) + ); + } + + // Handle all other returned values + } else { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Identity ) { + that = undefined; + args = [ returned ]; + } + + // Process the value(s) + // Default process is resolve + ( special || deferred.resolveWith )( that, args ); + } + }, + + // Only normal processors (resolve) catch and reject exceptions + process = special ? + mightThrow : + function() { + try { + mightThrow(); + } catch ( e ) { + + if ( jQuery.Deferred.exceptionHook ) { + jQuery.Deferred.exceptionHook( e, + process.stackTrace ); + } + + // Support: Promises/A+ section 2.3.3.3.4.1 + // https://promisesaplus.com/#point-61 + // Ignore post-resolution exceptions + if ( depth + 1 >= maxDepth ) { + + // Only substitute handlers pass on context + // and multiple values (non-spec behavior) + if ( handler !== Thrower ) { + that = undefined; + args = [ e ]; + } + + deferred.rejectWith( that, args ); + } + } + }; + + // Support: Promises/A+ section 2.3.3.3.1 + // https://promisesaplus.com/#point-57 + // Re-resolve promises immediately to dodge false rejection from + // subsequent errors + if ( depth ) { + process(); + } else { + + // Call an optional hook to record the stack, in case of exception + // since it's otherwise lost when execution goes async + if ( jQuery.Deferred.getStackHook ) { + process.stackTrace = jQuery.Deferred.getStackHook(); + } + window.setTimeout( process ); + } + }; + } + + return jQuery.Deferred( function( newDefer ) { + + // progress_handlers.add( ... ) + tuples[ 0 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onProgress ) ? + onProgress : + Identity, + newDefer.notifyWith + ) + ); + + // fulfilled_handlers.add( ... ) + tuples[ 1 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onFulfilled ) ? + onFulfilled : + Identity + ) + ); + + // rejected_handlers.add( ... ) + tuples[ 2 ][ 3 ].add( + resolve( + 0, + newDefer, + isFunction( onRejected ) ? + onRejected : + Thrower + ) + ); + } ).promise(); + }, + + // Get a promise for this deferred + // If obj is provided, the promise aspect is added to the object + promise: function( obj ) { + return obj != null ? jQuery.extend( obj, promise ) : promise; + } + }, + deferred = {}; + + // Add list-specific methods + jQuery.each( tuples, function( i, tuple ) { + var list = tuple[ 2 ], + stateString = tuple[ 5 ]; + + // promise.progress = list.add + // promise.done = list.add + // promise.fail = list.add + promise[ tuple[ 1 ] ] = list.add; + + // Handle state + if ( stateString ) { + list.add( + function() { + + // state = "resolved" (i.e., fulfilled) + // state = "rejected" + state = stateString; + }, + + // rejected_callbacks.disable + // fulfilled_callbacks.disable + tuples[ 3 - i ][ 2 ].disable, + + // rejected_handlers.disable + // fulfilled_handlers.disable + tuples[ 3 - i ][ 3 ].disable, + + // progress_callbacks.lock + tuples[ 0 ][ 2 ].lock, + + // progress_handlers.lock + tuples[ 0 ][ 3 ].lock + ); + } + + // progress_handlers.fire + // fulfilled_handlers.fire + // rejected_handlers.fire + list.add( tuple[ 3 ].fire ); + + // deferred.notify = function() { deferred.notifyWith(...) } + // deferred.resolve = function() { deferred.resolveWith(...) } + // deferred.reject = function() { deferred.rejectWith(...) } + deferred[ tuple[ 0 ] ] = function() { + deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments ); + return this; + }; + + // deferred.notifyWith = list.fireWith + // deferred.resolveWith = list.fireWith + // deferred.rejectWith = list.fireWith + deferred[ tuple[ 0 ] + "With" ] = list.fireWith; + } ); + + // Make the deferred a promise + promise.promise( deferred ); + + // Call given func if any + if ( func ) { + func.call( deferred, deferred ); + } + + // All done! + return deferred; + }, + + // Deferred helper + when: function( singleValue ) { + var + + // count of uncompleted subordinates + remaining = arguments.length, + + // count of unprocessed arguments + i = remaining, + + // subordinate fulfillment data + resolveContexts = Array( i ), + resolveValues = slice.call( arguments ), + + // the primary Deferred + primary = jQuery.Deferred(), + + // subordinate callback factory + updateFunc = function( i ) { + return function( value ) { + resolveContexts[ i ] = this; + resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value; + if ( !( --remaining ) ) { + primary.resolveWith( resolveContexts, resolveValues ); + } + }; + }; + + // Single- and empty arguments are adopted like Promise.resolve + if ( remaining <= 1 ) { + adoptValue( singleValue, primary.done( updateFunc( i ) ).resolve, primary.reject, + !remaining ); + + // Use .then() to unwrap secondary thenables (cf. gh-3000) + if ( primary.state() === "pending" || + isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) { + + return primary.then(); + } + } + + // Multiple arguments are aggregated like Promise.all array elements + while ( i-- ) { + adoptValue( resolveValues[ i ], updateFunc( i ), primary.reject ); + } + + return primary.promise(); + } +} ); + + +// These usually indicate a programmer mistake during development, +// warn about them ASAP rather than swallowing them by default. +var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/; + +jQuery.Deferred.exceptionHook = function( error, stack ) { + + // Support: IE 8 - 9 only + // Console exists when dev tools are open, which can happen at any time + if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) { + window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack ); + } +}; + + + + +jQuery.readyException = function( error ) { + window.setTimeout( function() { + throw error; + } ); +}; + + + + +// The deferred used on DOM ready +var readyList = jQuery.Deferred(); + +jQuery.fn.ready = function( fn ) { + + readyList + .then( fn ) + + // Wrap jQuery.readyException in a function so that the lookup + // happens at the time of error handling instead of callback + // registration. + .catch( function( error ) { + jQuery.readyException( error ); + } ); + + return this; +}; + +jQuery.extend( { + + // Is the DOM ready to be used? Set to true once it occurs. + isReady: false, + + // A counter to track how many items to wait for before + // the ready event fires. See #6781 + readyWait: 1, + + // Handle when the DOM is ready + ready: function( wait ) { + + // Abort if there are pending holds or we're already ready + if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) { + return; + } + + // Remember that the DOM is ready + jQuery.isReady = true; + + // If a normal DOM Ready event fired, decrement, and wait if need be + if ( wait !== true && --jQuery.readyWait > 0 ) { + return; + } + + // If there are functions bound, to execute + readyList.resolveWith( document, [ jQuery ] ); + } +} ); + +jQuery.ready.then = readyList.then; + +// The ready event handler and self cleanup method +function completed() { + document.removeEventListener( "DOMContentLoaded", completed ); + window.removeEventListener( "load", completed ); + jQuery.ready(); +} + +// Catch cases where $(document).ready() is called +// after the browser event has already occurred. +// Support: IE <=9 - 10 only +// Older IE sometimes signals "interactive" too soon +if ( document.readyState === "complete" || + ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) { + + // Handle it asynchronously to allow scripts the opportunity to delay ready + window.setTimeout( jQuery.ready ); + +} else { + + // Use the handy event callback + document.addEventListener( "DOMContentLoaded", completed ); + + // A fallback to window.onload, that will always work + window.addEventListener( "load", completed ); +} + + + + +// Multifunctional method to get and set values of a collection +// The value/s can optionally be executed if it's a function +var access = function( elems, fn, key, value, chainable, emptyGet, raw ) { + var i = 0, + len = elems.length, + bulk = key == null; + + // Sets many values + if ( toType( key ) === "object" ) { + chainable = true; + for ( i in key ) { + access( elems, fn, i, key[ i ], true, emptyGet, raw ); + } + + // Sets one value + } else if ( value !== undefined ) { + chainable = true; + + if ( !isFunction( value ) ) { + raw = true; + } + + if ( bulk ) { + + // Bulk operations run against the entire set + if ( raw ) { + fn.call( elems, value ); + fn = null; + + // ...except when executing function values + } else { + bulk = fn; + fn = function( elem, _key, value ) { + return bulk.call( jQuery( elem ), value ); + }; + } + } + + if ( fn ) { + for ( ; i < len; i++ ) { + fn( + elems[ i ], key, raw ? + value : + value.call( elems[ i ], i, fn( elems[ i ], key ) ) + ); + } + } + } + + if ( chainable ) { + return elems; + } + + // Gets + if ( bulk ) { + return fn.call( elems ); + } + + return len ? fn( elems[ 0 ], key ) : emptyGet; +}; + + +// Matches dashed string for camelizing +var rmsPrefix = /^-ms-/, + rdashAlpha = /-([a-z])/g; + +// Used by camelCase as callback to replace() +function fcamelCase( _all, letter ) { + return letter.toUpperCase(); +} + +// Convert dashed to camelCase; used by the css and data modules +// Support: IE <=9 - 11, Edge 12 - 15 +// Microsoft forgot to hump their vendor prefix (#9572) +function camelCase( string ) { + return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase ); +} +var acceptData = function( owner ) { + + // Accepts only: + // - Node + // - Node.ELEMENT_NODE + // - Node.DOCUMENT_NODE + // - Object + // - Any + return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType ); +}; + + + + +function Data() { + this.expando = jQuery.expando + Data.uid++; +} + +Data.uid = 1; + +Data.prototype = { + + cache: function( owner ) { + + // Check if the owner object already has a cache + var value = owner[ this.expando ]; + + // If not, create one + if ( !value ) { + value = {}; + + // We can accept data for non-element nodes in modern browsers, + // but we should not, see #8335. + // Always return an empty object. + if ( acceptData( owner ) ) { + + // If it is a node unlikely to be stringify-ed or looped over + // use plain assignment + if ( owner.nodeType ) { + owner[ this.expando ] = value; + + // Otherwise secure it in a non-enumerable property + // configurable must be true to allow the property to be + // deleted when data is removed + } else { + Object.defineProperty( owner, this.expando, { + value: value, + configurable: true + } ); + } + } + } + + return value; + }, + set: function( owner, data, value ) { + var prop, + cache = this.cache( owner ); + + // Handle: [ owner, key, value ] args + // Always use camelCase key (gh-2257) + if ( typeof data === "string" ) { + cache[ camelCase( data ) ] = value; + + // Handle: [ owner, { properties } ] args + } else { + + // Copy the properties one-by-one to the cache object + for ( prop in data ) { + cache[ camelCase( prop ) ] = data[ prop ]; + } + } + return cache; + }, + get: function( owner, key ) { + return key === undefined ? + this.cache( owner ) : + + // Always use camelCase key (gh-2257) + owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ]; + }, + access: function( owner, key, value ) { + + // In cases where either: + // + // 1. No key was specified + // 2. A string key was specified, but no value provided + // + // Take the "read" path and allow the get method to determine + // which value to return, respectively either: + // + // 1. The entire cache object + // 2. The data stored at the key + // + if ( key === undefined || + ( ( key && typeof key === "string" ) && value === undefined ) ) { + + return this.get( owner, key ); + } + + // When the key is not a string, or both a key and value + // are specified, set or extend (existing objects) with either: + // + // 1. An object of properties + // 2. A key and value + // + this.set( owner, key, value ); + + // Since the "set" path can have two possible entry points + // return the expected data based on which path was taken[*] + return value !== undefined ? value : key; + }, + remove: function( owner, key ) { + var i, + cache = owner[ this.expando ]; + + if ( cache === undefined ) { + return; + } + + if ( key !== undefined ) { + + // Support array or space separated string of keys + if ( Array.isArray( key ) ) { + + // If key is an array of keys... + // We always set camelCase keys, so remove that. + key = key.map( camelCase ); + } else { + key = camelCase( key ); + + // If a key with the spaces exists, use it. + // Otherwise, create an array by matching non-whitespace + key = key in cache ? + [ key ] : + ( key.match( rnothtmlwhite ) || [] ); + } + + i = key.length; + + while ( i-- ) { + delete cache[ key[ i ] ]; + } + } + + // Remove the expando if there's no more data + if ( key === undefined || jQuery.isEmptyObject( cache ) ) { + + // Support: Chrome <=35 - 45 + // Webkit & Blink performance suffers when deleting properties + // from DOM nodes, so set to undefined instead + // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted) + if ( owner.nodeType ) { + owner[ this.expando ] = undefined; + } else { + delete owner[ this.expando ]; + } + } + }, + hasData: function( owner ) { + var cache = owner[ this.expando ]; + return cache !== undefined && !jQuery.isEmptyObject( cache ); + } +}; +var dataPriv = new Data(); + +var dataUser = new Data(); + + + +// Implementation Summary +// +// 1. Enforce API surface and semantic compatibility with 1.9.x branch +// 2. Improve the module's maintainability by reducing the storage +// paths to a single mechanism. +// 3. Use the same single mechanism to support "private" and "user" data. +// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData) +// 5. Avoid exposing implementation details on user objects (eg. expando properties) +// 6. Provide a clear path for implementation upgrade to WeakMap in 2014 + +var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/, + rmultiDash = /[A-Z]/g; + +function getData( data ) { + if ( data === "true" ) { + return true; + } + + if ( data === "false" ) { + return false; + } + + if ( data === "null" ) { + return null; + } + + // Only convert to a number if it doesn't change the string + if ( data === +data + "" ) { + return +data; + } + + if ( rbrace.test( data ) ) { + return JSON.parse( data ); + } + + return data; +} + +function dataAttr( elem, key, data ) { + var name; + + // If nothing was found internally, try to fetch any + // data from the HTML5 data-* attribute + if ( data === undefined && elem.nodeType === 1 ) { + name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase(); + data = elem.getAttribute( name ); + + if ( typeof data === "string" ) { + try { + data = getData( data ); + } catch ( e ) {} + + // Make sure we set the data so it isn't changed later + dataUser.set( elem, key, data ); + } else { + data = undefined; + } + } + return data; +} + +jQuery.extend( { + hasData: function( elem ) { + return dataUser.hasData( elem ) || dataPriv.hasData( elem ); + }, + + data: function( elem, name, data ) { + return dataUser.access( elem, name, data ); + }, + + removeData: function( elem, name ) { + dataUser.remove( elem, name ); + }, + + // TODO: Now that all calls to _data and _removeData have been replaced + // with direct calls to dataPriv methods, these can be deprecated. + _data: function( elem, name, data ) { + return dataPriv.access( elem, name, data ); + }, + + _removeData: function( elem, name ) { + dataPriv.remove( elem, name ); + } +} ); + +jQuery.fn.extend( { + data: function( key, value ) { + var i, name, data, + elem = this[ 0 ], + attrs = elem && elem.attributes; + + // Gets all values + if ( key === undefined ) { + if ( this.length ) { + data = dataUser.get( elem ); + + if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) { + i = attrs.length; + while ( i-- ) { + + // Support: IE 11 only + // The attrs elements can be null (#14894) + if ( attrs[ i ] ) { + name = attrs[ i ].name; + if ( name.indexOf( "data-" ) === 0 ) { + name = camelCase( name.slice( 5 ) ); + dataAttr( elem, name, data[ name ] ); + } + } + } + dataPriv.set( elem, "hasDataAttrs", true ); + } + } + + return data; + } + + // Sets multiple values + if ( typeof key === "object" ) { + return this.each( function() { + dataUser.set( this, key ); + } ); + } + + return access( this, function( value ) { + var data; + + // The calling jQuery object (element matches) is not empty + // (and therefore has an element appears at this[ 0 ]) and the + // `value` parameter was not undefined. An empty jQuery object + // will result in `undefined` for elem = this[ 0 ] which will + // throw an exception if an attempt to read a data cache is made. + if ( elem && value === undefined ) { + + // Attempt to get data from the cache + // The key will always be camelCased in Data + data = dataUser.get( elem, key ); + if ( data !== undefined ) { + return data; + } + + // Attempt to "discover" the data in + // HTML5 custom data-* attrs + data = dataAttr( elem, key ); + if ( data !== undefined ) { + return data; + } + + // We tried really hard, but the data doesn't exist. + return; + } + + // Set the data... + this.each( function() { + + // We always store the camelCased key + dataUser.set( this, key, value ); + } ); + }, null, value, arguments.length > 1, null, true ); + }, + + removeData: function( key ) { + return this.each( function() { + dataUser.remove( this, key ); + } ); + } +} ); + + +jQuery.extend( { + queue: function( elem, type, data ) { + var queue; + + if ( elem ) { + type = ( type || "fx" ) + "queue"; + queue = dataPriv.get( elem, type ); + + // Speed up dequeue by getting out quickly if this is just a lookup + if ( data ) { + if ( !queue || Array.isArray( data ) ) { + queue = dataPriv.access( elem, type, jQuery.makeArray( data ) ); + } else { + queue.push( data ); + } + } + return queue || []; + } + }, + + dequeue: function( elem, type ) { + type = type || "fx"; + + var queue = jQuery.queue( elem, type ), + startLength = queue.length, + fn = queue.shift(), + hooks = jQuery._queueHooks( elem, type ), + next = function() { + jQuery.dequeue( elem, type ); + }; + + // If the fx queue is dequeued, always remove the progress sentinel + if ( fn === "inprogress" ) { + fn = queue.shift(); + startLength--; + } + + if ( fn ) { + + // Add a progress sentinel to prevent the fx queue from being + // automatically dequeued + if ( type === "fx" ) { + queue.unshift( "inprogress" ); + } + + // Clear up the last queue stop function + delete hooks.stop; + fn.call( elem, next, hooks ); + } + + if ( !startLength && hooks ) { + hooks.empty.fire(); + } + }, + + // Not public - generate a queueHooks object, or return the current one + _queueHooks: function( elem, type ) { + var key = type + "queueHooks"; + return dataPriv.get( elem, key ) || dataPriv.access( elem, key, { + empty: jQuery.Callbacks( "once memory" ).add( function() { + dataPriv.remove( elem, [ type + "queue", key ] ); + } ) + } ); + } +} ); + +jQuery.fn.extend( { + queue: function( type, data ) { + var setter = 2; + + if ( typeof type !== "string" ) { + data = type; + type = "fx"; + setter--; + } + + if ( arguments.length < setter ) { + return jQuery.queue( this[ 0 ], type ); + } + + return data === undefined ? + this : + this.each( function() { + var queue = jQuery.queue( this, type, data ); + + // Ensure a hooks for this queue + jQuery._queueHooks( this, type ); + + if ( type === "fx" && queue[ 0 ] !== "inprogress" ) { + jQuery.dequeue( this, type ); + } + } ); + }, + dequeue: function( type ) { + return this.each( function() { + jQuery.dequeue( this, type ); + } ); + }, + clearQueue: function( type ) { + return this.queue( type || "fx", [] ); + }, + + // Get a promise resolved when queues of a certain type + // are emptied (fx is the type by default) + promise: function( type, obj ) { + var tmp, + count = 1, + defer = jQuery.Deferred(), + elements = this, + i = this.length, + resolve = function() { + if ( !( --count ) ) { + defer.resolveWith( elements, [ elements ] ); + } + }; + + if ( typeof type !== "string" ) { + obj = type; + type = undefined; + } + type = type || "fx"; + + while ( i-- ) { + tmp = dataPriv.get( elements[ i ], type + "queueHooks" ); + if ( tmp && tmp.empty ) { + count++; + tmp.empty.add( resolve ); + } + } + resolve(); + return defer.promise( obj ); + } +} ); +var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source; + +var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" ); + + +var cssExpand = [ "Top", "Right", "Bottom", "Left" ]; + +var documentElement = document.documentElement; + + + + var isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ); + }, + composed = { composed: true }; + + // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only + // Check attachment across shadow DOM boundaries when possible (gh-3504) + // Support: iOS 10.0-10.2 only + // Early iOS 10 versions support `attachShadow` but not `getRootNode`, + // leading to errors. We need to check for `getRootNode`. + if ( documentElement.getRootNode ) { + isAttached = function( elem ) { + return jQuery.contains( elem.ownerDocument, elem ) || + elem.getRootNode( composed ) === elem.ownerDocument; + }; + } +var isHiddenWithinTree = function( elem, el ) { + + // isHiddenWithinTree might be called from jQuery#filter function; + // in that case, element will be second argument + elem = el || elem; + + // Inline style trumps all + return elem.style.display === "none" || + elem.style.display === "" && + + // Otherwise, check computed style + // Support: Firefox <=43 - 45 + // Disconnected elements can have computed display: none, so first confirm that elem is + // in the document. + isAttached( elem ) && + + jQuery.css( elem, "display" ) === "none"; + }; + + + +function adjustCSS( elem, prop, valueParts, tween ) { + var adjusted, scale, + maxIterations = 20, + currentValue = tween ? + function() { + return tween.cur(); + } : + function() { + return jQuery.css( elem, prop, "" ); + }, + initial = currentValue(), + unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ), + + // Starting value computation is required for potential unit mismatches + initialInUnit = elem.nodeType && + ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) && + rcssNum.exec( jQuery.css( elem, prop ) ); + + if ( initialInUnit && initialInUnit[ 3 ] !== unit ) { + + // Support: Firefox <=54 + // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144) + initial = initial / 2; + + // Trust units reported by jQuery.css + unit = unit || initialInUnit[ 3 ]; + + // Iteratively approximate from a nonzero starting point + initialInUnit = +initial || 1; + + while ( maxIterations-- ) { + + // Evaluate and update our best guess (doubling guesses that zero out). + // Finish if the scale equals or crosses 1 (making the old*new product non-positive). + jQuery.style( elem, prop, initialInUnit + unit ); + if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) { + maxIterations = 0; + } + initialInUnit = initialInUnit / scale; + + } + + initialInUnit = initialInUnit * 2; + jQuery.style( elem, prop, initialInUnit + unit ); + + // Make sure we update the tween properties later on + valueParts = valueParts || []; + } + + if ( valueParts ) { + initialInUnit = +initialInUnit || +initial || 0; + + // Apply relative offset (+=/-=) if specified + adjusted = valueParts[ 1 ] ? + initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] : + +valueParts[ 2 ]; + if ( tween ) { + tween.unit = unit; + tween.start = initialInUnit; + tween.end = adjusted; + } + } + return adjusted; +} + + +var defaultDisplayMap = {}; + +function getDefaultDisplay( elem ) { + var temp, + doc = elem.ownerDocument, + nodeName = elem.nodeName, + display = defaultDisplayMap[ nodeName ]; + + if ( display ) { + return display; + } + + temp = doc.body.appendChild( doc.createElement( nodeName ) ); + display = jQuery.css( temp, "display" ); + + temp.parentNode.removeChild( temp ); + + if ( display === "none" ) { + display = "block"; + } + defaultDisplayMap[ nodeName ] = display; + + return display; +} + +function showHide( elements, show ) { + var display, elem, + values = [], + index = 0, + length = elements.length; + + // Determine new display value for elements that need to change + for ( ; index < length; index++ ) { + elem = elements[ index ]; + if ( !elem.style ) { + continue; + } + + display = elem.style.display; + if ( show ) { + + // Since we force visibility upon cascade-hidden elements, an immediate (and slow) + // check is required in this first loop unless we have a nonempty display value (either + // inline or about-to-be-restored) + if ( display === "none" ) { + values[ index ] = dataPriv.get( elem, "display" ) || null; + if ( !values[ index ] ) { + elem.style.display = ""; + } + } + if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) { + values[ index ] = getDefaultDisplay( elem ); + } + } else { + if ( display !== "none" ) { + values[ index ] = "none"; + + // Remember what we're overwriting + dataPriv.set( elem, "display", display ); + } + } + } + + // Set the display of the elements in a second loop to avoid constant reflow + for ( index = 0; index < length; index++ ) { + if ( values[ index ] != null ) { + elements[ index ].style.display = values[ index ]; + } + } + + return elements; +} + +jQuery.fn.extend( { + show: function() { + return showHide( this, true ); + }, + hide: function() { + return showHide( this ); + }, + toggle: function( state ) { + if ( typeof state === "boolean" ) { + return state ? this.show() : this.hide(); + } + + return this.each( function() { + if ( isHiddenWithinTree( this ) ) { + jQuery( this ).show(); + } else { + jQuery( this ).hide(); + } + } ); + } +} ); +var rcheckableType = ( /^(?:checkbox|radio)$/i ); + +var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i ); + +var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i ); + + + +( function() { + var fragment = document.createDocumentFragment(), + div = fragment.appendChild( document.createElement( "div" ) ), + input = document.createElement( "input" ); + + // Support: Android 4.0 - 4.3 only + // Check state lost if the name is set (#11217) + // Support: Windows Web Apps (WWA) + // `name` and `type` must use .setAttribute for WWA (#14901) + input.setAttribute( "type", "radio" ); + input.setAttribute( "checked", "checked" ); + input.setAttribute( "name", "t" ); + + div.appendChild( input ); + + // Support: Android <=4.1 only + // Older WebKit doesn't clone checked state correctly in fragments + support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked; + + // Support: IE <=11 only + // Make sure textarea (and checkbox) defaultValue is properly cloned + div.innerHTML = ""; + support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue; + + // Support: IE <=9 only + // IE <=9 replaces "; + support.option = !!div.lastChild; +} )(); + + +// We have to close these tags to support XHTML (#13200) +var wrapMap = { + + // XHTML parsers do not magically insert elements in the + // same way that tag soup parsers do. So we cannot shorten + // this by omitting or other required elements. + thead: [ 1, "", "
    " ], + col: [ 2, "", "
    " ], + tr: [ 2, "", "
    " ], + td: [ 3, "", "
    " ], + + _default: [ 0, "", "" ] +}; + +wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead; +wrapMap.th = wrapMap.td; + +// Support: IE <=9 only +if ( !support.option ) { + wrapMap.optgroup = wrapMap.option = [ 1, "" ]; +} + + +function getAll( context, tag ) { + + // Support: IE <=9 - 11 only + // Use typeof to avoid zero-argument method invocation on host objects (#15151) + var ret; + + if ( typeof context.getElementsByTagName !== "undefined" ) { + ret = context.getElementsByTagName( tag || "*" ); + + } else if ( typeof context.querySelectorAll !== "undefined" ) { + ret = context.querySelectorAll( tag || "*" ); + + } else { + ret = []; + } + + if ( tag === undefined || tag && nodeName( context, tag ) ) { + return jQuery.merge( [ context ], ret ); + } + + return ret; +} + + +// Mark scripts as having already been evaluated +function setGlobalEval( elems, refElements ) { + var i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + dataPriv.set( + elems[ i ], + "globalEval", + !refElements || dataPriv.get( refElements[ i ], "globalEval" ) + ); + } +} + + +var rhtml = /<|&#?\w+;/; + +function buildFragment( elems, context, scripts, selection, ignored ) { + var elem, tmp, tag, wrap, attached, j, + fragment = context.createDocumentFragment(), + nodes = [], + i = 0, + l = elems.length; + + for ( ; i < l; i++ ) { + elem = elems[ i ]; + + if ( elem || elem === 0 ) { + + // Add nodes directly + if ( toType( elem ) === "object" ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem ); + + // Convert non-html into a text node + } else if ( !rhtml.test( elem ) ) { + nodes.push( context.createTextNode( elem ) ); + + // Convert html into DOM nodes + } else { + tmp = tmp || fragment.appendChild( context.createElement( "div" ) ); + + // Deserialize a standard representation + tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase(); + wrap = wrapMap[ tag ] || wrapMap._default; + tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ]; + + // Descend through wrappers to the right content + j = wrap[ 0 ]; + while ( j-- ) { + tmp = tmp.lastChild; + } + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( nodes, tmp.childNodes ); + + // Remember the top-level container + tmp = fragment.firstChild; + + // Ensure the created nodes are orphaned (#12392) + tmp.textContent = ""; + } + } + } + + // Remove wrapper from fragment + fragment.textContent = ""; + + i = 0; + while ( ( elem = nodes[ i++ ] ) ) { + + // Skip elements already in the context collection (trac-4087) + if ( selection && jQuery.inArray( elem, selection ) > -1 ) { + if ( ignored ) { + ignored.push( elem ); + } + continue; + } + + attached = isAttached( elem ); + + // Append to fragment + tmp = getAll( fragment.appendChild( elem ), "script" ); + + // Preserve script evaluation history + if ( attached ) { + setGlobalEval( tmp ); + } + + // Capture executables + if ( scripts ) { + j = 0; + while ( ( elem = tmp[ j++ ] ) ) { + if ( rscriptType.test( elem.type || "" ) ) { + scripts.push( elem ); + } + } + } + } + + return fragment; +} + + +var rtypenamespace = /^([^.]*)(?:\.(.+)|)/; + +function returnTrue() { + return true; +} + +function returnFalse() { + return false; +} + +// Support: IE <=9 - 11+ +// focus() and blur() are asynchronous, except when they are no-op. +// So expect focus to be synchronous when the element is already active, +// and blur to be synchronous when the element is not already active. +// (focus and blur are always synchronous in other supported browsers, +// this just defines when we can count on it). +function expectSync( elem, type ) { + return ( elem === safeActiveElement() ) === ( type === "focus" ); +} + +// Support: IE <=9 only +// Accessing document.activeElement can throw unexpectedly +// https://bugs.jquery.com/ticket/13393 +function safeActiveElement() { + try { + return document.activeElement; + } catch ( err ) { } +} + +function on( elem, types, selector, data, fn, one ) { + var origFn, type; + + // Types can be a map of types/handlers + if ( typeof types === "object" ) { + + // ( types-Object, selector, data ) + if ( typeof selector !== "string" ) { + + // ( types-Object, data ) + data = data || selector; + selector = undefined; + } + for ( type in types ) { + on( elem, type, selector, data, types[ type ], one ); + } + return elem; + } + + if ( data == null && fn == null ) { + + // ( types, fn ) + fn = selector; + data = selector = undefined; + } else if ( fn == null ) { + if ( typeof selector === "string" ) { + + // ( types, selector, fn ) + fn = data; + data = undefined; + } else { + + // ( types, data, fn ) + fn = data; + data = selector; + selector = undefined; + } + } + if ( fn === false ) { + fn = returnFalse; + } else if ( !fn ) { + return elem; + } + + if ( one === 1 ) { + origFn = fn; + fn = function( event ) { + + // Can use an empty set, since event contains the info + jQuery().off( event ); + return origFn.apply( this, arguments ); + }; + + // Use same guid so caller can remove using origFn + fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ ); + } + return elem.each( function() { + jQuery.event.add( this, types, fn, data, selector ); + } ); +} + +/* + * Helper functions for managing events -- not part of the public interface. + * Props to Dean Edwards' addEvent library for many of the ideas. + */ +jQuery.event = { + + global: {}, + + add: function( elem, types, handler, data, selector ) { + + var handleObjIn, eventHandle, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.get( elem ); + + // Only attach events to objects that accept data + if ( !acceptData( elem ) ) { + return; + } + + // Caller can pass in an object of custom data in lieu of the handler + if ( handler.handler ) { + handleObjIn = handler; + handler = handleObjIn.handler; + selector = handleObjIn.selector; + } + + // Ensure that invalid selectors throw exceptions at attach time + // Evaluate against documentElement in case elem is a non-element node (e.g., document) + if ( selector ) { + jQuery.find.matchesSelector( documentElement, selector ); + } + + // Make sure that the handler has a unique ID, used to find/remove it later + if ( !handler.guid ) { + handler.guid = jQuery.guid++; + } + + // Init the element's event structure and main handler, if this is the first + if ( !( events = elemData.events ) ) { + events = elemData.events = Object.create( null ); + } + if ( !( eventHandle = elemData.handle ) ) { + eventHandle = elemData.handle = function( e ) { + + // Discard the second event of a jQuery.event.trigger() and + // when an event is called after a page has unloaded + return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ? + jQuery.event.dispatch.apply( elem, arguments ) : undefined; + }; + } + + // Handle multiple events separated by a space + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // There *must* be a type, no attaching namespace-only handlers + if ( !type ) { + continue; + } + + // If event changes its type, use the special event handlers for the changed type + special = jQuery.event.special[ type ] || {}; + + // If selector defined, determine special event api type, otherwise given type + type = ( selector ? special.delegateType : special.bindType ) || type; + + // Update special based on newly reset type + special = jQuery.event.special[ type ] || {}; + + // handleObj is passed to all event handlers + handleObj = jQuery.extend( { + type: type, + origType: origType, + data: data, + handler: handler, + guid: handler.guid, + selector: selector, + needsContext: selector && jQuery.expr.match.needsContext.test( selector ), + namespace: namespaces.join( "." ) + }, handleObjIn ); + + // Init the event handler queue if we're the first + if ( !( handlers = events[ type ] ) ) { + handlers = events[ type ] = []; + handlers.delegateCount = 0; + + // Only use addEventListener if the special events handler returns false + if ( !special.setup || + special.setup.call( elem, data, namespaces, eventHandle ) === false ) { + + if ( elem.addEventListener ) { + elem.addEventListener( type, eventHandle ); + } + } + } + + if ( special.add ) { + special.add.call( elem, handleObj ); + + if ( !handleObj.handler.guid ) { + handleObj.handler.guid = handler.guid; + } + } + + // Add to the element's handler list, delegates in front + if ( selector ) { + handlers.splice( handlers.delegateCount++, 0, handleObj ); + } else { + handlers.push( handleObj ); + } + + // Keep track of which events have ever been used, for event optimization + jQuery.event.global[ type ] = true; + } + + }, + + // Detach an event or set of events from an element + remove: function( elem, types, handler, selector, mappedTypes ) { + + var j, origCount, tmp, + events, t, handleObj, + special, handlers, type, namespaces, origType, + elemData = dataPriv.hasData( elem ) && dataPriv.get( elem ); + + if ( !elemData || !( events = elemData.events ) ) { + return; + } + + // Once for each type.namespace in types; type may be omitted + types = ( types || "" ).match( rnothtmlwhite ) || [ "" ]; + t = types.length; + while ( t-- ) { + tmp = rtypenamespace.exec( types[ t ] ) || []; + type = origType = tmp[ 1 ]; + namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort(); + + // Unbind all events (on this namespace, if provided) for the element + if ( !type ) { + for ( type in events ) { + jQuery.event.remove( elem, type + types[ t ], handler, selector, true ); + } + continue; + } + + special = jQuery.event.special[ type ] || {}; + type = ( selector ? special.delegateType : special.bindType ) || type; + handlers = events[ type ] || []; + tmp = tmp[ 2 ] && + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ); + + // Remove matching events + origCount = j = handlers.length; + while ( j-- ) { + handleObj = handlers[ j ]; + + if ( ( mappedTypes || origType === handleObj.origType ) && + ( !handler || handler.guid === handleObj.guid ) && + ( !tmp || tmp.test( handleObj.namespace ) ) && + ( !selector || selector === handleObj.selector || + selector === "**" && handleObj.selector ) ) { + handlers.splice( j, 1 ); + + if ( handleObj.selector ) { + handlers.delegateCount--; + } + if ( special.remove ) { + special.remove.call( elem, handleObj ); + } + } + } + + // Remove generic event handler if we removed something and no more handlers exist + // (avoids potential for endless recursion during removal of special event handlers) + if ( origCount && !handlers.length ) { + if ( !special.teardown || + special.teardown.call( elem, namespaces, elemData.handle ) === false ) { + + jQuery.removeEvent( elem, type, elemData.handle ); + } + + delete events[ type ]; + } + } + + // Remove data and the expando if it's no longer used + if ( jQuery.isEmptyObject( events ) ) { + dataPriv.remove( elem, "handle events" ); + } + }, + + dispatch: function( nativeEvent ) { + + var i, j, ret, matched, handleObj, handlerQueue, + args = new Array( arguments.length ), + + // Make a writable jQuery.Event from the native event object + event = jQuery.event.fix( nativeEvent ), + + handlers = ( + dataPriv.get( this, "events" ) || Object.create( null ) + )[ event.type ] || [], + special = jQuery.event.special[ event.type ] || {}; + + // Use the fix-ed jQuery.Event rather than the (read-only) native event + args[ 0 ] = event; + + for ( i = 1; i < arguments.length; i++ ) { + args[ i ] = arguments[ i ]; + } + + event.delegateTarget = this; + + // Call the preDispatch hook for the mapped type, and let it bail if desired + if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) { + return; + } + + // Determine handlers + handlerQueue = jQuery.event.handlers.call( this, event, handlers ); + + // Run delegates first; they may want to stop propagation beneath us + i = 0; + while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) { + event.currentTarget = matched.elem; + + j = 0; + while ( ( handleObj = matched.handlers[ j++ ] ) && + !event.isImmediatePropagationStopped() ) { + + // If the event is namespaced, then each handler is only invoked if it is + // specially universal or its namespaces are a superset of the event's. + if ( !event.rnamespace || handleObj.namespace === false || + event.rnamespace.test( handleObj.namespace ) ) { + + event.handleObj = handleObj; + event.data = handleObj.data; + + ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle || + handleObj.handler ).apply( matched.elem, args ); + + if ( ret !== undefined ) { + if ( ( event.result = ret ) === false ) { + event.preventDefault(); + event.stopPropagation(); + } + } + } + } + } + + // Call the postDispatch hook for the mapped type + if ( special.postDispatch ) { + special.postDispatch.call( this, event ); + } + + return event.result; + }, + + handlers: function( event, handlers ) { + var i, handleObj, sel, matchedHandlers, matchedSelectors, + handlerQueue = [], + delegateCount = handlers.delegateCount, + cur = event.target; + + // Find delegate handlers + if ( delegateCount && + + // Support: IE <=9 + // Black-hole SVG instance trees (trac-13180) + cur.nodeType && + + // Support: Firefox <=42 + // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861) + // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click + // Support: IE 11 only + // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343) + !( event.type === "click" && event.button >= 1 ) ) { + + for ( ; cur !== this; cur = cur.parentNode || this ) { + + // Don't check non-elements (#13208) + // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764) + if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) { + matchedHandlers = []; + matchedSelectors = {}; + for ( i = 0; i < delegateCount; i++ ) { + handleObj = handlers[ i ]; + + // Don't conflict with Object.prototype properties (#13203) + sel = handleObj.selector + " "; + + if ( matchedSelectors[ sel ] === undefined ) { + matchedSelectors[ sel ] = handleObj.needsContext ? + jQuery( sel, this ).index( cur ) > -1 : + jQuery.find( sel, this, null, [ cur ] ).length; + } + if ( matchedSelectors[ sel ] ) { + matchedHandlers.push( handleObj ); + } + } + if ( matchedHandlers.length ) { + handlerQueue.push( { elem: cur, handlers: matchedHandlers } ); + } + } + } + } + + // Add the remaining (directly-bound) handlers + cur = this; + if ( delegateCount < handlers.length ) { + handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } ); + } + + return handlerQueue; + }, + + addProp: function( name, hook ) { + Object.defineProperty( jQuery.Event.prototype, name, { + enumerable: true, + configurable: true, + + get: isFunction( hook ) ? + function() { + if ( this.originalEvent ) { + return hook( this.originalEvent ); + } + } : + function() { + if ( this.originalEvent ) { + return this.originalEvent[ name ]; + } + }, + + set: function( value ) { + Object.defineProperty( this, name, { + enumerable: true, + configurable: true, + writable: true, + value: value + } ); + } + } ); + }, + + fix: function( originalEvent ) { + return originalEvent[ jQuery.expando ] ? + originalEvent : + new jQuery.Event( originalEvent ); + }, + + special: { + load: { + + // Prevent triggered image.load events from bubbling to window.load + noBubble: true + }, + click: { + + // Utilize native event to ensure correct state for checkable inputs + setup: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Claim the first handler + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + // dataPriv.set( el, "click", ... ) + leverageNative( el, "click", returnTrue ); + } + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function( data ) { + + // For mutual compressibility with _default, replace `this` access with a local var. + // `|| data` is dead code meant only to preserve the variable through minification. + var el = this || data; + + // Force setup before triggering a click + if ( rcheckableType.test( el.type ) && + el.click && nodeName( el, "input" ) ) { + + leverageNative( el, "click" ); + } + + // Return non-false to allow normal event-path propagation + return true; + }, + + // For cross-browser consistency, suppress native .click() on links + // Also prevent it if we're currently inside a leveraged native-event stack + _default: function( event ) { + var target = event.target; + return rcheckableType.test( target.type ) && + target.click && nodeName( target, "input" ) && + dataPriv.get( target, "click" ) || + nodeName( target, "a" ); + } + }, + + beforeunload: { + postDispatch: function( event ) { + + // Support: Firefox 20+ + // Firefox doesn't alert if the returnValue field is not set. + if ( event.result !== undefined && event.originalEvent ) { + event.originalEvent.returnValue = event.result; + } + } + } + } +}; + +// Ensure the presence of an event listener that handles manually-triggered +// synthetic events by interrupting progress until reinvoked in response to +// *native* events that it fires directly, ensuring that state changes have +// already occurred before other listeners are invoked. +function leverageNative( el, type, expectSync ) { + + // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add + if ( !expectSync ) { + if ( dataPriv.get( el, type ) === undefined ) { + jQuery.event.add( el, type, returnTrue ); + } + return; + } + + // Register the controller as a special universal handler for all event namespaces + dataPriv.set( el, type, false ); + jQuery.event.add( el, type, { + namespace: false, + handler: function( event ) { + var notAsync, result, + saved = dataPriv.get( this, type ); + + if ( ( event.isTrigger & 1 ) && this[ type ] ) { + + // Interrupt processing of the outer synthetic .trigger()ed event + // Saved data should be false in such cases, but might be a leftover capture object + // from an async native handler (gh-4350) + if ( !saved.length ) { + + // Store arguments for use when handling the inner native event + // There will always be at least one argument (an event object), so this array + // will not be confused with a leftover capture object. + saved = slice.call( arguments ); + dataPriv.set( this, type, saved ); + + // Trigger the native event and capture its result + // Support: IE <=9 - 11+ + // focus() and blur() are asynchronous + notAsync = expectSync( this, type ); + this[ type ](); + result = dataPriv.get( this, type ); + if ( saved !== result || notAsync ) { + dataPriv.set( this, type, false ); + } else { + result = {}; + } + if ( saved !== result ) { + + // Cancel the outer synthetic event + event.stopImmediatePropagation(); + event.preventDefault(); + + // Support: Chrome 86+ + // In Chrome, if an element having a focusout handler is blurred by + // clicking outside of it, it invokes the handler synchronously. If + // that handler calls `.remove()` on the element, the data is cleared, + // leaving `result` undefined. We need to guard against this. + return result && result.value; + } + + // If this is an inner synthetic event for an event with a bubbling surrogate + // (focus or blur), assume that the surrogate already propagated from triggering the + // native event and prevent that from happening again here. + // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the + // bubbling surrogate propagates *after* the non-bubbling base), but that seems + // less bad than duplication. + } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) { + event.stopPropagation(); + } + + // If this is a native event triggered above, everything is now in order + // Fire an inner synthetic event with the original arguments + } else if ( saved.length ) { + + // ...and capture the result + dataPriv.set( this, type, { + value: jQuery.event.trigger( + + // Support: IE <=9 - 11+ + // Extend with the prototype to reset the above stopImmediatePropagation() + jQuery.extend( saved[ 0 ], jQuery.Event.prototype ), + saved.slice( 1 ), + this + ) + } ); + + // Abort handling of the native event + event.stopImmediatePropagation(); + } + } + } ); +} + +jQuery.removeEvent = function( elem, type, handle ) { + + // This "if" is needed for plain objects + if ( elem.removeEventListener ) { + elem.removeEventListener( type, handle ); + } +}; + +jQuery.Event = function( src, props ) { + + // Allow instantiation without the 'new' keyword + if ( !( this instanceof jQuery.Event ) ) { + return new jQuery.Event( src, props ); + } + + // Event object + if ( src && src.type ) { + this.originalEvent = src; + this.type = src.type; + + // Events bubbling up the document may have been marked as prevented + // by a handler lower down the tree; reflect the correct value. + this.isDefaultPrevented = src.defaultPrevented || + src.defaultPrevented === undefined && + + // Support: Android <=2.3 only + src.returnValue === false ? + returnTrue : + returnFalse; + + // Create target properties + // Support: Safari <=6 - 7 only + // Target should not be a text node (#504, #13143) + this.target = ( src.target && src.target.nodeType === 3 ) ? + src.target.parentNode : + src.target; + + this.currentTarget = src.currentTarget; + this.relatedTarget = src.relatedTarget; + + // Event type + } else { + this.type = src; + } + + // Put explicitly provided properties onto the event object + if ( props ) { + jQuery.extend( this, props ); + } + + // Create a timestamp if incoming event doesn't have one + this.timeStamp = src && src.timeStamp || Date.now(); + + // Mark it as fixed + this[ jQuery.expando ] = true; +}; + +// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding +// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html +jQuery.Event.prototype = { + constructor: jQuery.Event, + isDefaultPrevented: returnFalse, + isPropagationStopped: returnFalse, + isImmediatePropagationStopped: returnFalse, + isSimulated: false, + + preventDefault: function() { + var e = this.originalEvent; + + this.isDefaultPrevented = returnTrue; + + if ( e && !this.isSimulated ) { + e.preventDefault(); + } + }, + stopPropagation: function() { + var e = this.originalEvent; + + this.isPropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopPropagation(); + } + }, + stopImmediatePropagation: function() { + var e = this.originalEvent; + + this.isImmediatePropagationStopped = returnTrue; + + if ( e && !this.isSimulated ) { + e.stopImmediatePropagation(); + } + + this.stopPropagation(); + } +}; + +// Includes all common event props including KeyEvent and MouseEvent specific props +jQuery.each( { + altKey: true, + bubbles: true, + cancelable: true, + changedTouches: true, + ctrlKey: true, + detail: true, + eventPhase: true, + metaKey: true, + pageX: true, + pageY: true, + shiftKey: true, + view: true, + "char": true, + code: true, + charCode: true, + key: true, + keyCode: true, + button: true, + buttons: true, + clientX: true, + clientY: true, + offsetX: true, + offsetY: true, + pointerId: true, + pointerType: true, + screenX: true, + screenY: true, + targetTouches: true, + toElement: true, + touches: true, + which: true +}, jQuery.event.addProp ); + +jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) { + jQuery.event.special[ type ] = { + + // Utilize native event if possible so blur/focus sequence is correct + setup: function() { + + // Claim the first handler + // dataPriv.set( this, "focus", ... ) + // dataPriv.set( this, "blur", ... ) + leverageNative( this, type, expectSync ); + + // Return false to allow normal processing in the caller + return false; + }, + trigger: function() { + + // Force setup before trigger + leverageNative( this, type ); + + // Return non-false to allow normal event-path propagation + return true; + }, + + // Suppress native focus or blur as it's already being fired + // in leverageNative. + _default: function() { + return true; + }, + + delegateType: delegateType + }; +} ); + +// Create mouseenter/leave events using mouseover/out and event-time checks +// so that event delegation works in jQuery. +// Do the same for pointerenter/pointerleave and pointerover/pointerout +// +// Support: Safari 7 only +// Safari sends mouseenter too often; see: +// https://bugs.chromium.org/p/chromium/issues/detail?id=470258 +// for the description of the bug (it existed in older Chrome versions as well). +jQuery.each( { + mouseenter: "mouseover", + mouseleave: "mouseout", + pointerenter: "pointerover", + pointerleave: "pointerout" +}, function( orig, fix ) { + jQuery.event.special[ orig ] = { + delegateType: fix, + bindType: fix, + + handle: function( event ) { + var ret, + target = this, + related = event.relatedTarget, + handleObj = event.handleObj; + + // For mouseenter/leave call the handler if related is outside the target. + // NB: No relatedTarget if the mouse left/entered the browser window + if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) { + event.type = handleObj.origType; + ret = handleObj.handler.apply( this, arguments ); + event.type = fix; + } + return ret; + } + }; +} ); + +jQuery.fn.extend( { + + on: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn ); + }, + one: function( types, selector, data, fn ) { + return on( this, types, selector, data, fn, 1 ); + }, + off: function( types, selector, fn ) { + var handleObj, type; + if ( types && types.preventDefault && types.handleObj ) { + + // ( event ) dispatched jQuery.Event + handleObj = types.handleObj; + jQuery( types.delegateTarget ).off( + handleObj.namespace ? + handleObj.origType + "." + handleObj.namespace : + handleObj.origType, + handleObj.selector, + handleObj.handler + ); + return this; + } + if ( typeof types === "object" ) { + + // ( types-object [, selector] ) + for ( type in types ) { + this.off( type, selector, types[ type ] ); + } + return this; + } + if ( selector === false || typeof selector === "function" ) { + + // ( types [, fn] ) + fn = selector; + selector = undefined; + } + if ( fn === false ) { + fn = returnFalse; + } + return this.each( function() { + jQuery.event.remove( this, types, fn, selector ); + } ); + } +} ); + + +var + + // Support: IE <=10 - 11, Edge 12 - 13 only + // In IE/Edge using regex groups here causes severe slowdowns. + // See https://connect.microsoft.com/IE/feedback/details/1736512/ + rnoInnerhtml = /\s*$/g; + +// Prefer a tbody over its parent table for containing new rows +function manipulationTarget( elem, content ) { + if ( nodeName( elem, "table" ) && + nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) { + + return jQuery( elem ).children( "tbody" )[ 0 ] || elem; + } + + return elem; +} + +// Replace/restore the type attribute of script elements for safe DOM manipulation +function disableScript( elem ) { + elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type; + return elem; +} +function restoreScript( elem ) { + if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) { + elem.type = elem.type.slice( 5 ); + } else { + elem.removeAttribute( "type" ); + } + + return elem; +} + +function cloneCopyEvent( src, dest ) { + var i, l, type, pdataOld, udataOld, udataCur, events; + + if ( dest.nodeType !