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normal_dist_calculator.py
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normal_dist_calculator.py
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# -*- coding: utf-8 -*-
"""
Created on Mon Jul 6 15:52:45 2020
@author: Martin Sánner
normDistGenerator returns a list of tensorflow tensors with the value of the cdf of a normal distribution centered on mu and with variance var.
The latest values are stored in the class instance
"""
import numpy as np
import tensorflow as tf
import tensorflow_probability as tfp
import scipy as scp
import matplotlib.pyplot as plt
import logging
import scipy.stats
from datetime import datetime
import sys
now = datetime.now()
d_string = now.strftime("%d/%m/%Y, %H:%M:%S")
logging.basicConfig(
level=logging.INFO,
format="%(asctime)s [%(levelname)s] %(message)s",
handlers=[
logging.FileHandler("logfile_{}_{}.log".format(now.day,now.month)),
logging.StreamHandler(sys.stdout)
]
)
onedivsqrttwoPi = 1/np.sqrt(2*np.pi)
class normalDistCalc:
def __init__(self,mu = 0.0,var = 1.0):
'''
Parameters
----------
mu : float
Mean value of distribution
var : Variance > 0
applies absolute value function if necessary. If 0, reset to 1
Returns
-------
None.
'''
self.mu = mu
self.var = tf.abs(var) if var < 0 else var
if var == 0:
self.var = 1
def generate_distribution(self,x):
premult = tf.cast(onedivsqrttwoPi*(1/tf.sqrt(self.var)),dtype = tf.float64)
diff = tf.math.subtract(x,self.mu)
diffsqr = diff**2
expon = -diffsqr/(2*self.var)
return premult*tf.exp(expon)
class normalMixtureCalculator:
def __init__(self):
self.kg = 1
self.pis = np.asarray([1/self.kg for i in range(self.kg)]) #uniform
self.mus = np.asarray([0 for i in range(self.kg)])
self.var = np.asarray([1 for i in range(self.kg)])
def calculate_mixture_distributions(self,xs,pis,mus,var):
n,k = np.asarray(pis).shape
n2,k2 = np.asarray(mus).shape
n3,k3 = np.asarray(var).shape
assert n == n2 and n2 == n3 and k == k2 and k2 == k3, "Mixture parameters dont have matching shapes, {},{},{}".format(pis.shape,mus.shape,var.shape)
self.kg = k
mixture_sources = []
mixtures = []
for mix_index in range(n):
x = xs[n % len(xs)]
probability_array = []
for kd in range(self.kg):
probability_array.append(pis[mix_index][kd]*normalDistCalc(mus[mix_index][kd], var[mix_index][kd]).generate_distribution(x))
mixture = tf.add_n(probability_array)
mixtures.append(mixture)
mixture_sources.append(np.asarray(probability_array))
return np.asarray(mixtures), mixture_sources
def calculate_mixture_pre_distribution(self,xs,pres,mus,var):
n,k = np.asarray(pres).shape
n2,k2 = np.asarray(mus).shape
n3,k3 = np.asarray(var).shape
assert n == n2 and n2 == n3 and k == k2 and k2 == k3, "Mixture parameters dont have matching shapes, {},{},{}".format(pis.shape,mus.shape,var.shape)
self.kg = k
mixture_sources = []
mixtures = []
for mix_index in range(n):
x = xs[n % len(xs)]
probability_array = []
for kd in range(self.kg):
diff = x-mus[mix_index][kd]
diffsqr = diff**2
expon = -diffsqr/(2*var[mix_index][kd])
probability_array.append(pres[mix_index][kd]*tf.exp(expon))
mixture = tf.add_n(probability_array)
mixtures.append(mixture)
mixture_sources.append(np.asarray(probability_array))
return np.asarray(mixtures), mixture_sources
def generate_vector_random_gauss_mixture(r_values, kg):
n = len(r_values)
mixtures = []
mixture_pdfs = []
parameters = []
