def GENERATE_RANDOM_EXPANDERS(K, size_H, EPSILON, samples):
NAME = '[RANDOM' + str(K) + ']'
print NAME + " Generating " + str(
samples) + " H (adjacency list matrices) of size " + str(
size_H) + " x " + str(K) + " ... "
print "\n"
eigenvalue = 0
for sampling in range(samples):
print NAME + " ## " + str(sampling) + " // " + str(
samples) + " ## "
H = generate_expander(K, size_H)
eigenvalue_aux = helpers.generate_eigenvalue(H, size_H, K, EPSILON,
NAME)
eigenvalue += eigenvalue_aux
eigenvalue = eigenvalue / samples
print NAME + " Calculated average of second highest eigenvalue for " + str(
samples) + " matrices H."
helpers.write_result(NAME, size_H, K, eigenvalue)
helpers.cleanup(".aux")
def GENERATE_ANGLUIN_EXPANDERS(size, A_indices, n, EPSILON):
size_H = 2 * size
print NAME + " Generating H (adjacency list matrix) of size " + str(
size_H) + " x " + str(K) + " ... "
H = numpy.empty(
shape=(size_H, K),
dtype=numpy.int32) # Generate H, empty adjacency list matrix
for row in A_indices:
for element_index in row: # Get the tuple index from the matrix of indices (A)
x0 = element_index / n # Grab first value
y0 = element_index % n # Grab second value
i = element_index # Grab the index of the (x0, y0) element
# connect to (x, y) in B
x = x0
y = y0
j = (x * n + y % n) + size # add the shift in the H indexing
H[i][0] = j # node with index i is connected to node with index j
H[j][0] = i # vice-versa
# connect to (x + y, y) in B
x = (x0 + y0) % n
y = y0
j = (x * n + y % n) + size
H[i][1] = j
H[j][1] = i
# connect to (y + 1, -x) in B
x = (y0 + 1) % n
y = (-x0) % n
j = (x * n + y % n) + size
H[i][2] = j
H[j][2] = i
print NAME + " Generated adjacency list matrix H."
print NAME + " Calculating second highest eigenvalue of H ... "
eigenvalue = helpers.generate_eigenvalue(H, size_H, K, EPSILON, NAME)
print NAME + " Calculated second highest eigenvalue of H."
helpers.write_result(NAME, size_H, K, eigenvalue)
helpers.cleanup(".aux")
def GENERATE_ANGLUIN_EXPANDERS(size, A_indices, n, EPSILON):
size_H = 2 * size
print NAME + " Generating H (adjacency list matrix) of size " + str(size_H) + " x " + str(K) + " ... "
H = numpy.empty(shape=(size_H, K), dtype=numpy.int32) # Generate H, empty adjacency list matrix
for row in A_indices:
for element_index in row: # Get the tuple index from the matrix of indices (A)
x0 = element_index / n # Grab first value
y0 = element_index % n # Grab second value
i = element_index # Grab the index of the (x0, y0) element
# connect to (x, y) in B
x = x0
y = y0
j = (x * n + y % n) + size # add the shift in the H indexing
H[i][0] = j # node with index i is connected to node with index j
H[j][0] = i # vice-versa
# connect to (x + y, y) in B
x = (x0 + y0) % n
y = y0
j = (x * n + y % n) + size
H[i][1] = j
H[j][1] = i
# connect to (y + 1, -x) in B
x = (y0 + 1) % n
y = (-x0) % n
j = (x * n + y % n) + size
H[i][2] = j
H[j][2] = i
print NAME + " Generated adjacency list matrix H."
print NAME + " Calculating second highest eigenvalue of H ... "
eigenvalue = helpers.generate_eigenvalue(H, size_H, K, EPSILON, NAME)
print NAME + " Calculated second highest eigenvalue of H."
helpers.write_result(NAME, size_H, K, eigenvalue)
helpers.cleanup(".aux")
def GENERATE_RANDOM_EXPANDERS(K, size_H, EPSILON, samples):
NAME = '[RANDOM' + str(K) + ']'
print NAME + " Generating " + str(samples) + " H (adjacency list matrices) of size " + str(size_H) + " x " + str(K) + " ... "
print "\n"
eigenvalue = 0
for sampling in range(samples):
print NAME + " ## " + str(sampling) + " // " + str(samples) + " ## "
H = generate_expander(K, size_H)
eigenvalue_aux = helpers.generate_eigenvalue(H, size_H, K, EPSILON, NAME)
eigenvalue += eigenvalue_aux
eigenvalue = eigenvalue / samples
print NAME + " Calculated average of second highest eigenvalue for " + str(samples) + " matrices H."
helpers.write_result(NAME, size_H, K, eigenvalue)
helpers.cleanup(".aux")
