local_low_rank_demo.py

import numpy as np
%pylab inline


def generate_raw_weights(n, a, b, p):
    res = np.zeros((n, n))
    for i in range(n):
        for j in range(n):
            sq_dist = ((i - a)**2 + (j - b)**2) *1.0/ n**2
            res[i,j] = exp(-sq_dist*p)
    return res


n = 100
k = 3
A = np.random.rand(n, k).dot(np.random.rand(n, k).T)
B = np.random.rand(n, k).dot(np.random.rand(n, k).T)


raw_mask1 = generate_raw_weights(n, 10, 10, 2)
raw_mask2 = generate_raw_weights(n, n-10, n-10, 5)

# normalization
mask1 = raw_mask1 / (raw_mask1 + raw_mask2)
mask2 = raw_mask2 / (raw_mask1 + raw_mask2)

# plot
figsize(10, 4)
subplot(121)
title('w_a')
imshow(mask1, interpolation='None')
colorbar()
subplot(122)
title('w_b')
imshow(mask2, interpolation='None')
colorbar()
print 'shape(A)={}, shape(B)={}'.format(A.shape, B.shape)
print 'rank(A) = {}, rank(B) = {}'.format(np.linalg.matrix_rank(A), np.linalg.matrix_rank(B))
print 'rank(A+B) = {}'.format(np.linalg.matrix_rank(A + B))
print 'rank(w_a*A + w_b*B) = {}'.format(np.linalg.matrix_rank(mask1*A + mask2*B))