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VAE_util.py
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VAE_util.py
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# -*- coding: utf-8 -*-
"""
Created on Thu Jun 9 12:12:57 2016
@author: rob
"""
import numpy as np
import tensorflow as tf
from scipy.stats import multivariate_normal
import matplotlib.pyplot as plt
# Extracts form the implementation by https://github.com/hardmaru/write-rnn-tensorflow
def tf_2d_normal(x1, x2, mu1, mu2, s1, s2, rho):
""" 2D normal distribution
input
- x,mu: input vectors
- s1,s2: standard deviances over x1 and x2
- rho: correlation coefficient in x1-x2 plane
"""
# eq # 24 and 25 of http://arxiv.org/abs/1308.0850
norm1 = tf.sub(x1, mu1)
norm2 = tf.sub(x2, mu2)
s1s2 = tf.mul(s1, s2)
z = tf.square(tf.div(norm1, s1))+tf.square(tf.div(norm2, s2))-2.0*tf.div(tf.mul(rho, tf.mul(norm1, norm2)), s1s2)
negRho = 1-tf.square(rho)
result = tf.exp(tf.div(-1.0*z,2.0*negRho))
denom = 2*np.pi*tf.mul(s1s2, tf.sqrt(negRho))
px1x2 = tf.div(result, denom)
return px1x2
def tf_1d_normal(x3,mu3,s3):
""" 3D normal distribution Under assumption that x3 is uncorrelated with x1 and x2
input
- x,mu: input vectors
- s1,s2,s3: standard deviances over x1 and x2 and x3
- rho: correlation coefficient in x1-x2 plane
"""
norm3 = tf.sub(x3, mu3)
z = tf.square(tf.div(norm3, s3))
result = tf.exp(tf.div(-z,2))
denom = 2.0*np.pi*s3
px3 = tf.div(result, denom) #probability in x3 dimension
return px3
#def plot_traj_MDN(sess,val_dict,batch,sl_plot = 5, ind = -1):