== 1 ) { + return; + } + + // 1. Copy private data: events, handlers, etc. + if ( dataPriv.hasData( src ) ) { + pdataOld = dataPriv.get( src ); + events = pdataOld.events; + + if ( events ) { + dataPriv.remove( dest, "handle events" ); + + for ( type in events ) { + for ( i = 0, l = events[ type ].length; i < l; i++ ) { + jQuery.event.add( dest, type, events[ type ][ i ] ); + } + } + } + } + + // 2. Copy user data + if ( dataUser.hasData( src ) ) { + udataOld = dataUser.access( src ); + udataCur = jQuery.extend( {}, udataOld ); + + dataUser.set( dest, udataCur ); + } +} + +// Fix IE bugs, see support tests +function fixInput( src, dest ) { + var nodeName = dest.nodeName.toLowerCase(); + + // Fails to persist the checked state of a cloned checkbox or radio button. + if ( nodeName === "input" && rcheckableType.test( src.type ) ) { + dest.checked = src.checked; + + // Fails to return the selected option to the default selected state when cloning options + } else if ( nodeName === "input" || nodeName === "textarea" ) { + dest.defaultValue = src.defaultValue; + } +} + +function domManip( collection, args, callback, ignored ) { + + // Flatten any nested arrays + args = flat( args ); + + var fragment, first, scripts, hasScripts, node, doc, + i = 0, + l = collection.length, + iNoClone = l - 1, + value = args[ 0 ], + valueIsFunction = isFunction( value ); + + // We can't cloneNode fragments that contain checked, in WebKit + if ( valueIsFunction || + ( l > 1 && typeof value === "string" && + !support.checkClone && rchecked.test( value ) ) ) { + return collection.each( function( index ) { + var self = collection.eq( index ); + if ( valueIsFunction ) { + args[ 0 ] = value.call( this, index, self.html() ); + } + domManip( self, args, callback, ignored ); + } ); + } + + if ( l ) { + fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored ); + first = fragment.firstChild; + + if ( fragment.childNodes.length === 1 ) { + fragment = first; + } + + // Require either new content or an interest in ignored elements to invoke the callback + if ( first || ignored ) { + scripts = jQuery.map( getAll( fragment, "script" ), disableScript ); + hasScripts = scripts.length; + + // Use the original fragment for the last item + // instead of the first because it can end up + // being emptied incorrectly in certain situations (#8070). + for ( ; i < l; i++ ) { + node = fragment; + + if ( i !== iNoClone ) { + node = jQuery.clone( node, true, true ); + + // Keep references to cloned scripts for later restoration + if ( hasScripts ) { + + // Support: Android <=4.0 only, PhantomJS 1 only + // push.apply(_, arraylike) throws on ancient WebKit + jQuery.merge( scripts, getAll( node, "script" ) ); + } + } + + callback.call( collection[ i ], node, i ); + } + + if ( hasScripts ) { + doc = scripts[ scripts.length - 1 ].ownerDocument; + + // Reenable scripts + jQuery.map( scripts, restoreScript ); + + // Evaluate executable scripts on first document insertion + for ( i = 0; i < hasScripts; i++ ) { + node = scripts[ i ]; + if ( rscriptType.test( node.type || "" ) && + !dataPriv.access( node, "globalEval" ) && + jQuery.contains( doc, node ) ) { + + if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) { + + // Optional AJAX dependency, but won't run scripts if not present + if ( jQuery._evalUrl && !node.noModule ) { + jQuery._evalUrl( node.src, { + nonce: node.nonce || node.getAttribute( "nonce" ) + }, doc ); + } + } else { + DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc ); + } + } + } + } + } + } + + return collection; +} + +function remove( elem, selector, keepData ) { + var node, + nodes = selector ? jQuery.filter( selector, elem ) : elem, + i = 0; + + for ( ; ( node = nodes[ i ] ) != null; i++ ) { + if ( !keepData && node.nodeType === 1 ) { + jQuery.cleanData( getAll( node ) ); + } + + if ( node.parentNode ) { + if ( keepData && isAttached( node ) ) { + setGlobalEval( getAll( node, "script" ) ); + } + node.parentNode.removeChild( node ); + } + } + + return elem; +} + +jQuery.extend( { + htmlPrefilter: function( html ) { + return html; + }, + + clone: function( elem, dataAndEvents, deepDataAndEvents ) { + var i, l, srcElements, destElements, + clone = elem.cloneNode( true ), + inPage = isAttached( elem ); + + // Fix IE cloning issues + if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) && + !jQuery.isXMLDoc( elem ) ) { + + // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2 + destElements = getAll( clone ); + srcElements = getAll( elem ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + fixInput( srcElements[ i ], destElements[ i ] ); + } + } + + // Copy the events from the original to the clone + if ( dataAndEvents ) { + if ( deepDataAndEvents ) { + srcElements = srcElements || getAll( elem ); + destElements = destElements || getAll( clone ); + + for ( i = 0, l = srcElements.length; i < l; i++ ) { + cloneCopyEvent( srcElements[ i ], destElements[ i ] ); + } + } else { + cloneCopyEvent( elem, clone ); + } + } + + // Preserve script evaluation history + destElements = getAll( clone, "script" ); + if ( destElements.length > 0 ) { + setGlobalEval( destElements, !inPage && getAll( elem, "script" ) ); + } + + // Return the cloned set + return clone; + }, + + cleanData: function( elems ) { + var data, elem, type, + special = jQuery.event.special, + i = 0; + + for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) { + if ( acceptData( elem ) ) { + if ( ( data = elem[ dataPriv.expando ] ) ) { + if ( data.events ) { + for ( type in data.events ) { + if ( special[ type ] ) { + jQuery.event.remove( elem, type ); + + // This is a shortcut to avoid jQuery.event.remove's overhead + } else { + jQuery.removeEvent( elem, type, data.handle ); + } + } + } + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataPriv.expando ] = undefined; + } + if ( elem[ dataUser.expando ] ) { + + // Support: Chrome <=35 - 45+ + // Assign undefined instead of using delete, see Data#remove + elem[ dataUser.expando ] = undefined; + } + } + } + } +} ); + +jQuery.fn.extend( { + detach: function( selector ) { + return remove( this, selector, true ); + }, + + remove: function( selector ) { + return remove( this, selector ); + }, + + text: function( value ) { + return access( this, function( value ) { + return value === undefined ? + jQuery.text( this ) : + this.empty().each( function() { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + this.textContent = value; + } + } ); + }, null, value, arguments.length ); + }, + + append: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.appendChild( elem ); + } + } ); + }, + + prepend: function() { + return domManip( this, arguments, function( elem ) { + if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) { + var target = manipulationTarget( this, elem ); + target.insertBefore( elem, target.firstChild ); + } + } ); + }, + + before: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this ); + } + } ); + }, + + after: function() { + return domManip( this, arguments, function( elem ) { + if ( this.parentNode ) { + this.parentNode.insertBefore( elem, this.nextSibling ); + } + } ); + }, + + empty: function() { + var elem, + i = 0; + + for ( ; ( elem = this[ i ] ) != null; i++ ) { + if ( elem.nodeType === 1 ) { + + // Prevent memory leaks + jQuery.cleanData( getAll( elem, false ) ); + + // Remove any remaining nodes + elem.textContent = ""; + } + } + + return this; + }, + + clone: function( dataAndEvents, deepDataAndEvents ) { + dataAndEvents = dataAndEvents == null ? false : dataAndEvents; + deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents; + + return this.map( function() { + return jQuery.clone( this, dataAndEvents, deepDataAndEvents ); + } ); + }, + + html: function( value ) { + return access( this, function( value ) { + var elem = this[ 0 ] || {}, + i = 0, + l = this.length; + + if ( value === undefined && elem.nodeType === 1 ) { + return elem.innerHTML; + } + + // See if we can take a shortcut and just use innerHTML + if ( typeof value === "string" && !rnoInnerhtml.test( value ) && + !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) { + + value = jQuery.htmlPrefilter( value ); + + try { + for ( ; i < l; i++ ) { + elem = this[ i ] || {}; + + // Remove element nodes and prevent memory leaks + if ( elem.nodeType === 1 ) { + jQuery.cleanData( getAll( elem, false ) ); + elem.innerHTML = value; + } + } + + elem = 0; + + // If using innerHTML throws an exception, use the fallback method + } catch ( e ) {} + } + + if ( elem ) { + this.empty().append( value ); + } + }, null, value, arguments.length ); + }, + + replaceWith: function() { + var ignored = []; + + // Make the changes, replacing each non-ignored context element with the new content + return domManip( this, arguments, function( elem ) { + var parent = this.parentNode; + + if ( jQuery.inArray( this, ignored ) < 0 ) { + jQuery.cleanData( getAll( this ) ); + if ( parent ) { + parent.replaceChild( elem, this ); + } + } + + // Force callback invocation + }, ignored ); + } +} ); + +jQuery.each( { + appendTo: "append", + prependTo: "prepend", + insertBefore: "before", + insertAfter: "after", + replaceAll: "replaceWith" +}, function( name, original ) { + jQuery.fn[ name ] = function( selector ) { + var elems, + ret = [], + insert = jQuery( selector ), + last = insert.length - 1, + i = 0; + + for ( ; i <= last; i++ ) { + elems = i === last ? this : this.clone( true ); + jQuery( insert[ i ] )[ original ]( elems ); + + // Support: Android <=4.0 only, PhantomJS 1 only + // .get() because push.apply(_, arraylike) throws on ancient WebKit + push.apply( ret, elems.get() ); + } + + return this.pushStack( ret ); + }; +} ); +var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" ); + +var getStyles = function( elem ) { + + // Support: IE <=11 only, Firefox <=30 (#15098, #14150) + // IE throws on elements created in popups + // FF meanwhile throws on frame elements through "defaultView.getComputedStyle" + var view = elem.ownerDocument.defaultView; + + if ( !view || !view.opener ) { + view = window; + } + + return view.getComputedStyle( elem ); + }; + +var swap = function( elem, options, callback ) { + var ret, name, + old = {}; + + // Remember the old values, and insert the new ones + for ( name in options ) { + old[ name ] = elem.style[ name ]; + elem.style[ name ] = options[ name ]; + } + + ret = callback.call( elem ); + + // Revert the old values + for ( name in options ) { + elem.style[ name ] = old[ name ]; + } + + return ret; +}; + + +var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" ); + + + +( function() { + + // Executing both pixelPosition & boxSizingReliable tests require only one layout + // so they're executed at the same time to save the second computation. + function computeStyleTests() { + + // This is a singleton, we need to execute it only once + if ( !div ) { + return; + } + + container.style.cssText = "position:absolute;left:-11111px;width:60px;" + + "margin-top:1px;padding:0;border:0"; + div.style.cssText = + "position:relative;display:block;box-sizing:border-box;overflow:scroll;" + + "margin:auto;border:1px;padding:1px;" + + "width:60%;top:1%"; + documentElement.appendChild( container ).appendChild( div ); + + var divStyle = window.getComputedStyle( div ); + pixelPositionVal = divStyle.top !== "1%"; + + // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44 + reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12; + + // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3 + // Some styles come back with percentage values, even though they shouldn't + div.style.right = "60%"; + pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36; + + // Support: IE 9 - 11 only + // Detect misreporting of content dimensions for box-sizing:border-box elements + boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36; + + // Support: IE 9 only + // Detect overflow:scroll screwiness (gh-3699) + // Support: Chrome <=64 + // Don't get tricked when zoom affects offsetWidth (gh-4029) + div.style.position = "absolute"; + scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12; + + documentElement.removeChild( container ); + + // Nullify the div so it wouldn't be stored in the memory and + // it will also be a sign that checks already performed + div = null; + } + + function roundPixelMeasures( measure ) { + return Math.round( parseFloat( measure ) ); + } + + var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal, + reliableTrDimensionsVal, reliableMarginLeftVal, + container = document.createElement( "div" ), + div = document.createElement( "div" ); + + // Finish early in limited (non-browser) environments + if ( !div.style ) { + return; + } + + // Support: IE <=9 - 11 only + // Style of cloned element affects source element cloned (#8908) + div.style.backgroundClip = "content-box"; + div.cloneNode( true ).style.backgroundClip = ""; + support.clearCloneStyle = div.style.backgroundClip === "content-box"; + + jQuery.extend( support, { + boxSizingReliable: function() { + computeStyleTests(); + return boxSizingReliableVal; + }, + pixelBoxStyles: function() { + computeStyleTests(); + return pixelBoxStylesVal; + }, + pixelPosition: function() { + computeStyleTests(); + return pixelPositionVal; + }, + reliableMarginLeft: function() { + computeStyleTests(); + return reliableMarginLeftVal; + }, + scrollboxSize: function() { + computeStyleTests(); + return scrollboxSizeVal; + }, + + // Support: IE 9 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Behavior in IE 9 is more subtle than in newer versions & it passes + // some versions of this test; make sure not to make it pass there! + // + // Support: Firefox 70+ + // Only Firefox includes border widths + // in computed dimensions. (gh-4529) + reliableTrDimensions: function() { + var table, tr, trChild, trStyle; + if ( reliableTrDimensionsVal == null ) { + table = document.createElement( "table" ); + tr = document.createElement( "tr" ); + trChild = document.createElement( "div" ); + + table.style.cssText = "position:absolute;left:-11111px;border-collapse:separate"; + tr.style.cssText = "border:1px solid"; + + // Support: Chrome 86+ + // Height set through cssText does not get applied. + // Computed height then comes back as 0. + tr.style.height = "1px"; + trChild.style.height = "9px"; + + // Support: Android 8 Chrome 86+ + // In our bodyBackground.html iframe, + // display for all div elements is set to "inline", + // which causes a problem only in Android 8 Chrome 86. + // Ensuring the div is display: block + // gets around this issue. + trChild.style.display = "block"; + + documentElement + .appendChild( table ) + .appendChild( tr ) + .appendChild( trChild ); + + trStyle = window.getComputedStyle( tr ); + reliableTrDimensionsVal = ( parseInt( trStyle.height, 10 ) + + parseInt( trStyle.borderTopWidth, 10 ) + + parseInt( trStyle.borderBottomWidth, 10 ) ) === tr.offsetHeight; + + documentElement.removeChild( table ); + } + return reliableTrDimensionsVal; + } + } ); +} )(); + + +function curCSS( elem, name, computed ) { + var width, minWidth, maxWidth, ret, + + // Support: Firefox 51+ + // Retrieving style before computed somehow + // fixes an issue with getting wrong values + // on detached elements + style = elem.style; + + computed = computed || getStyles( elem ); + + // getPropertyValue is needed for: + // .css('filter') (IE 9 only, #12537) + // .css('--customProperty) (#3144) + if ( computed ) { + ret = computed.getPropertyValue( name ) || computed[ name ]; + + if ( ret === "" && !isAttached( elem ) ) { + ret = jQuery.style( elem, name ); + } + + // A tribute to the "awesome hack by Dean Edwards" + // Android Browser returns percentage for some values, + // but width seems to be reliably pixels. + // This is against the CSSOM draft spec: + // https://drafts.csswg.org/cssom/#resolved-values + if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) { + + // Remember the original values + width = style.width; + minWidth = style.minWidth; + maxWidth = style.maxWidth; + + // Put in the new values to get a computed value out + style.minWidth = style.maxWidth = style.width = ret; + ret = computed.width; + + // Revert the changed values + style.width = width; + style.minWidth = minWidth; + style.maxWidth = maxWidth; + } + } + + return ret !== undefined ? + + // Support: IE <=9 - 11 only + // IE returns zIndex value as an integer. + ret + "" : + ret; +} + + +function addGetHookIf( conditionFn, hookFn ) { + + // Define the hook, we'll check on the first run if it's really needed. + return { + get: function() { + if ( conditionFn() ) { + + // Hook not needed (or it's not possible to use it due + // to missing dependency), remove it. + delete this.get; + return; + } + + // Hook needed; redefine it so that the support test is not executed again. + return ( this.get = hookFn ).apply( this, arguments ); + } + }; +} + + +var cssPrefixes = [ "Webkit", "Moz", "ms" ], + emptyStyle = document.createElement( "div" ).style, + vendorProps = {}; + +// Return a vendor-prefixed property or undefined +function vendorPropName( name ) { + + // Check for vendor prefixed names + var capName = name[ 0 ].toUpperCase() + name.slice( 1 ), + i = cssPrefixes.length; + + while ( i-- ) { + name = cssPrefixes[ i ] + capName; + if ( name in emptyStyle ) { + return name; + } + } +} + +// Return a potentially-mapped jQuery.cssProps or vendor prefixed property +function finalPropName( name ) { + var final = jQuery.cssProps[ name ] || vendorProps[ name ]; + + if ( final ) { + return final; + } + if ( name in emptyStyle ) { + return name; + } + return vendorProps[ name ] = vendorPropName( name ) || name; +} + + +var + + // Swappable if display is none or starts with table + // except "table", "table-cell", or "table-caption" + // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display + rdisplayswap = /^(none|table(?!-c[ea]).+)/, + rcustomProp = /^--/, + cssShow = { position: "absolute", visibility: "hidden", display: "block" }, + cssNormalTransform = { + letterSpacing: "0", + fontWeight: "400" + }; + +function setPositiveNumber( _elem, value, subtract ) { + + // Any relative (+/-) values have already been + // normalized at this point + var matches = rcssNum.exec( value ); + return matches ? + + // Guard against undefined "subtract", e.g., when used as in cssHooks + Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) : + value; +} + +function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) { + var i = dimension === "width" ? 1 : 0, + extra = 0, + delta = 0; + + // Adjustment may not be necessary + if ( box === ( isBorderBox ? "border" : "content" ) ) { + return 0; + } + + for ( ; i < 4; i += 2 ) { + + // Both box models exclude margin + if ( box === "margin" ) { + delta += jQuery.css( elem, box + cssExpand[ i ], true, styles ); + } + + // If we get here with a content-box, we're seeking "padding" or "border" or "margin" + if ( !isBorderBox ) { + + // Add padding + delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + + // For "border" or "margin", add border + if ( box !== "padding" ) { + delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + + // But still keep track of it otherwise + } else { + extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + + // If we get here with a border-box (content + padding + border), we're seeking "content" or + // "padding" or "margin" + } else { + + // For "content", subtract padding + if ( box === "content" ) { + delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles ); + } + + // For "content" or "padding", subtract border + if ( box !== "margin" ) { + delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles ); + } + } + } + + // Account for positive content-box scroll gutter when requested by providing computedVal + if ( !isBorderBox && computedVal >= 0 ) { + + // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border + // Assuming integer scroll gutter, subtract the rest and round down + delta += Math.max( 0, Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + computedVal - + delta - + extra - + 0.5 + + // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter + // Use an explicit zero to avoid NaN (gh-3964) + ) ) || 0; + } + + return delta; +} + +function getWidthOrHeight( elem, dimension, extra ) { + + // Start with computed style + var styles = getStyles( elem ), + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322). + // Fake content-box until we know it's needed to know the true value. + boxSizingNeeded = !support.boxSizingReliable() || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + valueIsBorderBox = isBorderBox, + + val = curCSS( elem, dimension, styles ), + offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ); + + // Support: Firefox <=54 + // Return a confounding non-pixel value or feign ignorance, as appropriate. + if ( rnumnonpx.test( val ) ) { + if ( !extra ) { + return val; + } + val = "auto"; + } + + + // Support: IE 9 - 11 only + // Use offsetWidth/offsetHeight for when box sizing is unreliable. + // In those cases, the computed value can be trusted to be border-box. + if ( ( !support.boxSizingReliable() && isBorderBox || + + // Support: IE 10 - 11+, Edge 15 - 18+ + // IE/Edge misreport `getComputedStyle` of table rows with width/height + // set in CSS while `offset*` properties report correct values. + // Interestingly, in some cases IE 9 doesn't suffer from this issue. + !support.reliableTrDimensions() && nodeName( elem, "tr" ) || + + // Fall back to offsetWidth/offsetHeight when value is "auto" + // This happens for inline elements with no explicit setting (gh-3571) + val === "auto" || + + // Support: Android <=4.1 - 4.3 only + // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602) + !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) && + + // Make sure the element is visible & connected + elem.getClientRects().length ) { + + isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box"; + + // Where available, offsetWidth/offsetHeight approximate border box dimensions. + // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the + // retrieved value as a content box dimension. + valueIsBorderBox = offsetProp in elem; + if ( valueIsBorderBox ) { + val = elem[ offsetProp ]; + } + } + + // Normalize "" and auto + val = parseFloat( val ) || 0; + + // Adjust for the element's box model + return ( val + + boxModelAdjustment( + elem, + dimension, + extra || ( isBorderBox ? "border" : "content" ), + valueIsBorderBox, + styles, + + // Provide the current computed size to request scroll gutter calculation (gh-3589) + val + ) + ) + "px"; +} + +jQuery.extend( { + + // Add in style property hooks for overriding the default + // behavior of getting and setting a style property + cssHooks: { + opacity: { + get: function( elem, computed ) { + if ( computed ) { + + // We should always get a number back from opacity + var ret = curCSS( elem, "opacity" ); + return ret === "" ? "1" : ret; + } + } + } + }, + + // Don't automatically add "px" to these possibly-unitless properties + cssNumber: { + "animationIterationCount": true, + "columnCount": true, + "fillOpacity": true, + "flexGrow": true, + "flexShrink": true, + "fontWeight": true, + "gridArea": true, + "gridColumn": true, + "gridColumnEnd": true, + "gridColumnStart": true, + "gridRow": true, + "gridRowEnd": true, + "gridRowStart": true, + "lineHeight": true, + "opacity": true, + "order": true, + "orphans": true, + "widows": true, + "zIndex": true, + "zoom": true + }, + + // Add in properties whose names you wish to fix before + // setting or getting the value + cssProps: {}, + + // Get and set the style property on a DOM Node + style: function( elem, name, value, extra ) { + + // Don't set styles on text and comment nodes + if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) { + return; + } + + // Make sure that we're working with the right name + var ret, type, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ), + style = elem.style; + + // Make sure that we're working with the right name. We don't + // want to query the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Gets hook for the prefixed version, then unprefixed version + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // Check if we're setting a value + if ( value !== undefined ) { + type = typeof value; + + // Convert "+=" or "-=" to relative numbers (#7345) + if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) { + value = adjustCSS( elem, name, ret ); + + // Fixes bug #9237 + type = "number"; + } + + // Make sure that null and NaN values aren't set (#7116) + if ( value == null || value !== value ) { + return; + } + + // If a number was passed in, add the unit (except for certain CSS properties) + // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append + // "px" to a few hardcoded values. + if ( type === "number" && !isCustomProp ) { + value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" ); + } + + // background-* props affect original clone's values + if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) { + style[ name ] = "inherit"; + } + + // If a hook was provided, use that value, otherwise just set the specified value + if ( !hooks || !( "set" in hooks ) || + ( value = hooks.set( elem, value, extra ) ) !== undefined ) { + + if ( isCustomProp ) { + style.setProperty( name, value ); + } else { + style[ name ] = value; + } + } + + } else { + + // If a hook was provided get the non-computed value from there + if ( hooks && "get" in hooks && + ( ret = hooks.get( elem, false, extra ) ) !== undefined ) { + + return ret; + } + + // Otherwise just get the value from the style object + return style[ name ]; + } + }, + + css: function( elem, name, extra, styles ) { + var val, num, hooks, + origName = camelCase( name ), + isCustomProp = rcustomProp.test( name ); + + // Make sure that we're working with the right name. We don't + // want to modify the value if it is a CSS custom property + // since they are user-defined. + if ( !isCustomProp ) { + name = finalPropName( origName ); + } + + // Try prefixed name followed by the unprefixed name + hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ]; + + // If a hook was provided get the computed value from there + if ( hooks && "get" in hooks ) { + val = hooks.get( elem, true, extra ); + } + + // Otherwise, if a way to get the computed value exists, use that + if ( val === undefined ) { + val = curCSS( elem, name, styles ); + } + + // Convert "normal" to computed value + if ( val === "normal" && name in cssNormalTransform ) { + val = cssNormalTransform[ name ]; + } + + // Make numeric if forced or a qualifier was provided and val looks numeric + if ( extra === "" || extra ) { + num = parseFloat( val ); + return extra === true || isFinite( num ) ? num || 0 : val; + } + + return val; + } +} ); + +jQuery.each( [ "height", "width" ], function( _i, dimension ) { + jQuery.cssHooks[ dimension ] = { + get: function( elem, computed, extra ) { + if ( computed ) { + + // Certain elements can have dimension info if we invisibly show them + // but it must have a current display style that would benefit + return rdisplayswap.test( jQuery.css( elem, "display" ) ) && + + // Support: Safari 8+ + // Table columns in Safari have non-zero offsetWidth & zero + // getBoundingClientRect().width unless display is changed. + // Support: IE <=11 only + // Running getBoundingClientRect on a disconnected node + // in IE throws an error. + ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ? + swap( elem, cssShow, function() { + return getWidthOrHeight( elem, dimension, extra ); + } ) : + getWidthOrHeight( elem, dimension, extra ); + } + }, + + set: function( elem, value, extra ) { + var matches, + styles = getStyles( elem ), + + // Only read styles.position if the test has a chance to fail + // to avoid forcing a reflow. + scrollboxSizeBuggy = !support.scrollboxSize() && + styles.position === "absolute", + + // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991) + boxSizingNeeded = scrollboxSizeBuggy || extra, + isBorderBox = boxSizingNeeded && + jQuery.css( elem, "boxSizing", false, styles ) === "border-box", + subtract = extra ? + boxModelAdjustment( + elem, + dimension, + extra, + isBorderBox, + styles + ) : + 0; + + // Account for unreliable border-box dimensions by comparing offset* to computed and + // faking a content-box to get border and padding (gh-3699) + if ( isBorderBox && scrollboxSizeBuggy ) { + subtract -= Math.ceil( + elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] - + parseFloat( styles[ dimension ] ) - + boxModelAdjustment( elem, dimension, "border", false, styles ) - + 0.5 + ); + } + + // Convert to pixels if value adjustment is needed + if ( subtract && ( matches = rcssNum.exec( value ) ) && + ( matches[ 3 ] || "px" ) !== "px" ) { + + elem.style[ dimension ] = value; + value = jQuery.css( elem, dimension ); + } + + return setPositiveNumber( elem, value, subtract ); + } + }; +} ); + +jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft, + function( elem, computed ) { + if ( computed ) { + return ( parseFloat( curCSS( elem, "marginLeft" ) ) || + elem.getBoundingClientRect().left - + swap( elem, { marginLeft: 0 }, function() { + return elem.getBoundingClientRect().left; + } ) + ) + "px"; + } + } +); + +// These hooks are used by animate to expand properties +jQuery.each( { + margin: "", + padding: "", + border: "Width" +}, function( prefix, suffix ) { + jQuery.cssHooks[ prefix + suffix ] = { + expand: function( value ) { + var i = 0, + expanded = {}, + + // Assumes a single number if not a string + parts = typeof value === "string" ? value.split( " " ) : [ value ]; + + for ( ; i < 4; i++ ) { + expanded[ prefix + cssExpand[ i ] + suffix ] = + parts[ i ] || parts[ i - 2 ] || parts[ 0 ]; + } + + return expanded; + } + }; + + if ( prefix !== "margin" ) { + jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber; + } +} ); + +jQuery.fn.extend( { + css: function( name, value ) { + return access( this, function( elem, name, value ) { + var styles, len, + map = {}, + i = 0; + + if ( Array.isArray( name ) ) { + styles = getStyles( elem ); + len = name.length; + + for ( ; i < len; i++ ) { + map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles ); + } + + return map; + } + + return value !== undefined ? + jQuery.style( elem, name, value ) : + jQuery.css( elem, name ); + }, name, value, arguments.length > 1 ); + } +} ); + + +function Tween( elem, options, prop, end, easing ) { + return new Tween.prototype.init( elem, options, prop, end, easing ); +} +jQuery.Tween = Tween; + +Tween.prototype = { + constructor: Tween, + init: function( elem, options, prop, end, easing, unit ) { + this.elem = elem; + this.prop = prop; + this.easing = easing || jQuery.easing._default; + this.options = options; + this.start = this.now = this.cur(); + this.end = end; + this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" ); + }, + cur: function() { + var hooks = Tween.propHooks[ this.prop ]; + + return hooks && hooks.get ? + hooks.get( this ) : + Tween.propHooks._default.get( this ); + }, + run: function( percent ) { + var eased, + hooks = Tween.propHooks[ this.prop ]; + + if ( this.options.duration ) { + this.pos = eased = jQuery.easing[ this.easing ]( + percent, this.options.duration * percent, 0, 1, this.options.duration + ); + } else { + this.pos = eased = percent; + } + this.now = ( this.end - this.start ) * eased + this.start; + + if ( this.options.step ) { + this.options.step.call( this.elem, this.now, this ); + } + + if ( hooks && hooks.set ) { + hooks.set( this ); + } else { + Tween.propHooks._default.set( this ); + } + return this; + } +}; + +Tween.prototype.init.prototype = Tween.prototype; + +Tween.propHooks = { + _default: { + get: function( tween ) { + var result; + + // Use a property on the element directly when it is not a DOM element, + // or when there is no matching style property that exists. + if ( tween.elem.nodeType !== 1 || + tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) { + return tween.elem[ tween.prop ]; + } + + // Passing an empty string as a 3rd parameter to .css will automatically + // attempt a parseFloat and fallback to a string if the parse fails. + // Simple values such as "10px" are parsed to Float; + // complex values such as "rotate(1rad)" are returned as-is. + result = jQuery.css( tween.elem, tween.prop, "" ); + + // Empty strings, null, undefined and "auto" are converted to 0. + return !result || result === "auto" ? 0 : result; + }, + set: function( tween ) { + + // Use step hook for back compat. + // Use cssHook if its there. + // Use .style if available and use plain properties where available. + if ( jQuery.fx.step[ tween.prop ] ) { + jQuery.fx.step[ tween.prop ]( tween ); + } else if ( tween.elem.nodeType === 1 && ( + jQuery.cssHooks[ tween.prop ] || + tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) { + jQuery.style( tween.elem, tween.prop, tween.now + tween.unit ); + } else { + tween.elem[ tween.prop ] = tween.now; + } + } + } +}; + +// Support: IE <=9 only +// Panic based approach to setting things on disconnected nodes +Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = { + set: function( tween ) { + if ( tween.elem.nodeType && tween.elem.parentNode ) { + tween.elem[ tween.prop ] = tween.now; + } + } +}; + +jQuery.easing = { + linear: function( p ) { + return p; + }, + swing: function( p ) { + return 0.5 - Math.cos( p * Math.PI ) / 2; + }, + _default: "swing" +}; + +jQuery.fx = Tween.prototype.init; + +// Back compat <1.8 extension point +jQuery.fx.step = {}; + + + + +var + fxNow, inProgress, + rfxtypes = /^(?:toggle|show|hide)$/, + rrun = /queueHooks$/; + +function schedule() { + if ( inProgress ) { + if ( document.hidden === false && window.requestAnimationFrame ) { + window.requestAnimationFrame( schedule ); + } else { + window.setTimeout( schedule, jQuery.fx.interval ); + } + + jQuery.fx.tick(); + } +} + +// Animations created synchronously will run synchronously +function createFxNow() { + window.setTimeout( function() { + fxNow = undefined; + } ); + return ( fxNow = Date.now() ); +} + +// Generate parameters to create a standard animation +function genFx( type, includeWidth ) { + var which, + i = 0, + attrs = { height: type }; + + // If we include width, step value is 1 to do all cssExpand values, + // otherwise step value is 2 to skip over Left and Right + includeWidth = includeWidth ? 1 : 0; + for ( ; i < 4; i += 2 - includeWidth ) { + which = cssExpand[ i ]; + attrs[ "margin" + which ] = attrs[ "padding" + which ] = type; + } + + if ( includeWidth ) { + attrs.opacity = attrs.width = type; + } + + return attrs; +} + +function createTween( value, prop, animation ) { + var tween, + collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ), + index = 0, + length = collection.length; + for ( ; index < length; index++ ) { + if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) { + + // We're done with this property + return tween; + } + } +} + +function defaultPrefilter( elem, props, opts ) { + var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display, + isBox = "width" in props || "height" in props, + anim = this, + orig = {}, + style = elem.style, + hidden = elem.nodeType && isHiddenWithinTree( elem ), + dataShow = dataPriv.get( elem, "fxshow" ); + + // Queue-skipping animations hijack the fx hooks + if ( !opts.queue ) { + hooks = jQuery._queueHooks( elem, "fx" ); + if ( hooks.unqueued == null ) { + hooks.unqueued = 0; + oldfire = hooks.empty.fire; + hooks.empty.fire = function() { + if ( !hooks.unqueued ) { + oldfire(); + } + }; + } + hooks.unqueued++; + + anim.always( function() { + + // Ensure the complete handler is called before this completes + anim.always( function() { + hooks.unqueued--; + if ( !jQuery.queue( elem, "fx" ).length ) { + hooks.empty.fire(); + } + } ); + } ); + } + + // Detect show/hide animations + for ( prop in props ) { + value = props[ prop ]; + if ( rfxtypes.test( value ) ) { + delete props[ prop ]; + toggle = toggle || value === "toggle"; + if ( value === ( hidden ? "hide" : "show" ) ) { + + // Pretend to be hidden if this is a "show" and + // there is still data from a stopped show/hide + if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) { + hidden = true; + + // Ignore all other no-op show/hide data + } else { + continue; + } + } + orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop ); + } + } + + // Bail out if this is a no-op like .hide().hide() + propTween = !jQuery.isEmptyObject( props ); + if ( !propTween && jQuery.isEmptyObject( orig ) ) { + return; + } + + // Restrict "overflow" and "display" styles during box animations + if ( isBox && elem.nodeType === 1 ) { + + // Support: IE <=9 - 11, Edge 12 - 15 + // Record all 3 overflow attributes because IE does not infer the shorthand + // from identically-valued overflowX and overflowY and Edge just mirrors + // the overflowX value there. + opts.overflow = [ style.overflow, style.overflowX, style.overflowY ]; + + // Identify a display type, preferring old show/hide data over the CSS cascade + restoreDisplay = dataShow && dataShow.display; + if ( restoreDisplay == null ) { + restoreDisplay = dataPriv.get( elem, "display" ); + } + display = jQuery.css( elem, "display" ); + if ( display === "none" ) { + if ( restoreDisplay ) { + display = restoreDisplay; + } else { + + // Get nonempty value(s) by temporarily forcing visibility + showHide( [ elem ], true ); + restoreDisplay = elem.style.display || restoreDisplay; + display = jQuery.css( elem, "display" ); + showHide( [ elem ] ); + } + } + + // Animate inline elements as inline-block + if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) { + if ( jQuery.css( elem, "float" ) === "none" ) { + + // Restore the original display value at the end of pure show/hide animations + if ( !propTween ) { + anim.done( function() { + style.display = restoreDisplay; + } ); + if ( restoreDisplay == null ) { + display = style.display; + restoreDisplay = display === "none" ? "" : display; + } + } + style.display = "inline-block"; + } + } + } + + if ( opts.overflow ) { + style.overflow = "hidden"; + anim.always( function() { + style.overflow = opts.overflow[ 0 ]; + style.overflowX = opts.overflow[ 1 ]; + style.overflowY = opts.overflow[ 2 ]; + } ); + } + + // Implement show/hide animations + propTween = false; + for ( prop in orig ) { + + // General show/hide setup for this element animation + if ( !propTween ) { + if ( dataShow ) { + if ( "hidden" in dataShow ) { + hidden = dataShow.hidden; + } + } else { + dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } ); + } + + // Store hidden/visible for toggle so `.stop().toggle()` "reverses" + if ( toggle ) { + dataShow.hidden = !hidden; + } + + // Show elements before animating them + if ( hidden ) { + showHide( [ elem ], true ); + } + + /* eslint-disable no-loop-func */ + + anim.done( function() { + + /* eslint-enable no-loop-func */ + + // The final step of a "hide" animation is actually hiding the element + if ( !hidden ) { + showHide( [ elem ] ); + } + dataPriv.remove( elem, "fxshow" ); + for ( prop in orig ) { + jQuery.style( elem, prop, orig[ prop ] ); + } + } ); + } + + // Per-property setup + propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim ); + if ( !( prop in dataShow ) ) { + dataShow[ prop ] = propTween.start; + if ( hidden ) { + propTween.end = propTween.start; + propTween.start = 0; + } + } + } +} + +function propFilter( props, specialEasing ) { + var index, name, easing, value, hooks; + + // camelCase, specialEasing and expand cssHook pass + for ( index in props ) { + name = camelCase( index ); + easing = specialEasing[ name ]; + value = props[ index ]; + if ( Array.isArray( value ) ) { + easing = value[ 1 ]; + value = props[ index ] = value[ 0 ]; + } + + if ( index !== name ) { + props[ name ] = value; + delete props[ index ]; + } + + hooks = jQuery.cssHooks[ name ]; + if ( hooks && "expand" in hooks ) { + value = hooks.expand( value ); + delete props[ name ]; + + // Not quite $.extend, this won't overwrite existing keys. + // Reusing 'index' because we have the correct "name" + for ( index in value ) { + if ( !( index in props ) ) { + props[ index ] = value[ index ]; + specialEasing[ index ] = easing; + } + } + } else { + specialEasing[ name ] = easing; + } + } +} + +function Animation( elem, properties, options ) { + var result, + stopped, + index = 0, + length = Animation.prefilters.length, + deferred = jQuery.Deferred().always( function() { + + // Don't match elem in the :animated selector + delete tick.elem; + } ), + tick = function() { + if ( stopped ) { + return false; + } + var currentTime = fxNow || createFxNow(), + remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ), + + // Support: Android 2.3 only + // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497) + temp = remaining / animation.duration || 0, + percent = 1 - temp, + index = 0, + length = animation.tweens.length; + + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( percent ); + } + + deferred.notifyWith( elem, [ animation, percent, remaining ] ); + + // If there's more to do, yield + if ( percent < 1 && length ) { + return remaining; + } + + // If this was an empty animation, synthesize a final progress notification + if ( !length ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + } + + // Resolve the animation and report its conclusion + deferred.resolveWith( elem, [ animation ] ); + return false; + }, + animation = deferred.promise( { + elem: elem, + props: jQuery.extend( {}, properties ), + opts: jQuery.extend( true, { + specialEasing: {}, + easing: jQuery.easing._default + }, options ), + originalProperties: properties, + originalOptions: options, + startTime: fxNow || createFxNow(), + duration: options.duration, + tweens: [], + createTween: function( prop, end ) { + var tween = jQuery.Tween( elem, animation.opts, prop, end, + animation.opts.specialEasing[ prop ] || animation.opts.easing ); + animation.tweens.push( tween ); + return tween; + }, + stop: function( gotoEnd ) { + var index = 0, + + // If we are going to the end, we want to run all the tweens + // otherwise we skip this part + length = gotoEnd ? animation.tweens.length : 0; + if ( stopped ) { + return this; + } + stopped = true; + for ( ; index < length; index++ ) { + animation.tweens[ index ].run( 1 ); + } + + // Resolve when we played the last frame; otherwise, reject + if ( gotoEnd ) { + deferred.notifyWith( elem, [ animation, 1, 0 ] ); + deferred.resolveWith( elem, [ animation, gotoEnd ] ); + } else { + deferred.rejectWith( elem, [ animation, gotoEnd ] ); + } + return this; + } + } ), + props = animation.props; + + propFilter( props, animation.opts.specialEasing ); + + for ( ; index < length; index++ ) { + result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts ); + if ( result ) { + if ( isFunction( result.stop ) ) { + jQuery._queueHooks( animation.elem, animation.opts.queue ).stop = + result.stop.bind( result ); + } + return result; + } + } + + jQuery.map( props, createTween, animation ); + + if ( isFunction( animation.opts.start ) ) { + animation.opts.start.call( elem, animation ); + } + + // Attach callbacks from options + animation + .progress( animation.opts.progress ) + .done( animation.opts.done, animation.opts.complete ) + .fail( animation.opts.fail ) + .always( animation.opts.always ); + + jQuery.fx.timer( + jQuery.extend( tick, { + elem: elem, + anim: animation, + queue: animation.opts.queue + } ) + ); + + return animation; +} + +jQuery.Animation = jQuery.extend( Animation, { + + tweeners: { + "*": [ function( prop, value ) { + var tween = this.createTween( prop, value ); + adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween ); + return tween; + } ] + }, + + tweener: function( props, callback ) { + if ( isFunction( props ) ) { + callback = props; + props = [ "*" ]; + } else { + props = props.match( rnothtmlwhite ); + } + + var prop, + index = 0, + length = props.length; + + for ( ; index < length; index++ ) { + prop = props[ index ]; + Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || []; + Animation.tweeners[ prop ].unshift( callback ); + } + }, + + prefilters: [ defaultPrefilter ], + + prefilter: function( callback, prepend ) { + if ( prepend ) { + Animation.prefilters.unshift( callback ); + } else { + Animation.prefilters.push( callback ); + } + } +} ); + +jQuery.speed = function( speed, easing, fn ) { + var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : { + complete: fn || !fn && easing || + isFunction( speed ) && speed, + duration: speed, + easing: fn && easing || easing && !isFunction( easing ) && easing + }; + + // Go to the end state if fx are off + if ( jQuery.fx.off ) { + opt.duration = 0; + + } else { + if ( typeof opt.duration !== "number" ) { + if ( opt.duration in jQuery.fx.speeds ) { + opt.duration = jQuery.fx.speeds[ opt.duration ]; + + } else { + opt.duration = jQuery.fx.speeds._default; + } + } + } + + // Normalize opt.queue - true/undefined/null -> "fx" + if ( opt.queue == null || opt.queue === true ) { + opt.queue = "fx"; + } + + // Queueing + opt.old = opt.complete; + + opt.complete = function() { + if ( isFunction( opt.old ) ) { + opt.old.call( this ); + } + + if ( opt.queue ) { + jQuery.dequeue( this, opt.queue ); + } + }; + + return opt; +}; + +jQuery.fn.extend( { + fadeTo: function( speed, to, easing, callback ) { + + // Show any hidden elements after setting opacity to 0 + return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show() + + // Animate to the value specified + .end().animate( { opacity: to }, speed, easing, callback ); + }, + animate: function( prop, speed, easing, callback ) { + var empty = jQuery.isEmptyObject( prop ), + optall = jQuery.speed( speed, easing, callback ), + doAnimation = function() { + + // Operate on a copy of prop so per-property easing won't be lost + var anim = Animation( this, jQuery.extend( {}, prop ), optall ); + + // Empty animations, or finishing resolves immediately + if ( empty || dataPriv.get( this, "finish" ) ) { + anim.stop( true ); + } + }; + + doAnimation.finish = doAnimation; + + return empty || optall.queue === false ? + this.each( doAnimation ) : + this.queue( optall.queue, doAnimation ); + }, + stop: function( type, clearQueue, gotoEnd ) { + var stopQueue = function( hooks ) { + var stop = hooks.stop; + delete hooks.stop; + stop( gotoEnd ); + }; + + if ( typeof type !== "string" ) { + gotoEnd = clearQueue; + clearQueue = type; + type = undefined; + } + if ( clearQueue ) { + this.queue( type || "fx", [] ); + } + + return this.each( function() { + var dequeue = true, + index = type != null && type + "queueHooks", + timers = jQuery.timers, + data = dataPriv.get( this ); + + if ( index ) { + if ( data[ index ] && data[ index ].stop ) { + stopQueue( data[ index ] ); + } + } else { + for ( index in data ) { + if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) { + stopQueue( data[ index ] ); + } + } + } + + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && + ( type == null || timers[ index ].queue === type ) ) { + + timers[ index ].anim.stop( gotoEnd ); + dequeue = false; + timers.splice( index, 1 ); + } + } + + // Start the next in the queue if the last step wasn't forced. + // Timers currently will call their complete callbacks, which + // will dequeue but only if they were gotoEnd. + if ( dequeue || !gotoEnd ) { + jQuery.dequeue( this, type ); + } + } ); + }, + finish: function( type ) { + if ( type !== false ) { + type = type || "fx"; + } + return this.each( function() { + var index, + data = dataPriv.get( this ), + queue = data[ type + "queue" ], + hooks = data[ type + "queueHooks" ], + timers = jQuery.timers, + length = queue ? queue.length : 0; + + // Enable finishing flag on private data + data.finish = true; + + // Empty the queue first + jQuery.queue( this, type, [] ); + + if ( hooks && hooks.stop ) { + hooks.stop.call( this, true ); + } + + // Look for any active animations, and finish them + for ( index = timers.length; index--; ) { + if ( timers[ index ].elem === this && timers[ index ].queue === type ) { + timers[ index ].anim.stop( true ); + timers.splice( index, 1 ); + } + } + + // Look for any animations in the old queue and finish them + for ( index = 0; index < length; index++ ) { + if ( queue[ index ] && queue[ index ].finish ) { + queue[ index ].finish.call( this ); + } + } + + // Turn off finishing flag + delete data.finish; + } ); + } +} ); + +jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) { + var cssFn = jQuery.fn[ name ]; + jQuery.fn[ name ] = function( speed, easing, callback ) { + return speed == null || typeof speed === "boolean" ? + cssFn.apply( this, arguments ) : + this.animate( genFx( name, true ), speed, easing, callback ); + }; +} ); + +// Generate shortcuts for custom animations +jQuery.each( { + slideDown: genFx( "show" ), + slideUp: genFx( "hide" ), + slideToggle: genFx( "toggle" ), + fadeIn: { opacity: "show" }, + fadeOut: { opacity: "hide" }, + fadeToggle: { opacity: "toggle" } +}, function( name, props ) { + jQuery.fn[ name ] = function( speed, easing, callback ) { + return this.animate( props, speed, easing, callback ); + }; +} ); + +jQuery.timers = []; +jQuery.fx.tick = function() { + var timer, + i = 0, + timers = jQuery.timers; + + fxNow = Date.now(); + + for ( ; i < timers.length; i++ ) { + timer = timers[ i ]; + + // Run the timer and safely remove it when done (allowing for external removal) + if ( !timer() && timers[ i ] === timer ) { + timers.splice( i--, 1 ); + } + } + + if ( !timers.length ) { + jQuery.fx.stop(); + } + fxNow = undefined; +}; + +jQuery.fx.timer = function( timer ) { + jQuery.timers.push( timer ); + jQuery.fx.start(); +}; + +jQuery.fx.interval = 13; +jQuery.fx.start = function() { + if ( inProgress ) { + return; + } + + inProgress = true; + schedule(); +}; + +jQuery.fx.stop = function() { + inProgress = null; +}; + +jQuery.fx.speeds = { + slow: 600, + fast: 200, + + // Default speed + _default: 400 +}; + + +// Based off of the plugin by Clint Helfers, with permission. +// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/ +jQuery.fn.delay = function( time, type ) { + time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time; + type = type || "fx"; + + return this.queue( type, function( next, hooks ) { + var timeout = window.setTimeout( next, time ); + hooks.stop = function() { + window.clearTimeout( timeout ); + }; + } ); +}; + + +( function() { + var input = document.createElement( "input" ), + select = document.createElement( "select" ), + opt = select.appendChild( document.createElement( "option" ) ); + + input.type = "checkbox"; + + // Support: Android <=4.3 only + // Default value for a checkbox should be "on" + support.checkOn = input.value !== ""; + + // Support: IE <=11 only + // Must access selectedIndex to make default options select + support.optSelected = opt.selected; + + // Support: IE <=11 only + // An input loses its value after becoming a radio + input = document.createElement( "input" ); + input.value = "t"; + input.type = "radio"; + support.radioValue = input.value === "t"; +} )(); + + +var boolHook, + attrHandle = jQuery.expr.attrHandle; + +jQuery.fn.extend( { + attr: function( name, value ) { + return access( this, jQuery.attr, name, value, arguments.length > 1 ); + }, + + removeAttr: function( name ) { + return this.each( function() { + jQuery.removeAttr( this, name ); + } ); + } +} ); + +jQuery.extend( { + attr: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set attributes on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + // Fallback to prop when attributes are not supported + if ( typeof elem.getAttribute === "undefined" ) { + return jQuery.prop( elem, name, value ); + } + + // Attribute hooks are determined by the lowercase version + // Grab necessary hook if one is defined + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + hooks = jQuery.attrHooks[ name.toLowerCase() ] || + ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined ); + } + + if ( value !