Removing py35 support (#297)

* Removing py35 support
* update convergence results

.circleci/config.yml

@@ -78,7 +78,7 @@ jobs:
             coverage run --source=chaospy/ --module \
                 pytest --nbval-lax --doctest-modules \
                 docs/tutorials/*.ipynb docs/tutorials/*/*.ipynb \
-                chaospy/ tests/ docs/*.rst docs/*/*.rst
+                chaospy/ tests/ README.rst docs/*.rst docs/*/*.rst
             bash <(curl -s https://codecov.io/bash)
   deploy:
     executor: python-container

CHANGELOG.rst

@@ -1,20 +1,24 @@
 Master Branch
 =============
 
+Version 4.1.1 (2020-11-13)
+==========================
+
 ADDED:
   * `include_axis_dim` flag added to `Distribution.sample` to force the
     inclusion of extra dimension. (Currently first dimension is omitted is
     `len(dist) == 1`.)
-
 CHANGED:
   * `chaospy.E_cond` changed to accept simple polynomials as second argument,
     allowing for e.g. `chaospy.E_cond(q0*q1, q0, dist)` which can be
     interpreted as "expectation of `q0*q1` given `q0` with respect to `dist`".
   * Bugfixes to `chaospy.Spearman`
-
+  * Updates to the documentation.
 REMOVED:
   * Deprecated `report_on_exception`. Caused recursion problems, and only a
     semi-useful diagnostic tool to begin with.
+  * No more support for Python 3.5. This allows the poetry install to use
+    newer version of `numpy` and `scipy`.
 
 Version 4.1.0 (2020-11-05)
 ==========================
@@ -36,7 +40,6 @@ CHANGED:
   * Discretization default in Lanczos and Stieltjes changed from `fejer` to
     `clenshaw_curtis` as edge evaluation is better handled these days, and the
     latter is better for when edges are finite.
-
 REMOVED:
   * `chaospy.basis` and `chaospy.prange` (which was superseded by
     `chaospy.monomial` in June).

README.rst

@@ -29,74 +29,105 @@ Python.
 Installation
 ------------
 
-Installation should be straight forward::
+Installation should be straight forward from `PyPI <https://pypi.org/>`_:
 
-    pip install chaospy
+.. code-block:: bash
 
-And you should be ready to go.
+    $ pip install chaospy
 
 Example Usage
 -------------
 
-``chaospy`` is created to be simple and modular. A simple script to implement
-point collocation method will look as follows:
+``chaospy`` is created to work well inside numerical Python ecosystem. You
+therefore typically need to import `Numpy <https://numpy.org/>`_ along side
+``chaospy``:
 
 .. code-block:: python
 
-    import numpy
-    import chaospy
+    >>> import numpy
+    >>> import chaospy
 
-Wrap your code in a function:
+``chaospy`` is problem agnostic, so you can use your own code using any means
+you find fit. The only requirement is that the output is compatible with
+`numpy.ndarray` format:
 
 .. code-block:: python
 
-    coordinates = numpy.linspace(0, 10, 100)
-    def foo(coordinates, params):
-        """Function to do uncertainty quantification on."""
-        param_init, param_rate = params
-        return param_init*numpy.e**(-param_rate*coordinates)
+    >>> coordinates = numpy.linspace(0, 10, 100)
+    >>> def forward_solver(coordinates, parameters):
+    ...     """Function to do uncertainty quantification on."""
+    ...     param_init, param_rate = parameters
+    ...     return param_init*numpy.e**(-param_rate*coordinates)
 
-Construct a multivariate probability distribution:
+We here assume that ``parameters`` contains aleatory variability with known
+probability. We formalize this probability in ``chaospy`` as a joint
+probability distribution. For example:
 
 .. code-block:: python
 
-    distribution = chaospy.J(chaospy.Uniform(1, 2), chaospy.Uniform(0.1, 0.2))
+    >>> distribution = chaospy.J(
+    ...     chaospy.Uniform(1, 2), chaospy.Normal(0, 2))
+    >>> print(distribution)
+    J(Uniform(lower=1, upper=2), Normal(mu=0, sigma=2))
 
-Construct polynomial chaos expansion:
+Most probability distributions have an associated expansion of orthogonal
+polynomials. These can be automatically constructed:
 
 .. code-block:: python
 
-    polynomial_expansion = chaospy.generate_expansion(8, distribution)
+    >>> expansion = chaospy.generate_expansion(8, distribution)
+    >>> print(expansion[:5].round(8))
+    [1.0 q1 q0-1.5 q0*q1-1.5*q1 q0**2-3.0*q0+2.16666667]
 
-Generate random samples from for example Halton low-discrepancy sequence:
+Here the polynomial is defined positional, such that ``q0`` and ``q1`` refers
+to the uniform and normal distribution respectively.
+
+The distribution can also be used to create (pseudo-)random samples and
+low-discrepancy sequences. For example to create Sobol sequence samples:
 
 .. code-block:: python
 
-    samples = distribution.sample(1000, rule="halton")
+    >>> samples = distribution.sample(1000, rule="sobol")
+    >>> print(samples[:, :4].round(8))
+    [[ 1.5         1.75        1.25        1.375     ]
+     [ 0.         -1.3489795   1.3489795  -0.63727873]]
 
-Evaluate function for each sample:
+We can evaluating the forward solver using these samples:
 
 .. code-block:: python
 
-    evals = numpy.array([foo(coordinates, sample) for sample in samples.T])
+    >>> evaluations = numpy.array([
+    ...     forward_solver(coordinates, sample) for sample in samples.T])
+    >>> print(evaluations[:3, :5].round(8))
+    [[1.5        1.5        1.5        1.5        1.5       ]
+     [1.75       2.00546578 2.29822457 2.63372042 3.0181921 ]
+     [1.25       1.09076905 0.95182169 0.83057411 0.72477163]]
 
-Bring the parts together using point collocation method:
+Having all these components in place, we have enough components to perform
+point collocation. Or in other words, we can create a polynomial approximation
+of ``forward_solver``:
 
 .. code-block:: python
 
-    foo_approx = chaospy.fit_regression(
-        polynomial_expansion, samples, evals)
+    >>> approx_solver = chaospy.fit_regression(
+    ...     expansion, samples, evaluations)
+    >>> print(approx_solver[:2].round(4))
+    [q0 -0.0002*q0*q1**3+0.0051*q0*q1**2-0.101*q0*q1+q0]
 
-Derive statistics from model approximation:
+Since the model approximations are polynomials, we can do inference on them
+directly. For example:
 
 .. code-block:: python
 
-    expected = chaospy.E(foo_approx, distribution)
-    deviation = chaospy.Std(foo_approx, distribution)
-    sobol_main = chaospy.Sens_m(foo_approx, distribution)
-    sobol_total = chaospy.Sens_t(foo_approx, distribution)
+    >>> expected = chaospy.E(approx_solver, distribution)
+    >>> print(expected[:5].round(8))
+    [1.5        1.53092356 1.62757217 1.80240142 2.07915608]
+    >>> deviation = chaospy.Std(approx_solver, distribution)
+    >>> print(deviation[:5].round(8))
+    [0.28867513 0.43364958 0.76501802 1.27106355 2.07110879]
 
-For a more extensive guides on what is going on, see the `tutorial collection`_.
+For more extensive guides on this approach an others, see the `tutorial
+collection`_.
 
 .. _tutorial collection: https://chaospy.readthedocs.io/en/master/tutorials