# """Plots the trajectory. At given time-stamp, it plots the probability distributions
# of where the next point will be
# input:
# - sess: the TF session
# - val_dict: a dictionary with which to evaluate the model
# - batch: the batch X_val[some_indices] that you feed into val_dict.
# we could also pick this from val-dict, but this workflow is cleaner
# - sl_plot: the time-stamp where you'd like to visualize
# - ind: some index into the batch. if -1, we'll pick a random one"""
# try:
# result = sess.run([model.mu1,model.mu2,model.mu3,model.s1,model.s2,model.s3,model.rho],feed_dict=val_dict)
# except:
# print('We cannot fetch all variables for the MDN')
# batch_size,crd,seq_len = batch.shape
# assert ind < batch_size, 'Your index is outside batch'
# assert sl_plot < seq_len, 'Your sequence index is outside sequence'
# if ind == -1: ind = np.random.randint(0,batch_size)
# delta = 0.025 #Grid size to evaluate the PDF
# width = 1.0 # how far to evaluate the pdf?
#
# fig = plt.figure()
# ax = fig.add_subplot(2,2,1,projection='3d')
# ax.plot(batch[ind,0,:], batch[ind,1,:], batch[ind,2,:],'r')
# ax.scatter(batch[ind,0,sl_plot], batch[ind,1,sl_plot], batch[ind,2,sl_plot])
# ax.set_xlabel('x coordinate')
# ax.set_ylabel('y coordinate')
# ax.set_zlabel('z coordinate')
#
# mean1 = result[0][ind,0,sl_plot]
# mean2 = result[1][ind,0,sl_plot]
# mean3 = result[2][ind,0,sl_plot]
# sigma1 = result[3][ind,0,sl_plot]
# sigma2 = result[4][ind,0,sl_plot]
# sigma3 = result[5][ind,0,sl_plot]
# sigma12 = result[6][ind,0,sl_plot]*sigma1*sigma2
#
# ax = fig.add_subplot(2,2,2)
#
# x1 = np.arange(-width, width, delta)
# x2 = np.arange(-width, width, delta)
# X1, X2 = np.meshgrid(x1, x2)
# Z = mlab.bivariate_normal(X1, X2, sigma1, sigma2, mean1, mean2,sigma12)
# CS = ax.contour(X1, X2, Z)
# plt.clabel(CS, inline=1, fontsize=10)
# ax.set_xlabel('x coordinate')
# ax.set_ylabel('y coordinate')
#
# ax = fig.add_subplot(2,2,3)
# x3 = np.arange(-width, width, delta)
# X1, X3 = np.meshgrid(x1, x3)
# Z = mlab.bivariate_normal(X1, X3, sigma1, sigma3, mean1, mean3)
# CS = ax.contour(X1, X3, Z)
# plt.clabel(CS, inline=1, fontsize=10)
# ax.set_xlabel('x coordinate')
# ax.set_ylabel('Z coordinate')
#
# ax = fig.add_subplot(2,2,4)
# X2, X3 = np.meshgrid(x2, x3)
# Z = mlab.bivariate_normal(X2, X3, sigma2, sigma3, mean2, mean3)
# CS = ax.contour(X2, X3, Z)
# plt.clabel(CS, inline=1, fontsize=10)
# ax.set_xlabel('y coordinate')
# ax.set_ylabel('Z coordinate')
def plot_traj_MDN_mult(model,sess,val_dict,batch,sl_plot = 5, ind = -1):
"""Plots the trajectory. At given time-stamp, it plots the probability distributions
of where the next point will be
THIS IS FOR MULTIPLE MIXTURES
input:
- sess: the TF session
- val_dict: a dictionary with which to evaluate the model
- batch: the batch X_val[some_indices] that you feed into val_dict.
we could also pick this from val-dict, but this workflow is cleaner
- sl_plot: the time-stamp where you'd like to visualize
- ind: some index into the batch. if -1, we'll pick a random one"""
result = sess.run([model.mu1,model.mu2,model.mu3,model.s1,model.s2,model.s3,model.rho,model.theta],feed_dict=val_dict)
batch_size,crd,seq_len = batch.shape
assert ind < batch_size, 'Your index is outside batch'
assert sl_plot < seq_len, 'Your sequence index is outside sequence'
if ind == -1: ind = np.random.randint(0,batch_size)
delta = 0.025 #Grid size to evaluate the PDF
width = 1.0 # how far to evaluate the pdf?
fig = plt.figure()
ax = fig.add_subplot(2,2,1,projection='3d')
ax.plot(batch[ind,0,:], batch[ind,1,:], batch[ind,2,:],'r')
ax.scatter(batch[ind,0,sl_plot], batch[ind,1,sl_plot], batch[ind,2,sl_plot])
ax.set_xlabel('x coordinate')
ax.set_ylabel('y coordinate')
ax.set_zlabel('z coordinate')
# lower-case x1,x2,x3 are indezing the grid
# upper-case X1,X2,X3 are coordinates in the mesh
x1 = np.arange(-width, width+0.1, delta)
x2 = np.arange(-width, width+0.2, delta)
x3 = np.arange(-width, width+0.3, delta)
X1,X2,X3 = np.meshgrid(x1,x2,x3,indexing='ij')
XX = np.stack((X1,X2,X3),axis=3)
PP = []
mixtures = result[0].shape[1]
for m in range(mixtures):
mean = np.zeros((3))
mean[0] = result[0][ind,m,sl_plot]
mean[1] = result[1][ind,m,sl_plot]
mean[2] = result[2][ind,m,sl_plot]
cov = np.zeros((3,3))
sigma1 = result[3][ind,m,sl_plot]
sigma2 = result[4][ind,m,sl_plot]
sigma3 = result[5][ind,m,sl_plot]
sigma12 = result[6][ind,m,sl_plot]*sigma1*sigma2
cov[0,0] = np.square(sigma1)
cov[1,1] = np.square(sigma2)
cov[2,2] = np.square(sigma3)
cov[1,2] = sigma12
cov[2,1] = sigma12
rv = multivariate_normal(mean,cov)
P = rv.pdf(XX) #P is now in [x1,x2,x3]
PP.append(P)
# PP is now a list
PP = np.stack(PP,axis=3)
# PP is now in [x1,x2,x3,mixtures]
#Multiply with the mixture
theta_local = result[7][ind,:,sl_plot]
ZZ = np.dot(PP,theta_local)
#ZZ is now in [x1,x2,x3]
print('The theta variables %s'%theta_local)
#Every Z is a marginalization of ZZ.