== undefined ) { + if ( value === null ) { + jQuery.removeAttr( elem, name ); + return; + } + + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + elem.setAttribute( name, value + "" ); + return value; + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + ret = jQuery.find.attr( elem, name ); + + // Non-existent attributes return null, we normalize to undefined + return ret == null ? undefined : ret; + }, + + attrHooks: { + type: { + set: function( elem, value ) { + if ( !support.radioValue && value === "radio" && + nodeName( elem, "input" ) ) { + var val = elem.value; + elem.setAttribute( "type", value ); + if ( val ) { + elem.value = val; + } + return value; + } + } + } + }, + + removeAttr: function( elem, value ) { + var name, + i = 0, + + // Attribute names can contain non-HTML whitespace characters + // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2 + attrNames = value && value.match( rnothtmlwhite ); + + if ( attrNames && elem.nodeType === 1 ) { + while ( ( name = attrNames[ i++ ] ) ) { + elem.removeAttribute( name ); + } + } + } +} ); + +// Hooks for boolean attributes +boolHook = { + set: function( elem, value, name ) { + if ( value === false ) { + + // Remove boolean attributes when set to false + jQuery.removeAttr( elem, name ); + } else { + elem.setAttribute( name, name ); + } + return name; + } +}; + +jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) { + var getter = attrHandle[ name ] || jQuery.find.attr; + + attrHandle[ name ] = function( elem, name, isXML ) { + var ret, handle, + lowercaseName = name.toLowerCase(); + + if ( !isXML ) { + + // Avoid an infinite loop by temporarily removing this function from the getter + handle = attrHandle[ lowercaseName ]; + attrHandle[ lowercaseName ] = ret; + ret = getter( elem, name, isXML ) != null ? + lowercaseName : + null; + attrHandle[ lowercaseName ] = handle; + } + return ret; + }; +} ); + + + + +var rfocusable = /^(?:input|select|textarea|button)$/i, + rclickable = /^(?:a|area)$/i; + +jQuery.fn.extend( { + prop: function( name, value ) { + return access( this, jQuery.prop, name, value, arguments.length > 1 ); + }, + + removeProp: function( name ) { + return this.each( function() { + delete this[ jQuery.propFix[ name ] || name ]; + } ); + } +} ); + +jQuery.extend( { + prop: function( elem, name, value ) { + var ret, hooks, + nType = elem.nodeType; + + // Don't get/set properties on text, comment and attribute nodes + if ( nType === 3 || nType === 8 || nType === 2 ) { + return; + } + + if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) { + + // Fix name and attach hooks + name = jQuery.propFix[ name ] || name; + hooks = jQuery.propHooks[ name ]; + } + + if ( value !== undefined ) { + if ( hooks && "set" in hooks && + ( ret = hooks.set( elem, value, name ) ) !== undefined ) { + return ret; + } + + return ( elem[ name ] = value ); + } + + if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) { + return ret; + } + + return elem[ name ]; + }, + + propHooks: { + tabIndex: { + get: function( elem ) { + + // Support: IE <=9 - 11 only + // elem.tabIndex doesn't always return the + // correct value when it hasn't been explicitly set + // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/ + // Use proper attribute retrieval(#12072) + var tabindex = jQuery.find.attr( elem, "tabindex" ); + + if ( tabindex ) { + return parseInt( tabindex, 10 ); + } + + if ( + rfocusable.test( elem.nodeName ) || + rclickable.test( elem.nodeName ) && + elem.href + ) { + return 0; + } + + return -1; + } + } + }, + + propFix: { + "for": "htmlFor", + "class": "className" + } +} ); + +// Support: IE <=11 only +// Accessing the selectedIndex property +// forces the browser to respect setting selected +// on the option +// The getter ensures a default option is selected +// when in an optgroup +// eslint rule "no-unused-expressions" is disabled for this code +// since it considers such accessions noop +if ( !support.optSelected ) { + jQuery.propHooks.selected = { + get: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent && parent.parentNode ) { + parent.parentNode.selectedIndex; + } + return null; + }, + set: function( elem ) { + + /* eslint no-unused-expressions: "off" */ + + var parent = elem.parentNode; + if ( parent ) { + parent.selectedIndex; + + if ( parent.parentNode ) { + parent.parentNode.selectedIndex; + } + } + } + }; +} + +jQuery.each( [ + "tabIndex", + "readOnly", + "maxLength", + "cellSpacing", + "cellPadding", + "rowSpan", + "colSpan", + "useMap", + "frameBorder", + "contentEditable" +], function() { + jQuery.propFix[ this.toLowerCase() ] = this; +} ); + + + + + // Strip and collapse whitespace according to HTML spec + // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace + function stripAndCollapse( value ) { + var tokens = value.match( rnothtmlwhite ) || []; + return tokens.join( " " ); + } + + +function getClass( elem ) { + return elem.getAttribute && elem.getAttribute( "class" ) || ""; +} + +function classesToArray( value ) { + if ( Array.isArray( value ) ) { + return value; + } + if ( typeof value === "string" ) { + return value.match( rnothtmlwhite ) || []; + } + return []; +} + +jQuery.fn.extend( { + addClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).addClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + if ( cur.indexOf( " " + clazz + " " ) < 0 ) { + cur += clazz + " "; + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + removeClass: function( value ) { + var classes, elem, cur, curValue, clazz, j, finalValue, + i = 0; + + if ( isFunction( value ) ) { + return this.each( function( j ) { + jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) ); + } ); + } + + if ( !arguments.length ) { + return this.attr( "class", "" ); + } + + classes = classesToArray( value ); + + if ( classes.length ) { + while ( ( elem = this[ i++ ] ) ) { + curValue = getClass( elem ); + + // This expression is here for better compressibility (see addClass) + cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " ); + + if ( cur ) { + j = 0; + while ( ( clazz = classes[ j++ ] ) ) { + + // Remove *all* instances + while ( cur.indexOf( " " + clazz + " " ) > -1 ) { + cur = cur.replace( " " + clazz + " ", " " ); + } + } + + // Only assign if different to avoid unneeded rendering. + finalValue = stripAndCollapse( cur ); + if ( curValue !== finalValue ) { + elem.setAttribute( "class", finalValue ); + } + } + } + } + + return this; + }, + + toggleClass: function( value, stateVal ) { + var type = typeof value, + isValidValue = type === "string" || Array.isArray( value ); + + if ( typeof stateVal === "boolean" && isValidValue ) { + return stateVal ? this.addClass( value ) : this.removeClass( value ); + } + + if ( isFunction( value ) ) { + return this.each( function( i ) { + jQuery( this ).toggleClass( + value.call( this, i, getClass( this ), stateVal ), + stateVal + ); + } ); + } + + return this.each( function() { + var className, i, self, classNames; + + if ( isValidValue ) { + + // Toggle individual class names + i = 0; + self = jQuery( this ); + classNames = classesToArray( value ); + + while ( ( className = classNames[ i++ ] ) ) { + + // Check each className given, space separated list + if ( self.hasClass( className ) ) { + self.removeClass( className ); + } else { + self.addClass( className ); + } + } + + // Toggle whole class name + } else if ( value === undefined || type === "boolean" ) { + className = getClass( this ); + if ( className ) { + + // Store className if set + dataPriv.set( this, "__className__", className ); + } + + // If the element has a class name or if we're passed `false`, + // then remove the whole classname (if there was one, the above saved it). + // Otherwise bring back whatever was previously saved (if anything), + // falling back to the empty string if nothing was stored. + if ( this.setAttribute ) { + this.setAttribute( "class", + className || value === false ? + "" : + dataPriv.get( this, "__className__" ) || "" + ); + } + } + } ); + }, + + hasClass: function( selector ) { + var className, elem, + i = 0; + + className = " " + selector + " "; + while ( ( elem = this[ i++ ] ) ) { + if ( elem.nodeType === 1 && + ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) { + return true; + } + } + + return false; + } +} ); + + + + +var rreturn = /\r/g; + +jQuery.fn.extend( { + val: function( value ) { + var hooks, ret, valueIsFunction, + elem = this[ 0 ]; + + if ( !arguments.length ) { + if ( elem ) { + hooks = jQuery.valHooks[ elem.type ] || + jQuery.valHooks[ elem.nodeName.toLowerCase() ]; + + if ( hooks && + "get" in hooks && + ( ret = hooks.get( elem, "value" ) ) !== undefined + ) { + return ret; + } + + ret = elem.value; + + // Handle most common string cases + if ( typeof ret === "string" ) { + return ret.replace( rreturn, "" ); + } + + // Handle cases where value is null/undef or number + return ret == null ? "" : ret; + } + + return; + } + + valueIsFunction = isFunction( value ); + + return this.each( function( i ) { + var val; + + if ( this.nodeType !== 1 ) { + return; + } + + if ( valueIsFunction ) { + val = value.call( this, i, jQuery( this ).val() ); + } else { + val = value; + } + + // Treat null/undefined as ""; convert numbers to string + if ( val == null ) { + val = ""; + + } else if ( typeof val === "number" ) { + val += ""; + + } else if ( Array.isArray( val ) ) { + val = jQuery.map( val, function( value ) { + return value == null ? "" : value + ""; + } ); + } + + hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ]; + + // If set returns undefined, fall back to normal setting + if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) { + this.value = val; + } + } ); + } +} ); + +jQuery.extend( { + valHooks: { + option: { + get: function( elem ) { + + var val = jQuery.find.attr( elem, "value" ); + return val != null ? + val : + + // Support: IE <=10 - 11 only + // option.text throws exceptions (#14686, #14858) + // Strip and collapse whitespace + // https://html.spec.whatwg.org/#strip-and-collapse-whitespace + stripAndCollapse( jQuery.text( elem ) ); + } + }, + select: { + get: function( elem ) { + var value, option, i, + options = elem.options, + index = elem.selectedIndex, + one = elem.type === "select-one", + values = one ? null : [], + max = one ? index + 1 : options.length; + + if ( index < 0 ) { + i = max; + + } else { + i = one ? index : 0; + } + + // Loop through all the selected options + for ( ; i < max; i++ ) { + option = options[ i ]; + + // Support: IE <=9 only + // IE8-9 doesn't update selected after form reset (#2551) + if ( ( option.selected || i === index ) && + + // Don't return options that are disabled or in a disabled optgroup + !option.disabled && + ( !option.parentNode.disabled || + !nodeName( option.parentNode, "optgroup" ) ) ) { + + // Get the specific value for the option + value = jQuery( option ).val(); + + // We don't need an array for one selects + if ( one ) { + return value; + } + + // Multi-Selects return an array + values.push( value ); + } + } + + return values; + }, + + set: function( elem, value ) { + var optionSet, option, + options = elem.options, + values = jQuery.makeArray( value ), + i = options.length; + + while ( i-- ) { + option = options[ i ]; + + /* eslint-disable no-cond-assign */ + + if ( option.selected = + jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1 + ) { + optionSet = true; + } + + /* eslint-enable no-cond-assign */ + } + + // Force browsers to behave consistently when non-matching value is set + if ( !optionSet ) { + elem.selectedIndex = -1; + } + return values; + } + } + } +} ); + +// Radios and checkboxes getter/setter +jQuery.each( [ "radio", "checkbox" ], function() { + jQuery.valHooks[ this ] = { + set: function( elem, value ) { + if ( Array.isArray( value ) ) { + return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 ); + } + } + }; + if ( !support.checkOn ) { + jQuery.valHooks[ this ].get = function( elem ) { + return elem.getAttribute( "value" ) === null ? "on" : elem.value; + }; + } +} ); + + + + +// Return jQuery for attributes-only inclusion + + +support.focusin = "onfocusin" in window; + + +var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/, + stopPropagationCallback = function( e ) { + e.stopPropagation(); + }; + +jQuery.extend( jQuery.event, { + + trigger: function( event, data, elem, onlyHandlers ) { + + var i, cur, tmp, bubbleType, ontype, handle, special, lastElement, + eventPath = [ elem || document ], + type = hasOwn.call( event, "type" ) ? event.type : event, + namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : []; + + cur = lastElement = tmp = elem = elem || document; + + // Don't do events on text and comment nodes + if ( elem.nodeType === 3 || elem.nodeType === 8 ) { + return; + } + + // focus/blur morphs to focusin/out; ensure we're not firing them right now + if ( rfocusMorph.test( type + jQuery.event.triggered ) ) { + return; + } + + if ( type.indexOf( "." ) > -1 ) { + + // Namespaced trigger; create a regexp to match event type in handle() + namespaces = type.split( "." ); + type = namespaces.shift(); + namespaces.sort(); + } + ontype = type.indexOf( ":" ) < 0 && "on" + type; + + // Caller can pass in a jQuery.Event object, Object, or just an event type string + event = event[ jQuery.expando ] ? + event : + new jQuery.Event( type, typeof event === "object" && event ); + + // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true) + event.isTrigger = onlyHandlers ? 2 : 3; + event.namespace = namespaces.join( "." ); + event.rnamespace = event.namespace ? + new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) : + null; + + // Clean up the event in case it is being reused + event.result = undefined; + if ( !event.target ) { + event.target = elem; + } + + // Clone any incoming data and prepend the event, creating the handler arg list + data = data == null ? + [ event ] : + jQuery.makeArray( data, [ event ] ); + + // Allow special events to draw outside the lines + special = jQuery.event.special[ type ] || {}; + if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) { + return; + } + + // Determine event propagation path in advance, per W3C events spec (#9951) + // Bubble up to document, then to window; watch for a global ownerDocument var (#9724) + if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) { + + bubbleType = special.delegateType || type; + if ( !rfocusMorph.test( bubbleType + type ) ) { + cur = cur.parentNode; + } + for ( ; cur; cur = cur.parentNode ) { + eventPath.push( cur ); + tmp = cur; + } + + // Only add window if we got to document (e.g., not plain obj or detached DOM) + if ( tmp === ( elem.ownerDocument || document ) ) { + eventPath.push( tmp.defaultView || tmp.parentWindow || window ); + } + } + + // Fire handlers on the event path + i = 0; + while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) { + lastElement = cur; + event.type = i > 1 ? + bubbleType : + special.bindType || type; + + // jQuery handler + handle = ( dataPriv.get( cur, "events" ) || Object.create( null ) )[ event.type ] && + dataPriv.get( cur, "handle" ); + if ( handle ) { + handle.apply( cur, data ); + } + + // Native handler + handle = ontype && cur[ ontype ]; + if ( handle && handle.apply && acceptData( cur ) ) { + event.result = handle.apply( cur, data ); + if ( event.result === false ) { + event.preventDefault(); + } + } + } + event.type = type; + + // If nobody prevented the default action, do it now + if ( !onlyHandlers && !event.isDefaultPrevented() ) { + + if ( ( !special._default || + special._default.apply( eventPath.pop(), data ) === false ) && + acceptData( elem ) ) { + + // Call a native DOM method on the target with the same name as the event. + // Don't do default actions on window, that's where global variables be (#6170) + if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) { + + // Don't re-trigger an onFOO event when we call its FOO() method + tmp = elem[ ontype ]; + + if ( tmp ) { + elem[ ontype ] = null; + } + + // Prevent re-triggering of the same event, since we already bubbled it above + jQuery.event.triggered = type; + + if ( event.isPropagationStopped() ) { + lastElement.addEventListener( type, stopPropagationCallback ); + } + + elem[ type ](); + + if ( event.isPropagationStopped() ) { + lastElement.removeEventListener( type, stopPropagationCallback ); + } + + jQuery.event.triggered = undefined; + + if ( tmp ) { + elem[ ontype ] = tmp; + } + } + } + } + + return event.result; + }, + + // Piggyback on a donor event to simulate a different one + // Used only for `focus(in | out)` events + simulate: function( type, elem, event ) { + var e = jQuery.extend( + new jQuery.Event(), + event, + { + type: type, + isSimulated: true + } + ); + + jQuery.event.trigger( e, null, elem ); + } + +} ); + +jQuery.fn.extend( { + + trigger: function( type, data ) { + return this.each( function() { + jQuery.event.trigger( type, data, this ); + } ); + }, + triggerHandler: function( type, data ) { + var elem = this[ 0 ]; + if ( elem ) { + return jQuery.event.trigger( type, data, elem, true ); + } + } +} ); + + +// Support: Firefox <=44 +// Firefox doesn't have focus(in | out) events +// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787 +// +// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1 +// focus(in | out) events fire after focus & blur events, +// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order +// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857 +if ( !support.focusin ) { + jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) { + + // Attach a single capturing handler on the document while someone wants focusin/focusout + var handler = function( event ) { + jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) ); + }; + + jQuery.event.special[ fix ] = { + setup: function() { + + // Handle: regular nodes (via `this.ownerDocument`), window + // (via `this.document`) & document (via `this`). + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ); + + if ( !attaches ) { + doc.addEventListener( orig, handler, true ); + } + dataPriv.access( doc, fix, ( attaches || 0 ) + 1 ); + }, + teardown: function() { + var doc = this.ownerDocument || this.document || this, + attaches = dataPriv.access( doc, fix ) - 1; + + if ( !attaches ) { + doc.removeEventListener( orig, handler, true ); + dataPriv.remove( doc, fix ); + + } else { + dataPriv.access( doc, fix, attaches ); + } + } + }; + } ); +} +var location = window.location; + +var nonce = { guid: Date.now() }; + +var rquery = ( /\?/ ); + + + +// Cross-browser xml parsing +jQuery.parseXML = function( data ) { + var xml, parserErrorElem; + if ( !data || typeof data !== "string" ) { + return null; + } + + // Support: IE 9 - 11 only + // IE throws on parseFromString with invalid input. + try { + xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" ); + } catch ( e ) {} + + parserErrorElem = xml && xml.getElementsByTagName( "parsererror" )[ 0 ]; + if ( !xml || parserErrorElem ) { + jQuery.error( "Invalid XML: " + ( + parserErrorElem ? + jQuery.map( parserErrorElem.childNodes, function( el ) { + return el.textContent; + } ).join( "\n" ) : + data + ) ); + } + return xml; +}; + + +var + rbracket = /\[\]$/, + rCRLF = /\r?\n/g, + rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i, + rsubmittable = /^(?:input|select|textarea|keygen)/i; + +function buildParams( prefix, obj, traditional, add ) { + var name; + + if ( Array.isArray( obj ) ) { + + // Serialize array item. + jQuery.each( obj, function( i, v ) { + if ( traditional || rbracket.test( prefix ) ) { + + // Treat each array item as a scalar. + add( prefix, v ); + + } else { + + // Item is non-scalar (array or object), encode its numeric index. + buildParams( + prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]", + v, + traditional, + add + ); + } + } ); + + } else if ( !traditional && toType( obj ) === "object" ) { + + // Serialize object item. + for ( name in obj ) { + buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add ); + } + + } else { + + // Serialize scalar item. + add( prefix, obj ); + } +} + +// Serialize an array of form elements or a set of +// key/values into a query string +jQuery.param = function( a, traditional ) { + var prefix, + s = [], + add = function( key, valueOrFunction ) { + + // If value is a function, invoke it and use its return value + var value = isFunction( valueOrFunction ) ? + valueOrFunction() : + valueOrFunction; + + s[ s.length ] = encodeURIComponent( key ) + "=" + + encodeURIComponent( value == null ? "" : value ); + }; + + if ( a == null ) { + return ""; + } + + // If an array was passed in, assume that it is an array of form elements. + if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) { + + // Serialize the form elements + jQuery.each( a, function() { + add( this.name, this.value ); + } ); + + } else { + + // If traditional, encode the "old" way (the way 1.3.2 or older + // did it), otherwise encode params recursively. + for ( prefix in a ) { + buildParams( prefix, a[ prefix ], traditional, add ); + } + } + + // Return the resulting serialization + return s.join( "&" ); +}; + +jQuery.fn.extend( { + serialize: function() { + return jQuery.param( this.serializeArray() ); + }, + serializeArray: function() { + return this.map( function() { + + // Can add propHook for "elements" to filter or add form elements + var elements = jQuery.prop( this, "elements" ); + return elements ? jQuery.makeArray( elements ) : this; + } ).filter( function() { + var type = this.type; + + // Use .is( ":disabled" ) so that fieldset[disabled] works + return this.name && !jQuery( this ).is( ":disabled" ) && + rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) && + ( this.checked || !rcheckableType.test( type ) ); + } ).map( function( _i, elem ) { + var val = jQuery( this ).val(); + + if ( val == null ) { + return null; + } + + if ( Array.isArray( val ) ) { + return jQuery.map( val, function( val ) { + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ); + } + + return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) }; + } ).get(); + } +} ); + + +var + r20 = /%20/g, + rhash = /#.*$/, + rantiCache = /([?&])_=[^&]*/, + rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg, + + // #7653, #8125, #8152: local protocol detection + rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/, + rnoContent = /^(?:GET|HEAD)$/, + rprotocol = /^\/\//, + + /* Prefilters + * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example) + * 2) These are called: + * - BEFORE asking for a transport + * - AFTER param serialization (s.data is a string if s.processData is true) + * 3) key is the dataType + * 4) the catchall symbol "*" can be used + * 5) execution will start with transport dataType and THEN continue down to "*" if needed + */ + prefilters = {}, + + /* Transports bindings + * 1) key is the dataType + * 2) the catchall symbol "*" can be used + * 3) selection will start with transport dataType and THEN go to "*" if needed + */ + transports = {}, + + // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression + allTypes = "*/".concat( "*" ), + + // Anchor tag for parsing the document origin + originAnchor = document.createElement( "a" ); + +originAnchor.href = location.href; + +// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport +function addToPrefiltersOrTransports( structure ) { + + // dataTypeExpression is optional and defaults to "*" + return function( dataTypeExpression, func ) { + + if ( typeof dataTypeExpression !== "string" ) { + func = dataTypeExpression; + dataTypeExpression = "*"; + } + + var dataType, + i = 0, + dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || []; + + if ( isFunction( func ) ) { + + // For each dataType in the dataTypeExpression + while ( ( dataType = dataTypes[ i++ ] ) ) { + + // Prepend if requested + if ( dataType[ 0 ] === "+" ) { + dataType = dataType.slice( 1 ) || "*"; + ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func ); + + // Otherwise append + } else { + ( structure[ dataType ] = structure[ dataType ] || [] ).push( func ); + } + } + } + }; +} + +// Base inspection function for prefilters and transports +function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) { + + var inspected = {}, + seekingTransport = ( structure === transports ); + + function inspect( dataType ) { + var selected; + inspected[ dataType ] = true; + jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) { + var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR ); + if ( typeof dataTypeOrTransport === "string" && + !seekingTransport && !inspected[ dataTypeOrTransport ] ) { + + options.dataTypes.unshift( dataTypeOrTransport ); + inspect( dataTypeOrTransport ); + return false; + } else if ( seekingTransport ) { + return !( selected = dataTypeOrTransport ); + } + } ); + return selected; + } + + return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" ); +} + +// A special extend for ajax options +// that takes "flat" options (not to be deep extended) +// Fixes #9887 +function ajaxExtend( target, src ) { + var key, deep, + flatOptions = jQuery.ajaxSettings.flatOptions || {}; + + for ( key in src ) { + if ( src[ key ] !== undefined ) { + ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ]; + } + } + if ( deep ) { + jQuery.extend( true, target, deep ); + } + + return target; +} + +/* Handles responses to an ajax request: + * - finds the right dataType (mediates between content-type and expected dataType) + * - returns the corresponding response + */ +function ajaxHandleResponses( s, jqXHR, responses ) { + + var ct, type, finalDataType, firstDataType, + contents = s.contents, + dataTypes = s.dataTypes; + + // Remove auto dataType and get content-type in the process + while ( dataTypes[ 0 ] === "*" ) { + dataTypes.shift(); + if ( ct === undefined ) { + ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" ); + } + } + + // Check if we're dealing with a known content-type + if ( ct ) { + for ( type in contents ) { + if ( contents[ type ] && contents[ type ].test( ct ) ) { + dataTypes.unshift( type ); + break; + } + } + } + + // Check to see if we have a response for the expected dataType + if ( dataTypes[ 0 ] in responses ) { + finalDataType = dataTypes[ 0 ]; + } else { + + // Try convertible dataTypes + for ( type in responses ) { + if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) { + finalDataType = type; + break; + } + if ( !firstDataType ) { + firstDataType = type; + } + } + + // Or just use first one + finalDataType = finalDataType || firstDataType; + } + + // If we found a dataType + // We add the dataType to the list if needed + // and return the corresponding response + if ( finalDataType ) { + if ( finalDataType !== dataTypes[ 0 ] ) { + dataTypes.unshift( finalDataType ); + } + return responses[ finalDataType ]; + } +} + +/* Chain conversions given the request and the original response + * Also sets the responseXXX fields on the jqXHR instance + */ +function ajaxConvert( s, response, jqXHR, isSuccess ) { + var conv2, current, conv, tmp, prev, + converters = {}, + + // Work with a copy of dataTypes in case we need to modify it for conversion + dataTypes = s.dataTypes.slice(); + + // Create converters map with lowercased keys + if ( dataTypes[ 1 ] ) { + for ( conv in s.converters ) { + converters[ conv.toLowerCase() ] = s.converters[ conv ]; + } + } + + current = dataTypes.shift(); + + // Convert to each sequential dataType + while ( current ) { + + if ( s.responseFields[ current ] ) { + jqXHR[ s.responseFields[ current ] ] = response; + } + + // Apply the dataFilter if provided + if ( !prev && isSuccess && s.dataFilter ) { + response = s.dataFilter( response, s.dataType ); + } + + prev = current; + current = dataTypes.shift(); + + if ( current ) { + + // There's only work to do if current dataType is non-auto + if ( current === "*" ) { + + current = prev; + + // Convert response if prev dataType is non-auto and differs from current + } else if ( prev !== "*" && prev !== current ) { + + // Seek a direct converter + conv = converters[ prev + " " + current ] || converters[ "* " + current ]; + + // If none found, seek a pair + if ( !conv ) { + for ( conv2 in converters ) { + + // If conv2 outputs current + tmp = conv2.split( " " ); + if ( tmp[ 1 ] === current ) { + + // If prev can be converted to accepted input + conv = converters[ prev + " " + tmp[ 0 ] ] || + converters[ "* " + tmp[ 0 ] ]; + if ( conv ) { + + // Condense equivalence converters + if ( conv === true ) { + conv = converters[ conv2 ]; + + // Otherwise, insert the intermediate dataType + } else if ( converters[ conv2 ] !== true ) { + current = tmp[ 0 ]; + dataTypes.unshift( tmp[ 1 ] ); + } + break; + } + } + } + } + + // Apply converter (if not an equivalence) + if ( conv !== true ) { + + // Unless errors are allowed to bubble, catch and return them + if ( conv && s.throws ) { + response = conv( response ); + } else { + try { + response = conv( response ); + } catch ( e ) { + return { + state: "parsererror", + error: conv ? e : "No conversion from " + prev + " to " + current + }; + } + } + } + } + } + } + + return { state: "success", data: response }; +} + +jQuery.extend( { + + // Counter for holding the number of active queries + active: 0, + + // Last-Modified header cache for next request + lastModified: {}, + etag: {}, + + ajaxSettings: { + url: location.href, + type: "GET", + isLocal: rlocalProtocol.test( location.protocol ), + global: true, + processData: true, + async: true, + contentType: "application/x-www-form-urlencoded; charset=UTF-8", + + /* + timeout: 0, + data: null, + dataType: null, + username: null, + password: null, + cache: null, + throws: false, + traditional: false, + headers: {}, + */ + + accepts: { + "*": allTypes, + text: "text/plain", + html: "text/html", + xml: "application/xml, text/xml", + json: "application/json, text/javascript" + }, + + contents: { + xml: /\bxml\b/, + html: /\bhtml/, + json: /\bjson\b/ + }, + + responseFields: { + xml: "responseXML", + text: "responseText", + json: "responseJSON" + }, + + // Data converters + // Keys separate source (or catchall "*") and destination types with a single space + converters: { + + // Convert anything to text + "* text": String, + + // Text to html (true = no transformation) + "text html": true, + + // Evaluate text as a json expression + "text json": JSON.parse, + + // Parse text as xml + "text xml": jQuery.parseXML + }, + + // For options that shouldn't be deep extended: + // you can add your own custom options here if + // and when you create one that shouldn't be + // deep extended (see ajaxExtend) + flatOptions: { + url: true, + context: true + } + }, + + // Creates a full fledged settings object into target + // with both ajaxSettings and settings fields. + // If target is omitted, writes into ajaxSettings. + ajaxSetup: function( target, settings ) { + return settings ? + + // Building a settings object + ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) : + + // Extending ajaxSettings + ajaxExtend( jQuery.ajaxSettings, target ); + }, + + ajaxPrefilter: addToPrefiltersOrTransports( prefilters ), + ajaxTransport: addToPrefiltersOrTransports( transports ), + + // Main method + ajax: function( url, options ) { + + // If url is an object, simulate pre-1.5 signature + if ( typeof url === "object" ) { + options = url; + url = undefined; + } + + // Force options to be an object + options = options || {}; + + var transport, + + // URL without anti-cache param + cacheURL, + + // Response headers + responseHeadersString, + responseHeaders, + + // timeout handle + timeoutTimer, + + // Url cleanup var + urlAnchor, + + // Request state (becomes false upon send and true upon completion) + completed, + + // To know if global events are to be dispatched + fireGlobals, + + // Loop variable + i, + + // uncached part of the url + uncached, + + // Create the final options object + s = jQuery.ajaxSetup( {}, options ), + + // Callbacks context + callbackContext = s.context || s, + + // Context for global events is callbackContext if it is a DOM node or jQuery collection + globalEventContext = s.context && + ( callbackContext.nodeType || callbackContext.jquery ) ? + jQuery( callbackContext ) : + jQuery.event, + + // Deferreds + deferred = jQuery.Deferred(), + completeDeferred = jQuery.Callbacks( "once memory" ), + + // Status-dependent callbacks + statusCode = s.statusCode || {}, + + // Headers (they are sent all at once) + requestHeaders = {}, + requestHeadersNames = {}, + + // Default abort message + strAbort = "canceled", + + // Fake xhr + jqXHR = { + readyState: 0, + + // Builds headers hashtable if needed + getResponseHeader: function( key ) { + var match; + if ( completed ) { + if ( !responseHeaders ) { + responseHeaders = {}; + while ( ( match = rheaders.exec( responseHeadersString ) ) ) { + responseHeaders[ match[ 1 ].toLowerCase() + " " ] = + ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] ) + .concat( match[ 2 ] ); + } + } + match = responseHeaders[ key.toLowerCase() + " " ]; + } + return match == null ? null : match.join( ", " ); + }, + + // Raw string + getAllResponseHeaders: function() { + return completed ? responseHeadersString : null; + }, + + // Caches the header + setRequestHeader: function( name, value ) { + if ( completed == null ) { + name = requestHeadersNames[ name.toLowerCase() ] = + requestHeadersNames[ name.toLowerCase() ] || name; + requestHeaders[ name ] = value; + } + return this; + }, + + // Overrides response content-type header + overrideMimeType: function( type ) { + if ( completed == null ) { + s.mimeType = type; + } + return this; + }, + + // Status-dependent callbacks + statusCode: function( map ) { + var code; + if ( map ) { + if ( completed ) { + + // Execute the appropriate callbacks + jqXHR.always( map[ jqXHR.status ] ); + } else { + + // Lazy-add the new callbacks in a way that preserves old ones + for ( code in map ) { + statusCode[ code ] = [ statusCode[ code ], map[ code ] ]; + } + } + } + return this; + }, + + // Cancel the request + abort: function( statusText ) { + var finalText = statusText || strAbort; + if ( transport ) { + transport.abort( finalText ); + } + done( 0, finalText ); + return this; + } + }; + + // Attach deferreds + deferred.promise( jqXHR ); + + // Add protocol if not provided (prefilters might expect it) + // Handle falsy url in the settings object (#10093: consistency with old signature) + // We also use the url parameter if available + s.url = ( ( url || s.url || location.href ) + "" ) + .replace( rprotocol, location.protocol + "//" ); + + // Alias method option to type as per ticket #12004 + s.type = options.method || options.type || s.method || s.type; + + // Extract dataTypes list + s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ]; + + // A cross-domain request is in order when the origin doesn't match the current origin. + if ( s.crossDomain == null ) { + urlAnchor = document.createElement( "a" ); + + // Support: IE <=8 - 11, Edge 12 - 15 + // IE throws exception on accessing the href property if url is malformed, + // e.g. http://example.com:80x/ + try { + urlAnchor.href = s.url; + + // Support: IE <=8 - 11 only + // Anchor's host property isn't correctly set when s.url is relative + urlAnchor.href = urlAnchor.href; + s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !== + urlAnchor.protocol + "//" + urlAnchor.host; + } catch ( e ) { + + // If there is an error parsing the URL, assume it is crossDomain, + // it can be rejected by the transport if it is invalid + s.crossDomain = true; + } + } + + // Convert data if not already a string + if ( s.data && s.processData && typeof s.data !== "string" ) { + s.data = jQuery.param( s.data, s.traditional ); + } + + // Apply prefilters + inspectPrefiltersOrTransports( prefilters, s, options, jqXHR ); + + // If request was aborted inside a prefilter, stop there + if ( completed ) { + return jqXHR; + } + + // We can fire global events as of now if asked to + // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118) + fireGlobals = jQuery.event && s.global; + + // Watch for a new set of requests + if ( fireGlobals && jQuery.active++ === 0 ) { + jQuery.event.trigger( "ajaxStart" ); + } + + // Uppercase the type + s.type = s.type.toUpperCase(); + + // Determine if request has content + s.hasContent = !rnoContent.test( s.type ); + + // Save the URL in case we're toying with the If-Modified-Since + // and/or If-None-Match header later on + // Remove hash to simplify url manipulation + cacheURL = s.url.replace( rhash, "" ); + + // More options handling for requests with no content + if ( !s.hasContent ) { + + // Remember the hash so we can put it back + uncached = s.url.slice( cacheURL.length ); + + // If data is available and should be processed, append data to url + if ( s.data && ( s.processData || typeof s.data === "string" ) ) { + cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data; + + // #9682: remove data so that it's not used in an eventual retry + delete s.data; + } + + // Add or update anti-cache param if needed + if ( s.cache === false ) { + cacheURL = cacheURL.replace( rantiCache, "$1" ); + uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) + + uncached; + } + + // Put hash and anti-cache on the URL that will be requested (gh-1732) + s.url = cacheURL + uncached; + + // Change '%20' to '+' if this is encoded form body content (gh-2658) + } else if ( s.data && s.processData && + ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) { + s.data = s.data.replace( r20, "+" ); + } + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + if ( jQuery.lastModified[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] ); + } + if ( jQuery.etag[ cacheURL ] ) { + jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] ); + } + } + + // Set the correct header, if data is being sent + if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) { + jqXHR.setRequestHeader( "Content-Type", s.contentType ); + } + + // Set the Accepts header for the server, depending on the dataType + jqXHR.setRequestHeader( + "Accept", + s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ? + s.accepts[ s.dataTypes[ 0 ] ] + + ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) : + s.accepts[ "*" ] + ); + + // Check for headers option + for ( i in s.headers ) { + jqXHR.setRequestHeader( i, s.headers[ i ] ); + } + + // Allow custom headers/mimetypes and early abort + if ( s.beforeSend && + ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) { + + // Abort if not done already and return + return jqXHR.abort(); + } + + // Aborting is no longer a cancellation + strAbort = "abort"; + + // Install callbacks on deferreds + completeDeferred.add( s.complete ); + jqXHR.done( s.success ); + jqXHR.fail( s.error ); + + // Get transport + transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR ); + + // If no transport, we auto-abort + if ( !transport ) { + done( -1, "No Transport" ); + } else { + jqXHR.readyState = 1; + + // Send global event + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] ); + } + + // If request was aborted inside ajaxSend, stop there + if ( completed ) { + return jqXHR; + } + + // Timeout + if ( s.async && s.timeout > 0 ) { + timeoutTimer = window.setTimeout( function() { + jqXHR.abort( "timeout" ); + }, s.timeout ); + } + + try { + completed = false; + transport.send( requestHeaders, done ); + } catch ( e ) { + + // Rethrow post-completion exceptions + if ( completed ) { + throw e; + } + + // Propagate others as results + done( -1, e ); + } + } + + // Callback for when everything is done + function done( status, nativeStatusText, responses, headers ) { + var isSuccess, success, error, response, modified, + statusText = nativeStatusText; + + // Ignore repeat invocations + if ( completed ) { + return; + } + + completed = true; + + // Clear timeout if it exists + if ( timeoutTimer ) { + window.clearTimeout( timeoutTimer ); + } + + // Dereference transport for early garbage collection + // (no matter how long the jqXHR object will be used) + transport = undefined; + + // Cache response headers + responseHeadersString = headers || ""; + + // Set readyState + jqXHR.readyState = status > 0 ? 4 : 0; + + // Determine if successful + isSuccess = status >= 200 && status < 300 || status === 304; + + // Get response data + if ( responses ) { + response = ajaxHandleResponses( s, jqXHR, responses ); + } + + // Use a noop converter for missing script but not if jsonp + if ( !isSuccess && + jQuery.inArray( "script", s.dataTypes ) > -1 && + jQuery.inArray( "json", s.dataTypes ) < 0 ) { + s.converters[ "text script" ] = function() {}; + } + + // Convert no matter what (that way responseXXX fields are always set) + response = ajaxConvert( s, response, jqXHR, isSuccess ); + + // If successful, handle type chaining + if ( isSuccess ) { + + // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode. + if ( s.ifModified ) { + modified = jqXHR.getResponseHeader( "Last-Modified" ); + if ( modified ) { + jQuery.lastModified[ cacheURL ] = modified; + } + modified = jqXHR.getResponseHeader( "etag" ); + if ( modified ) { + jQuery.etag[ cacheURL ] = modified; + } + } + + // if no content + if ( status === 204 || s.type === "HEAD" ) { + statusText = "nocontent"; + + // if not modified + } else if ( status === 304 ) { + statusText = "notmodified"; + + // If we have data, let's convert it + } else { + statusText = response.state; + success = response.data; + error = response.error; + isSuccess = !error; + } + } else { + + // Extract error from statusText and normalize for non-aborts + error = statusText; + if ( status || !statusText ) { + statusText = "error"; + if ( status < 0 ) { + status = 0; + } + } + } + + // Set data for the fake xhr object + jqXHR.status = status; + jqXHR.statusText = ( nativeStatusText || statusText ) + ""; + + // Success/Error + if ( isSuccess ) { + deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] ); + } else { + deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] ); + } + + // Status-dependent callbacks + jqXHR.statusCode( statusCode ); + statusCode = undefined; + + if ( fireGlobals ) { + globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError", + [ jqXHR, s, isSuccess ? success : error ] ); + } + + // Complete + completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] ); + + if ( fireGlobals ) { + globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] ); + + // Handle the global AJAX counter + if ( !( --jQuery.active ) ) { + jQuery.event.trigger( "ajaxStop" ); + } + } + } + + return jqXHR; + }, + + getJSON: function( url, data, callback ) { + return jQuery.get( url, data, callback, "json" ); + }, + + getScript: function( url, callback ) { + return jQuery.get( url, undefined, callback, "script" ); + } +} ); + +jQuery.each( [ "get", "post" ], function( _i, method ) { + jQuery[ method ] = function( url, data, callback, type ) { + + // Shift arguments if data argument was omitted + if ( isFunction( data ) ) { + type = type || callback; + callback = data; + data = undefined; + } + + // The url can be an options object (which then must have .url) + return jQuery.ajax( jQuery.extend( { + url: url, + type: method, + dataType: type, + data: data, + success: callback + }, jQuery.isPlainObject( url ) && url ) ); + }; +} ); + +jQuery.ajaxPrefilter( function( s ) { + var i; + for ( i in s.headers ) { + if ( i.toLowerCase() === "content-type" ) { + s.contentType = s.headers[ i ] || ""; + } + } +} ); + + +jQuery._evalUrl = function( url, options, doc ) { + return jQuery.ajax( { + url: url, + + // Make this explicit, since user can override this through ajaxSetup (#11264) + type: "GET", + dataType: "script", + cache: true, + async: false, + global: false, + + // Only evaluate the response if it is successful (gh-4126) + // dataFilter is not invoked for failure responses, so using it instead + // of the default converter is kludgy but it works. + converters: { + "text script": function() {} + }, + dataFilter: function( response ) { + jQuery.globalEval( response, options, doc ); + } + } ); +}; + + +jQuery.fn.extend( { + wrapAll: function( html ) { + var wrap; + + if ( this[ 0 ] ) { + if ( isFunction( html ) ) { + html = html.call( this[ 0 ] ); + } + + // The elements to wrap the target around + wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true ); + + if ( this[ 0 ].parentNode ) { + wrap.insertBefore( this[ 0 ] ); + } + + wrap.map( function() { + var elem = this; + + while ( elem.firstElementChild ) { + elem = elem.firstElementChild; + } + + return elem; + } ).append( this ); + } + + return this; + }, + + wrapInner: function( html ) { + if ( isFunction( html ) ) { + return this.each( function( i ) { + jQuery( this ).wrapInner( html.call( this, i ) ); + } ); + } + + return this.each( function() { + var self = jQuery( this ), + contents = self.contents(); + + if ( contents.length ) { + contents.wrapAll( html ); + + } else { + self.append( html ); + } + } ); + }, + + wrap: function( html ) { + var htmlIsFunction = isFunction( html ); + + return this.each( function( i ) { + jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html ); + } ); + }, + + unwrap: function( selector ) { + this.parent( selector ).not( "body" ).each( function() { + jQuery( this ).replaceWith( this.childNodes ); + } ); + return this; + } +} ); + + +jQuery.expr.pseudos.hidden = function( elem ) { + return !jQuery.expr.pseudos.visible( elem ); +}; +jQuery.expr.pseudos.visible = function( elem ) { + return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length ); +}; + + + + +jQuery.ajaxSettings.xhr = function() { + try { + return new window.XMLHttpRequest(); + } catch ( e ) {} +}; + +var xhrSuccessStatus = { + + // File protocol always yields status code 0, assume 200 + 0: 200, + + // Support: IE <=9 only + // #1450: sometimes IE returns 1223 when it should be 204 + 1223: 204 + }, + xhrSupported = jQuery.ajaxSettings.xhr(); + +support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported ); +support.ajax = xhrSupported = !!xhrSupported; + +jQuery.ajaxTransport( function( options ) { + var callback, errorCallback; + + // Cross domain only allowed if supported through XMLHttpRequest + if ( support.cors || xhrSupported && !options.crossDomain ) { + return { + send: function( headers, complete ) { + var i, + xhr = options.xhr(); + + xhr.open( + options.type, + options.url, + options.async, + options.username, + options.password + ); + + // Apply custom fields if provided + if ( options.xhrFields ) { + for ( i in options.xhrFields ) { + xhr[ i ] = options.xhrFields[ i ]; + } + } + + // Override mime type if needed + if ( options.mimeType && xhr.overrideMimeType ) { + xhr.overrideMimeType( options.mimeType ); + } + + // X-Requested-With header + // For cross-domain requests, seeing as conditions for a preflight are + // akin to a jigsaw puzzle, we simply never set it to be sure. + // (it can always be set on a per-request basis or even using ajaxSetup) + // For same-domain requests, won't change header if already provided. + if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) { + headers[ "X-Requested-With" ] = "XMLHttpRequest"; + } + + // Set headers + for ( i in headers ) { + xhr.setRequestHeader( i, headers[ i ] ); + } + + // Callback + callback = function( type ) { + return function() { + if ( callback ) { + callback = errorCallback = xhr.onload = + xhr.onerror = xhr.onabort = xhr.ontimeout = + xhr.onreadystatechange = null; + + if ( type === "abort" ) { + xhr.abort(); + } else if ( type === "error" ) { + + // Support: IE <=9 only + // On a manual native abort, IE9 throws + // errors on any property access that is not readyState + if ( typeof xhr.status !== "number" ) { + complete( 0, "error" ); + } else { + complete( + + // File: protocol always yields status 0; see #8605, #14207 + xhr.status, + xhr.statusText + ); + } + } else { + complete( + xhrSuccessStatus[ xhr.status ] || xhr.status, + xhr.statusText, + + // Support: IE <=9 only + // IE9 has no XHR2 but throws on binary (trac-11426) + // For XHR2 non-text, let the caller handle it (gh-2498) + ( xhr.responseType || "text" ) !== "text" || + typeof xhr.responseText !== "string" ? + { binary: xhr.response } : + { text: xhr.responseText }, + xhr.getAllResponseHeaders() + ); + } + } + }; + }; + + // Listen to events + xhr.onload = callback(); + errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" ); + + // Support: IE 9 only + // Use onreadystatechange to replace onabort + // to handle uncaught aborts + if ( xhr.onabort !== undefined ) { + xhr.onabort = errorCallback; + } else { + xhr.onreadystatechange = function() { + + // Check readyState before timeout as it changes + if ( xhr.readyState === 4 ) { + + // Allow onerror to be called first, + // but that will not handle a native abort + // Also, save errorCallback to a variable + // as xhr.onerror cannot be accessed + window.setTimeout( function() { + if ( callback ) { + errorCallback(); + } + } ); + } + }; + } + + // Create the abort callback + callback = callback( "abort" ); + + try { + + // Do send the request (this may raise an exception) + xhr.send( options.hasContent && options.data || null ); + } catch ( e ) { + + // #14683: Only rethrow if this hasn't been notified as an error yet + if ( callback ) { + throw e; + } + } + }, + + abort: function() { + if ( callback ) { + callback(); + } + } + }; + } +} ); + + + + +// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432) +jQuery.ajaxPrefilter( function( s ) { + if ( s.crossDomain ) { + s.contents.script = false; + } +} ); + +// Install script dataType +jQuery.ajaxSetup( { + accepts: { + script: "text/javascript, application/javascript, " + + "application/ecmascript, application/x-ecmascript" + }, + contents: { + script: /\b(?:java|ecma)script\b/ + }, + converters: { + "text script": function( text ) { + jQuery.globalEval( text ); + return text; + } + } +} ); + +// Handle cache's special case and crossDomain +jQuery.ajaxPrefilter( "script", function( s ) { + if ( s.cache === undefined ) { + s.cache = false; + } + if ( s.crossDomain ) { + s.type = "GET"; + } +} ); + +// Bind script tag hack transport +jQuery.ajaxTransport( "script", function( s ) { + + // This transport only deals with cross domain or forced-by-attrs requests + if ( s.crossDomain || s.scriptAttrs ) { + var script, callback; + return { + send: function( _, complete ) { + script = jQuery( " + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    + Made with Sphinx and @pradyunsg's + + Furo + +
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    + + + + + \ No newline at end of file diff --git a/cpp/index.html b/cpp/index.html new file mode 100644 index 000000000..344e8ec8b --- /dev/null +++ b/cpp/index.html @@ -0,0 +1,269 @@ + + + + + + + + + dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    + + + + + \ No newline at end of file diff --git a/cpp/objects.inv b/cpp/objects.inv new file mode 100644 index 0000000000000000000000000000000000000000..0dce3850824519def54e1c38ac063f6384e09769 GIT binary patch literal 3262 zcmV;v3_NERX>N99Zgg*Qc_4OWa&u{KZXhxWBOp+6Z)#;@bUGkpb#rtI zBOq2~a&u{KZaN?^E-^JOF$yCfRA^-&a%F8{X>Md?av*PJAarPHb0B7EY-J#6b0A}H zZE$jBb8}^6Aa!$TZf78RY-wUH3V7PpT-k0LM;3k8R}h%I1rBOo_!ij2jK_$g$ns!- z!GNe$Vul-qtaPevVt>1qA=kM1iy!QF>l-I6) zz4`c$m%sM)=KAyH-;a7P-cP3O_WXXk?fSQ)qBp(6$Kj|LxPB{)$L%z{A3TA?-eg+z z{QVS2lQ~rP3UIZW1W`_W@}aNqBzVnv(^HystV=_z@_K1#}X z)OU@mkTcYy`2XtN-rj??X$fWt{9J|a4M&6CV$$>dFqF_o5Pl}4vq5T>NF7@w*Y8fh zkJB|3#qhQ}nYwA3U3j|n^r=!3?6RTi$`x*KF4D&5EA8o-QsOiX#(f~2m&E1EXKcld zm(R_V>2W+7rs1@Sl}qUw+HuPE=_xNZHL=Z0Yj$lkudmsK@p}5s%!qfmSlp)3Ab~X0 zUlL*y@TKeZXr=A;{~DUkt=u`hG!3RNdVD z+Pcnh8YjKK&cI%4o3}3t-`&gS`?g!6mY3`9S}gZDS9~W<Pb9*8;?i5$z(LFy_2ICKqu}iE#5{o?gl=(W;)uYG&Q_M(3q@d`~Sve zosr4#X%M5!(Q7 zB5Co!+{4NbFQk8>s9@N$cXJ%WVsoeh{?Pu=aUAPADiuVl)qV0fW{dEPD*KD>^h@uH ze;cMMkJ!tQ(LVR$AZpQIGueDJS9`r`3#RzIf%NV|flijdDX z9A2DvMF~+Ex$37qIoH21;yxN=l=^dafUan_-K0A+>$ZzLF%|pjAzDzn2GLn_ip%YS zZ_P_Oml9-@iV3QY&H-KcclVGBpM%Jw>*)6pTfU02e28?=z1`YiJzksKg6Uk%9PRVA zw51+O)9|5JjD~|WoOXIg2t%+24w{3(q|S`Lh0u}z^V}si=ar4Co&DVfUR6XbdV}7y z_mK9VBa=k53?3q!%fxmAvVZX8?ch=8B z=~0_k=b`kN{jBp+dftXD->4T0=^E1hC0jnxOf-Bc=eKv@Y$_ri!8-{6_Uk{j@x(Hd zQT^iyt5-YKsOS;;_mj#WggBN#lqd&j8lf^vq`h=NE6V@t(=Cy9&{a1%<*mK@zO!1K z-k5tNLnU_fQnkU$FCguQKd@e#8ABr^$BgArOV`wJn&CNWM2DhG6IA!ZUPgwge*m}u zs(m84z-hM!?y;eht>&fmhUY4+>BGwA1vY$a`FaA+(TtCyVl=r!8%&v5rPIyb&;6N= zs%?nQL6Vb*7}*80pKK#*pH5btvL9<2PdpwpU2Vfr^LUimY8!2x=%C4%RP{`@060WY z&tz*L`-tkBYz?H6NK#hMWD9^p1ocd|2C|Q+zRA`=Dv8!I!`62-o{^x7UYtX8*E*f8 z9(n`z0BgH_xwle%0|7VhE#TkpE#Ud_@*oX-I=XS&;@ke-%OUzb-@14a@18GTY%z|; z^Um}?|E=owUc%dZtUR2nO}C0Gwfsr0ym%I#$_Kl&yWGaX zr`cCTCezsNJD>Wk4;2TjKkY~8Qb!f_EGV62jMf_>lqQT(u3a#k$<6DZLBA6X_s6E1IKGk|*vYn&~D;WZ;@|Vw0d!CCwevMteeJ zFMyVPhaojT^gCj!XlXsMxY$yxSWe#U+#=BgEaflOId3bZy zJ~8EUw#*6UId8_hJe4+EYblW|lN3qhK}nLS%y5F-%t&&|${QG8I87*Ff<{3p_Z9&F zf600z%P_X6uy$dsMZ%+j${9eU(4NH{B&Hz?CsZ_%a1$^CIyK6b7$qWF%rEs)sgz6q z&5p%LISr9D$(1D~@Tw54;5ze^NsfXW%XPApdfF%#Vy<*FTA6*YhJiW|$4Wwk`@|dN ziYhRph=q$G!X!=wSI!ENG}Wde9&d5oreSXw)8po|%d4~JTA$007f+AHQ79i;d!iKE z`uOwDE!?^PL`-kO?`P;vZ;(b3YXohZ(CSw=Ua|5hS+DiZNUI-JS z4AcZg635UHxTEsYMi<4-vG3UCDQ(aYr6XAE-02Vzk%{C1_d_Iz{=zEZ)w^htRuK_0 zktVpnA<7_0cswU{H1MAH(3Fwnu_z&q5bq)r3R%(_t!(ht3f+*V0$Kp55!ww=Jc(q3 zNy5rBTax%k#gr6B!vizBoRuIf@f=x-B07!#sJBv7toCEz9Z}Bb5JWWIp)L^`fl)Zc zj6oqJRYmczd04rhfpYE=OhY9KuAmq}>EJ2qEd_4{%Q4Yo54x2uMa+7%8l{im6!Fk= zA2~^&+MQ^hjzRW=GbC#s7$;O)l-5LJ983j^a@RXl+e&o+Of}2T?xYGUE@!5cwf z8rX>2NEK6AvxI`VrgWV{R)lCBd}JWWiqS|^$c$vEP5o6XqqHb6l2%4XjtVUxjwXv0 z7VwADh9)?c)qc>77>Z)qP$R8F29q$C2#z-F?|S`L8AfO5v6zfMUqj?&l}v|y+*Fc6gE^$c_f-IbZbgtE9wkx3E| zw`@YMDQ6*)yf%G=|Cx|IcO)8S5ht@mvy&W*j4q44GJUd$o!s%P9T+L15Ml&Fd6yjW zzEJh(tw48^(T8fJov2W9X@b}qqGw)3!Rp6Ui+yfG6&9Wl$6bwot zBpt;x5}8I%;Up%-`*K~^MEB)(7)LxnyNn27wI>Ln5*@ooVU%k{hOA+AEwCChvNG|C zaRZ;^Wqh-d9kn#qI@SZN?A7<_-DtSk(atf~JLmb8`5V{syTkk0W;Pn{ayP$ho_G1# zbC4Z=*!r}7>0-@ZJ6>OzvGr?waKq3W-nOQ9X>ofgYrfU=&~vTw`4#4J&uRzm#&%Zg zYWd(M?8yI_!t`Q$&F+HRSkJAi)uTm)`C7} + + + + + + + + Distributions - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
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    Distributions#

