def base_counts(coeff_set):
""" Count the number of additions, reads, and writes for this coefficient set (A, B, or C).
For A and B, these are the adds used to form the 'S' and 'T' matrices.
If an S or T matrix is just a length-1 addition chain, then no additions are counted.
"""
cols = subexpr_elim.transpose(coeff_set)
num_adds = sum([gen.num_nonzero(col) - 1 for col in cols])
num_reads = sum([gen.num_nonzero(col) for col in cols])
num_writes = sum([1 for col in cols if gen.num_nonzero(col) > 1])
return (num_adds, num_reads, num_writes)
def main():
try:
coeff_file = sys.argv[1]
dims = tuple([int(d) for d in sys.argv[2].split(',')])
except:
raise Exception('USAGE: python stability_vector.py coeff_file m,k,n')
full_stab_mat = 0
if len(sys.argv) > 3:
full_stab_mat = sys.argv[3]
coeffs = read_coeffs(coeff_file)
# Using the notation from our paper
a_vec = np.array(
[sum(np.abs([float(x) for x in row])) for row in transpose(coeffs[0])])
b_vec = np.array(
[sum(np.abs([float(x) for x in row])) for row in transpose(coeffs[1])])
e_vec = [
np.dot(np.abs([float(x) for x in row]), a_vec * b_vec)
for row in coeffs[2]
]
alpha_vec = np.array([num_nonzero(row) for row in transpose(coeffs[0])])
beta_vec = np.array([num_nonzero(row) for row in transpose(coeffs[1])])
ab_vec = alpha_vec + beta_vec
gamma_vec = [num_nonzero(row) for row in coeffs[2]]
W_ind = np.array([[float(val) for val in row] for row in coeffs[2]])
W_ind[np.nonzero(W_ind)] = 1
q_vec = [gamma_vec[k] + np.max(ab_vec * W_ind[k,:]) \
for k in range(W_ind.shape[0])]
# Number of additions
nnz = sum([val for val in ab_vec]) + sum([val for val in gamma_vec])
# print as q_vec emax
rank = len(coeffs[0][0])
mkn = dims[0] * dims[1] * dims[2]
print mkn, rank, nnz, int(np.max(q_vec)), int(np.max(e_vec))
if full_stab_mat:
# Print in the same style as D'Alberto presents in his 2014 paper.
print 'e vector:'
for i in range(dims[0]):
out_format = '\t' + ' '.join(['%4d' for _ in range(dims[2])])
vals = e_vec[(i * dims[2]):(i * dims[2] + dims[2])]
print out_format % tuple(vals)
print 'q vector:'
for i in range(dims[0]):
out_format = '\t' + ' '.join(['%4d' for _ in range(dims[2])])
vals = q_vec[(i * dims[2]):(i * dims[2] + dims[2])]
print out_format % tuple(vals)
def elim_counts(elim_info):
""" Count the number of additions, reads, and writes for the elimination variables of
a single coefficient set (for S matrices, T matrix, or M matrices).
"""
if any(map(lambda x: len(x) == 0, elim_info)):
return (0, 0, 0)
num_adds = sum([gen.num_nonzero(row) - 1 for row in elim_info])
num_reads = sum([gen.num_nonzero(row) for row in elim_info])
num_writes = len(elim_info)
return (num_adds, num_reads, num_writes)
def main():
try:
coeff_file = sys.argv[1]
dims = tuple([int(d) for d in sys.argv[2].split(',')])
except:
raise Exception('USAGE: python stability_vector.py coeff_file m,k,n')
full_stab_mat = 0
if len(sys.argv) > 3:
full_stab_mat = sys.argv[3]
coeffs = read_coeffs(coeff_file)
# Using the notation from our paper
a_vec = np.array([sum(np.abs([float(x) for x in row])) for row in transpose(coeffs[0])])
b_vec = np.array([sum(np.abs([float(x) for x in row])) for row in transpose(coeffs[1])])
e_vec = [np.dot(np.abs([float(x) for x in row]), a_vec * b_vec) for row in coeffs[2]]
alpha_vec = np.array([num_nonzero(row) for row in transpose(coeffs[0])])
beta_vec = np.array([num_nonzero(row) for row in transpose(coeffs[1])])
ab_vec = alpha_vec + beta_vec
gamma_vec = [num_nonzero(row) for row in coeffs[2]]
W_ind = np.array([[float(val) for val in row] for row in coeffs[2]])
W_ind[np.nonzero(W_ind)] = 1
q_vec = [gamma_vec[k] + np.max(ab_vec * W_ind[k,:]) \
for k in range(W_ind.shape[0])]
# Number of additions
nnz = sum([val for val in ab_vec]) + sum([val for val in gamma_vec])
# print as q_vec emax
rank = len(coeffs[0][0])
mkn = dims[0] * dims[1] * dims[2]
print mkn, rank, nnz, int(np.max(q_vec)), int(np.max(e_vec))
if full_stab_mat:
# Print in the same style as D'Alberto presents in his 2014 paper.
print 'e vector:'
for i in range(dims[0]):
out_format = '\t' + ' '.join(['%4d' for _ in range(dims[2])])
vals = e_vec[(i * dims[2]):(i * dims[2] + dims[2])]
print out_format % tuple(vals)
print 'q vector:'
for i in range(dims[0]):
out_format = '\t' + ' '.join(['%4d' for _ in range(dims[2])])
vals = q_vec[(i * dims[2]):(i * dims[2] + dims[2])]
print out_format % tuple(vals)