for mix_index in range(n):
r = r_values[mix_index]
mus = [np.random.uniform(-1.0,1.0) for k in range(kg)]
var = [np.random.uniform(0.0,1.0) for k in range(kg)]
pis = [np.random.rand() for k in range(kg)]
spi = np.sum(pis)
pis = [cp/spi for cp in pis] # sum(pi) = 1
gm = tfp.distributions.MixtureSameFamily(mixture_distribution = tfp.distributions.Categorical(probs = pis),
components_distribution = tfp.distributions.Normal(loc = mus,scale =var))
mixtures.append(gm)
mixture_pdfs.append(gm.prob(r))
parameters.append(np.asarray(pis+mus+var))
return np.asarray(mixture_pdfs),np.asarray(parameters),mixtures
def generate_vector_gauss_mixture(r_values, pi_values, mu_values, var_values):
n,k = np.asarray(pi_values).shape
n2,k2 = np.asarray(mu_values).shape
n3,k3 = np.asarray(var_values).shape
assert n == n2 and n2 == n3 and k == k2 and k2 == k3, "Mixture parameters dont have matching shapes, {},{},{}".format(pi_values.shape,mu_values.shape,var_values.shape)
mixtures = []
mixture_pdfs = []
for mix_index in range(n):
gm = tfp.distributions.MixtureSameFamily(mixture_distribution = tfp.distributions.Categorical(probs = pi_values[mix_index]),components_distribution = tfp.distributions.Normal(loc = mu_values[mix_index],scale = var_values[mix_index]),allow_nan_stats = False)
mixtures.append(gm)
mixture_pdfs.append(gm.prob(r_values[mix_index]))
return tf.stack(mixture_pdfs),mixtures
def generate_tensor_mixture_model(r_values, pi_values, mu_values, var_values):
n,k = pi_values.shape
n2,k2 = mu_values.shape
n3,k3 = var_values.shape
assert n == n2 and n2 == n3 and k == k2 and k2 == k3, "Mixture parameters dont have matching shapes, {},{},{}".format(pi_values.shape,mu_values.shape,var_values.shape)
mixtures = []
probabilities = []
for mix_index in range(n):
probability_array = []
for kd in range(k):
probability_array.append(pi_values[mix_index,kd]*tfp.distributions.normal.Normal(mu_values[mix_index,kd],tf.cast(tf.sqrt(var_values[mix_index,kd]),tf.float64)).prob(r_values[mix_index]))
mixture = tf.add_n(probability_array)
mixtures.append(mixture)
probabilities.append(probability_array)
return tf.stack(mixtures),probabilities
if __name__ == "__main__":
#num_profiles = 10#args.num_profile
#kg = 4
plt.close("all")
r = np.linspace(-10,10,1001)
mu = 0
var = 0.5
calcul = normalDistCalc(mu,var)
sample_dist = calcul.generate_distribution(r)
other_dist = tfp.distributions.Normal(loc = mu, scale = tf.sqrt(var))
diff = tf.cast(sample_dist,tf.float64) - tf.cast(other_dist.prob(r),tf.float64)
plt.figure()
plt.plot(r,sample_dist,label = "Calculator distribution")
plt.plot(r,other_dist.prob(r),label = "TFP dist")
plt.legend()
plt.figure()
plt.plot(r,diff)
num_gen = 5
kg = 4
rs = [r for i in range(num_gen)]
pis = [tf.cast(tf.nn.softmax([np.random.rand() for j in range(kg)]),dtype = tf.float64) for i in range(num_gen)]
mus = [[np.random.choice(r,replace = False) for j in range(kg)] for i in range(num_gen)]
var = [[np.random.rand() for j in range(kg)] for i in range(num_gen)]
mix_gen = normalMixtureCalculator()
mixtures,mixture_sources = mix_gen.calculate_mixture_distributions(rs,pis,mus,var)
tf_mixtures_pdfs,tf_mixture_sources = generate_vector_gauss_mixture(rs,pis,mus,tf.cast(tf.sqrt(var),tf.float64))
for i in range(num_gen):
plt.figure()
plt.plot(r,mixtures[i],label = "Self generated distribution")
plt.plot(r,tf_mixtures_pdfs[i],label = "TF generated dist")
plt.legend()