    +

    Our distribution support will grow over time. If you need a distribution that is not yet supported please post an issue <https://github.com/mrc-ide/dust/issues/>.

    +
    +

    Uniform#

    +
    +
    +template<typename real_type, typename rng_state_type>
    __nv_exec_check_disable__ __host__ __device__ real_type dust::random::uniform(rng_state_type &rng_state, real_type min, real_type max)#
    +

    Draw a uniformly distributed random number with arbitrary bounds. This function simply scales the output of dust::random::random_real

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • rng_state_type – The random number state type

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • min, max – The minimum and maximum values for the distribution

      • +
    +
    +
    +
    + +
    +
    +

    Normal#

    +
    +
    +template<typename real_type, algorithm::normal algorithm = algorithm::normal::box_muller, typename rng_state_type>
    __nv_exec_check_disable__ __host__ __device__ real_type dust::random::normal(rng_state_type &rng_state, real_type mean, real_type sd)#
    +

    Draw a normally distributed random number with arbitrary bounds. This function simply scales the output of dust::random::random_real

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • The – algorithm to use; the default is Box-Muller which is slowest on CPU but simple.

      • +

    • rng_state_type – The random number state type

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • mean – The mean of the distribution

      • +

    • sd – The standard deviation of the distribution

      • +
    +
    +
    +
    + +

    The enum dust::random::algorithm::normal controls the normal algorithm used for a given draw

    +
    +
    +enum class dust::random::algorithm::normal#
    +

    Values:

    +
    +
    +enumerator box_muller#
    +

    Box-Muller method (transformation)

    +
    + +
    +
    +enumerator polar#
    +

    Polar method (rejection)

    +
    + +
    +
    +enumerator ziggurat#
    +

    Ziggurat method (rejection)

    +
    + +
    + +
    +
    +

    Binomial#

    +
    +
    +template<typename real_type, typename rng_state_type>
    __host__ __device__ real_type dust::random::binomial(rng_state_type &rng_state, real_type n, real_type p)#
    +

    Draw a binomially distributed random number; the number of successes given n trials each with probability p. Generation is performed using a rejection-sampling algorithm or inversion depending on the expected mean (n * p).

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • rng_state_type – The random number state type

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • n – The number of trials

      • +

    • p – The probability of success of each trial

      • +
    +
    +
    +
    + +
    +
    +

    Hypergeometric#

    +
    +
    +template<typename real_type, typename rng_state_type>
    __host__ __device__ real_type dust::random::hypergeometric(rng_state_type &rng_state, real_type n1, real_type n2, real_type k)#
    +

    Draw random number from the hypergeometric distribution. This is often descrribed as sampling k elements without replacement from an urn with n1 white balls and n2 black balls, where the outcome is the number of white balls retrieved.

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • rng_state_type – The random number state type

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • n1 – The number of white balls in the urn

      • +

    • n2 – The number of black balls in the urn

      • +

    • k – The number of draws

      • +
    +
    +
    +
    + +
    +
    +

    Exponential#

    +
    +
    +template<typename real_type, typename rng_state_type>
    __nv_exec_check_disable__ __host__ __device__ real_type dust::random::exponential(rng_state_type &rng_state, real_type rate)#
    +

    Draw a exponentially distributed random number given a rate parameter. Generation is performed using inversion (faster algorithms exist but are not yet implemented).

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • rng_state_type – The random number state type

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • rate – The rate of the process

      • +
    +
    +
    +
    + +
    +
    +

    Poisson#

    +
    +
    +template<typename real_type, typename rng_state_type>
    __nv_exec_check_disable__ __host__ __device__ real_type dust::random::poisson(rng_state_type &rng_state, real_type lambda)#
    +

    Draw a Poisson distributed random number given a mean parameter. Generation is performed using either Knuth’s algorithm (small lambda) or Hormann’s rejection sampling algorithm (medium lambda), or rejection based on the Cauchy (large lambda)

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • rng_state_type – The random number state type

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • lambda – The mean of the distribution

      • +
    +
    +
    Returns:
    +

    We return a real_type, not an int, as with deterministic mode this will not necessarily be an integer

    +
    +
    +
    + +
    +
    +

    Multinomial#

    +
    +
    +template<typename real_type, typename rng_state_type, typename T, typename U>
    __host__ __device__ void dust::random::multinomial(rng_state_type &rng_state, int size, const T &prob, int prob_len, U &ret)#
    +

    Draw one sample from the multinomial distribution.

    +

    This is written assuming that prob and ret are arbitrary containers; they could be pointers, vectors or anything else that supports random access. We could also do this with iterators but they always feel a bit weird really.

    +

    Note that prob and ret will ordinarily be containers of real_type but that might not be the case, in particular when calling from R where we want calculations to happen in single precision but the inputs (and destination) are double precision.

    +

    Later we will provide some helpers that will allow setting a stride over these containers; this will help with use from odin code.

    +
    +
    Template Parameters:
    +
      +

    • real_type – The underlying real number type, typically double or float. A compile-time error will be thrown if you attempt to use a non-floating point type (based on `std::is_floating_point).

      • +

    • rng_state_type – The random number state type

      • +

    • T, U – The type of the containers for prob and ret. This might be double* or std::vector<double> depending on use.

      • +
    +
    +
    Parameters:
    +
      +

    • rng_state – Reference to the random number state, will be modified as a side-effect

      • +

    • size – The number of trials (analagous to size in binomial)

      • +

    • prob – The set of probabilities. In a binomial trial we only provide a single probability of success but here there is a vector/array of such probabilities. These need not sum to one as they will be normalised, however they must all be non-negative and at least one must be positive.

      • +

    • prob_len – The number of probabilities (or outcomes)

      • +

    • ret – Container for the return value

      • +
    +
    +
    +
    + +
    +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+void show_numbers(std::vector<double> numbers, const char * label) {
+  std::cout << label << ":";
+  for (size_t i = 0; i < numbers.size(); ++i) {
+    std::cout << " " << numbers[i];
+  }
+  std::cout << std::endl;
+}
+
+int main() {
+  using rng_state_type = dust::random::generator<double>;
+
+  auto state = dust::random::seed<rng_state_type>(42);
+  size_t n = 10;
+
+  // A place to store numbers:
+  std::vector<double> numbers(n);
+
+  for (size_t i = 0; i < n; ++i) {
+    numbers[i] = dust::random::uniform<double>(state, 10, 20);
+  }
+  show_numbers(numbers, "Uniform(10, 20)");
+
+  for (size_t i = 0; i < n; ++i) {
+    numbers[i] = dust::random::normal<double>(state, 5, 2);
+  }
+  show_numbers(numbers, "Normal(5, 2)");
+
+  for (size_t i = 0; i < n; ++i) {
+    numbers[i] = dust::random::exponential<double>(state, 6);
+  }
+  show_numbers(numbers, "Exponential(6)");
+
+  for (size_t i = 0; i < n; ++i) {
+    numbers[i] = dust::random::poisson<double>(state, 3);
+  }
+  show_numbers(numbers, "Poisson(3)");
+
+  for (size_t i = 0; i < n; ++i) {
+    numbers[i] = dust::random::binomial<double>(state, 10, 0.3);
+  }
+  show_numbers(numbers, "Binomial(10, 0.3)");
+
+  for (size_t i = 0; i < n; ++i) {
+    numbers[i] = dust::random::hypergeometric<double>(state, 10, 3, 7);
+  }
+  show_numbers(numbers, "Hypergeometric(10, 3, 7)");
+}
+
    +
    +
    Uniform(10, 20): 14.9695 16.8962 13.6696 13.6204 19.2999 10.7353 13.6703 10.8023 16.4116 18.2632
+Normal(5, 2): 5.02109 6.01904 5.15919 6.38409 2.67724 6.1001 4.48944 5.31519 3.86882 5.23517
+Exponential(6): 0.0231662 0.0920166 0.238532 0.0190538 0.241245 0.128207 0.13686 0.0170973 0.0575175 0.097848
+Poisson(3): 2 0 2 2 4 3 4 3 2 4
+Binomial(10, 0.3): 3 4 3 1 4 2 3 4 4 3
+Hypergeometric(10, 3, 7): 6 6 6 6 7 5 6 6 5 6
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-jump.html b/cpp/random-jump.html new file mode 100644 index 000000000..ca39982d9 --- /dev/null +++ b/cpp/random-jump.html @@ -0,0 +1,354 @@ + + + + + + + + + Advancing the random number state via jumps - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    dust 0.15.1 documentation
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    + +
    + +
    + +
    +
    +
    +

    Advancing the random number state via jumps#

    +

    There are two functions for jumping the random number state:

    +
    +
    +template<typename T>
    __host__ inline void dust::random::jump(T &state)#
    +

    Jump the random number state forward by a number of steps equal to the square root of the sequence length. The xoshiro256 generators have a sequence length of 2^256 and so each of these jumps is equivalent to 2^128 steps.

    +
    +
    Template Parameters:
    +

    T – The random number generator state type; this will be inferred based on the argument

    +
    +
    Parameters:
    +

    state – The random number state, will be updated as a side effect

    +
    +
    +
    + +
    +
    +template<typename T>
    __host__ inline void dust::random::long_jump(T &state)#
    +

    Jump the random number state forward by a number of steps equal to the period raised to 3/4s. The xoshiro256 generators have a sequence length of 2^256 and so each of these jumps is equivalent to 2^192 steps.

    +
    +
    Template Parameters:
    +

    T – The random number generator state type; this will be inferred based on the argument

    +
    +
    Parameters:
    +

    state – The random number state, will be updated as a side effect

    +
    +
    +
    + +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+template <typename T>
+void show_state(T& state, const char * label) {
+  std::cout << label << std::endl;
+  std::cout << std::hex;
+  for (size_t i = 0; i < T::size(); ++i) {
+    std::cout << state[i] << std::endl;
+  }
+}
+
+int main() {
+  using rng_state_type = dust::random::xoroshiro128plusplus;
+
+  auto state = dust::random::seed<rng_state_type>(42);
+  show_state(state, "Initial state");
+
+  dust::random::jump(state);
+  show_state(state, "\nAfter one jump");
+
+  dust::random::long_jump(state);
+  show_state(state, "\nAfter long jump");
+}
+
    +
    +
    Initial state
+bdd732262feb6e95
+57e1faba65107204
+
+After one jump
+7be6cde51a8a4905
+93dc62917e1a6b74
+
+After long jump
+2902cc414b8cdb97
+ba4b52663a54c408
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-parallel.html b/cpp/random-parallel.html new file mode 100644 index 000000000..628e6e666 --- /dev/null +++ b/cpp/random-parallel.html @@ -0,0 +1,455 @@ + + + + + + + + + Parallel random number object - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    dust 0.15.1 documentation
     +
    +
    +
    + +
    + +
    +
    + +
    +
    +
    + + + + + Back to top + +
    + +
    + +
    + +
    +
    +
    +

    Parallel random number object#

    +
    +
    +template<typename T>
    class prng#
    +

    Container class for parallel random number streams. This class does not do any actual running of random numbers (and nothing in parallel) but acts to hold together the state and ease some bookkeeping.

    +
    +
    Template Parameters:
    +

    T – Random number state type to use

    +
    +
    +
    +

    Public Types

    +
    +
    +using rng_state = T#
    +

    The random number state type.

    +
    + +
    +
    +using int_type = typename rng_state::int_type#
    +

    The underlying integer type used by rng_state

    +
    + +
    +
    +

    Public Functions

    +
    +
    +inline prng(const size_t n, const int seed, const bool deterministic = false)#
    +

    Construct a new prng object from a single integer seed

    +
    +
    Parameters:
    +
      +

    • n – The number of streams

      • +

    • seed – An integer to use as a seed

      • +

    • deterministic – Selects use of the “deterministic” generator

      • +
    +
    +
    +
    + +
    +
    +inline prng(const size_t n, const std::vector<int_type> &seed, const bool deterministic = false)#
    +

    Construct a new prng object from a vector of seed data. We will consume as many items of seed as possible, then start jumping

    +
    +
    Parameters:
    +

    seed – A vector of integers to seed the generator with

    +
    +
    +
    + +
    +
    +inline size_t size() const#
    +

    The number of streams within the object.

    +
    + +
    +
    +inline void jump()#
    +

    Jump all generators forward.

    +
    + +
    +
    +inline void long_jump()#
    +

    Take a long jump for every generator.

    +
    + +
    +
    +inline rng_state &state(size_t i)#
    +

    Return the ith state, as an rng_state reference. This is the workhorse method and the main one likely to be used once the object is constructed.

    +
    +
    Parameters:
    +

    i – The index of the stream (0, 1, …, size() - 1)

    +
    +
    +
    + +
    +
    +inline std::vector<int_type> export_state()#
    +

    Convert the random number state of all generators into a single vector. This can be used to save the state to restore using import_state()

    +
    + +
    +
    +inline void import_state(const std::vector<int_type> &state)#
    +

    Import a vector of random number state, previously saved by export_state()

    +
    +
    Parameters:
    +

    state – A vector of state

    +
    +
    +
    + +
    +
    +inline bool deterministic() const#
    +

    Indicates if the generators are deterministic.

