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util.py
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util.py
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# Title: util.py
# Description: Various utilities useful for online NICA tests
# Author: David Lipshutz ([email protected])
##############################
# Imports
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import linear_sum_assignment
##############################
def synthetic_data(s_dim, x_dim, samples):
"""
Parameters:
====================
s_dim -- The dimension of sources
x_dim -- The dimension of mixtures
samples -- The number of samples
Output:
====================
S -- The source data matrix
X -- The mixture data matrix
"""
print(f'Generating {s_dim}-dimensional sparse uniform source data...')
# Generate sparse random samples
U = np.random.uniform(0,np.sqrt(48/5),(s_dim,samples)) # independent non-negative uniform source RVs with variance 1
B = np.random.binomial(1, .5, (s_dim,samples)) # binomial RVs to sparsify the source
S = U*B # sources
print(f'Generating {x_dim}-dimensional mixtures...')
A = np.random.randn(x_dim,s_dim) # random mixing matrix
# Generate mixtures
X = A@S
np.save(f'datasets/{s_dim}-dim_synthetic/sources.npy', S)
np.save(f'datasets/{s_dim}-dim_synthetic/mixtures.npy', X)
def image_data(s_dim, x_dim):
"""
Parameters:
====================
s_dim -- The dimension of sources
x_dim -- The dimension of mixtures
Output:
====================
S -- The source data matrix
X -- The mixture data matrix
"""
print(f'Generating {s_dim}-dimensional image source data...')
# Generate image sources
image_numbers = [5, 6, 11]; winsize=252 # 3 pre-specified image patches
posx = [220, 250, 200]
posy = [1, 1, 1]
S = np.zeros((s_dim, winsize**2))
plt.figure(figsize=(15,10))
for i in range(s_dim):
image = imageio.imread(f"images/{image_numbers[i]}.tiff")
window = image[posy[i]:posy[i] + winsize, posx[i]:posx[i] + winsize]
plt.subplot(s_dim, 1, i+1)
plt.imshow(window, cmap="gray")
window = window.reshape(1,-1)
window = window - window.min(axis=1)
window_var = np.cov(window)
window = window*(window_var**-.5)
S[i,:] = window
plt.show()
S = np.array(S)
print(f'Generating {x_dim}-dimensional mixtures...')
A = np.random.randn(x_dim,s_dim) # random mixing matrix
# Generate mixtures
X = A@S
np.save(f'datasets/image/sources.npy', S)
np.save(f'datasets/image/mixtures.npy', X)
def permutation_error(S_perm, Y):
"""
Parameters:
====================
S_perm -- The data matrix of permuted sources
Y -- The data matrix of recovered sources
Output:
====================
err -- the (relative) Frobenius norm error
"""
assert S_perm.shape==Y.shape, "The shape of the permuted sources S_perm must equal the shape of the recovered sources Y"
s_dim = S_perm.shape[0]
iters = S_perm.shape[1]
err = np.zeros(iters)
# Determine the optimal permutation at the final time point.
# We solve the linear assignment problem using the linear_sum_assignment package
# Calculate cost matrix:
C = np.zeros((s_dim,s_dim))
for i in range(s_dim):
for j in range(s_dim):
C[i,j] = ((S_perm[i] - Y[j])**2).sum()
# Find the optimal assignment for the cost matrix C
row_ind, col_ind = linear_sum_assignment(C)
for t in range(iters):
diff_t = (S_perm[row_ind[:],t] - Y[col_ind[:],t])**2
error_t = diff_t.sum()/s_dim
if t==0:
err[t] = error_t
elif t>0:
# err[t] = err[t-1] + (error_t - err[t-1])/t
err[t] = err[t-1] + (error_t - err[t-1])/1000
return err
def add_fill_lines(axis, t, err, plot_kwargs=None, ci_kwargs=None):
"""
Parameters:
====================
axis -- Axis variable
t -- Array of time points
err -- The data matrix of errors over multiple trials
plot_kwargs -- Arguments for axis.plot()
ci_kwargs -- Arguments for axis.fill_between()
Output:
====================
plot -- Function axis.plot()
fill -- Function axis.fill_between() with standard deviation computed on a log scale
"""
log_err = np.log(err+10**-5) # add 10**-5 to ensure the logarithm is well defined
log_mu = log_err.mean(axis=0)
sigma = np.std(log_err,axis=0)
ci_lo, ci_hi = log_mu - sigma, log_mu + sigma
plot_kwargs = plot_kwargs or {}
ci_kwargs = ci_kwargs or {}
plot = axis.plot(t, np.exp(log_mu), **plot_kwargs)
fill = axis.fill_between(t, np.exp(ci_lo), np.exp(ci_hi), alpha=.1, **ci_kwargs)
return plot, fill