# summing over axis 2, gives the pdf over x1,x2
# summing over axis 1, gives the pdf over x1,x3
# summing over axis 0, gives the pdf over x2,x3
ax = fig.add_subplot(2,2,2)
X1, X2 = np.meshgrid(x1, x2)
Z = np.sum(ZZ,axis=2)
CS = ax.contour(X1, X2, Z.T)
plt.clabel(CS, inline=1, fontsize=10)
ax.set_xlabel('x coordinate')
ax.set_ylabel('y coordinate')
ax = fig.add_subplot(2,2,3)
X1, X3 = np.meshgrid(x1, x3)
Z = np.sum(ZZ,axis=1)
CS = ax.contour(X1, X3, Z.T)
plt.clabel(CS, inline=1, fontsize=10)
ax.set_xlabel('x coordinate')
ax.set_ylabel('Z coordinate')
ax = fig.add_subplot(2,2,4)
X2, X3 = np.meshgrid(x2, x3)
Z = np.sum(ZZ,axis=0)
CS = ax.contour(X2, X3, Z.T)
plt.clabel(CS, inline=1, fontsize=10)
ax.set_xlabel('y coordinate')
ax.set_ylabel('Z coordinate')
# Piece of code doesn;t work yet
#def tf_3d_normal(x_in, mu_in, s1, s2, s3, rho12, rho13, rho23):
#
# x = tf.sub(x_in,mu_in)
# V11 = tf.pow(s1,2)
# V12 = tf.mul(tf.mul(rho12,s1),s2)
# V13 = tf.mul(tf.mul(rho13,s1),s3)
# V22 = tf.pow(s2,2)
# V23 = tf.mul(tf.mul(rho23,s2),s3)
# V22 = tf.pow(s3,2)
#
# cov = tf.pack([tf.pack([V11,V12.V13]),tf.pack([V12,V22,V23]),tf.pack([V13,V23,V33])])
# quad = tf.matmul(x,tf.matmul(tf.inv(cov),tf.transpose(x)))
# expo = tf.exp(tf.mul(tf.constant([-0.5]),quad))
# den = tf.mul(tf.pow((tf.constant([2*3.1415])),tf.constant([3.0/2.0])),
# determinant = tf.mul(V11,tf.mul(V22,V33)) - tf.mul(V11,tf.pow(V23,2)) + tf.mul(V12,tf.sub(tf.mul(tf.mul(tf.constant([2]),V13),V23),tf.mul(V12,V33))) - tf.mul(V22,tf.pow(V13,2))
#
#
# w = tf.pow(x1,2)
#
## s1s2 = tf.mul(s1, s2)
## z = tf.square(tf.div(norm1, s1))+tf.square(tf.div(norm2, s2))-2*tf.div(tf.mul(rho, tf.mul(norm1, norm2)), s1s2)
## negRho = 1-tf.square(rho)
## result = tf.exp(tf.div(-z,2*negRho))
## denom = 2*np.pi*tf.mul(s1s2, tf.sqrt(negRho))
## result = tf.div(result, denom)
# return result