    +
    + +
    +
    + +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+template <typename T>
+void show_state(T& state, const char * label) {
+  std::cout << label << std::endl;
+  std::cout << std::hex;
+  for (size_t i = 0; i < T::size(); ++i) {
+    std::cout << state[i] << std::endl;
+  }
+}
+
+int main() {
+  // Using a small state so it's easier to see the output
+  using rng_state_type = dust::random::xoroshiro128plus;
+
+  // Create a prng object with 4 streams (and initial seed 42)
+  auto obj = dust::random::prng<rng_state_type>(4, 42);
+  show_state(obj.state(0), "first stream");
+
+  // An equivalently created state
+  auto cmp = dust::random::seed<rng_state_type>(42);
+  show_state(cmp, "\nequivalent state");
+
+  // The second stream
+  show_state(obj.state(1), "\nsecond stream");
+
+  // Jumping our state forward gets to the same place
+  dust::random::jump(cmp);
+  show_state(cmp, "\nequivalent state");
+}
+
    +
    +
    first stream
+bdd732262feb6e95
+57e1faba65107204
+
+equivalent state
+bdd732262feb6e95
+57e1faba65107204
+
+second stream
+1b3c79462edc2ed4
+871ea92fbd8aefdf
+
+equivalent state
+1b3c79462edc2ed4
+871ea92fbd8aefdf
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-primitive.html b/cpp/random-primitive.html new file mode 100644 index 000000000..2879ef719 --- /dev/null +++ b/cpp/random-primitive.html @@ -0,0 +1,394 @@ + + + + + + + + + Primitive random number generation functions - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    dust 0.15.1 documentation
     +
    +
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    +
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    + + + + + Back to top + +
    + +
    + +
    + +
    +
    +
    +

    Primitive random number generation functions#

    +
    +

    Uniform#

    +

    The workhorse random number generating function is random_real:

    +
    +
    +template<typename T, typename U>
    __host__ __device__ T dust::random::random_real(U &state)#
    +

    Generate a real number U(0, 1)

    +
    +
    Template Parameters:
    +
      +

    • T – The real type to return, typically double or float; because this affects the return value only it must be provided.

      • +

    • U – The random number generator state type; this will be inferred based on the argument

      • +
    +
    +
    Parameters:
    +

    state – The random number state, will be updated as a side effect

    +
    +
    Returns:
    +

    A real-valued random number on (0, 1]

    +
    +
    +
    + +
    +
    +

    Integer#

    +

    There is also a low-level function for generating integers of a given width:

    +
    +
    +template<typename T, typename U>
    __host__ __device__ T dust::random::random_int(U &state)#
    +

    Generate a random integer of a given width

    +
    +
    Template Parameters:
    +
      +

    • T – The integer type to generate, such as uint64_t. Both signed and unsigned integers can be provided here. Because this affects the return value only it must be provided.

      • +

    • U – The random number generator state type; this will be inferred based on the argument

      • +
    +
    +
    Parameters:
    +

    state – The random number state, will be updated as a side effect

    +
    +
    Returns:
    +

    An integer valued number, uniformly distributed anywhere within the range of the given integer type.

    +
    +
    +
    + +

    Note that this does not generate an arbitrary integer within some specified range; you are limited to C++ integer types.

    +
    +
    +

    Normal#

    +

    The standard normal distribution also gets special treatment.

    +
    +
    +template<typename real_type, algorithm::normal algorithm = algorithm::normal::box_muller, typename rng_state_type>
    __nv_exec_check_disable__ __host__ __device__ real_type dust::random::random_normal(rng_state_type &rng_state)#
    +

    Draw a standard normally distributed random number (with mean 0 and standard deviation 1)

    +
    +
    Template Parameters:
    +
      +

    • T – The real type to return, typically double or float; because this affects the return value only it must be provided.

      • +

    • The – algorithm to use; the default is Box-Muller which is slowest on CPU but simple. Other alternatives are ziggurat (fast) or polar (medium).

      • +

    • U – The random number generator state type; this will be inferred based on the argument

      • +
    +
    +
    Parameters:
    +

    state – The random number state, will be updated as a side effect

    +
    +
    Returns:
    +

    A real-valued random number on (-inf, inf)

    +
    +
    +
    + +
    +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+int main() {
+  using rng_state_type = dust::random::generator<double>;
+  auto state = dust::random::seed<rng_state_type>(42);
+
+  std::cout << "uniform: " <<
+    dust::random::random_real<double>(state) << std::endl;
+  std::cout << "normal: " <<
+    dust::random::random_normal<double>(state) << std::endl;
+  std::cout << "unsigned integer: " <<
+    dust::random::random_int<uint32_t>(state) << std::endl;
+  std::cout << "signed integer: " <<
+    dust::random::random_int<int16_t>(state) << std::endl;
+}
+
    +
    +
    uniform: 0.496954
+normal: -0.578048
+unsigned integer: 2064508910
+signed integer: -13454
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-r.html b/cpp/random-r.html new file mode 100644 index 000000000..dd490df46 --- /dev/null +++ b/cpp/random-r.html @@ -0,0 +1,327 @@ + + + + + + + + + Random number interface from R - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    dust 0.15.1 documentation
     +
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    +
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    +
    + + + + + Back to top + +
    + +
    + +
    + +
    +
    +
    +

    Random number interface from R#

    +

    We provide several functions for use from within R packages, all of which are in the namespace dust::random::r. These are further described in the package vignette

    +

    To access these functions you must have the cpp11 package available and include <dust/r/random.hpp>.

    +
    +

    Seeding the generator#

    +

    As a slightly more convienient interace for seeding generators

    +
    +
    +template<typename rng_state_type>
    std::vector<typename rng_state_type::int_type> dust::random::r::as_rng_seed(cpp11::sexp r_seed)#
    +

    Create a seed vector from an R object

    +
    +
    Template Parameters:
    +

    rng_state_type – The random number state type to use; this is used to work out what type of integer is required and how many of them.

    +
    +
    Parameters:
    +

    r_seed – An R object to use as a seed. Valid options are:

      +

    • a scalar integer (or integer-like number) which we pass to dust::random::seed

      • +

    • a vector of raw values, which we take as a serialised vector of integers of appropriate width.

      • +

    • the R value NULL (i.e., R_NilValue, not a C++ nullptr), in which case we draw a random integer from R’s random number generator and pass that to dust::random::seed

      • +
    +

    +
    +
    +
    + +

    Once you have a seed, there’s no direct interaction with the dust R API any further - you have a seed and can draw numbers as described elsewhere in this manual.

    +
    +
    +

    Persistent streams#

    +

    To provide access to persistent streams (see also the reference documentation)

    +
    +
    +template<typename rng_state_type>
    prng<rng_state_type> *dust::random::r::rng_pointer_get(cpp11::environment obj, int n_streams = 0)#
    +

    Recieve and check the pointer to rng state. This checks that the object is valid, is of the correct state type, has sufficient streams and has not been invalidated by serialisation.

    +
    +
    Template Parameters:
    +

    rng_state_type – The random number state type to use

    +
    +
    Parameters:
    +
      +

    • obj – An dust_rng_pointer object, created in R with dust::dust_rng_pointer

      • +

    • n_streams – The number of required streams. Set this to 0 to disable the check. If you are going to use 100 streams pass 100 here, and a runtime error will be thrown if the object does not contain enough streams, which is nicer than a crash when prng::state fails.

      • +
    +
    +
    +
    + +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-seed.html b/cpp/random-seed.html new file mode 100644 index 000000000..3253476e4 --- /dev/null +++ b/cpp/random-seed.html @@ -0,0 +1,383 @@ + + + + + + + + + Seeding - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
    +
    +
    dust 0.15.1 documentation
     +
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    +
    + + + + + Back to top + +
    + +
    + +
    + +
    +
    +
    +

    Seeding#

    +

    We can initialise the random number state with any state that is not zero everywhere. Do do this, we take an integer and pass it through the splitmix64 algorithm until we have enough random state; this depends on the generator involved; a xoshiro512 generator requires more starting seed than a xoshiro128 generator.

    +

    These seedings functions are designed so that any single integer may be passed into them. The first form returns an initialised state:

    +
    +
    +template<typename T>
    __host__ T dust::random::seed(uint64_t seed)#
    +
    +
    Template Parameters:
    +

    T – The generator type

    +
    +
    Parameters:
    +

    seed – integer seed

    +
    +
    Returns:
    +

    A generator state (type T)

    +
    +
    +
    + +

    The second initialises a state in-place:

    +
    +
    +template<typename T>
    __host__ void dust::random::seed(T &state, uint64_t seed)#
    +
    +
    Template Parameters:
    +

    T – The generator type

    +
    +
    Parameters:
    +
      +

    • state – A generator state to write to

      • +

    • seed – integer seed; any value is suitable as it will be passed though splitmix64

      • +
    +
    +
    +
    + +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+template <typename T>
+void show_state(T& state, const char * label) {
+  std::cout << label << std::endl;
+  std::cout << std::hex;
+  for (size_t i = 0; i < T::size(); ++i) {
+    std::cout << state[i] << std::endl;
+  }
+}
+
+template <typename T>
+void draw_numbers(T& state, int n, const char * label) {
+  std::cout << label << std::endl;
+  for (int i = 0; i < n; ++i) {
+    std::cout << dust::random::random_normal<double>(state) << std::endl;
+  }
+}
+
+int main() {
+  using rng_state_type = dust::random::generator<double>;
+  // construct a state as a value
+  auto state = dust::random::seed<rng_state_type>(1);
+
+  show_state(state, "Initial state");
+  draw_numbers(state, 5, "\nRandom samples");
+
+  // construct a state in place
+  dust::random::seed(state, 2);
+  show_state(state, "\nState with slightly different seed");
+  draw_numbers(state, 5, "\nRandom samples");
+}
+
    +
    +
    Initial state
+910a2dec89025cc1
+5e41ab087439611e
+b18a02f46d8d86c3
+e28195ddd9ee4956
+
+Random samples
+1.1291
+0.537807
+-1.26699
+0.958293
+3.21195
+
+State with slightly different seed
+975835de1c9756ce
+64684c4f0fd784b4
+1956ecd1a275ec95
+90a5cb3b55b40acf
+
+Random samples
+0.965992
+0.881319
+-0.716755
+0.551913
+0.180611
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-state.html b/cpp/random-state.html new file mode 100644 index 000000000..7b34b6056 --- /dev/null +++ b/cpp/random-state.html @@ -0,0 +1,503 @@ + + + + + + + + + Random number state - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
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    dust 0.15.1 documentation
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    + +
    +
    +
    +

    Random number state#

    +

    Typically, you don’t need to think much about the state used; in the simple example we do

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+int main() {
+  using rng_state_type = dust::random::generator<double>;
+  auto state = dust::random::seed<rng_state_type>(42);
+  for (int i = 0; i < 5; ++i) {
+    std::cout << dust::random::random_real<double>(state) << std::endl;
+  }
+}
+
    +
    +

    This pattern will typically be sufficient - use dust::random::generator to select an appropriate algorithm for your floating point type, and use auto to save it. This will select dust::random::xoshiro256plus for double and dust::random::xoshiro128plus for float

    +
    +

    Core state class#

    +

    Every random number state is built on the same core class

    +
    +
    +template<typename T, size_t N, scrambler X>
    class xoshiro_state#
    +

    Basic struct to hold random number state for a single stream

    +
    +
    Template Parameters:
    +
      +

    • T – The integer type (uint32_t or uint64_t)

      • +

    • N – The number of integers included in the state (2, 4, or 8)

      • +

    • X – The scrambler type

      • +
    +
    +
    +
    +

    Public Types

    +
    +
    +using int_type = T#
    +

    Type alias used to find the integer type.

    +
    + +
    +
    +

    Public Functions

    +
    +
    +__host__ __device__ inline int_type &operator[](size_t i)#
    +

    Accessor method, used to both get and set the underlying state.

    +
    + +
    +
    +

    Public Members

    +
    +
    +int_type state[N]#
    +

    Array of state.

    +
    + +
    +
    +bool deterministic = false#
    +

    This flag indicates that the distributions should return the deterministic expectation of the draw, and not use any random numbers

    +
    + +
    +
    +

    Public Static Functions

    +
    +
    +__host__ __device__ static inline constexpr size_t size()#
    +

    Static method, returning the number of integers per state.

    +
    + +
    +
    + +

    Every random number state uses one of the three scrambler options, described based on the mathematical operations they perform when creating the final integer from the generator

    +
    +
    +enum class dust::random::scrambler#
    +

    Values:

    +
    +
    +enumerator starstar#
    +

    Two multiplications.

    +
    + +
    +
    +enumerator plusplus#
    +

    Two additions.

    +
    + +
    +
    +enumerator plus#
    +

    One addition.

    +
    + +
    + +
    +
    +

    Random number generation algorithms#

    +

    We then define 12 user-usable types, each representing a different algorithm:

    +

    32-bit generators, suitable for generating float values

    +
    +
    +using dust::random::xoshiro128starstar = xoshiro_state<uint32_t, 4, scrambler::starstar>#
    +
    + +
    +
    +using dust::random::xoshiro128plusplus = xoshiro_state<uint32_t, 4, scrambler::plusplus>#
    +
    + +
    +
    +using dust::random::xoshiro128plus = xoshiro_state<uint32_t, 4, scrambler::plus>#
    +
    + +

    64 bit generators, suitable for generating either double or float values, but differing in the size of the internal state:

    +

    128 bits:

    +
    +
    +using dust::random::xoroshiro128starstar = xoshiro_state<uint64_t, 2, scrambler::starstar>#
    +
    + +
    +
    +using dust::random::xoroshiro128plusplus = xoshiro_state<uint64_t, 2, scrambler::plusplus>#
    +
    + +
    +
    +using dust::random::xoroshiro128plus = xoshiro_state<uint64_t, 2, scrambler::plus>#
    +
    + +

    256 bits:

    +
    +
    +using dust::random::xoshiro256starstar = xoshiro_state<uint64_t, 4, scrambler::starstar>#
    +
    + +
    +
    +using dust::random::xoshiro256plusplus = xoshiro_state<uint64_t, 4, scrambler::plusplus>#
    +
    + +
    +
    +using dust::random::xoshiro256plus = xoshiro_state<uint64_t, 4, scrambler::plus>#
    +
    + +

    512 bits:

    +
    +
    +using dust::random::xoshiro512starstar = xoshiro_state<uint64_t, 8, scrambler::starstar>#
    +
    + +
    +
    +using dust::random::xoshiro512plusplus = xoshiro_state<uint64_t, 8, scrambler::plusplus>#
    +
    + +
    +
    +using dust::random::xoshiro512plus = xoshiro_state<uint64_t, 8, scrambler::plus>#
    +
    + +
    +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+int main() {
+  using rng_state_type = dust::random::xoroshiro128plusplus;
+  std::cout << "Using " << rng_state_type::size() << " " <<
+    std::numeric_limits<rng_state_type::int_type>::digits <<
+    " bit unsigned integers" << std::endl;
+
+  auto state = dust::random::seed<rng_state_type>(42);
+  std::cout << std::hex << state[0] << " " << state[1] << std::endl;
+}
+
    +
    +
    Using 2 64 bit unsigned integers
+bdd732262feb6e95 57e1faba65107204
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random-version.html b/cpp/random-version.html new file mode 100644 index 000000000..5a98608cd --- /dev/null +++ b/cpp/random-version.html @@ -0,0 +1,325 @@ + + + + + + + + + Query version information - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
    +
    + +
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    +
    dust 0.15.1 documentation
     +
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    +
    +
    +

    Query version information#

    +

    We define several constants that can be used for feature testing and reporting:

    +
    +
    +DUST_VERSION_MAJOR 0#
    +
    + +
    +
    +DUST_VERSION_MINOR 15#
    +
    + +
    +
    +DUST_VERSION_PATCH 1#
    +
    + +
    +
    +DUST_VERSION_STRING "0.15.1"#
    +
    + +

    The most useful for testing is DUST_VERSION_CODE which is built from the major, minor and patch numbers (10000 * major + 100 + minor + patch), so version 1.23.45 would be 12345 and 0.4.8 would be 408

    +
    +
    +DUST_VERSION_CODE 1501#
    +
    + +
    +

    Example#

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+int main() {
+  // Check version compatibility at compile time or runtime
+  static_assert(DUST_VERSION_CODE > 1110, // requires at least 0.11.10
+                "Your version of dust is too old, please upgrade");
+  std::cout << DUST_VERSION_STRING << std::endl;
+}
+
    +
    +
    0.15.1
+
    +
    +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/random.html b/cpp/random.html new file mode 100644 index 000000000..1fe5ec9f8 --- /dev/null +++ b/cpp/random.html @@ -0,0 +1,303 @@ + + + + + + + + + Random number generation - dust 0.15.1 documentation + + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
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    dust 0.15.1 documentation
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    + +
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    +
    +
    +

    Random number generation#

    +

    To generate random numbers we need to

    +
      +

    1. include <dust/random/random.hpp>

      2. +

    2. decide on the generator algorithm to use

      3. +

    3. seed a random number state

      4. +

    4. draw numbers using some distribution function

      5. +
    +

    A simple complete example looks like

    +
    #include <iostream>
+#include <dust/random/random.hpp>
+
+int main() {
+  using rng_state_type = dust::random::generator<double>;
+  auto state = dust::random::seed<rng_state_type>(42);
+  for (int i = 0; i < 5; ++i) {
+    std::cout << dust::random::random_real<double>(state) << std::endl;
+  }
+}
+
    +
    +

    which produces output:

    +
    0.496954
+0.689618
+0.366961
+0.362038
+0.929985
+
    +
    +
    +

    Contents:

    + +
    +
    + +
    +
    + +
    + +
    +
    + + + + + \ No newline at end of file diff --git a/cpp/search.html b/cpp/search.html new file mode 100644 index 000000000..3427769d7 --- /dev/null +++ b/cpp/search.html @@ -0,0 +1,251 @@ + + + + + + + Search - dust 0.15.1 documentation + + + + + + + + + + + + + + + Contents + + + + + + Menu + + + + + + + + Expand + + + + + + Light mode + + + + + + + + + + + + + + Dark mode + + + + + + + Auto light/dark mode + + + + + + + + + + + + + + + + + + + +
    +
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    dust 0.15.1 documentation
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    + Copyright © 2021, Imperial College of Science, Technology and Medicine +
    + Made with Sphinx and @pradyunsg's + + Furo + +
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    + + + + + + + + \ No newline at end of file diff --git a/cpp/searchindex.js b/cpp/searchindex.js new file mode 100644 index 000000000..1d0abf4c2 --- /dev/null +++ b/cpp/searchindex.js @@ -0,0 +1 @@ +Search.setIndex({"docnames": ["index", "random", "random-distributions", "random-jump", "random-parallel", "random-primitive", "random-r", "random-seed", "random-state", "random-version"], "filenames": ["index.rst", "random.rst", "random-distributions.rst", "random-jump.rst", "random-parallel.rst", "random-primitive.rst", "random-r.rst", "random-seed.rst", "random-state.rst", "random-version.rst"], "titles": ["dust C++ documentation", "Random number generation", "Distributions", "Advancing the random number state via jumps", "Parallel random number object", "Primitive random number generation functions", "Random number interface from R", "Seeding", "Random number state", "Query version information"], "terms": {"random": [0, 2, 7, 9], "number": [0, 2, 7, 9], "gener": [0, 2, 3, 4, 7], "state": [0, 1, 2, 4, 5, 6, 7], "seed": [0, 1, 2, 3, 4, 5, 8], "primit": [0, 1], "function": [0, 1, 2, 3, 4, 6, 7, 8], "distribut": [0, 1, 5, 8], "advanc": [0, 1], "via": [0, 1], "jump": [0, 1, 4], "parallel": [0, 1], "object": [0, 1, 6], "queri": [0, 1], "version": [0, 1], "inform": [0, 1], "interfac": [0, 1], "from": [0, 1, 2, 4, 8, 9], "r": [0, 1, 2], "thi": [0, 2, 3, 4, 5, 6, 7, 8], "set": [0, 2, 6, 8], "page": 0, "describ": [0, 6, 8], "api": [0, 6], "more": [0, 6, 7], "detail": 0, "than": [0, 6, 7], "discuss": 0, "main": [0, 1, 2, 3, 4, 5, 7, 8, 9], "princip": 0, "cover": 0, "librari": 0, "To": [1, 6], "we": [1, 2, 4, 6, 7, 8, 9], "need": [1, 2, 8], "includ": [1, 2, 3, 4, 5, 6, 7, 8, 9], "dust": [1, 2, 3, 4, 5, 6, 7, 8, 9], "hpp": [1, 2, 3, 4, 5, 6, 7, 8, 9], "decid": 1, "algorithm": [1, 2, 5, 7], "us": [1, 2, 3, 4, 5, 6, 7, 8, 9], "draw": [1, 2, 5, 6, 8], "some": [1, 2, 4, 5], "A": [1, 2, 4, 5, 7], "simpl": [1, 2, 5, 8], "complet": 1, "exampl": 1, "look": 1, "like": [1, 4, 6], "iostream": [1, 2, 3, 4, 5, 7, 8, 9], "int": [1, 2, 3, 4, 5, 6, 7, 8, 9], "rng_state_typ": [1, 2, 3, 4, 5, 6, 7, 8], "doubl": [1, 2, 5, 7, 8], "auto": [1, 2, 3, 4, 5, 7, 8], "42": [1, 2, 3, 4, 5, 8], "i": [1, 2, 3, 4, 5, 6, 7, 8, 9], "0": [1, 2, 3, 4, 5, 6, 7, 8, 9], "5": [1, 2, 7, 8], "std": [1, 2, 3, 4, 5, 6, 7, 8, 9], "cout": [1, 2, 3, 4, 5, 7, 8, 9], "random_r": [1, 2, 5, 8], "endl": [1, 2, 3, 4, 5, 7, 8, 9], "which": [1, 2, 5, 6, 9], "produc": 1, "output": [1, 2, 4], "496954": [1, 5], "689618": 1, "366961": 1, "362038": 1, "929985": 1, "our": [2, 4], "support": 2, "grow": 2, "over": 2, "time": [2, 9], "If": [2, 6], "you": [2, 5, 6, 8], "yet": 2, "pleas": [2, 9], "post": 2, "an": [2, 4, 5, 6, 7, 8], "issu": 2, "http": 2, "github": 2, "com": 2, "mrc": 2, "id": 2, "templat": [2, 3, 4, 5, 6, 7, 8], "typenam": [2, 3, 4, 5, 6, 7, 8], "real_typ": [2, 5], "__nv_exec_check_disable__": [2, 5], "__host__": [2, 3, 5, 7, 8], "__device__": [2, 5, 8], "rng_state": [2, 4, 5], "min": 2, "max": 2, 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    +
    + + + +
    +
    +
    +

    Developing dust

    +
    + +
    + +

    As the project has grown, we’ve added a few processes around updating parts of the package.

    +
    +

    Adding features

    +

    Adding new methods to the dust object requires a few steps (most of which will be caught by CI)

    +
    • If you’re doing something complicated, you’ll find it more pleasant to delete all example .cpp files from src/ (sir.cpp, sirs.cpp, variable.cpp, volatility.cpp, walk.cpp) particularly if your changes break compilation. Then you’ll be in a position to iterate faster and control where the compilation errors are thrown (package tests will fail with this change, but the package will work fine). You can use ./script/remove_examples to automate this.
      • +
    • If you have made any change to the dust class (updating a method, adding an argument etc) you must regenerate the examples by running ./scripts/update_example - be sure to edit both the .cpp and .hpp files or you will get compilation errors as the definitions will not match.
      • +
    • If you make any changes to the dust class interface (updating a method, adding an argument or changing the documentation) you must run ./scripts/update_dust_generator before running devtools::document(). Running make roxygen will do this for you
      • +
    • The gpu vignette is built offline because it requires access to a CUDA toolchain and compatible device. The script ./scripts/build_gpu_vignette will update the version in the package
      • +
    +
    +

    Versioning

    +

    All PRs, no matter small, must increase the version number. This is enforced by github actions. We aim to use semanitic versioning as much as is reasonable, but our main aim is that all commits to master are easily findable in future.

    +
    • If you make any change you will need to increase the version number in DESCRIPTION before the GitHub actions checks will pass
      • +
    • If you make any changes in inst/include/dust then you also need to run ./scripts/update_version to reflect this new version number into the header file contents. This is also automatically checked on GitHub actions.
      • +
    +
    +

    Random number library

    +

    We keep the random number library in inst/include/dust so that it does not depend on anything else in the source tree so that it could be reused in other projects (R or otherwise).

    +

    To update the underlying generator code with the reference implementations at https://prng.di.unimi.it/ you should run the script at ./extra/generate.sh which will download, compile, and run small programs with the upstream implementation and write out reference output in the test directory.

    +
    +
    +

    Headers

    +

    As the project has become more complex, keeping the headers under control has become harder. Basic principles here:

    +
    • Every header must be self-contained (in that it can be included in any order and pulls in all its dependencies)
      • +
    • Includes should be grouped by (1) System (stdlib, omp etc), (2) cpp11 (if an interface file), (3) dust’s includes. Each block should be alphabetical - any deviations required to support something compiled correctly should be removed. There are exceptions to this: for example random/random.hpp imports all distributions alphabetically separately from the generators so that it’s clearer.
      • +
    • Only include cpp11 (or R) files from files within dust/r/; within these files throw errors only with throw, not with cpp11::stop (these errors will be correctly caught).
      • +

    The script scripts/check_headers will validate that headers are self contained and that only interface headers include cpp11 files (directly or indirectly).

    +
    +
    +

    Documentation

    +

    There are lots of places to consider putting documentation

    +
    • Following R package standards, all user facing functions must be documented and have examples, we use roxygen for this (generates files in man/).
      • +
    • Vignettes form the backbone of the documentation. Mostof these are directly built as normal (in vignettes/) but a few are precomputed (see vignettes_src/) where they need special resources such as access to a GPU or more cores than usually available.
      • +
    • The C++ interface is documented using doxygen tags within API functions, and then compiled to html using sphinx/breathe. Running ./scripts/docs_build_cpp will build these at sphinx/_build/html for local development
      • +
    +
    +

    Debugging cuda

    +
    R -d cuda-gdb
    +

    It might be useful to set this:

    +
    set cuda api_failures stop
    +

    Then start the process by running r <enter> and all the usual gdb things work reasonably well.

    +

    To find memory errors, compile a model with gpu = dust::dust_cuda_options(debug = TRUE) to enable debug symbols, then run with

    +
    R -d cuda-memcheck
    +

    which will report the location of invalid access.

    +

    Using printf() within kernels works fine, though it does make a mess of the screen.

    +
    +
    +

    Finding unexpcted double precision code

    +

    You want the -warn-double-usage argument, passed via -Xptxas.

    +
    gpu <- dust::dust_cuda_options(
+  fast_math = TRUE, profile = FALSE, quiet = FALSE, debug = FALSE,
+  flags = paste("--keep --source-in-ptx --generate-line-info",
+                "-Xptxas -warn-double-usage"))
    +

    The additional flags are required to make this nice to use:

    +
    • +--source-in-ptx: interleaves the source with the ptx so you know where the f64 calls come from
      • +
    • +--keep: retains the ptx so that you can read it (otherwise it is deleted) *--generate-line-info is required for the --source-in-ptx option to do anything
      • +
    +
    + +
    + + + +
    + + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/docsearch.css b/docsearch.css new file mode 100644 index 000000000..e5f1fe1df --- /dev/null +++ b/docsearch.css @@ -0,0 +1,148 @@ +/* Docsearch -------------------------------------------------------------- */ +/* + Source: https://github.com/algolia/docsearch/ + License: MIT +*/ + +.algolia-autocomplete { + display: block; + -webkit-box-flex: 1; + -ms-flex: 1; + flex: 1 +} + +.algolia-autocomplete .ds-dropdown-menu { + width: 100%; + min-width: none; + max-width: none; + padding: .75rem 0; + background-color: #fff; + background-clip: padding-box; + border: 1px solid rgba(0, 0, 0, .1); + box-shadow: 0 .5rem 1rem rgba(0, 0, 0, .175); +} + +@media (min-width:768px) { + .algolia-autocomplete .ds-dropdown-menu { + width: 175% + } +} + +.algolia-autocomplete .ds-dropdown-menu::before { + display: none +} + +.algolia-autocomplete .ds-dropdown-menu [class^=ds-dataset-] { + padding: 0; + background-color: rgb(255,255,255); + border: 0; + max-height: 80vh; +} + +.algolia-autocomplete .ds-dropdown-menu .ds-suggestions { + margin-top: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion { + padding: 0; + overflow: visible +} + +.algolia-autocomplete .algolia-docsearch-suggestion--category-header { + padding: .125rem 1rem; + margin-top: 0; + font-size: 1.3em; + font-weight: 500; + color: #00008B; + border-bottom: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--wrapper { + float: none; + padding-top: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--subcategory-column { + float: none; + width: auto; + padding: 0; + text-align: left +} + +.algolia-autocomplete .algolia-docsearch-suggestion--content { + float: none; + width: auto; + padding: 0 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--content::before { + display: none +} + +.algolia-autocomplete .ds-suggestion:not(:first-child) .algolia-docsearch-suggestion--category-header { + padding-top: .75rem; + margin-top: .75rem; + border-top: 1px solid rgba(0, 0, 0, .1) +} + +.algolia-autocomplete .ds-suggestion .algolia-docsearch-suggestion--subcategory-column { + display: block; + padding: .1rem 1rem; + margin-bottom: 0.1; + font-size: 1.0em; + font-weight: 400 + /* display: none */ +} + +.algolia-autocomplete .algolia-docsearch-suggestion--title { + display: block; + padding: .25rem 1rem; + margin-bottom: 0; + font-size: 0.9em; + font-weight: 400 +} + +.algolia-autocomplete .algolia-docsearch-suggestion--text { + padding: 0 1rem .5rem; + margin-top: -.25rem; + font-size: 0.8em; + font-weight: 400; + line-height: 1.25 +} + +.algolia-autocomplete .algolia-docsearch-footer { + width: 110px; + height: 20px; + z-index: 3; + margin-top: 10.66667px; + float: right; + font-size: 0; + line-height: 0; +} + +.algolia-autocomplete .algolia-docsearch-footer--logo { + background-image: url("data:image/svg+xml;utf8,"); + background-repeat: no-repeat; + background-position: 50%; + background-size: 100%; + overflow: hidden; + text-indent: -9000px; + width: 100%; + height: 100%; + display: block; + transform: translate(-8px); +} + +.algolia-autocomplete .algolia-docsearch-suggestion--highlight { + color: #FF8C00; + background: rgba(232, 189, 54, 0.1) +} + + +.algolia-autocomplete .algolia-docsearch-suggestion--text .algolia-docsearch-suggestion--highlight { + box-shadow: inset 0 -2px 0 0 rgba(105, 105, 105, .5) +} + +.algolia-autocomplete .ds-suggestion.ds-cursor .algolia-docsearch-suggestion--content { + background-color: rgba(192, 192, 192, .15) +} diff --git a/docsearch.js b/docsearch.js new file mode 100644 index 000000000..b35504cd3 --- /dev/null +++ b/docsearch.js @@ -0,0 +1,85 @@ +$(function() { + + // register a handler to move the focus to the search bar + // upon pressing shift + "/" (i.e. "?") + $(document).on('keydown', function(e) { + if (e.shiftKey && e.keyCode == 191) { + e.preventDefault(); + $("#search-input").focus(); + } + }); + + $(document).ready(function() { + // do keyword highlighting + /* modified from https://jsfiddle.net/julmot/bL6bb5oo/ */ + var mark = function() { + + var referrer = document.URL ; + var paramKey = "q" ; + + if (referrer.indexOf("?") !== -1) { + var qs = referrer.substr(referrer.indexOf('?') + 1); + var qs_noanchor = qs.split('#')[0]; + var qsa = qs_noanchor.split('&'); + var keyword = ""; + + for (var i = 0; i < qsa.length; i++) { + var currentParam = qsa[i].split('='); + + if (currentParam.length !== 2) { + continue; + } + + if (currentParam[0] == paramKey) { + keyword = decodeURIComponent(currentParam[1].replace(/\+/g, "%20")); + } + } + + if (keyword !== "") { + $(".contents").unmark({ + done: function() { + $(".contents").mark(keyword); + } + }); + } + } + }; + + mark(); + }); +}); + +/* Search term highlighting ------------------------------*/ + +function matchedWords(hit) { + var words = []; + + var hierarchy = hit._highlightResult.hierarchy; + // loop to fetch from lvl0, lvl1, etc. + for (var idx in hierarchy) { + words = 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    +
    + + + + +
    +
    +
    +

    dust +

    + + +

    Stochastic models appear in many domains as they are easy to write out, but hard to analyse without running many realisations of the process. dust provides an engine for running stochastic models, taking care of many bookkeeping details such as:

    +
      +
    • Running stochastic models in parallel on multi-core machines
      • +
    • Running models massively in parallel on GPU without writing any low-level code
      • +
    • Reducing output by filtering over steps or intermediate outputs
      • +
    • Providing useful verbs for working with stochastic models (for initialisation, state setting, parameter updating, and inspection)
      • +
    • Combining multiple realisations due to stochastic variability and due to different parameter sets
      • +
    +
    +

    Get started +

    +

    Two vignettes provide an overview of the package, depending on your tastes:

    + +

    There are further vignettes describing details:

    + +

    And several on the random number generator, around which dust is built:

    + +

    The C++ API is documented in a separate set of documentation

    +

    You can also read our open access paper describing dust and some related tools that use it:

    +
    +

    FitzJohn, Knock, Whittles, Perez-Guizman, Bhatia, Guntoro, Watson, Whittaker, Ferguson, Cori, Baguelin, Lees 2021: Reproducible parallel inference and simulation of stochastic state space models using odin, dust, and mcstate, Wellcome Open Research 5, 288

    +
    +
    +
    +

    Higher-level +

    +

    The dust package, while designed to be user-friendly, is lower-level than many users need. The odin.dust package provides a way of compiling stochastic odin models to work with dust. For example, to create a parallel epidemiological model, one might write simply:

    +
    +sir <- odin.dust::odin_dust({
+  update(S) <- S - n_SI
+  update(I) <- I + n_SI - n_IR
+  update(R) <- R + n_IR
+
+  n_IR <- rbinom(I, 1 - exp(-beta * I / (S + I + R)))
+  n_SI <- rbinom(S, 1 - exp(-gamma))
+
+  initial(S) <- S_ini
+  initial(I) <- I_ini
+  initial(R) <- 0
+
+  S_ini <- user(1000)
+  I_ini <- user(10)
+  beta <- user(0.2)
+  gamma <- user(0.1)
+})
    +
    +
    +

    Use-cases +

    +

    We use dust to power several epidemiological models. Public examples include:

    +
      +
    • +sircovid - a large model (over 15k states) of COVID-19 in the UK
      • +
    • +gonovaxdust - a model of gonorrhoea infection with vaccination
      • +
    +
    +
    +

    Installation +

    +

    To install dust:

    +
    +# install.packages("drat") # -- if you don't have drat installed
+drat:::add("ncov-ic")
+install.packages("dust")
    +

    You will need a compiler to install dependencies for the package, and to build any models with dust. dust uses pkgbuild to build its shared libraries so use pkgbuild::check_build_tools() to see if your system is ok to use.

    +

    The development version of the package can be installed directly from GitHub if you prefer with:

    +
    +remotes::install_github("mrc-ide/dust", upgrade = FALSE)
    +
    +
    +

    License +

    +

    MIT © Imperial College of Science, Technology and Medicine

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    +
    +
    + + +
    + + +
    +

    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    +

    Site built with pkgdown 2.0.7.

    +
    + +
    +
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000000000..b73decc46 --- /dev/null +++ b/news/index.html @@ -0,0 +1,471 @@ + +Changelog • dust + + +
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    +
    +

    Changelog

    + Source: NEWS.md +
    + +
    +

    dust 0.13.12

    +
    • New method $time_type() to determine of a model uses discrete time (discrete) or continuous time (continuous).
      • +
    +
    +

    dust 0.13.10

    +
    • Avoid integer overflow in binomial(); previously n of greater than 2^31 - 1 (.Machine$integer.max) would overflow and error (mrc-4046, reported by Jørgen Eriksson Midtbø).
      • +
    +
    +

    dust 0.13.8

    +
    • Support for solving ODE models (based on a prototype implementation in mode; full documentation forthcoming.
      • +
    +
    +

    dust 0.12.5

    +
    • Allow control over the C++ specification using the argument cpp_std, and including other packages’ headers using the argument linking_to in dust::dust() +
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    +
    +

    dust 0.12.1

    +
    • The update_state() method gains an index argument for setting just some variables in an update.
      • +
    +
    +

    dust 0.12.0

    +
    • Breaking change, with step (and so on with step_end) changing to time everywhere, in order to smooth the inclusion of continuous time models. This affects quite a few methods: +
      • +step() and set_step() become time() and set_time() +
        • +
      • +update_state()’s argument changes from step to time +
        • +
      • +
    +
    +

    dust 0.11.24

    +
    • Add min_log_likelihood support to $filter() (#361)
      • +
    +
    +

    dust 0.11.23

    +
    • Allow use of $filter() with deterministic models (that support it)
      • +
    • Allow partial running of the filter from the current step up to some step part way through the data (#177)
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    +
    +

    dust 0.11.22

    +
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    +

    dust 0.11.21

    +
    • Remove the functionality that allowed a vector of start times to be provided, as we were never using it and it simplifes things to remove it (#310)
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    +

    dust 0.11.17

    +
    • Remove dust::dust_rng_state_long_jump now that we have proper distributed RNG state support (#343)
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    +
    +

    dust 0.11.15

    +
    +
    +

    dust 0.11.11

    +
    • Removed methods $set_state, $reset and $set_pars which were deprecated in favour of $update_state in 0.9.21 (#273)
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    +
    +

    dust 0.11.10

    +
    • The names of different generator internal states has been simplified to lose the trailing state, e.g. xoshiro256star_state becomes xoshiro256star (#332)
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    +
    +

    dust 0.11.8

    +
    • Improved the interface for using dust’s random number support from other packages (#329)
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    dust 0.11.7

    +
    • New polar algorithm for normally distributed random numbers; faster than Box-Muller but slower than Ziggurat
      • +
    • Tweaked algorithm for Ziggurat so now ~10% faster by avoiding drawing a second random number when working with 64 bit integers
      • +
    • Added a new vignette describing the internals of the normal sampling algorithms (#325)
      • +
    +
    +

    dust 0.11.6

    +
    • Added support for drawing normally distributed random numbers using the ziggurat method. Currently this is only efficient on a CPU, though supported on a GPU (#308)
      • +
    +
    +

    dust 0.11.5

    +
    • Major header reorganisation, the dust::cuda namespace is now dust::gpu, most user-facing uses of cuda and device now replaced with gpu (#298, #317)
      • +
    • New (static) method real_size on every dust class for accessing the size of real_type, in bits (#301)
      • +
    +
    +

    dust 0.11.1

    +
    • Support for the multinomial distribution. This differs from most other random number support because it returns a vector of values not a single number (#307)
      • +
    +
    +

    dust 0.11.0

    +
    • Rationalised the GPU interface, now once created models can only be used on either the GPU or CPU which simplifies the internal bookkeeping (#292, #302)
      • +
    +
    +

    dust 0.10.0

    +
    • Improved and generalised RNG interface, with more algorithms and more control +
      • Expand set of included generators to 12 with different storage types, period and precision (#281)
        • +
      • Faster random number generation with single precision, using xoshiro128plus (#282)
        • +
      • Slightly faster real number generation for all generators by avoiding division (#280)
        • +
      • The dust_rng object has been refactored with methods changing names, a new behaviour when using multiple generators, and parallelisation (#279)
        • +
      • +
    • Type names have been standardised and we now avoid _t in favour of _type in line with the POSIX standard; this impacts all existing dust-using code (#278)
      • +
    • Density function names have changed from dust::dbinom to dust::density::binomial (and so on, #291)
      • +
    +
    +

    dust 0.9.21

    +
    • Deprecate the previous state update methods ($reset(), $set_pars() and $set_state()) in favour of a single method that can update any or all of parameters, model state and time, $update_state() (#180)
      • +
    • Model determinism is now fixed at creation, rather than being settable via run and simulate, with deterministic now an argument to the constructor (#270)
      • +
    +
    +

    dust 0.9.20

    +
    • Change to the dust::densities::dnbinom() to offer both of the same parameterisations as R’s dnbinom, explicitly as dust::densities::dnbinom_mu() and dust::densities::dnbinom_prob() (#171)
      • +
    +
    +

    dust 0.9.18

    +
    • New function dust::dust_generate for creating a mini-package from a dust model for inspection or later loading (#204)
      • +
    • New option to dust::dust to skip the model cache, which may be useful when compiling with (say) different GPU options (#248)
      • +
    +
    +

    dust 0.9.14

    +
    • Add two new vignettes covering model/data comparison and use on GPUs; see vignette("data") and vignette("cuda") (#183, #229)
      • +
    +
    +

    dust 0.9.10

    +
    • Finer control over GPU settings, with the block size of run() now (optionally) exposed
      • +
    • On the GPU integers are kept in shared memory even where reals will no longer fit (#245)
      • +
    +
    +

    dust 0.9.8

    +
    • Fix infinite loop with rbinom using floats
      • +
    +
    +

    dust 0.9.7

    +
    • Synchronise possible divergences in the density functions (CUDA only) (#243)
      • +
    +
    +

    dust 0.9.6

    +
    • Fix a possible issue with dnbinom in float mode with a small mean (#240)
      • +
    +
    +

    dust 0.9.5

    +
    • Fix a bug when running the systematic resample in the particle filter in float mode (#238)
      • +
    +
    +

    dust 0.9.4

    +
    • Fix a bug when running the CUDA version of the particle filter without history/trajectories.
      • +
    +
    +

    dust 0.9.3

    +
    • Change real_t at compilation, and return information about the size of real_t from model objects (#233)
      • +
    +
    +

    dust 0.9.2

    +
    • Add a CUDA version of the simulate method.
      • +
    +
    +

    dust 0.9.1

    +
    • Move history and snapshot saving out of VRAM, and make it asynchronous.
      • +
    +
    +

    dust 0.9.0

    +
    • Added CUDA version of the particle filter, run with model$filter(device = TRUE) (#224)
      • +
    +
    +

    dust 0.8.15

    +
    • Removed functions dust::dust_simulate and dust::dust_iterate, which were deprecated in 0.7.9 (#215)
      • +
    +
    +

    dust 0.8.7

    +
    • Invalid inputs in rbinom are converted into exceptions which are safely thrown even from parallel code (#190)
      • +
    +
    +

    dust 0.8.5

    +
    • The filter method can save snapshots at points along a run (#176)
      • +
    +
    +

    dust 0.8.4

    +
    • Reduce host and memcpy usage in device reorder by computing scatter index within the kernel (#198)
      • +
    +
    +

    dust 0.8.3

    +
    • Fix issue with rnorm() running on a GPU (device code).
      • +
    • Fix issue with unaligned shared copy in CUDA code.
      • +
    +
    +

    dust 0.8.2

    +
    • Don’t rewrite files with identical content during generation; this avoids recompilation of code across sessions when the argument workdir is used with dust::dust (#195)
      • +
    +
    +

    dust 0.8.0

    +
    • Add GPU support (#73)
      • +
    +
    +

    dust 0.7.15

    +
    +
    +

    dust 0.7.13

    +
    • Improved handling of multi-parameter models, allowing parameter sets to be structured and handling of the special case of one particle per parameter set, outlined in vignette("multi") (#169)
      • +
    +
    +

    dust 0.7.9

    +
    • Deprecate dust::dust_simulate and dust::dust_iterate which are replaced with a new method $simulate on the object which retains state and makes this more powerful (#100, #119, #121)
      • +
    +
    +

    dust 0.7.8

    +
    • Allow set_pars method to be used with multiparameter dust objects (#125)
      • +
    • Enforce rule that once created a dust object may not change state size (i.e., the number of particles, state elements and number of parameter sets may not change). This was already assumed by mcstate
      • +
    +
    +

    dust 0.7.5

    +
    • Beginnings of particle filter support, with a new $filter() method (only works for models with a compiled “compare” method) (#155)
      • +
    +
    +

    dust 0.7.4

    +
    • More complete handling of $compare_data() with multiple parameters, with the dust::dust_data function now expanded to support this (#152)
      • +
    +
    +

    dust 0.7.3

    +
    • Added new method $resample() which implements the resampling algorithm used by the mcstate particle filter (#137)
      • +
    • The $compare_data() method is better behaved with multi-parameter dust objects, returning a matrix (#136)
      • +
    +
    +

    dust 0.7.2

    +
    • Added new methods $n_particles() and $n_state() to every dust model which can be used to query the size of the state (#149)
      • +
    +
    +

    dust 0.7.0

    +
    • Dust models must now specify two internal types, internal_t and shared_t. The latter is a pointer to constant data shared across all particles within a parameter set (#143)
      • +
    +
    +

    dust 0.6.2

    +
    • Support for some basic density functions within the header <dust/densities.hpp>. Supported distributions include dbinom, dnbinom, dbetabinom and dpois. These are included for use within comparison functions (#134)
      • +
    +
    +

    dust 0.6.1

    +
    • Compiled “comparison” functions are supported, designed to compute likelihoods for mcstate; this interface will be expanded and documented in a future release (#129)
      • +
    +
    +

    dust 0.6.0

    +
    • The data argument (and along with it things like set_data) have moved to become pars as that is how we’re using it, and to make space for a future data element (#130)
      • +
    +
    +

    dust 0.5.10

    +
    • Add support for rexp from dust model, just using inversion for now (#127)
      • +
    +
    +

    dust 0.5.9

    +
    • Start of support for running dust objects with multiple data/parameter sets at once (#92)
      • +
    +
    +

    dust 0.5.7

    +
    • New method set_n_threads() for changing the number of OpenMP threads after initialisation (#122)
      • +
    +
    +

    dust 0.5.6

    +
    • +dust::dust_simulate() can return the entire model end state (#119)
      • +
    +
    +

    dust 0.5.4

    +
    • New $set_data() method, similar to reset but changing only the data/parameters mid-model run, holding state and everything else identical (#114)
      • +
    +
    +

    dust 0.5.3

    +
    • Add support for configuring dust generation using C++ pseudo-attributes.
      • +
    +
    +

    dust 0.5.2

    +
    • Back out the interleaved rng state from 0.5.0, which is causing a performance regression
      • +
    +
    +

    dust 0.5.1

    +
    • Remove prototype GPU interface, in preparation for a new version (#109)
      • +
    +
    +

    dust 0.5.0

    +
    • The rng objects (dust_rng) also get a $set_state() method (primarily of debugging interest)
      • +
    +
    +

    dust 0.4.12

    +
    • New $set_rng_state() method, the inverse to $rng_state() for taking a previously saved state and setting it into a model (#??)
      • +
    +
    +

    dust 0.4.11

    +
    • +dust::dust_iterate now copies names from the index as rownames (#101)
      • +
    +
    +

    dust 0.4.9

    +
    • The “low n * p” branch of the binomial distribution now uses a slightly faster algorithm (#91)
      • +
    +
    +

    dust 0.4.8

    +
    +
    +

    dust 0.4.7

    +
    • +dust::dust_package() validates that the package contains a suitable src/Makevars for use with openmp, or creates one if missing (#95)
      • +
    +
    +

    dust 0.4.6

    +
    • Some examples are now compiled into the package and available via dust::dust_example(), reducing the need for a compiler for exploration and making examples and testing faster (#89)
      • +
    +
    +

    dust 0.4.5

    +
    • Change of behaviour for seed, which now seeds from R’s random number if given the default value of NULL (#85, #87)
      • +
    • The rng_state method can optionally advance the random number stream, making it more suitable for use with dust::dust_simulate +
      • +
    • A new utility dust::dust_rng_long_jump which can advance the saved state of a dust RNG, suitable for creating independent streams from one saved state.
      • +
    +
    +

    dust 0.4.4

    +
    • Helper function dust::dust_simulate is renamed to dust::dust_iterate +
      • +
    • New function dust::dust_simulate which simulates many parameter sets and starting points at once, possibly in parallel (#84)
      • +
    +
    +

    dust 0.4.3

    +
    • If $set_index() uses a named index vector, then those names are copied back as rownames on the returned matrix. Similarly, if $state() is used with a named index then those names are used as rownames (#81)
      • +
    +
    +

    dust 0.4.0

    +
    • Can now generate dust objects that run on the GPU (#69)
      • +
    +
    +

    dust 0.3.0

    +
    • Overhaul of the RNG interface, where we now pass state and use free functions; this is needed to support future development work (#60)
      • +
    +
    +

    dust 0.2.2

    +
    • New $rng_state() method for getting the RNG state as a raw vector
      • +
    +
    +

    dust 0.2.0

    +
    • Use cpp11 as the backend (#22)
      • +
    +
    +

    dust 0.1.5

    +
    • Simpler RNG interface; we now always use as many RNG streams as there are particles (#51)
      • +
    +
    +

    dust 0.1.4

    +
    • New function dust::dust_simulate which provides a helper for running a simulation while collecting output (#7)
      • +
    +
    +

    dust 0.1.3

    +
    • Allow $set_state() to accept an initial state of NULL, in which case only the time is set (#48)
      • +
    +
    +

    dust 0.1.2

    +
    • Allow $set_state() to accept an initial step too. This can be a vector if particles start at different initial steps, in which case all particles are run up to the latest step (#45)
      • +
    +
    +

    dust 0.1.1

    +
    • Allow $set_state() to accept a matrix in order to start particles with different starting values (#43)
      • +
    +
    + + + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
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  • , and enclosing
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    +
    + + + +
    +
    +
    +

    Create a dust model from a C++ input file

    + Source: R/interface.R + +
    + +
    +

    Create a dust model from a C++ input file. This function will +compile the dust support around your model and return an object +that can be used to work with the model (see the Details below, +and dust_generator).

    +
    + +
    + 
    dust(
+  filename,
+  quiet = FALSE,
+  workdir = NULL,
+  gpu = FALSE,
+  real_type = NULL,
+  linking_to = NULL,
+  cpp_std = NULL,
+  compiler_options = NULL,
+  optimisation_level = NULL,
+  skip_cache = FALSE
+)
    +
    + +
    +

    Arguments

    +
    filename
    +

    The path to a single C++ file

    + + +
    quiet
    +

    Logical, indicating if compilation messages from +pkgbuild should be displayed. Error messages will be +displayed on compilation failure regardless of the value used.

    + + +
    workdir
    +

    Optional working directory to use. If NULL +uses a temporary directory. By using a different directory of +your choosing you can see the generated code.

    + + +
    gpu
    +

    Logical, indicating if we should generate GPU +code. This requires a considerable amount of additional software +installed (CUDA toolkit and drivers) as well as a +CUDA-compatible GPU. If TRUE, then we call +dust_cuda_options with no arguments. Alternatively, call +that function and pass the value here (e.g, gpu = dust::dust_cuda_options(debug = TRUE)). Note that due to the +use of the __syncwarp() primitive this may require a GPU with +compute version 70 or higher.

    + + +
    real_type
    +

    Optionally, a string indicating a substitute type to +swap in for your model's real_type declaration. If given, then we +replace the string using real_type = (double|float) with the +given type. This is primarily intended to be used as gpu = TRUE, real_type = "float" in order to create model for the GPU +that will use 32 bit floats (rather than 64 bit doubles, which +are much slower). For CPU models decreasing precision of your +real type will typically just decrease precision for no +additional performance.

    + + +
    linking_to
    +

    Optionally, a character vector of additional +packages to add to the DESCRIPTION's LinkingTo field. Use +this when your model pulls in C++ code that is packaged within +another package's header-only library.

    + + +
    cpp_std
    +

    The C++ standard to use, if you need to set one +explicitly. See the section "Using C++ code" in "Writing R +extensions" for the details of this, and how it interacts with +the R version currently being used. For R 4.0.0 and above, C++11 +will be used; as dust depends on at least this version of R you +will never need to specify a version this low. Sensible options +are C++14, C++17, etc, depending on the features you need +and what your compiler supports.

    + + +
    compiler_options
    +

    A character vector of additional options +to pass through to the C++ compiler. These will be passed +through without any shell quoting or validation, so check the +generated commands and outputs carefully in case of error. Note +that R will apply these before anything in your personal +Makevars.

    + + +
    optimisation_level
    +

    A shorthand way of specifying common +compiler options that control optimisation level. By default +(NULL) no options are generated from this, and the +optimisation level will depend on your user Makevars file. +Valid options are none which disables optimisation (-O0), +which will be faster to compile but much slower, standard +which enables standard level of optimisation (-O2), useful if +your Makevars/pkgload configuration is disabling optimisation, +or max (-O3 and --fast-math) which enables some +slower-to-compile and potentially unsafe +optimisations. These options are applied after +compiler_options and may override options provided there. +Note that as for compiler_options, R will apply these before +anything in your personal Makevars

    + + +
    skip_cache
    +

    Logical, indicating if the cache of previously +compiled models should be skipped. If TRUE then your model will +not be looked for in the cache, nor will it be added to the +cache after compilation.

    + +
    +
    +

    Value

    + + +

    A dust_generator object based on your source files

    +
    +
    +

    Input requirements

    + + + +

    Your input dust model must satisfy a few requirements.

    • Define some class that implements your model (below model is +assumed to be the class name)

      • +

    • That class must define a type internal_type (so +model::internal_type) that contains its internal data that the +model may change during execution (i.e., that is not shared +between particles). If no such data is needed, you can do +using internal_type = dust::no_internal; to indicate this.

      • +

    • We also need a type shared_type that contains constant internal +data is shared between particles (e.g., dimensions, arrays that +are read but not written). If no such data is needed, you can do +using share_type = dust::no_shared; to indicate this.

      • +

    • That class must also include a type alias that describes the +model's floating point type, real_type. Most models can include +using real_type = double; in their public section.

      • +

    • The class must also include a type alias that describes the model's +data type. If your model does not support data, then write +using data_type = dust::no_data;, which disables the +compare_data and set_data methods. Otherwise see +vignette("data") for more information.

      • +

    • The class must have a constructor that accepts const dust::pars_type<model>& pars for your type model. This will have +elements shared and internal which you can assign into your +model if needed.

      • +

    • The model must have a method size() returning size_t which +returns the size of the system. This size may depend on values +in your initialisation object but is constant within a model +run.

      • +

    • The model must have a method initial (which may not be +const), taking a time step number (size_t) and returning a +std::vector<real_type> of initial state for the model.

      • +

    • The model must have a method update taking arguments:

      • size_t time: the time step number

        • +

      • const double * state: the state at the beginning of the +time step

        • +

      • dust::rng_state_type<real_type>& rng_state: the dust random number +generator state - this must be a reference, as it will be modified +as random numbers are drawn

        • +

      • double *state_next: the end state of the model +(to be written to by your function)

        • +
      • +

    Your update function is the core here and should update the +state of the system - you are expected to update all values of +state on return.

    +

    It is very important that none of the functions in the class use +the R API in any way as these functions will be called in +parallel.

    +

    You must also provide a data/parameter-wrangling function for +producing an object of type dust::pars_type<model> from an R list. We +use cpp11 for this. Your function will look like:

    +

    namespace dust {
+template <>
+dust::pars_type<model> dust_pars<model>(cpp11::list pars) {
+  // ...
+  return dust::pars_type<model>(shared, internal);
+}
+}

    +

    With the body interacting with pars to create an object of type +model::shared_type and model::internal_type before returning the +dust::pars_type object. This function will be called in serial +and may use anything in the cpp11 API. All elements of the +returned object must be standard C/C++ (e.g., STL) types and +not cpp11/R types. If your model uses only shared or internal, +you may use the single-argument constructor overload to +dust::pars_type which is equivalent to using dust::no_shared or +dust::no_internal for the missing argument.

    +

    Your model may provided a template specialisation +dust::dust_info<model>() returning a cpp11::sexp for +returning arbitrary information back to the R session:

    +

    namespace dust {
+template <>
+cpp11::sexp dust_info<model>(const dust::pars_type<sir>& pars) {
+  return cpp11::wrap(...);
+}
+}

    +

    What you do with this is up to you. If not present then the +info() method on the created object will return NULL. +Potential use cases for this are to return information about +variable ordering, or any processing done while accepting the +pars object used to create the pars fed into the particles.

    +
    +
    +

    Configuring your model

    + + + +

    You can optionally use C++ pseudo-attributes to configure the +generated code. Currently we support two attributes:

    • [[dust::class(classname)]] will tell dust the name of your +target C++ class (in this example classname). You will need to +use this if your file uses more than a single class, as +otherwise will try to detect this using extremely simple +heuristics.

      • +

    • [[dust::name(modelname)]] will tell dust the name to use for +the class in R code. For technical reasons this must be +alphanumeric characters only (sorry, no underscore) and must not +start with a number. If not included then the C++ type name will +be used (either specified with [[dust::class()]] or detected).

      • +
    +
    +

    Error handling

    + + + +

    Your model should only throw exceptions as a last resort. One such +last resort exists already if rbinom is given invalid inputs +to prevent an infinite loop. If an error is thrown, all +particles will complete their current run, and then the error +will be rethrown - this is required by our parallel processing +design. Once this happens though the state of the system is +"inconsistent" as it contains particles that have run for +different lengths of time. You can extract the state of the +system at the point of failure (which may help with debugging) +but you will be unable to continue running the object until +either you reset it (with $update_state()). An error will be +thrown otherwise.

    +

    Things are worse on a GPU; if an error is thrown by the RNG code +(happens in rbinom when given impossible inputs such as +negative sizes, probabilities less than zero or greater than 1) +then we currently use CUDA's __trap() function which will +require a process restart to be able to use anything that uses +the GPU again, covering all methods in the class. However, this +is preferable to the infinite loop that would otherwise be +caused.

    +
    +
    +

    See also

    +

    dust_generator for a description of the class +of created objects, and dust_example() for some +pre-built examples. If you want to just generate the code and +load it yourself with pkgload::load_all or some other means, +see dust_generate)

    +
    + +
    +

    Examples

    + 
    
+# dust includes a couple of very simple examples
+filename <- system.file("examples/walk.cpp", package = "dust")
+
+# This model implements a random walk with a parameter coming from
+# R representing the standard deviation of the walk
+writeLines(readLines(filename))
+#> class walk {
+#> public:
+#>   using real_type = double;
+#>   using data_type = dust::no_data;
+#>   using internal_type = dust::no_internal;
+#>   using rng_state_type = dust::random::generator<real_type>;
+#> 
+#>   struct shared_type {
+#>     real_type sd;
+#>     bool random_initial;
+#>   };
+#> 
+#>   walk(const dust::pars_type<walk>& pars) : shared(pars.shared) {
+#>   }
+#> 
+#>   size_t size() const {
+#>     return 1;
+#>   }
+#> 
+#>   std::vector<real_type> initial(size_t time, rng_state_type& rng_state) {
+#>     std::vector<real_type> ret = {0};
+#>     if (shared->random_initial) {
+#>       ret[0] = dust::random::normal<real_type>(rng_state, 0, shared->sd);
+#>     }
+#>     return ret;
+#>   }
+#> 
+#>   void update(size_t time, const real_type * state, rng_state_type& rng_state,
+#>               real_type * state_next) {
+#>     state_next[0] = state[0] +
+#>       dust::random::normal<real_type>(rng_state, 0, shared->sd);
+#>   }
+#> 
+#> private:
+#>   dust::shared_ptr<walk> shared;
+#> };
+#> 
+#> namespace dust {
+#> 
+#> template <>
+#> dust::pars_type<walk> dust_pars<walk>(cpp11::list pars) {
+#>   walk::real_type sd = cpp11::as_cpp<walk::real_type>(pars["sd"]);
+#>   const bool random_initial = pars["random_initial"] == R_NilValue ? false :
+#>     cpp11::as_cpp<bool>(pars["random_initial"]);
+#>   return dust::pars_type<walk>(walk::shared_type{sd, random_initial});
+#> }
+#> 
+#> }
+
+# The model can be compiled and loaded with dust::dust(filename)
+# but it's faster in this example to use the prebuilt version in
+# the package
+model <- dust::dust_example("walk")
+
+# Print the object and you can see the methods that it provides
+model
+#> <dust> object generator
+#>   Public:
+#>     initialize: function (pars, time, n_particles, n_threads = 1L, seed = NULL, 
+#>     name: function () 
+#>     param: function () 
+#>     run: function (time_end) 
+#>     simulate: function (time_end) 
+#>     run_adjoint: function () 
+#>     set_index: function (index) 
+#>     index: function () 
+#>     ode_control: function () 
+#>     ode_statistics: function () 
+#>     n_threads: function () 
+#>     n_state: function () 
+#>     n_particles: function () 
+#>     n_particles_each: function () 
+#>     shape: function () 
+#>     update_state: function (pars = NULL, state = NULL, time = NULL, set_initial_state = NULL, 
+#>     state: function (index = NULL) 
+#>     time: function () 
+#>     set_stochastic_schedule: function (time) 
+#>     reorder: function (index) 
+#>     resample: function (weights) 
+#>     info: function () 
+#>     pars: function () 
+#>     rng_state: function (first_only = FALSE, last_only = FALSE) 
+#>     set_rng_state: function (rng_state) 
+#>     has_openmp: function () 
+#>     has_gpu_support: function (fake_gpu = FALSE) 
+#>     has_compare: function () 
+#>     real_size: function () 
+#>     time_type: function () 
+#>     rng_algorithm: function () 
+#>     uses_gpu: function (fake_gpu = FALSE) 
+#>     n_pars: function () 
+#>     set_n_threads: function (n_threads) 
+#>     set_data: function (data, shared = FALSE) 
+#>     compare_data: function () 
+#>     filter: function (time_end = NULL, save_trajectories = FALSE, time_snapshot = NULL, 
+#>     gpu_info: function () 
+#>   Private:
+#>     pars_: NULL
+#>     pars_multi_: NULL
+#>     index_: NULL
+#>     info_: NULL
+#>     n_threads_: NULL
+#>     n_particles_: NULL
+#>     n_particles_each_: NULL
+#>     shape_: NULL
+#>     ptr_: NULL
+#>     gpu_config_: NULL
+#>     ode_control_: NULL
+#>     methods_: NULL
+#>     param_: NULL
+#>     reload_: NULL
+#>   Parent env: <environment: namespace:dust>
+#>   Locked objects: TRUE
+#>   Locked class: FALSE
+#>   Portable: TRUE
+
+# Create a model with standard deviation of 1, initial time step zero
+# and 30 particles
+obj <- model$new(list(sd = 1), 0, 30)
+obj
+#> <dust>
+#>   Public:
+#>     compare_data: function () 
+#>     filter: function (time_end = NULL, save_trajectories = FALSE, time_snapshot = NULL, 
+#>     gpu_info: function () 
+#>     has_compare: function () 
+#>     has_gpu_support: function (fake_gpu = FALSE) 
+#>     has_openmp: function () 
+#>     index: function () 
+#>     info: function () 
+#>     initialize: function (pars, time, n_particles, n_threads = 1L, seed = NULL, 
+#>     n_pars: function () 
+#>     n_particles: function () 
+#>     n_particles_each: function () 
+#>     n_state: function () 
+#>     n_threads: function () 
+#>     name: function () 
+#>     ode_control: function () 
+#>     ode_statistics: function () 
+#>     param: function () 
+#>     pars: function () 
+#>     real_size: function () 
+#>     reorder: function (index) 
+#>     resample: function (weights) 
+#>     rng_algorithm: function () 
+#>     rng_state: function (first_only = FALSE, last_only = FALSE) 
+#>     run: function (time_end) 
+#>     run_adjoint: function () 
+#>     set_data: function (data, shared = FALSE) 
+#>     set_index: function (index) 
+#>     set_n_threads: function (n_threads) 
+#>     set_rng_state: function (rng_state) 
+#>     set_stochastic_schedule: function (time) 
+#>     shape: function () 
+#>     simulate: function (time_end) 
+#>     state: function (index = NULL) 
+#>     time: function () 
+#>     time_type: function () 
+#>     update_state: function (pars = NULL, state = NULL, time = NULL, set_initial_state = NULL, 
+#>     uses_gpu: function (fake_gpu = FALSE) 
+#>   Private:
+#>     gpu_config_: NULL
+#>     index_: NULL
+#>     info_: NULL
+#>     methods_: list
+#>     n_particles_: 30
+#>     n_particles_each_: 30
+#>     n_threads_: 1
+#>     ode_control_: NULL
+#>     param_: NULL
+#>     pars_: list
+#>     pars_multi_: FALSE
+#>     ptr_: externalptr
+#>     reload_: NULL
+#>     shape_: 30
+
+# Curent state is all zero
+obj$state()
+#>      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13] [,14]
+#> [1,]    0    0    0    0    0    0    0    0    0     0     0     0     0     0
+#>      [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25] [,26]
+#> [1,]     0     0     0     0     0     0     0     0     0     0     0     0
+#>      [,27] [,28] [,29] [,30]
+#> [1,]     0     0     0     0
+
+# Current time is also zero
+obj$time()
+#> [1] 0
+
+# Run the model up to time step 100
+obj$run(100)
+#>          [,1]      [,2]     [,3]      [,4]     [,5]      [,6]    [,7]     [,8]
+#> [1,] 9.272973 0.2890321 15.55267 0.7687308 9.163547 -10.21083 12.4816 18.68955
+#>           [,9]    [,10]    [,11]    [,12]     [,13]    [,14]    [,15]    [,16]
+#> [1,] -18.29856 2.680278 6.473689 2.189865 -7.466181 4.665493 8.862259 11.83087
+#>        [,17]    [,18]     [,19]    [,20]     [,21]     [,22]     [,23]    [,24]
+#> [1,] 10.9931 17.21938 -5.345609 -3.92305 -4.798443 -7.233241 -12.60575 5.675072
+#>         [,25]    [,26]     [,27]    [,28]   [,29]     [,30]
+#> [1,] 7.550567 6.855366 -6.135951 5.013464 8.44695 -12.81809
+
+# Reorder/resample the particles:
+obj$reorder(sample(30, replace = TRUE))
+
+# See the state again
+obj$state()
+#>          [,1]      [,2]      [,3]    [,4]     [,5]      [,6]      [,7]
+#> [1,] 6.473689 -6.135951 -4.798443 10.9931 11.83087 0.7687308 -12.60575
+#>           [,8]      [,9]    [,10]     [,11]    [,12]     [,13]    [,14]
+#> [1,] -12.81809 0.2890321 15.55267 -18.29856 -3.92305 -5.345609 6.473689
+#>          [,15]    [,16]     [,17]    [,18]    [,19]    [,20]   [,21]     [,22]
+#> [1,] -6.135951 9.163547 -7.466181 5.675072 18.68955 7.550567 10.9931 0.7687308
+#>         [,23]     [,24]   [,25]     [,26]     [,27]    [,28]    [,29]    [,30]
+#> [1,] 4.665493 0.2890321 12.4816 -4.798443 -4.798443 5.675072 -3.92305 2.680278
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_cuda_configuration.html b/reference/dust_cuda_configuration.html new file mode 100644 index 000000000..7631fd4eb --- /dev/null +++ b/reference/dust_cuda_configuration.html @@ -0,0 +1,278 @@ + +Detect CUDA configuration — dust_cuda_configuration • dust + + +
    +
    + + + +
    +
    +
    +

    Detect CUDA configuration

    + Source: R/cuda.R + +
    + +
    +

    Detect CUDA configuration. This function tries to compile a small +program with nvcc and confirms that this can be loaded into R, +then uses that program to query the presence and capabilities of +your NVIDIA GPUs. If this works, then you can use the GPU-enabled +dust features, and the information returned will help us. It's +quite slow to execute (several seconds) so we cache the value +within a session. Later versions of dust will cache this across +sessions too.

    +
    + +
    + 
    dust_cuda_configuration(
+  path_cuda_lib = NULL,
+  path_cub_include = NULL,
+  quiet = TRUE,
+  forget = FALSE
+)
    +
    + +
    +

    Arguments

    +
    path_cuda_lib
    +

    Optional path to the CUDA libraries, if they +are not on system library paths. This will be added as +-L{path_cuda_lib} in calls to nvcc

    + + +
    path_cub_include
    +

    Optional path to the CUB headers, if using +CUDA < 11.0.0. See Details

    + + +
    quiet
    +

    Logical, indicating if compilation of test programs +should be quiet

    + + +
    forget
    +

    Logical, indicating if we should forget cached +values and recompute the configuration

    + +
    +
    +

    Value

    + + +

    A list of configuration information. This includes:

    • has_cuda: logical, indicating if it is possible to compile CUDA on +this machine (not necessarily use it though)

      • +

    • cuda_version: the version of CUDA found

      • +

    • devices: a data.frame of device information:

      • id: the device id (integer, typically in a sequence from 0)

        • +

      • name: the human-friendly name of the device

        • +

      • memory: the memory of the device, in MB

        • +

      • version: the compute version for this device

        • +
      • +

    • path_cuda_lib: path to CUDA libraries, if required

      • +

    • path_cub_include: path to CUB headers, if required

      • +

    If compilation of the test program fails, then has_cuda will be +FALSE and all other elements will be NULL.

    +
    +
    +

    Details

    +

    Not all installations leave the CUDA libraries on the default +paths, and you may need to provide it. Specifically, when we link +the dynamic library, if the linker complains about not being able +to find libcudart then your CUDA libraries are not in the +default location. You can manually pass in the path_cuda_lib +argument, or set the DUST_PATH_CUDA_LIB environment variable (in +that order of precedence).

    +

    If you are using older CUDA (< 11.0.0) then you need to provide +CUB headers, which we use to +manage state on the device (these are included in CUDA 11.0.0 and +higher). You can provide this as:

    • a path to this function (path_cub_include)

      • +

    • the environment variable DUST_PATH_CUB_INCLUDE

      • +

    • CUB headers installed into the default location (R >= 4.0.0, +see below).

      • +

    These are checked in turn with the first found taking +precedence. The default location is stored with +tools::R_user_dir("dust", "data"), but this functionality is +only available on R >= 4.0.0.

    +

    To install CUB you can do:

    +

    dust:::cuda_install_cub(NULL)

    +

    which will install CUB into the default path (provide a path on +older versions of R and set this path as DUST_PATH_CUB_INCLUDE).

    +

    For editing your .Renviron file to set these environment +variables, usethis::edit_r_environ() is very helpful.

    +
    +
    +

    See also

    +

    dust_cuda_options which controls additional CUDA +compilation options (e.g., profiling, debug mode or custom +flags)

    +
    + +
    +

    Examples

    + 
    # If you have your CUDA library in an unusual location, then you
+# may need to add a path_cuda_lib argument:
+dust::dust_cuda_configuration(
+  path_cuda_lib = "/usr/local/cuda-11.1/lib64",
+  forget = TRUE, quiet = FALSE)
+#> nvcc detection reported failure:
+#> Did not find 'libcudart' within '/usr/local/cuda-11.1/lib64' (via provided argument)
+#> $has_cuda
+#> [1] FALSE
+#> 
+#> $cuda_version
+#> NULL
+#> 
+#> $devices
+#> NULL
+#> 
+#> $path_cuda_lib
+#> NULL
+#> 
+#> $path_cub_include
+#> NULL
+#> 
+
+# However, if things are installed in the default location or you
+# have set the environment variables described above, then this
+# may work:
+dust::dust_cuda_configuration(forget = TRUE, quiet = FALSE)
+#> ℹ Loading dust8c59b949
+#> ℹ 1 functions decorated with [[cpp11::register]]
+#> ✔ generated file cpp11.R
+#> ✔ generated file cpp11.cpp
+#> ℹ Re-compiling dust8c59b949 (debug build)
+#> ── R CMD INSTALL ───────────────────────────────────────────────────────────────
+#> * installing *source* package ‘dust8c59b949’ ...
+#> ** using staged installation
+#> ** libs
+#> using C++ compiler: ‘g++ (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
+#> using C++14
+#> g++ -std=gnu++14 -I"/opt/R/4.3.1/lib/R/include" -DNDEBUG  -I'/home/runner/work/_temp/Library/cpp11/include' -I/usr/local/include   -I/home/runner/work/_temp/Library/dust/include -DHAVE_INLINE -fopenmp  -fpic  -g -O2  -UNDEBUG -Wall -pedantic -g -O0 -fdiagnostics-color=always -c cpp11.cpp -o cpp11.o
+#> nvcc -std=c++14 -O0 -I. -I/opt/R/4.3.1/lib/R/include -I/home/runner/work/_temp/Library/dust/include  -I'/home/runner/work/_temp/Library/cpp11/include'  -Xcompiler -fPIC -Xcompiler -fopenmp -x cu -c dust.cu -o dust.o
+#> /bin/bash: line 1: nvcc: command not found
+#> make: *** [Makevars:14: dust.o] Error 127
+#> ERROR: compilation failed for package ‘dust8c59b949’
+#> * removing ‘/tmp/RtmpuwDvZs/devtools_install_1bec7c4f4c53/dust8c59b949’
+#> nvcc detection reported failure:
+#> System command 'R' failed
+#> $has_cuda
+#> [1] FALSE
+#> 
+#> $cuda_version
+#> NULL
+#> 
+#> $devices
+#> NULL
+#> 
+#> $path_cuda_lib
+#> NULL
+#> 
+#> $path_cub_include
+#> NULL
+#> 
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_cuda_options.html b/reference/dust_cuda_options.html new file mode 100644 index 000000000..2507ffe17 --- /dev/null +++ b/reference/dust_cuda_options.html @@ -0,0 +1,187 @@ + +Create CUDA options — dust_cuda_options • dust + + +
    +
    + + + +
    +
    +
    +

    Create CUDA options

    + Source: R/cuda.R + +
    + +
    +

    Create options for compiling for CUDA. Unless you need to change +paths to libraries/headers, or change the debug level you will +probably not need to directly use this. However, it's potentially +useful to see what is being passed to the compiler.

    +
    + +
    + 
    dust_cuda_options(
+  ...,
+  debug = FALSE,
+  profile = FALSE,
+  fast_math = FALSE,
+  flags = NULL
+)
    +
    + +
    +

    Arguments

    +
    ...
    +

    Arguments passed to dust_cuda_configuration()

    + + +
    debug
    +

    Logical, indicating if we should compile for debug +(adding -g, -G and -O0)

    + + +
    profile
    +

    Logical, indicating if we should enable profiling

    + + +
    fast_math
    +

    Logical, indicating if we should enable "fast +maths", which lets the optimiser enable optimisations that break +IEEE compliance and disables some error checking (see the CUDA docs +for more details).

    + + +
    flags
    +

    Optional extra arguments to pass to nvcc. These +options will not be passed to your normal C++ compiler, nor the +linker (for that use R's user Makevars system). This can be used +to do things like tune the maximum number of registers +(--maxrregcount x). If not NULL, this must be a character +vector, which will be concatenated with spaces between options.

    + +
    +
    +

    Value

    + + +

    An object of type cuda_options, which can be passed into +dust as argument gpu

    + + +
    +
    +

    See also

    +

    dust_cuda_configuration which identifies and +returns the core CUDA configuration (often used implicitly by +this function).

    +
    + +
    +

    Examples

    + 
    tryCatch(
+  dust::dust_cuda_options(),
+  error = function(e) NULL)
+#> NULL
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_data.html b/reference/dust_data.html new file mode 100644 index 000000000..0ddd39d2b --- /dev/null +++ b/reference/dust_data.html @@ -0,0 +1,292 @@ + +Process data for dust — dust_data • dust + + +
    +
    + + + +
    +
    +
    +

    Process data for dust

    + Source: R/data.R + +
    + +
    +

    Prepare data for use with the $set_data() method. This is not +required for use but tries to simplify the most common use case +where you have a data.frame with some column indicating "dust +time step" (name_time), and other columns that might be use in +your data_compare function. Each row will be turned into a named +R list, which your dust_data function can then work with to get +this time-steps values. See Details for use with multi-pars +objects.

    +
    + +
    + 
    dust_data(object, name_time = "time", multi = NULL)
    +
    + +
    +

    Arguments

    +
    object
    +

    An object, at this point must be a data.frame

    + + +
    name_time
    +

    The name of the data column within object; this +column must be integer-like and every integer must be +nonnegative and unique

    + + +
    multi
    +

    Control how to interpret data for multi-parameter +dust object; see Details

    + +
    +
    +

    Value

    + + +

    A list of dust time/data pairs that will be used for the +compare function in a compiled model. Each element is a list of +length two or more where the first element is the time step and +the subsequent elements are data for that time step.

    +
    +
    +

    Details

    +

    Note that here "dust time step" (name_time) refers to the dust +time step (which will be a non-negative integer) and not the +rescaled value of time that you probably use within the model. See +dust_generator for more information.

    +

    The data object as accepted by data_set must be a list and +each element must itself be a list with two elements; the dust +time at which the data applies and any R object that corresponds +to data at that point. We expect that most of the time this second +element will be a key-value list with scalar keys, but more +flexibility may be required.

    +

    For multi-data objects, the final format is a bit more awkward; +each time step we have a list with elements time, data_1, +data_2, ..., data_n for n parameters. There are two ways of +creating this that might be useful: sharing the data across all +parameters and using some column as a grouping value.

    +

    The behaviour here is driven by the multi argument;

    • NULL: (the default) do nothing; this creates an object that +is suitable for use with a pars_multi = FALSE dust +object.

      • +

    • <integer> (e.g., multi = 3); share the data across 3 sets of +parameters. This number must match the number of parameter sets +that your dust object is created with

      • +

    • <column_name> (e.g., multi = "country"); the name of a column +within your data to split the data at. This column must be a +factor, and that factor must have levels that map to integers 1, +2, ..., n (e.g., unique(as.integer(object[[multi]])) returns +the integers 1:n).

      • +
    + +
    +

    Examples

    + 
    d <- data.frame(time = seq(0, 50, by = 10), a = runif(6), b = runif(6))
+dust::dust_data(d)
+#> [[1]]
+#> [[1]][[1]]
+#> [1] 0
+#> 
+#> [[1]][[2]]
+#> [[1]][[2]]$time
+#> [1] 0
+#> 
+#> [[1]][[2]]$a
+#> [1] 0.5969611
+#> 
+#> [[1]][[2]]$b
+#> [1] 0.4673645
+#> 
+#> 
+#> 
+#> [[2]]
+#> [[2]][[1]]
+#> [1] 10
+#> 
+#> [[2]][[2]]
+#> [[2]][[2]]$time
+#> [1] 10
+#> 
+#> [[2]][[2]]$a
+#> [1] 0.3528804
+#> 
+#> [[2]][[2]]$b
+#> [1] 0.9839092
+#> 
+#> 
+#> 
+#> [[3]]
+#> [[3]][[1]]
+#> [1] 20
+#> 
+#> [[3]][[2]]
+#> [[3]][[2]]$time
+#> [1] 20
+#> 
+#> [[3]][[2]]$a
+#> [1] 0.4643421
+#> 
+#> [[3]][[2]]$b
+#> [1] 0.5646604
+#> 
+#> 
+#> 
+#> [[4]]
+#> [[4]][[1]]
+#> [1] 30
+#> 
+#> [[4]][[2]]
+#> [[4]][[2]]$time
+#> [1] 30
+#> 
+#> [[4]][[2]]$a
+#> [1] 0.2981162
+#> 
+#> [[4]][[2]]$b
+#> [1] 0.904469
+#> 
+#> 
+#> 
+#> [[5]]
+#> [[5]][[1]]
+#> [1] 40
+#> 
+#> [[5]][[2]]
+#> [[5]][[2]]$time
+#> [1] 40
+#> 
+#> [[5]][[2]]$a
+#> [1] 0.8452975
+#> 
+#> [[5]][[2]]$b
+#> [1] 0.6275686
+#> 
+#> 
+#> 
+#> [[6]]
+#> [[6]][[1]]
+#> [1] 50
+#> 
+#> [[6]][[2]]
+#> [[6]][[2]]$time
+#> [1] 50
+#> 
+#> [[6]][[2]]$a
+#> [1] 0.8486128
+#> 
+#> [[6]][[2]]$b
+#> [1] 0.02699266
+#> 
+#> 
+#> 
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
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zD{{B@zCOWCz2o2?8H+mXg^vmWjKlE*dY1Arox2jrpWaJdBt+S;Zi4wjCN6iaQ+ik8l|9y&9`>Kirdd{Zn^j z)_fB<{3<~kHJWDOP_1~RTT1giwHUSIDHtKCpFOQ422+XDH)Jc?`+QIVUhp+kc^C82 zp*yyV%Aq!3oNV9dxYLAh{IW`^`>gk`>=AV#?(*S&o*1 zCMCR~RS4rEWI)||e<`)qEAXXUx#BleP;|w|p zEbOf=&Y%?BZWvTJ74}5MaRcfVsov)blJ~z%zeRVD(M%dhMV=!h$OdoChzl;AE3u4J zw?^+{e}Dixsfjk&6`fblwJEr7W{m-W-jsenCIITAg~?&S2Eh$~{=JuEqJ0zus=I!m z5wH+}oHT;=EUI!Z!^9zzK6ob~!U+|TN{t2gNN+_+F(Ce3Cs=i|1P91UDA-gs_$oo) zbfv*uV!ls`ZHIDz_=j!c_@%anr5G=-{H>c-nCwyj^I^Q<^`M=YeE=KiSe(A$kf-3i zQ=Ho=EgfqAIk(wL4H-9nS4}xkA&f1li+6qG93Wg;2*QO=8>Nv+Z#k4EC$v$T- zO$so5-ON03Z>hx=8hBlBxZ5|NzGfOV-n=nlzkZ}iEl|G!d4-@ZtC{L7qmarfBz{x+ zsn&dTrx8WvB0Vpw2G5`xwFp4$V0cjU6iX7&C^D$ccl{C234{#cnN);4ff0{o(f_;0 z`yAt}#04AI5yTAHaY-~~7#<J{7qEXV~hl|c${(3N#-zXd$r54+TC!o68GgGHR@7X(ELLH;RM z0cT4tHlJ_80{#W<_aK0&7UbFUO95(xh=w$-1E7}elK=}wW=%5^7TLBab;xphy%Z&l znl$eZ*m)(Q`=-l~_1*;nTW1u#4-)!WR9^6U99H`+wIA?45Ke;kf`0;C48hku*Y|nK zW6^-9j9}+ZZb+W?23~hr88Cw!XX}B>l1Nnn<))Rp=fQYgg4^I~4hUow`Zrsv*qN-T zfW1wM%UP{b{4(_@sxc}-YU>(c^9A1q__nIzq5-f8{{Qd)qQFQGn_oMZcr +Access dust's built-in examples — dust_example • dust + + +
    +
    + + + +
    +
    +
    +

    Access dust's built-in examples

    + Source: R/examples.R + +
    + +
    +

    Access dust's built-in examples. These are compiled into the +package so that examples and tests can be run more quickly without +having to compile code directly via dust(). These examples are +all "toy" examples, being small and fast to run.

    +
    + +
    + 
    dust_example(name)
    +
    + +
    +

    Arguments

    +
    name
    +

    The name of the example to use. There are five +examples: sir, sirs, variable, volatility, walk and logistic +(see Details).

    + +
    +
    +

    Value

    + + +

    A dust_generator object that can be used to create a +model. See examples for usage.

    +
    +
    +

    Details

    + +

    • sir: a basic SIR (Susceptible, Infected, Resistant) +epidemiological model. Draws from the binomial distribution to +update the population between each time step.

      • +

    • sirs: an SIRS model, the SIR model with an added R->S transition. +This has a non-zero steady state, so can be run indefinitely for testing.

      • +

    • volatility: A volatility model that might be applied to +currency fluctuations etc.

      • +

    • walk: A 1D random walk, following a Gaussian distribution each +time step.

      • +

    • logistic: Logistic growth in continuous time

      • +
    + +
    +

    Examples

    + 
    
+# A SIR (Susceptible, Infected, Resistant) epidemiological model
+sir <- dust::dust_example("sir")
+sir
+#> <dust> object generator
+#>   Public:
+#>     initialize: function (pars, time, n_particles, n_threads = 1L, seed = NULL, 
+#>     name: function () 
+#>     param: function () 
+#>     run: function (time_end) 
+#>     simulate: function (time_end) 
+#>     run_adjoint: function () 
+#>     set_index: function (index) 
+#>     index: function () 
+#>     ode_control: function () 
+#>     ode_statistics: function () 
+#>     n_threads: function () 
+#>     n_state: function () 
+#>     n_particles: function () 
+#>     n_particles_each: function () 
+#>     shape: function () 
+#>     update_state: function (pars = NULL, state = NULL, time = NULL, set_initial_state = NULL, 
+#>     state: function (index = NULL) 
+#>     time: function () 
+#>     set_stochastic_schedule: function (time) 
+#>     reorder: function (index) 
+#>     resample: function (weights) 
+#>     info: function () 
+#>     pars: function () 
+#>     rng_state: function (first_only = FALSE, last_only = FALSE) 
+#>     set_rng_state: function (rng_state) 
+#>     has_openmp: function () 
+#>     has_gpu_support: function (fake_gpu = FALSE) 
+#>     has_compare: function () 
+#>     real_size: function () 
+#>     time_type: function () 
+#>     rng_algorithm: function () 
+#>     uses_gpu: function (fake_gpu = FALSE) 
+#>     n_pars: function () 
+#>     set_n_threads: function (n_threads) 
+#>     set_data: function (data, shared = FALSE) 
+#>     compare_data: function () 
+#>     filter: function (time_end = NULL, save_trajectories = FALSE, time_snapshot = NULL, 
+#>     gpu_info: function () 
+#>   Private:
+#>     pars_: NULL
+#>     pars_multi_: NULL
+#>     index_: NULL
+#>     info_: NULL
+#>     n_threads_: NULL
+#>     n_particles_: NULL
+#>     n_particles_each_: NULL
+#>     shape_: NULL
+#>     ptr_: NULL
+#>     gpu_config_: NULL
+#>     ode_control_: NULL
+#>     methods_: NULL
+#>     param_: list
+#>     reload_: NULL
+#>   Parent env: <environment: namespace:dust>
+#>   Locked objects: TRUE
+#>   Locked class: FALSE
+#>   Portable: TRUE
+
+# Initialise the model at time step 0 with 50 independent trajectories
+mod <- sir$new(list(), 0, 50)
+
+# Run the model for 400 steps, collecting "infected" every 4th time step
+times <- seq(0, 400, by = 4)
+mod$set_index(2L)
+y <- mod$simulate(times)
+
+# A plot of our epidemic
+matplot(times, t(drop(y)), type = "l", lty = 1, col = "#00000044",
+        las = 1, xlab = "Time", ylab = "Number infected")
+
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_generate.html b/reference/dust_generate.html new file mode 100644 index 000000000..7c050719c --- /dev/null +++ b/reference/dust_generate.html @@ -0,0 +1,259 @@ + +Generate dust code — dust_generate • dust + + +
    +
    + + + +
    +
    +
    +

    Generate dust code

    + Source: R/interface.R + +
    + +
    +

    Generate a package out of a dust model. The resulting package can +be installed or loaded via pkgload::load_all() though it +contains minimal metadata and if you want to create a persistent +package you should use dust_package(). This function is +intended for cases where you either want to inspect the code or +generate it once and load multiple times (useful in some workflows +with CUDA models).

    +
    + +
    + 
    dust_generate(
+  filename,
+  quiet = FALSE,
+  workdir = NULL,
+  gpu = FALSE,
+  real_type = NULL,
+  linking_to = NULL,
+  cpp_std = NULL,
+  compiler_options = NULL,
+  optimisation_level = NULL,
+  mangle = FALSE
+)
    +
    + +
    +

    Arguments

    +
    filename
    +

    The path to a single C++ file

    + + +
    quiet
    +

    Logical, indicating if compilation messages from +pkgbuild should be displayed. Error messages will be +displayed on compilation failure regardless of the value used.

    + + +
    workdir
    +

    Optional working directory to use. If NULL +uses a temporary directory. By using a different directory of +your choosing you can see the generated code.

    + + +
    gpu
    +

    Logical, indicating if we should generate GPU +code. This requires a considerable amount of additional software +installed (CUDA toolkit and drivers) as well as a +CUDA-compatible GPU. If TRUE, then we call +dust_cuda_options with no arguments. Alternatively, call +that function and pass the value here (e.g, gpu = dust::dust_cuda_options(debug = TRUE)). Note that due to the +use of the __syncwarp() primitive this may require a GPU with +compute version 70 or higher.

    + + +
    real_type
    +

    Optionally, a string indicating a substitute type to +swap in for your model's real_type declaration. If given, then we +replace the string using real_type = (double|float) with the +given type. This is primarily intended to be used as gpu = TRUE, real_type = "float" in order to create model for the GPU +that will use 32 bit floats (rather than 64 bit doubles, which +are much slower). For CPU models decreasing precision of your +real type will typically just decrease precision for no +additional performance.

    + + +
    linking_to
    +

    Optionally, a character vector of additional +packages to add to the DESCRIPTION's LinkingTo field. Use +this when your model pulls in C++ code that is packaged within +another package's header-only library.

    + + +
    cpp_std
    +

    The C++ standard to use, if you need to set one +explicitly. See the section "Using C++ code" in "Writing R +extensions" for the details of this, and how it interacts with +the R version currently being used. For R 4.0.0 and above, C++11 +will be used; as dust depends on at least this version of R you +will never need to specify a version this low. Sensible options +are C++14, C++17, etc, depending on the features you need +and what your compiler supports.

    + + +
    compiler_options
    +

    A character vector of additional options +to pass through to the C++ compiler. These will be passed +through without any shell quoting or validation, so check the +generated commands and outputs carefully in case of error. Note +that R will apply these before anything in your personal +Makevars.

    + + +
    optimisation_level
    +

    A shorthand way of specifying common +compiler options that control optimisation level. By default +(NULL) no options are generated from this, and the +optimisation level will depend on your user Makevars file. +Valid options are none which disables optimisation (-O0), +which will be faster to compile but much slower, standard +which enables standard level of optimisation (-O2), useful if +your Makevars/pkgload configuration is disabling optimisation, +or max (-O3 and --fast-math) which enables some +slower-to-compile and potentially unsafe +optimisations. These options are applied after +compiler_options and may override options provided there. +Note that as for compiler_options, R will apply these before +anything in your personal Makevars

    + + +
    mangle
    +

    Logical, indicating if the model name should be +mangled when creating the package. This is safer if you will +load multiple copies of the package into a single session, but +is FALSE by default as the generated code is easier to read.

    + +
    +
    +

    Value

    + + +

    The path to the generated package (will be workdir if +that was provided, otherwise a temporary directory).

    +
    + +
    +

    Examples

    + 
    filename <- system.file("examples/walk.cpp", package = "dust")
+path <- dust::dust_generate(filename)
+#> ℹ 21 functions decorated with [[cpp11::register]]
+#> ✔ generated file cpp11.R
+#> ✔ generated file cpp11.cpp
+
+# Simple package created:
+dir(path)
+#> [1] "DESCRIPTION" "NAMESPACE"   "R"           "src"        
+dir(file.path(path, "R"))
+#> [1] "cpp11.R" "dust.R" 
+dir(file.path(path, "src"))
+#> [1] "Makevars"  "cpp11.cpp" "dust.cpp"  "dust.hpp" 
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_generator.html b/reference/dust_generator.html new file mode 100644 index 000000000..91e301bc2 --- /dev/null +++ b/reference/dust_generator.html @@ -0,0 +1,988 @@ + +The dust class — dust_generator • dust + + +
    +
    + + + +
    +
    +
    +

    The dust class

    + Source: R/dust_generator.R + +
    + +
    +

    All "dust" dust models are R6 objects and expose a +common set of "methods". To create a dust model of your own, +see dust and to interact with some built-in ones see +dust_example()

    +
    + + +
    +

    Value

    + + +

    A dust_generator object

    +
    +
    +

    Time

    + + + +

    For discrete time models, dust has an internal "time", which was +called step in version 0.11.x and below. This must always +be non-negative (i.e., zero or more) and always increases in +unit increments. Typically a model will remap this internal +time onto a more meaningful time in model space, e.g. by applying +the transform model_time = offset + time * dt; with this approach +you can start at any real valued time and scale the unit increments +to control the model dynamics.

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method new()

    +

    Create a new model. Note that the behaviour of this object +created by this function will change considerably based on +whether the pars_multi argument is TRUE. If not (the +default) then we create n_particles which all share the same +parameters as specified by the pars argument. If pars_multi +is TRUE then pars must be an unnamed list, and each element +of it represents a different set of parameters. We will +create length(pars) sets of n_particles particles which +will be simulated together. These particles must have the same +dimension - that is, they must correspond to model state that +is the same size.

    +

    Usage

    +

    dust_generator$new(
+  pars,
+  time,
+  n_particles,
+  n_threads = 1L,
+  seed = NULL,
+  pars_multi = FALSE,
+  deterministic = FALSE,
+  gpu_config = NULL,
+  ode_control = NULL
+)

    +
    + +
    +

    Arguments

    +

    pars
    +

    Data to initialise your model with; a list +object, but the required elements will depend on the details of +your model. If pars_multi is TRUE, then this must be an +unnamed list of pars objects (see Details).

    + + +
    time
    +

    Initial time - must be nonnegative

    + + +
    n_particles
    +

    Number of particles to create - must be at +least 1

    + + +
    n_threads
    +

    Number of OMP threads to use, if dust and +your model were compiled with OMP support (details to come). +n_particles should be a multiple of n_threads (e.g., if you use 8 +threads, then you should have 8, 16, 24, etc particles). However, this +is not compulsory.

    + + +
    seed
    +

    The seed to use for the random number generator. Can +be a positive integer, NULL (initialise with R's random number +generator) or a raw vector of a length that is a multiple of +32 to directly initialise the generator (e..g., from the +dust object's $rng_state() method).

    + + +
    pars_multi
    +

    Logical, indicating if pars should be +interpreted as a set of different initialisations, and that we +should prepare n_particles * length(pars) particles for +simulation. This has an effect on many of the other methods of +the object.

    + + +
    deterministic
    +

    Run random number generation deterministically, +replacing a random number from some distribution with its +expectation. Deterministic models are not compatible with running on +a a GPU.

    + + +
    gpu_config
    +

    GPU configuration, typically an integer +indicating the device to use, where the model has GPU support. +If not given, then the default value of NULL will fall back on the +first found device if any are available. An error is thrown if the +device id given is larger than those reported to be available (note +that CUDA numbers devices from 0, so that '0' is the first device, +and so on). See the method $gpu_info() for available device ids; +this can be called before object creation as +dust_generator$public_methods$gpu_info(). +For additional control, provide a list with elements device_id +and run_block_size. Further options (and validation) of this +list will be added in a future version!

    + + +
    ode_control
    +

    For ODE models, control over the integration; +must be a dust_ode_control model, produced by +dust_ode_control(). It is an error to provide a non-NULL +value for discrete time models.

    + + +

    +
    + +

    +

    Method name()

    +

    Returns friendly model name

    +

    Usage

    +

    dust_generator$name()

    +
    + + +

    +

    Method param()

    +

    Returns parameter information, if provided by the model. This +describes the contents of pars passed to the constructor or to +$update_state() as the pars argument, and the details depend +on the model.

    +

    Usage

    +

    dust_generator$param()

    +
    + + +

    +

    Method run()

    +

    Run the model up to a point in time, returning the filtered state +at that point.

    +

    Usage

    +

    dust_generator$run(time_end)

    +
    + +
    +

    Arguments

    +

    time_end
    +

    Time to run to (if less than or equal to the current +time(), silently nothing will happen)

    + + +

    +
    + +

    +

    Method simulate()

    +

    Iterate all particles forward in time over a series of times, +collecting output as they go. This is a helper around $run() +where you want to run to a series of points in time and save +output. The returned object will be filtered by your active index, +so that it has shape (n_state x n_particles x length(time_end)) +for single-parameter objects, and (n_state x n_particles x +n_pars x length(time_end)) for multiparameter objects. Note that +this method is very similar to $run() except that the rank of +the returned array is one less. For a scalar time_end you would +ordinarily want to use $run() but the resulting numbers would +be identical.

    +

    Usage

    +

    dust_generator$simulate(time_end)

    +
    + +
    +

    Arguments

    +

    time_end
    +

    A vector of time points that the simulation should +report output at. This the first time must be at least the same +as the current time, and every subsequent time must be equal or +greater than those before it (ties are allowed though probably +not wanted).

    + + +

    +
    + +

    +

    Method run_adjoint()

    +

    Run model with gradient information (if supported). The +interface here will change, and documentation written once it +stabilises.

    +

    Usage

    +

    dust_generator$run_adjoint()

    +
    + + +

    +

    Method set_index()

    +

    Set the "index" vector that is used to return a subset of pars +after using run(). If this is not used then run() returns +all elements in your state vector, which may be excessive and slower +than necessary.

    +

    Usage

    +

    dust_generator$set_index(index)

    +
    + +
    +

    Arguments

    +

    index
    +

    The index vector - must be an integer vector with +elements between 1 and the length of the state (this will be +validated, and an error thrown if an invalid index is given).

    + + +

    +
    + +

    +

    Method index()

    +

    Returns the index as set by $set_index

    +

    Usage

    +

    dust_generator$index()

    +
    + + +

    +

    Method ode_control()

    +

    Return the ODE control set into the object on creation. +For discrete-time models this always returns NULL.

    +

    Usage

    +

    dust_generator$ode_control()

    +
    + + +

    +

    Method ode_statistics()

    +

    Return statistics about the integration, for ODE models. +For discrete time models this makes little sense and so errors +if used.

    +

    Usage

    +

    dust_generator$ode_statistics()

    +
    + + +

    +

    Method n_threads()

    +

    Returns the number of threads that the model was constructed with

    +

    Usage

    +

    dust_generator$n_threads()

    +
    + + +

    +

    Method n_state()

    +

    Returns the length of the per-particle state

    +

    Usage

    +

    dust_generator$n_state()

    +
    + + +

    +

    Method n_particles()

    +

    Returns the number of particles

    +

    Usage

    +

    dust_generator$n_particles()

    +
    + + +

    +

    Method n_particles_each()

    +

    Returns the number of particles per parameter set

    +

    Usage

    +

    dust_generator$n_particles_each()

    +
    + + +

    +

    Method shape()

    +

    Returns the shape of the particles

    +

    Usage

    +

    dust_generator$shape()

    +
    + + +

    +

    Method update_state()

    +

    Update one or more components of the model state. +This method can be used to update any or all of pars, state and +time. If both pars and time are given and state is not, +then by default we will update the model internal state according +to your model's initial conditions - use set_initial_state = FALSE +to prevent this.

    +

    Usage

    +

    dust_generator$update_state(
+  pars = NULL,
+  state = NULL,
+  time = NULL,
+  set_initial_state = NULL,
+  index = NULL,
+  reset_step_size = NULL
+)

    +
    + +
    +

    Arguments

    +

    pars
    +

    New pars for the model (see constructor)

    + + +
    state
    +

    The state vector - can be either a numeric vector with the +same length as the model's current state (in which case the same +state is applied to all particles), or a numeric matrix with as +many rows as your model's state and as many columns as you have +particles (in which case you can set a number of different starting +states at once).

    + + +
    time
    +

    New initial time for the model. If this +is a vector (with the same length as the number of particles), then +particles are started from different initial times and run up to the +largest time given (i.e., max(time))

    + + +
    set_initial_state
    +

    Control if the model initial state +should be set while setting parameters. It is an error for +this to be TRUE when either pars is NULL or when state +is non-NULL.

    + + +
    index
    +

    Used in conjunction with state, use this to set a +fraction of the model state; the index vector provided must +be the same length as the number of provided states, and +indicates the index within the model state that should be updated. +For example, if your model has states [a, b, c, d] and +you provide an index of [1, 3] then of state was [10, 20] +you would set a to 10 and c to 20.

    + + +
    reset_step_size
    +

    Logical, indicating if we should +reset the initial step size. This only has an effect with +ode models and is silently ignored in discrete time models +where the step size is constant.

    + + +

    +
    + +

    +

    Method state()

    +

    Return full model state

    +

    Usage

    +

    dust_generator$state(index = NULL)

    +
    + +
    +

    Arguments

    +

    index
    +

    Optional index to select state using

    + + +

    +
    + +

    +

    Method time()

    +

    Return current model time +For ODE models, sets the schedule at which stochastic events are +handled. The timing here is quite subtle - an event happens +immediately after the time (so at time + eps). If your model +runs up to time an event is not triggered, but as soon as that +time is passed, by any amount of time, the event will trigger. It +is an error to set this to a non-NULL value in a discrete time +model; later we may generalise the approach here.

    +

    Usage

    +

    dust_generator$time()

    +
    + + +

    +

    Method set_stochastic_schedule()

    + +
    +

    Usage

    +

    dust_generator$set_stochastic_schedule(time)

    +
    + +
    +

    Arguments

    +

    time
    +

    A vector of times to run the stochastic update at

    + + +

    +
    + +

    +

    Method reorder()

    +

    Reorder particles.

    +

    Usage

    +

    dust_generator$reorder(index)

    +
    + +
    +

    Arguments

    +

    index
    +

    An integer vector, with values between 1 and n_particles, +indicating the index of the current particles that new particles should +take.

    + + +

    +
    + +

    +

    Method resample()

    +

    Resample particles according to some weight.

    +

    Usage

    +

    dust_generator$resample(weights)

    +
    + +
    +

    Arguments

    +

    weights
    +

    A numeric vector representing particle weights. +For a "multi-parameter" dust object this should be be a matrix +with the number of rows being the number of particles per +parameter set and the number of columns being the number of +parameter sets. +long as all particles or be a matrix.

    + + +

    +
    + +

    +

    Method info()

    +

    Returns information about the pars that your model was created with. +Only returns non-NULL if the model provides a dust_info template +specialisation.

    +

    Usage

    +

    dust_generator$info()

    +
    + + +

    +

    Method pars()

    +

    Returns the pars object that your model was constructed with.

    +

    Usage

    +

    dust_generator$pars()

    +
    + + +

    +

    Method rng_state()

    +

    Returns the state of the random number generator. This returns a +raw vector of length 32 * n_particles. This can be useful for +debugging or for initialising other dust objects. The arguments +first_only and last_only are mutually exclusive. If neither is +given then all all particles states are returned, being 32 bytes +per particle. The full returned state or first_only are most +suitable for reseeding a new dust object.

    +

    Usage

    +

    dust_generator$rng_state(first_only = FALSE, last_only = FALSE)

    +
    + +
    +

    Arguments

    +

    first_only
    +

    Logical, indicating if we should return only the +first random number state

    + + +
    last_only
    +

    Logical, indicating if we should return only the +last random number state, which does not belong to a particle.

    + + +

    +
    + +

    +

    Method set_rng_state()

    +

    Set the random number state for this model. This +replaces the RNG state that the model is using with a state of +your choosing, saved out from a different model object. This method +is designed to support advanced use cases where it is easier to +manipulate the state of the random number generator than the +internal state of the dust object.

    +

    Usage

    +

    dust_generator$set_rng_state(rng_state)

    +
    + +
    +

    Arguments

    +

    rng_state
    +

    A random number state, as saved out by the +$rng_state() method. Note that unlike seed as passed to the +constructor, this must be a raw vector of the expected length.

    + + +

    +
    + +

    +

    Method has_openmp()

    +

    Returns a logical, indicating if this model was compiled with +"OpenMP" support, in which case it will react to the n_threads +argument passed to the constructor. This method can also be used +as a static method by running it directly +as dust_generator$public_methods$has_openmp()

    +

    Usage

    +

    dust_generator$has_openmp()

    +
    + + +

    +

    Method has_gpu_support()

    +

    Returns a logical, indicating if this model was compiled with +"CUDA" support, in which case it will react to the device +argument passed to the run method. This method can also be used +as a static method by running it directly +as dust_generator$public_methods$has_gpu_support()

    +

    Usage

    +

    dust_generator$has_gpu_support(fake_gpu = FALSE)

    +
    + +
    +

    Arguments

    +

    fake_gpu
    +

    Logical, indicating if we count as TRUE +models that run on the "fake" GPU (i.e., using the GPU +version of the model but running on the CPU)

    + + +

    +
    + +

    +

    Method has_compare()

    +

    Returns a logical, indicating if this model was compiled with +"compare" support, in which case the set_data and compare_data +methods are available (otherwise these methods will error). This +method can also be used as a static method by running it directly +as dust_generator$public_methods$has_compare()

    +

    Usage

    +

    dust_generator$has_compare()

    +
    + + +

    +

    Method real_size()

    +

    Return the size of real numbers (in bits). Typically this will be +64 for double precision and 32 for float. This method can also be +used as a static method by running it directly as +dust_generator$public_methods$real_size()

    +

    Usage

    +

    dust_generator$real_size()

    +
    + + +

    +

    Method time_type()

    +

    Return the type of time this model uses; will be one of discrete +(for discrete time models) or continuous (for ODE models). +This method can also be used as a static method by running it +directly as dust_generator$public_methods$time_type()

    +

    Usage

    +

    dust_generator$time_type()

    +
    + + +

    +

    Method rng_algorithm()

    +

    Return the random number algorithm used. Typically this will be +xoshiro256plus for models using double precision reals and +xoshiro128plus for single precision (float). This method can +also be used as a static method by running it directly as +dust_generator$public_methods$rng_algorithm()

    +

    Usage

    +

    dust_generator$rng_algorithm()

    +
    + + +

    +

    Method uses_gpu()

    +

    Check if the model is running on a GPU

    +

    Usage

    +

    dust_generator$uses_gpu(fake_gpu = FALSE)

    +
    + +
    +

    Arguments

    +

    fake_gpu
    +

    Logical, indicating if we count as TRUE +models that run on the "fake" GPU (i.e., using the GPU +version of the model but running on the CPU)

    + + +

    +
    + +

    +

    Method n_pars()

    +

    Returns the number of distinct pars elements required. This is 0 +where the object was initialised with pars_multi = FALSE and +an integer otherwise. For multi-pars dust objects, Where pars +is accepted, you must provide an unnamed list of length $n_pars().

    +

    Usage

    +

    dust_generator$n_pars()

    +
    + + +

    +

    Method set_n_threads()

    +

    Change the number of threads that the dust object will use. Your +model must be compiled with "OpenMP" support for this to have an +effect. Returns (invisibly) the previous value.

    +

    Usage

    +

    dust_generator$set_n_threads(n_threads)

    +
    + +
    +

    Arguments

    +

    n_threads
    +

    The new number of threads to use. You may want to +wrap this argument in dust_openmp_threads() in order to +verify that you can actually use the number of threads +requested (based on environment variables and OpenMP support).

    + + +

    +
    + +

    +

    Method set_data()

    +

    Set "data" into the model for use with the $compare_data() method. +This is not supported by all models, depending on if they define a +data_type type. See dust_data() for a helper function to +construct suitable data and a description of the required format. You +will probably want to use that here, and definitely if using multiple +parameter sets.

    +

    Usage

    +

    dust_generator$set_data(data, shared = FALSE)

    +
    + +
    +

    Arguments

    +

    data
    +

    A list of data to set.

    + + +
    shared
    +

    Logical, indicating if the data should be shared +across all parameter sets, if your model is initialised to use +more than one parameter set (pars_multi = TRUE).

    + + +

    +
    + +

    +

    Method compare_data()

    +

    Compare the current model state against the data as set by +set_data. If there is no data set, or no data corresponding to +the current time then NULL is returned. Otherwise a numeric vector +the same length as the number of particles is returned. If model's +underlying compare_data function is stochastic, then each call to +this function may be result in a different answer.

    +

    Usage

    +

    dust_generator$compare_data()

    +
    + + +

    +

    Method filter()

    +

    Run a particle filter. The interface here will change a lot over the +next few versions. You must reset the dust object using +$update_state(pars = ..., time = ...) before using this method to +get sensible values.

    +

    Usage

    +

    dust_generator$filter(
+  time_end = NULL,
+  save_trajectories = FALSE,
+  time_snapshot = NULL,
+  min_log_likelihood = NULL
+)

    +
    + +
    +

    Arguments

    +

    time_end
    +

    The time to run to. If NULL, run to the end +of the last data. This value must be larger than the current +model time ($time()) and must exactly appear in the data.

    + + +
    save_trajectories
    +

    Logical, indicating if the filtered particle +trajectories should be saved. If TRUE then the trajectories element +will be a multidimensional array (state x <shape> x time) +containing the state values, selected according to the index set +with $set_index().

    + + +
    time_snapshot
    +

    Optional integer vector indicating times +that we should record a snapshot of the full particle filter state. +If given it must be strictly increasing vector whose elements +match times given in the data object. The return value with be +a multidimensional array (state x <shape> x time_snapshot) +containing full state values at the requested times.

    + + +
    min_log_likelihood
    +

    Optionally, a numeric value representing +the smallest likelihood we are interested in. If non-NULL +either a scalar value or vector the same length as the number +of parameter sets. Not yet supported, and included for future +compatibility.

    + + +

    +
    + +

    +

    Method gpu_info()

    +

    Return information about GPU devices, if the model +has been compiled with CUDA/GPU support. This can be called as a +static method by running dust_generator$public_methods$gpu_info(). +If run from a GPU enabled object, it will also have an element +config containing the computed device configuration: the device +id, shared memory and the block size for the run method on the +device.

    +

    Usage

    +

    dust_generator$gpu_info()

    +
    + + +
    + +
    + +
    +

    Examples

    + 
    # An example dust object from the package:
+walk <- dust::dust_example("walk")
+
+# The generator object has class "dust_generator"
+class(walk)
+#> [1] "dust_generator"   "R6ClassGenerator"
+
+# The methods below are are described in the documentation
+walk
+#> <dust> object generator
+#>   Public:
+#>     initialize: function (pars, time, n_particles, n_threads = 1L, seed = NULL, 
+#>     name: function () 
+#>     param: function () 
+#>     run: function (time_end) 
+#>     simulate: function (time_end) 
+#>     run_adjoint: function () 
+#>     set_index: function (index) 
+#>     index: function () 
+#>     ode_control: function () 
+#>     ode_statistics: function () 
+#>     n_threads: function () 
+#>     n_state: function () 
+#>     n_particles: function () 
+#>     n_particles_each: function () 
+#>     shape: function () 
+#>     update_state: function (pars = NULL, state = NULL, time = NULL, set_initial_state = NULL, 
+#>     state: function (index = NULL) 
+#>     time: function () 
+#>     set_stochastic_schedule: function (time) 
+#>     reorder: function (index) 
+#>     resample: function (weights) 
+#>     info: function () 
+#>     pars: function () 
+#>     rng_state: function (first_only = FALSE, last_only = FALSE) 
+#>     set_rng_state: function (rng_state) 
+#>     has_openmp: function () 
+#>     has_gpu_support: function (fake_gpu = FALSE) 
+#>     has_compare: function () 
+#>     real_size: function () 
+#>     time_type: function () 
+#>     rng_algorithm: function () 
+#>     uses_gpu: function (fake_gpu = FALSE) 
+#>     n_pars: function () 
+#>     set_n_threads: function (n_threads) 
+#>     set_data: function (data, shared = FALSE) 
+#>     compare_data: function () 
+#>     filter: function (time_end = NULL, save_trajectories = FALSE, time_snapshot = NULL, 
+#>     gpu_info: function () 
+#>   Private:
+#>     pars_: NULL
+#>     pars_multi_: NULL
+#>     index_: NULL
+#>     info_: NULL
+#>     n_threads_: NULL
+#>     n_particles_: NULL
+#>     n_particles_each_: NULL
+#>     shape_: NULL
+#>     ptr_: NULL
+#>     gpu_config_: NULL
+#>     ode_control_: NULL
+#>     methods_: NULL
+#>     param_: NULL
+#>     reload_: NULL
+#>   Parent env: <environment: namespace:dust>
+#>   Locked objects: TRUE
+#>   Locked class: FALSE
+#>   Portable: TRUE
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_ode_control.html b/reference/dust_ode_control.html new file mode 100644 index 000000000..cc90e6c25 --- /dev/null +++ b/reference/dust_ode_control.html @@ -0,0 +1,221 @@ + +Create a dust_ode_control object. — dust_ode_control • dust + + +
    +
    + + + +
    +
    +
    +

    Create a dust_ode_control object.

    + Source: R/ode_control.R + +
    + +
    +

    Create a control object for controlling the adaptive stepper for +systems of ordinary differential equations (ODEs). The returned +object can be passed into a continuous-time dust model on +initialisation.

    +
    + +
    + 
    dust_ode_control(
+  max_steps = NULL,
+  atol = NULL,
+  rtol = NULL,
+  step_size_min = NULL,
+  step_size_max = NULL,
+  debug_record_step_times = NULL
+)
    +
    + +
    +

    Arguments

    +
    max_steps
    +

    Maxmimum number of steps to take. If the +integration attempts to take more steps that this, it will +throw an error, stopping the integration.

    + + +
    atol
    +

    The per-step absolute tolerance.

    + + +
    rtol
    +

    The per-step relative tolerance. The total accuracy +will be less than this.

    + + +
    step_size_min
    +

    The minimum step size. The actual minimum +used will be the largest of the absolute value of this +step_size_min or .Machine$double.eps. If the +integration attempts to make a step smaller than this, it will +throw an error, stopping the integration.

    + + +
    step_size_max
    +

    The largest step size. By default there is +no maximum step size (Inf) so the solver can take as large a +step as it wants to. If you have short-lived fluctuations in +your rhs that the solver may skip over by accident, then specify +a smaller maximum step size here.

    + + +
    debug_record_step_times
    +

    Logical, indicating if we should record +the steps taken. This information will be available as part of +the statistics() output

    + +
    +
    +

    Value

    + + +

    A named list of class "dust_ode_control"

    +
    + +
    +

    Examples

    + 
    
+# We include an example of logistic growth with the package
+gen <- dust::dust_example("logistic")
+
+# Create a control object, then pass it through as the ode_control
+# parameter to the constructor:
+ctrl <- dust::dust_ode_control(atol = 1e-3, rtol = 1e-3)
+mod <- gen$new(list(r = 0.1, K = 100), 0, 1, ode_control = ctrl)
+
+# When the model runs, the control parameters passed in to the
+# constructor are used in the solution
+mod$run(10)
+#>          [,1]
+#> [1,] 2.672373
+#> [2,] 2.672373
+
+# The full set of control parameters can be extracted:
+mod$ode_control()
+#> $max_steps
+#> [1] 10000
+#> 
+#> $atol
+#> [1] 0.001
+#> 
+#> $rtol
+#> [1] 0.001
+#> 
+#> $step_size_min
+#> [1] 1e-08
+#> 
+#> $step_size_max
+#> [1] Inf
+#> 
+#> $debug_record_step_times
+#> [1] FALSE
+#> 
+#> attr(,"class")
+#> [1] "dust_ode_control"
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_openmp_support.html b/reference/dust_openmp_support.html new file mode 100644 index 000000000..638f84991 --- /dev/null +++ b/reference/dust_openmp_support.html @@ -0,0 +1,206 @@ + +Information about OpenMP support — dust_openmp_support • dust + + +
    +
    + + + +
    +
    +
    +

    Information about OpenMP support

    + Source: R/openmp.R + +
    + +
    +

    Return information about OpenMP support for this system. For +individual models look at the $has_openmp() method.

    +
    + +
    + 
    dust_openmp_support(check_compile = FALSE)
    +
    + +
    +

    Arguments

    +
    check_compile
    +

    Logical, indicating if we should check if we +can compile an openmp program - this is slow the first time.

    + +
    +
    +

    Value

    + + +

    A list with information about the openmp support on your +system.

    • The first few elements come from the openmp library directly: +num_proc, max_threads, thread_limit; these correspond to a +call to the function omp_get_<name>() in C and +openmp_version which is the value of the _OPENMP macro.

      • +

    • A logical has_openmp which is TRUE if it looks like runtime +OpenMP support is available

      • +

    • The next elements tell you about different sources that might +control the number of threads allowed to run: mc.cores (from +the R option with the same name), OMP_THREAD_LIMIT, +OMP_NUM_THREADS, MC_CORES (from environment variables), +limit_r (limit computed against R-related control variables), +limit_openmp (limit computed against OpenMP-related variables) +and limit the smaller of limit_r and limit_openmp

      • +
    +
    +

    See also

    +

    dust_openmp_threads() for setting a polite number of +threads.

    +
    + +
    +

    Examples

    + 
    # System wide support
+dust::dust_openmp_support()
+#> $num_procs
+#> [1] 2
+#> 
+#> $max_threads
+#> [1] 2
+#> 
+#> $thread_limit
+#> [1] 2147483647
+#> 
+#> $openmp_version
+#> [1] 201511
+#> 
+#> $has_openmp
+#> [1] TRUE
+#> 
+#> $mc.cores
+#> [1] NA
+#> 
+#> $OMP_THREAD_LIMIT
+#> [1] NA
+#> 
+#> $OMP_NUM_THREADS
+#> [1] NA
+#> 
+#> $MC_CORES
+#> [1] NA
+#> 
+#> $limit_r
+#> [1] 1
+#> 
+#> $limit_openmp
+#> [1] 2
+#> 
+#> $limit
+#> [1] 1
+#> 
+
+# Support compiled into a generator
+walk <- dust::dust_example("walk")
+walk$public_methods$has_openmp()
+#> [1] TRUE
+
+# Support from an instance of that model
+model <- walk$new(list(sd = 1), 0, 1)
+model$has_openmp()
+#> [1] TRUE
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_openmp_threads.html b/reference/dust_openmp_threads.html new file mode 100644 index 000000000..d68044268 --- /dev/null +++ b/reference/dust_openmp_threads.html @@ -0,0 +1,173 @@ + +Select number of threads — dust_openmp_threads • dust + + +
    +
    + + + +
    +
    +
    +

    Select number of threads

    + Source: R/openmp.R + +
    + +
    +

    Politely select a number of threads to use. See Details for the algorithm

    +
    + +
    + 
    dust_openmp_threads(n = NULL, action = "error")
    +
    + +
    +

    Arguments

    +
    n
    +

    Either NULL (select automatically) or an integer as +your proposed number of threads.

    + + +
    action
    +

    An action to perform if n exceeds the maximum +number of threads you can use. Options are "error" (the default, +throw an error), "fix" (print a message and reduce n down to +the limit) or "message" (print a message and continue anyway)

    + +
    +
    +

    Value

    + + +

    An integer, indicating the number of threads that you can use

    +
    +
    +

    Details

    +

    There are two limits and we will take the smaller of the two.

    +

    The first limit comes from piggy-backing off of R's normal +parallel configuration; we will use the MC_CORES environment +variable and mc.cores option as a guide to how many cores you +are happy to use. We take mc.cores first, then MC_CORES, which +is the same behaviour as parallel::mclapply and friends.

    +

    The second limit comes from openmp. If you do not have OpenMP +support, then we use one thread (higher numbers have no effect at +all in this case). If you do have OpenMP support, we take the +smallest of the number of "processors" (reported by +omp_get_num_procs()) the "max threads" (reported by +omp_get_max_threads() and "thread_limit" (reported by +omp_get_thread_limit().

    +

    See dust_openmp_support() for the values of all the values +that go into this calculation.

    +
    + +
    +

    Examples

    + 
    # Default number of threads; tries to pick something friendly,
+# erring on the conservative side.
+dust::dust_openmp_threads(NULL)
+#> [1] 1
+
+# Try to pick something silly and it will be reduced for you
+dust::dust_openmp_threads(1000, action = "fix")
+#> Requested number of threads '1000' exceeds a limit of '1'
+#>  See dust::dust_openmp_threads() for details
+#> [1] 1
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_package.html b/reference/dust_package.html new file mode 100644 index 000000000..70e14c501 --- /dev/null +++ b/reference/dust_package.html @@ -0,0 +1,209 @@ + +Create dust model in package — dust_package • dust + + +
    +
    + + + +
    +
    +
    +

    Create dust model in package

    + Source: R/package.R + +
    + +
    +

    Updates a dust model in a package. The user-provided code is +assumed to the in inst/dust as a series of C++ files; a file +inst/dust/model.cpp will be transformed into a file +src/model.cpp.

    +
    + +
    + 
    dust_package(path, quiet = FALSE)
    +
    + +
    +

    Arguments

    +
    path
    +

    Path to the package

    + + +
    quiet
    +

    Passed to cpp11::cpp_register, if TRUE suppresses +informational notices about updates to the cpp11 files

    + +
    +
    +

    Value

    + + +

    Nothing, this function is called for its side effects

    +
    +
    +

    Details

    +

    If your code provides a class model then dust will create C++ +functions such as dust_model_alloc - if your code also includes +names such as this, compilation will fail due to duplicate +symbols.

    +

    We add "cpp11 attributes" to the created functions, and will run +cpp11::cpp_register() on them once the generated code +has been created.

    +

    Your package needs a src/Makevars file to enable openmp (if your +system supports it). If it is not present then a suitable Makevars +will be written, containing

    +

    PKG_CXXFLAGS=$(SHLIB_OPENMP_CXXFLAGS)
+PKG_LIBS=$(SHLIB_OPENMP_CXXFLAGS)

    +

    following "Writing R Extensions" (see section "OpenMP support"). +If your package does contain a src/Makevars file we do not +attempt to edit it but will error if it looks like it does not +contain these lines or similar.

    +

    You also need to make sure that your package loads the dynamic +library; if you are using roxygen, then you might create a file +(say, R/zzz.R) containing

    +

    #' @useDynLib packagename, .registration = TRUE
+NULL

    +

    substituting packagename for your package name as +appropriate. This will create an entry in NAMESPACE.

    +
    +
    +

    See also

    +

    vignette("dust") which contains more discussion of this +process

    +
    + +
    +

    Examples

    + 
    # This is explained in more detail in the package vignette
+path <- system.file("examples/sir.cpp", package = "dust", mustWork = TRUE)
+dest <- tempfile()
+dir.create(dest)
+dir.create(file.path(dest, "inst/dust"), FALSE, TRUE)
+writeLines(c("Package: example",
+             "Version: 0.0.1",
+             "LinkingTo: cpp11, dust"),
+           file.path(dest, "DESCRIPTION"))
+writeLines("useDynLib('example', .registration = TRUE)",
+           file.path(dest, "NAMESPACE"))
+file.copy(path, file.path(dest, "inst/dust"))
+#> [1] TRUE
+
+# An absolutely minimal skeleton contains a DESCRIPTION, NAMESPACE
+# and one or more dust model files to compile:
+dir(dest, recursive = TRUE)
+#> [1] "DESCRIPTION"       "NAMESPACE"         "inst/dust/sir.cpp"
+
+# Running dust_package will fill in the rest
+dust::dust_package(dest)
+#> ℹ 21 functions decorated with [[cpp11::register]]
+#> ✔ generated file cpp11.R
+#> ✔ generated file cpp11.cpp
+
+# More files here now
+dir(dest, recursive = TRUE)
+#> [1] "DESCRIPTION"       "NAMESPACE"         "R/cpp11.R"        
+#> [4] "R/dust.R"          "inst/dust/sir.cpp" "src/Makevars"     
+#> [7] "src/cpp11.cpp"     "src/sir.cpp"      
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_repair_environment.html b/reference/dust_repair_environment.html new file mode 100644 index 000000000..5998c7456 --- /dev/null +++ b/reference/dust_repair_environment.html @@ -0,0 +1,146 @@ + +Repair dust environment — dust_repair_environment • dust + + +
    +
    + + + +
    +
    +
    +

    Repair dust environment

    + Source: R/compile.R + +
    + +
    +

    Repair the environment of a dust object created by [dust] +and then saved and reloaded by [saveRDS] and +[readRDS]. Because we use a fake temporary package to hold the +generated code, it will not ordinarily be loaded properly without +using this.

    +
    + +
    + 
    dust_repair_environment(generator, quiet = FALSE)
    +
    + +
    +

    Arguments

    +
    generator
    +

    The dust generator

    + + +
    quiet
    +

    Logical, indicating if we should be quiet (default +prints some progress information)

    + +
    +
    +

    Value

    + + +

    Nothing, called for its side effects

    +
    + +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_rng.html b/reference/dust_rng.html new file mode 100644 index 000000000..3fdab22a2 --- /dev/null +++ b/reference/dust_rng.html @@ -0,0 +1,698 @@ + +Dust Random Number Generator — dust_rng • dust + + +
    +
    + + + +
    +
    +
    +

    Dust Random Number Generator

    + Source: R/rng.R + +
    + +
    +

    Create an object that can be used to generate random +numbers with the same RNG as dust uses internally. This is +primarily meant for debugging and testing the underlying C++ +rather than a source of random numbers from R.

    +
    + + +
    +

    Value

    + + +

    A dust_rng object, which can be used to drawn random +numbers from dust's distributions.

    +
    +
    +

    Running multiple streams, perhaps in parallel

    + + + +

    The underlying random number generators are designed to work in +parallel, and with random access to parameters (see +vignette("rng") for more details). However, this is usually +done within the context of running a model where each particle +sees its own stream of numbers. We provide some support for +running random number generators in parallel, but any speed +gains from parallelisation are likely to be somewhat eroded by +the overhead of copying around a large number of random numbers.

    +

    All the random distribution functions support an argument +n_threads which controls the number of threads used. This +argument will silently have no effect if your installation +does not support OpenMP (see dust_openmp_support).

    +

    Parallelisation will be performed at the level of the stream, +where we draw n numbers from each stream for a total of n * n_streams random numbers using n_threads threads to do this. +Setting n_threads to be higher than n_streams will therefore +have no effect. If running on somebody else's system (e.g., an +HPC, CRAN) you must respect the various environment variables +that control the maximum allowable number of threads; consider +using dust_openmp_threads to select a safe number.

    +

    With the exception of random_real, each random number +distribution accepts parameters; the interpretations of these +will depend on n, n_streams and their rank.

    • If a scalar then we will use the same parameter value for every draw +from every stream

      • +

    • If a vector with length n then we will draw n random +numbers per stream, and every stream will use the same parameter +value for every stream for each draw (but a different, +shared, parameter value for subsequent draws).

      • +

    • If a matrix is provided with one row and n_streams +columns then we use different parameters for each stream, but +the same parameter for each draw.

      • +

    • If a matrix is provided with n rows and n_streams +columns then we use a parameter value [i, j] for the ith +draw on the jth stream.

      • +

    The rules are slightly different for the prob argument to +multinomial as for that prob is a vector of values. As such +we shift all dimensions by one:

    • If a vector we use same prob every draw from every stream +and there are length(prob) possible outcomes.

      • +

    • If a matrix with n columns then vary over each draw (the +ith draw using vector prob[, i] but shared across all +streams. There are nrow(prob) possible outcomes.

      • +

    • If a 3d array is provided with 1 column and n_streams +"layers" (the third dimension) then we use then we use different +parameters for each stream, but the same parameter for each +draw.

      • +

    • If a 3d array is provided with n columns and n_streams +"layers" then we vary over both draws and streams so that with +use vector prob[, i, j] for the ith draw on the jth +stream.

      • +

    The output will not differ based on the number of threads used, +only on the number of streams.

    +
    +
    +

    Public fields

    +

    info
    +

    Information about the generator (read-only)

    + + +

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method new()

    +

    Create a dust_rng object

    +

    Usage

    +

    dust_rng$new(
+  seed = NULL,
+  n_streams = 1L,
+  real_type = "double",
+  deterministic = FALSE
+)

    +
    + +
    +

    Arguments

    +

    seed
    +

    The seed, as an integer, a raw vector or NULL. +If an integer we will create a suitable seed via the "splitmix64" +algorithm, if a raw vector it must the correct length (a multiple +of either 32 or 16 for float = FALSE or float = TRUE +respectively). If NULL then we create a seed using R's random +number generator.

    + + +
    n_streams
    +

    The number of streams to use (see Details)

    + + +
    real_type
    +

    The type of floating point number to use. Currently +only float and double are supported (with double being +the default). This will have no (or negligible) impact on speed, +but exists to test the low-precision generators.

    + + +
    deterministic
    +

    Logical, indicating if we should use +"deterministic" mode where distributions return their +expectations and the state is never changed.

    + + +

    +
    + +

    +

    Method size()

    +

    Number of streams available

    +

    Usage

    +

    dust_rng$size()

    +
    + + +

    +

    Method jump()

    +

    The jump function updates the random number state for +each stream by advancing it to a state equivalent to +2^128 numbers drawn from each stream.

    +

    Usage

    +

    dust_rng$jump()

    +
    + + +

    +

    Method long_jump()

    +

    Longer than $jump, the $long_jump method is +equivalent to 2^192 numbers drawn from each stream.

    +

    Usage

    +

    dust_rng$long_jump()

    +
    + + +

    +

    Method random_real()

    +

    Generate n numbers from a standard uniform distribution

    +

    Usage

    +

    dust_rng$random_real(n, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method random_normal()

    +

    Generate n numbers from a standard normal distribution

    +

    Usage

    +

    dust_rng$random_normal(n, n_threads = 1L, algorithm = "box_muller")

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +
    algorithm
    +

    Name of the algorithm to use; currently box_muller +and ziggurat are supported, with the latter being considerably +faster.

    + + +

    +
    + +

    +

    Method uniform()

    +

    Generate n numbers from a uniform distribution

    +

    Usage

    +

    dust_rng$uniform(n, min, max, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    min
    +

    The minimum of the distribution (length 1 or n)

    + + +
    max
    +

    The maximum of the distribution (length 1 or n)

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method normal()

    +

    Generate n numbers from a normal distribution

    +

    Usage

    +

    dust_rng$normal(n, mean, sd, n_threads = 1L, algorithm = "box_muller")

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    mean
    +

    The mean of the distribution (length 1 or n)

    + + +
    sd
    +

    The standard deviation of the distribution (length 1 or n)

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +
    algorithm
    +

    Name of the algorithm to use; currently box_muller +and ziggurat are supported, with the latter being considerably +faster.

    + + +

    +
    + +

    +

    Method binomial()

    +

    Generate n numbers from a binomial distribution

    +

    Usage

    +

    dust_rng$binomial(n, size, prob, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    size
    +

    The number of trials (zero or more, length 1 or n)

    + + +
    prob
    +

    The probability of success on each trial +(between 0 and 1, length 1 or n)

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method nbinomial()

    +

    Generate n numbers from a negative binomial distribution

    +

    Usage

    +

    dust_rng$nbinomial(n, size, prob, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    size
    +

    The target number of successful trials +(zero or more, length 1 or n)

    + + +
    prob
    +

    The probability of success on each trial +(between 0 and 1, length 1 or n)

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method hypergeometric()

    +

    Generate n numbers from a hypergeometric distribution

    +

    Usage

    +

    dust_rng$hypergeometric(n, n1, n2, k, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    n1
    +

    The number of white balls in the urn (called n in +R's rhyper)

    + + +
    n2
    +

    The number of black balls in the urn (called m in +R's rhyper)

    + + +
    k
    +

    The number of balls to draw

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method gamma()

    +

    Generate n numbers from a gamma distribution

    +

    Usage

    +

    dust_rng$gamma(n, shape, scale, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    shape
    +

    Shape

    + + +
    scale
    +

    Scale +'

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method poisson()

    +

    Generate n numbers from a Poisson distribution

    +

    Usage

    +

    dust_rng$poisson(n, lambda, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    lambda
    +

    The mean (zero or more, length 1 or n). Only valid for +lambda <= 10^7

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method exponential()

    +

    Generate n numbers from a exponential distribution

    +

    Usage

    +

    dust_rng$exponential(n, rate, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    rate
    +

    The rate of the exponential

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method cauchy()

    +

    Generate n draws from a Cauchy distribution.

    +

    Usage

    +

    dust_rng$cauchy(n, location, scale, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    Number of samples to draw (per stream)

    + + +
    location
    +

    The location of the peak of the distribution +(also its median)

    + + +
    scale
    +

    A scale parameter, which specifies the distribution's +"half-width at half-maximum"

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method multinomial()

    +

    Generate n draws from a multinomial distribution. +In contrast with most of the distributions here, each draw is a +vector with the same length as prob.

    +

    Usage

    +

    dust_rng$multinomial(n, size, prob, n_threads = 1L)

    +
    + +
    +

    Arguments

    +

    n
    +

    The number of samples to draw (per stream)

    + + +
    size
    +

    The number of trials (zero or more, length 1 or n)

    + + +
    prob
    +

    A vector of probabilities for the success of each +trial. This does not need to sum to 1 (though all elements +must be non-negative), in which case we interpret prob as +weights and normalise so that they equal 1 before sampling.

    + + +
    n_threads
    +

    Number of threads to use; see Details

    + + +

    +
    + +

    +

    Method state()

    +

    Returns the state of the random number stream. This returns a +raw vector of length 32 * n_streams. It is primarily intended for +debugging as one cannot (yet) initialise a dust_rng object with this +state.

    +

    Usage

    +

    dust_rng$state()

    +
    + + +
    + +
    + +
    +

    Examples

    + 
    rng <- dust::dust_rng$new(42)
+
+# Shorthand for Uniform(0, 1)
+rng$random_real(5)
+#> [1] 0.4969537 0.6896184 0.3669609 0.3620384 0.9299854
+
+# Shorthand for Normal(0, 1)
+rng$random_normal(5)
+#> [1] -1.53271190 -1.41913805  0.02345789 -0.73297710 -1.23072552
+
+# Uniform random numbers between min and max
+rng$uniform(5, -2, 6)
+#> [1] -0.07182473  4.28030151 -1.86883075  1.79198057  2.40249777
+
+# Normally distributed random numbers with mean and sd
+rng$normal(5, 4, 2)
+#> [1] 5.100104 3.489436 4.315190 2.868816 4.235165
+
+# Binomially distributed random numbers with size and prob
+rng$binomial(5, 10, 0.3)
+#> [1] 5 3 2 5 2
+
+# Negative binomially distributed random numbers with size and prob
+rng$nbinomial(5, 10, 0.3)
+#> [1] 18 12 10 28 41
+
+# Hypergeometric distributed random numbers with parameters n1, n2 and k
+rng$hypergeometric(5, 6, 10, 4)
+#> [1] 2 2 2 0 2
+
+# Gamma distributed random numbers with parameters a and b
+rng$gamma(5, 0.5, 2)
+#> [1] 0.1440913 0.5461841 0.8933152 2.0532643 0.2496346
+
+# Poisson distributed random numbers with mean lambda
+rng$poisson(5, 2)
+#> [1] 6 2 2 2 1
+
+# Exponentially distributed random numbers with rate
+rng$exponential(5, 2)
+#> [1] 0.19990637 0.02665489 0.14149562 0.60697382 0.31936759
+
+# Multinomial distributed random numbers with size and vector of
+# probabiltiies prob
+rng$multinomial(5, 10, c(0.1, 0.3, 0.5, 0.1))
+#>      [,1] [,2] [,3] [,4] [,5]
+#> [1,]    0    2    0    0    0
+#> [2,]    3    2    3    3    4
+#> [3,]    7    6    7    6    6
+#> [4,]    0    0    0    1    0
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_rng_distributed.html b/reference/dust_rng_distributed.html new file mode 100644 index 000000000..3f36ec2bf --- /dev/null +++ b/reference/dust_rng_distributed.html @@ -0,0 +1,222 @@ + +Create a set of distributed seeds — dust_rng_distributed_state • dust + + +
    +
    + + + +
    +
    +
    +

    Create a set of distributed seeds

    + Source: R/rng_distributed.R + +
    + +
    +

    Create a set of initial random number seeds suitable for using +within a distributed context (over multiple processes or nodes) at +a level higher than a single group of synchronised threads.

    +
    + +
    + 
    dust_rng_distributed_state(
+  seed = NULL,
+  n_streams = 1L,
+  n_nodes = 1L,
+  algorithm = "xoshiro256plus"
+)
+
+dust_rng_distributed_pointer(
+  seed = NULL,
+  n_streams = 1L,
+  n_nodes = 1L,
+  algorithm = "xoshiro256plus"
+)
    +
    + +
    +

    Arguments

    +
    seed
    +

    Initial seed to use. As for dust_rng, this can +be NULL (create a seed using R's generators), an integer or a +raw vector of appropriate length.

    + + +
    n_streams
    +

    The number of streams to create per node. If +passing the results of this seed to a dust object's initialiser +(see dust_generator) you can safely leave this at 1, but +if using in a standalone setting, and especially if using +dust_rng_distributed_pointer, you may need to set this to the +appropriate length.

    + + +
    n_nodes
    +

    The number of separate seeds to create. Each will +be separated by a "long jump" for your generator.

    + + +
    algorithm
    +

    The name of an algorithm to use. Alternatively +pass a dust_generator or dust object here to select the +algorithm used by that object automatically.

    + +
    +
    +

    Value

    + + +

    A list of either raw vectors (for +dust_rng_distributed_state) or of dust_rng_pointer

    + + +

    objects (for dust_rng_distributed_pointer)

    +
    +
    +

    Details

    +

    See vignette("rng_distributed") for a proper introduction to +these functions.

    +
    + +
    +

    Examples

    + 
    dust::dust_rng_distributed_state(n_nodes = 2)
+#> [[1]]
+#>  [1] 8d a2 7e f2 dc 24 fa 89 45 7e d3 2a c5 d2 2a cf a6 10 e2 49 a6 3e b9 8c c6
+#> [26] e0 23 54 77 b6 75 7b
+#> 
+#> [[2]]
+#>  [1] 90 9c 59 93 55 7d 9e b8 19 07 9a d6 1c d0 98 0b 1d 13 83 b1 59 30 8f 22 64
+#> [26] d0 79 ab 1e ee 1b 5b
+#> 
+dust::dust_rng_distributed_pointer(n_nodes = 2)
+#> [[1]]
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus") 
+#>     is_current: function () 
+#>     n_streams: 1
+#>     state: function () 
+#>     sync: function () 
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 64 a2 c0 67 4a d6 59 d7 f4 58 2b 73 4f d2 da 23 a2 b3 02 ...
+#> 
+#> [[2]]
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus") 
+#>     is_current: function () 
+#>     n_streams: 1
+#>     state: function () 
+#>     sync: function () 
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 6e 75 1f c8 ca a4 f9 95 d7 a2 84 0f 53 3d c8 41 f3 c2 c1 ...
+#> 
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/dust_rng_pointer.html b/reference/dust_rng_pointer.html new file mode 100644 index 000000000..6c716f9d0 --- /dev/null +++ b/reference/dust_rng_pointer.html @@ -0,0 +1,237 @@ + +Create pointer to random number generator stream — dust_rng_pointer • dust + + +
    +
    + + + +
    +
    +
    +

    Create pointer to random number generator stream

    + Source: R/rng_pointer.R + +
    + +
    +

    This function exists to support use from other +packages that wish to use dust's random number support, and +creates an opaque pointer to a set of random number streams. It +is described more fully in vignette("rng_package.Rmd")

    +
    + + +
    +

    Public fields

    +

    algorithm
    +

    The name of the generator algorithm used (read-only)

    + + +
    n_streams
    +

    The number of streams of random numbers provided +(read-only)

    + + +

    +
    +
    +

    Methods

    + +
    +

    Public methods

    + +

    +

    Method new()

    +

    Create a new dust_rng_pointer object

    +

    Usage

    +

    dust_rng_pointer$new(
+  seed = NULL,
+  n_streams = 1L,
+  long_jump = 0L,
+  algorithm = "xoshiro256plus"
+)

    +
    + +
    +

    Arguments

    +

    seed
    +

    The random number seed to use (see dust_rng +for details)

    + + +
    n_streams
    +

    The number of independent random number streams to +create

    + + +
    long_jump
    +

    Optionally an integer indicating how many +"long jumps" should be carried out immediately on creation. +This can be used to create a distributed parallel random number +generator (see dust_rng_distributed_state)

    + + +
    algorithm
    +

    The random number algorithm to use. The default is +xoshiro256plus which is a good general choice

    + + +

    +
    + +

    +

    Method sync()

    +

    Synchronise the R copy of the random number state. +Typically this is only needed before serialisation if you have +ever used the object.

    +

    Usage

    +

    dust_rng_pointer$sync()

    +
    + + +

    +

    Method state()

    +

    Return a raw vector of state. This can be used to +create other generators with the same state.

    +

    Usage

    +

    dust_rng_pointer$state()

    +
    + + +

    +

    Method is_current()

    +

    Return a logical, indicating if the random number +state that would be returned by state() is "current" (i.e., the +same as the copy held in the pointer) or not. This is TRUE on +creation or immediately after calling $sync() or $state() +and FALSE after any use of the pointer.

    +

    Usage

    +

    dust_rng_pointer$is_current()

    +
    + + +
    + +
    + +
    +

    Examples

    + 
    dust::dust_rng_pointer$new()
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus") 
+#>     is_current: function () 
+#>     n_streams: 1
+#>     state: function () 
+#>     sync: function () 
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: b6 9a 70 44 13 1f 49 1c db ab 4e c4 77 1c 0d 57 80 62 7e ...
+
    +
    +
    + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/reference/figures/logo.png b/reference/figures/logo.png new file mode 100644 index 0000000000000000000000000000000000000000..b2c520439c62d1583667a3a1596bfc4c1ed3517d GIT binary patch literal 98467 zcmV*CKyAN?P)004R>004l5008;`004mK004C`008P>0026e000+ooVrmw00006 zVoOIv0RI600RN!9r;`8x010qNS#tmY3labT3lag+-G2N4000McNliru5*kXgR0vCe zWU$R(W4mo=8wq3gY7b4f!3HxJx&g!T!mHhFv)t~+HXa+=c*59BLVzrgN>UA3IY!3x z8{d0(IOpvCW1ssXN*RTULCPvAZ?33_iunEB?+y2yv-fv@2YBoHMRR?_H+%!CiuZmG z_&(r|1HTXWSO}qcv!CBv*IUiNfz42QX-SU5P&LzG;xhx_YebC^% zexa`cGz35Hua^JAV^@xU;9XBYxq9N-)i?X4zIFXwTyLGgU*eal@?ZYh|AEKj-|p5! z`-$7Hz3>Otm#6>qI1Nvz>Lbf#?*m=ivFut}9}%&~QPnqmZ7J%fl%Ab(`kpE0cP+a3 z$~S-YyI+0m`ZZpB?e?4f^543Cj!WL`C-Bzwg|Dyq_J4}7yy?d~Kk}jTlb3$;D=)wL ztGDa(1J&}#uNQH|*wD5uF?fP=NKqh@a%MXY^ut7X#6kve&e65atE;a069z{r3^j!buXJ2}=--@@cFL1qe0)Gi!U;nZ1;-!~AO;fgSd;NtU`=L9xKKJ`?-+JYn zhJMpp<@@=Uh!A5-+pTE3ju1RvAbL*>9v1>l6KUIq5F$mPls9eys>+no{+QA?k12oK 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000000000..46478ae3d --- /dev/null +++ b/reference/index.html @@ -0,0 +1,199 @@ + +Function reference • dust + + +
    +
    + + + +
    +
    +
    +

    Reference

    +
    + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +

    Generate a dust model

    +

    Convert a small section of C++ code into a model that can be run efficiently in parallel.

    +
    +

    dust()

    +

    Create a dust model from a C++ input file

    +

    dust_generate()

    +

    Generate dust code

    +

    dust_package()

    +

    Create dust model in package

    +

    Interact with the dust model

    +

    Every dust model shares the same (fairly large) set of methods

    +
    +

    dust_generator

    +

    The dust class

    +

    Random numbers

    +

    The core of dust is a parallel random number generator. These are also described in a series of vignettes.

    +
    +

    dust_rng

    +

    Dust Random Number Generator

    +

    dust_rng_pointer

    +

    Create pointer to random number generator stream

    +

    dust_rng_distributed_state() dust_rng_distributed_pointer()

    +

    Create a set of distributed seeds

    +

    ODE models

    +

    Additional support for ODE (ordinary differential equation) models

    +
    +

    dust_ode_control()

    +

    Create a dust_ode_control object.

    +

    Run in parallel with OpenMP

    +

    Detect OpenMP support

    +
    +

    dust_openmp_support()

    +

    Information about OpenMP support

    +

    dust_openmp_threads()

    +

    Select number of threads

    +

    Compile on GPUs

    +

    Control compilation options for creating models to run on a GPU

    +
    +

    dust_cuda_configuration()

    +

    Detect CUDA configuration

    +

    dust_cuda_options()

    +

    Create CUDA options

    +

    Other

    +

    +
    +

    dust_data()

    +

    Process data for dust

    +

    dust_example()

    +

    Access dust's built-in examples

    +

    dust_repair_environment()

    +

    Repair dust environment

    + + +
    + + +
    +

    Developed by Rich FitzJohn, Alex Hill, John Lees.

    +
    + +
    +

    Site built with pkgdown 2.0.7.

    +
    + +
    + + + + + + + + diff --git a/sitemap.xml b/sitemap.xml new file mode 100644 index 000000000..17dab5abe --- /dev/null +++ b/sitemap.xml @@ -0,0 +1,102 @@ + + + + /404.html + + + /LICENSE-text.html + + + /LICENSE.html + + + /articles/data.html + + + /articles/design.html + + + /articles/dust.html + + + /articles/gpu.html + + + /articles/index.html + + + /articles/multi.html + + + /articles/rng.html + + + /articles/rng_algorithms.html + + + /articles/rng_distributed.html + + + /articles/rng_package.html + + + /authors.html + + + /developing.html + + + /index.html + + + /news/index.html + + + /reference/dust.html + + + /reference/dust_cuda_configuration.html + + + /reference/dust_cuda_options.html + + + /reference/dust_data.html + + + /reference/dust_example.html + + + /reference/dust_generate.html + + + /reference/dust_generator.html + + + /reference/dust_ode_control.html + + + /reference/dust_openmp_support.html + + + /reference/dust_openmp_threads.html + + + /reference/dust_package.html + + + /reference/dust_repair_environment.html + + + /reference/dust_rng.html + + + /reference/dust_rng_distributed.html + + + /reference/dust_rng_pointer.html + + + /reference/index.html + +

    • +
    + + + + +
    +
    +
    +

    Distributed parallel random numbers

    + + + Source: vignettes/rng_distributed.Rmd + + +
    + + + + +

    This vignette assumes some familiarity with the dust approach to +random numbers, though we provide pointers below to the relevant +documentation for further discussion.

    +

    The random number generator in dust is well suited to +parallel calculations. On a single node we can set up a generator with +many streams and then parallelise the calculation using OpenMP. The +number of streams is either one per core or, typically better, one per +logical unit of calculation (which may be the maximum number of threads, +for example one stream per loop iteration). This is the approach taken +by dust objects (vignette("dust")) and described for +standalone use of the generators +(vignette("rng_package")).

    +

    When parallelising, you may also have separate ‘nodes’, which could +be separate processors, physical machines, or just processes on the same +machine. The difference between threads is that nodes will not share any +memory with each other during processing.

    +

    Some additional care is required to use multiple nodes for the +calculation so their streams do not overlap (“distributed parallel +computation”), and this vignette explains the problems and solutions. It +applies to both use with dust objects and for standalone +use of the random number generators.

    +
    +

    A note on seeding +

    +

    To seed multiple streams we begin by seeding the first generator. +Practically how this happens can be ignored for now.

    +
    +r <- dust::dust_rng$new(seed = 1)
+r$state()
+#>  [1] c1 5c 02 89 ec 2d 0a 91 1e 61 39 74 08 ab 41 5e c3 86 8d 6d f4 02 8a b1 56
+#> [26] 49 ee d9 dd 95 81 e2
    +

    To seed the next stream we “jump ahead” in the stream. The generators +provide pre-computed coefficients that jump the state of the generator +to a state equal to drawing a very large number of random numbers (or +equivalently steps of the Markov chains). For the default generator +(xoshiro256+) this is 2^128 draws, equal to the square root +of the period of the generator (22561).

    +
    +r$jump()
+r$state()
+#>  [1] 15 6e 10 9b 13 4b 6b 88 3a 50 b0 f1 ef 99 11 5c 6f 68 1c 0f e8 97 17 40 da
+#> [26] c7 c6 2e 27 b7 b7 5d
    +

    Constructing a generator with more than one stream does this +automatically:

    +
    +r2 <- dust::dust_rng$new(seed = 1, n_streams = 4)
+matrix(r2$state(), 32)
+#>       [,1] [,2] [,3] [,4]
+#>  [1,]   c1   15   56   f9
+#>  [2,]   5c   6e   fc   32
+#>  [3,]   02   10   6d   84
+#>  [4,]   89   9b   df   e6
+#>  [5,]   ec   13   7b   30
+#>  [6,]   2d   4b   10   34
+#>  [7,]   0a   6b   6e   d2
+#>  [8,]   91   88   ed   38
+#>  [9,]   1e   3a   cf   f3
+#> [10,]   61   50   0f   f2
+#> [11,]   39   b0   57   89
+#> [12,]   74   f1   0e   21
+#> [13,]   08   ef   3d   72
+#> [14,]   ab   99   3b   fd
+#> [15,]   41   11   a2   53
+#> [16,]   5e   5c   45   2b
+#> [17,]   c3   6f   87   b5
+#> [18,]   86   68   5d   92
+#> [19,]   8d   1c   4b   2c
+#> [20,]   6d   0f   86   8f
+#> [21,]   f4   e8   44   25
+#> [22,]   02   97   9a   9f
+#> [23,]   8a   17   7d   d8
+#> [24,]   b1   40   18   ae
+#> [25,]   56   da   f8   c6
+#> [26,]   49   c7   d0   89
+#> [27,]   ee   c6   ce   79
+#> [28,]   d9   2e   93   ef
+#> [29,]   dd   27   a8   b0
+#> [30,]   95   b7   63   42
+#> [31,]   81   b7   dd   ec
+#> [32,]   e2   5d   41   9f
    +

    Note here how the first 32 bytes (the first column) are the same as +the initial state of the generator r, the second set are +equal to the state after jumping once. The third is 2 * 2^128 steps +ahead and the fourth is 3 * 2^128 steps ahead.

    +

    We also have coefficients for a “long jump”, which is equivalent to +2^192 steps of the generator (generator period1). The point of the +original jump is that individual draws of random numbers will never +overlap; the point of the long jumps is that each long jump is so far +that we’ll never reach the next one by normal jumping (there are 2^64 ~= +10^19 jumps within a single long jump).

    +
    +
    +

    Distributed seeding +

    +

    The basic idea using the above primitives is that we could take a set +of “long jumps” to create a set of initial seeds, pass those to each +node that will do calculation, then on each node take a set of jumps to +create a locally parallel random number generator.

    +

    The function dust::dust_rng_distributed_state creates a +list of random number states that are suitable for use on a series of +nodes:

    +
    +dust::dust_rng_distributed_state(seed = 1, n_streams = 1, n_nodes = 2L)
+#> [[1]]
+#>  [1] c1 5c 02 89 ec 2d 0a 91 1e 61 39 74 08 ab 41 5e c3 86 8d 6d f4 02 8a b1 56
+#> [26] 49 ee d9 dd 95 81 e2
+#>
+#> [[2]]
+#>  [1] 77 69 c2 44 65 7b dc 93 49 c7 93 ef dd 06 fc 47 cf af f3 d0 80 97 01 68 45
+#> [26] a2 90 f4 38 dd 4d 0a
    +

    Each element of this list can be passed through to to +dust::dust_rng_pointer$new or to create +dust::dust_generator objects. It will depend on your +application how you do this of course.

    +

    We also include the convenience function +dust::dust_rng_distributed_pointer which returns a list of +pointer objects

    +
    +dust::dust_rng_distributed_pointer(seed = 1, n_streams = 1, n_nodes = 2L)
+#> [[1]]
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: c1 5c 02 89 ec 2d 0a 91 1e 61 39 74 08 ab 41 5e c3 86 8d ...
+#>
+#> [[2]]
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 77 69 c2 44 65 7b dc 93 49 c7 93 ef dd 06 fc 47 cf af f3 ...
    +

    We will illustrate the idea first with the pi estimation algorithm +from vignette("rng_package") and to start we will ignore +the within-host parallelism (imagine we’re trying to distribute the +calculation over a set of single core jobs). Because we need our code +available on multiple nodes we can’t use cpp11::source_cpp +and will have to create a package, which will be called +piparallel as before.

    +

    As a reminder, to use our pi estimation code on a single node we +first create a dust_rng_pointer object

    +
    +rng <- dust:::dust_rng_pointer$new()
    +

    We can call the function like so:

    +
    +piparallel::pi_dust_parallel(1e6, rng, 1)
+#> [1] 3.142492
    +

    To do this in parallel, we use the above functions to create a list +of pointers:

    +
    +ptrs <- dust::dust_rng_distributed_pointer(seed = 1, n_streams = 1,
+                                           n_nodes = 4L)
    +

    Next, we need a parallel cluster; we’ll use the parallel +package for this and create a cluster of two nodes (this could be +increased of course). This might be done via a cluster scheduler or the +more sophisticated tools in the future package.

    +
    +cl <- parallel::makeCluster(2, "PSOCK")
    +

    We’ve installed our package in lib so can make sure +that’s available on each node:

    +
    +parallel::clusterCall(cl, loadNamespace, "piparallel", lib)
+#> [[1]]
+#> <environment: namespace:piparallel>
+#>
+#> [[2]]
+#> <environment: namespace:piparallel>
    +

    Then we can call our pi estimation function. We take as arguments the +number of iterations, a pointer to random state and the number of +threads to use.

    +
    +ans <- parallel::clusterApply(cl, ptrs, function(r)
+                              piparallel::pi_dust_parallel(1e6, r, 1))
+ans
+#> [[1]]
+#> [1] 3.144028
+#>
+#> [[2]]
+#> [1] 3.141628
+#>
+#> [[3]]
+#> [1] 3.141232
+#>
+#> [[4]]
+#> [1] 3.141676
    +

    We now have four estimates of pi which are independent and can be +safely averaged:

    +
    +mean(unlist(ans))
+#> [1] 3.142141
    +

    These are the same numbers we would have found had we run things in +series locally:

    +
    +ptrs_local <- dust::dust_rng_distributed_pointer(seed = 1, n_streams = 1,
+                                                 n_nodes = 4L)
+ans_local <- lapply(ptrs_local, function(r)
+                    piparallel::pi_dust_parallel(1e6, r, 1))
+ans_local
+#> [[1]]
+#> [1] 3.144028
+#>
+#> [[2]]
+#> [1] 3.141628
+#>
+#> [[3]]
+#> [1] 3.141232
+#>
+#> [[4]]
+#> [1] 3.141676
    +

    If we’d run the clusterApply over a different number of +nodes, the calculation would also be unchanged.

    +

    The same approach works where we want each node to run in parallel. +So we might want to distribute calculations over 4 nodes which each have +8 cores say. Then we’d configure our pointers to have more streams (here +using 32 streams as that might represent our upper bound of per-node +compute capacity)

    +
    +ptrs <- dust::dust_rng_distributed_pointer(seed = 1, n_streams = 32,
+                                           n_nodes = 4L)
    +

    The state vector for each pointer is now considerably longer:

    +
    +length(ptrs[[1]]$state())
+#> [1] 1024
    +
    +ans <- lapply(ptrs, function(r)
+              piparallel::pi_dust_parallel(1e6, r, 8))
+ans
+#> [[1]]
+#> [1] 3.142302
+#>
+#> [[2]]
+#> [1] 3.141256
+#>
+#> [[3]]
+#> [1] 3.141828
+#>
+#> [[4]]
+#> [1] 3.140525
    +

    As before, this gives us four answers (two per node) but each node +ran 2 * 32 * 1e6 random draws, spread over 8 threads in two serial +jobs.

    +

    With this set-up we can change the number of nodes and number of +threads without affecting the calculation, but spread the work out over +the compute that we have available to us.

    +
    +
    +

    Continuing the streams +

    +

    The above set-up assumes that we want to establish our streams, do +some work with them, then throw them away. That is, we never want to run +calculations on the same nodes again. To sensibly we have several +choices:

    +

    Take another set of long jumps to jump over all partial +series used and continue from there. Possibly the simplest +solution; if we have set up initial states for n nodes and +we have our initial seed we can simply take n long jumps to +move away from our initial sequence, then configure seeds using the next +n states. This can be repeated without practical limit. It +has the advantage that no reverse communication needs to happen about +the random number seed - that is, the worker nodes never need to tell +our main node where they got to in the sequence.

    +

    Report back the final state reached by each node. A +more involved solution, but possibly more satisfying, involves each node +sending back its final state at the end of sampling (along with whatever +calculations were being performed). We then pass this state back to the +nodes when continuing so that all calculations are taken from an +unbroken set of streams.

    +
    +pi_estimate_continue <- function(n, ptr, n_threads) {
+  value <- piparallel::pi_dust_parallel(n, ptr, n_threads)
+  ptr$sync()
+  list(value = value,
+       ptr = ptr)
+}
+parallel::clusterExport(cl, "pi_estimate_continue")
    +
    +ptrs <- dust::dust_rng_distributed_pointer(seed = 1, n_streams = 1,
+                                           n_nodes = 4L)
+ans <- parallel::clusterApply(cl, ptrs, function(r)
+                              pi_estimate_continue(1e6, r, 1))
+ans
+#> [[1]]
+#> [[1]]$value
+#> [1] 3.144028
+#>
+#> [[1]]$ptr
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 3c 9a e0 2e ac 65 52 0d b4 be 20 c8 cd c5 9e 27 82 14 7e ...
+#>
+#>
+#> [[2]]
+#> [[2]]$value
+#> [1] 3.141628
+#>
+#> [[2]]$ptr
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 2e 3d 0e 9c fb a7 d3 08 f3 32 89 25 c1 38 b8 aa 95 0b 65 ...
+#>
+#>
+#> [[3]]
+#> [[3]]$value
+#> [1] 3.141232
+#>
+#> [[3]]$ptr
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: 7f b4 7d 26 a0 13 11 24 20 95 93 02 4b 3d 16 9d ba cf a2 ...
+#>
+#>
+#> [[4]]
+#> [[4]]$value
+#> [1] 3.141676
+#>
+#> [[4]]$ptr
+#> <dust_rng_pointer>
+#>   Public:
+#>     algorithm: xoshiro256plus
+#>     initialize: function (seed = NULL, n_streams = 1L, long_jump = 0L, algorithm = "xoshiro256plus")
+#>     is_current: function ()
+#>     n_streams: 1
+#>     state: function ()
+#>     sync: function ()
+#>   Private:
+#>     is_current_: TRUE
+#>     ptr_: externalptr
+#>     state_: a0 46 22 8e b9 e5 e8 fe 37 99 06 e4 18 2d 13 f3 25 33 fb ...
    +

    We can again assemble our answer, which agrees with above

    +
    +mean(vapply(ans, "[[", numeric(1), "value"))
+#> [1] 3.142141
    +

    The state of these pointers now also agrees with above;

    +
    +ptrs_local[[1]]$state()
+#>  [1] 3c 9a e0 2e ac 65 52 0d b4 be 20 c8 cd c5 9e 27 82 14 7e 79 c2 8f fb 47 4c
+#> [26] 00 da 0f 97 50 f7 f6
+ans[[1]]$ptr$state()
+#>  [1] 3c 9a e0 2e ac 65 52 0d b4 be 20 c8 cd c5 9e 27 82 14 7e 79 c2 8f fb 47 4c
+#> [26] 00 da 0f 97 50 f7 f6
    +

    This approach could be useful where the calculation is to be +continued (for example iterating until some convergence criteria is +met). The additional work of synchronising and returning the pointer +adds complexity though.

    +
    +
    +

    Considerations +

    +

    Ideally the calculations will not depend on number of nodes used, so +you should take the same approach as described in +vignette("rng_package") and try and identify the +“parallelisable” component (which might be larger than the number of +nodes) and parallelise based on that.

    +

    For example, suppose we want to run a multi-chain MCMC simulation. +Parallelising across chains is an obvious between-node target. We could +then send n chains over m nodes +(m <= n) and we’d want to arrange our seeds so that we +long-jump for each chain not over each node as that way no +matter how many nodes we had available we’d get the same results.

    +
    +
    +

    Use cases +

    +

    Here we show a more complete, and less contrived, use case with +dust’s “volatility” model. This example picks up from +vignette("data") and the reader is directed there for a +fuller explanation.

    +
    +volatility <- dust::dust_example("volatility")
    +

    The model was written to fit to a time series:

    +

    The model can run in parallel on a single node to produce a +likelihood estimate given parameters, we’ll write a small function to do +this:

    +
    +run_filter <- function(pars, mod) {
+  if (any(pars < 0)) {
+    return(-Inf)
+  }
+  pars <- list(alpha = pars[[1]], sigma = pars[[2]])
+  mod$update_state(pars = pars, time = 0)
+  mod$filter()$log_likelihood
+}
    +

    We assume that our parameter vector here is a length-2 numeric vector +with values alpha and sigma and ensure that +these are positive by returning -Inf if invalid values are +given.

    +

    We can create an instance of the model, set the data, and run the +filter (for details see vignette("data"))

    +
    +n_particles <- 128
+n_threads <- 4
+mod <- volatility$new(list(), 0, n_particles, n_threads = n_threads)
+mod$set_data(dust::dust_data(data))
+#> NULL
+run_filter(c(0.91, 1), mod)
+#> [1] -179.0706
    +

    We could also write a very simple MCMC using the Metropolis-Hastings +algorithm:

    +
    +mcmc <- function(mod, p, n_times, proposal_sd = 0.02) {
+  ll <- run_filter(p, mod)
+
+  ret <- matrix(NA_real_, n_times + 1, length(p) + 1)
+  ret[1, ] <- c(p, ll)
+
+  for (i in seq_len(n_times)) {
+    p_new <- rnorm(length(p), p, proposal_sd)
+    ll_new <- run_filter(p_new, mod)
+    if (ll_new > ll || runif(1) < exp(ll_new - ll)) {
+      ll <- ll_new
+      p <- p_new
+    }
+    ret[i + 1, ] <- c(p, ll)
+  }
+  ret
+}
    +

    We can run this for a number of steps and collect up sampled +parameters and their likelihoods

    +
    +ans <- mcmc(mod, c(0.91, 1), 20)
    +

    (We are cutting a lot of corners with the inference here; we have not +specified any priors and are assuming that the distribution can be +integrated over the parameters, and our proposal mechanism is extremely +simple supporting only orthogonal proposals of the two parameters which +are certainly correlated. However, the basic features are shared with +any more sophisticated approach.)

    +

    Our aim here is now to carry this out in parallel, where we run a +chain per node. To do this we need to do the same basic steps as above. +If we want to run 8 chains we’ll need 8 seeds, even if we run on fewer +nodes:

    +
    +seed <- dust::dust_rng_distributed_state(n_nodes = 8L, algorithm = volatility)
    +

    It will also be useful to write a little wrapper function that +repeats the setup from above, then runs the MCMC:

    +
    +run_mcmc <- function(seed, data, ...) {
+  volatility <- dust::dust_example("volatility")
+  mod <- volatility$new(list(), 0, 128, seed = seed, n_threads = 2)
+  mod$set_data(dust::dust_data(data))
+  mcmc(mod, ...)
+}
    +
    +parallel::clusterExport(cl, c("mcmc", "run_mcmc", "run_filter"))
+ans <- parallel::clusterApply(cl, seed, run_mcmc, data, c(0.91, 1), 20)
    +

    This produces a list of samples from each of the 8 chains, run over 2 +nodes, each of which ran using 2 threads. We can scale any of this +parallelism (increasing threads until we hit the total number of +particles, increasing nodes until we hit the number of chains) but the +results will be deterministic (except for the call to runif +that we use here for the acceptance test within the MCMC).

    +

    Note that in creating the seed above we left n_streams +as the default (1) because the dust model constructor will take care of +expanding out per-particle seeds via a series of jumps.

    +

    You should be careful with these approaches to not exceed the compute +available to you, especially when using a multi-user system such as an +HPC.

    +
    +
    +

    Summary +

    +
      +
    • +Simplest: create a set of suitable rng seeds on the +controlling node and send them to the worker nodes, don’t try and +continue calculations afterwards.
      • +
    • Create a set of pointer objects which could be used on the +controlling process first, then sent to the worker nodes
      • +
    • +Hardest: create a set of pointer objects and send them to +the worker nodes, then at the end of the calculation synchronise the +state and return to the controlling node
      • +
    +
    +

    [^1] It’s hard to get a sense of these numbers but 2^128 +is about 3 x 10^38 draws. If we draw a billion numbers +(10^9) a second (1ns per draw is the rate on a reasonable CPU) we can +draw 3 x 10^16 numbers a year, so at this rate it would take this would +take 10^22 years to reach the next stream. In contrast, the universe is +14 billion years old (1.4 x 10^10 years).

    +
    +
    +
    +
      +

    1. 3/4↩︎

      2. +
    +
    +
    + + + +
    + + + + +