def test_from_column_vector(self):
m = 3
n = 1
a = [1, 2, 3]
ia = [0, 1, 2, 3]
ja = [0, 0, 0]
input_vector = numpy.matrix([[1], [2], [3]])
expected_matrix = Matrix(m, n, a, ia, ja)
output_matrix = Matrix.from_column_vector(input_vector)
assert expected_matrix == output_matrix
def test_transpose(self):
m = n = 3
a = [1, 2, 3, 4, 5, 6, 7, 8, 9]
ia = [0, 3, 6, 9]
ja = [0, 1, 2, 0, 1, 2, 0, 1, 2]
initial_matrix = Matrix(m, n, a, ia, ja)
a_trans = [1, 4, 7, 2, 5, 8, 3, 6, 9]
expected_matrix = Matrix(m, n, a_trans, ia, ja)
output_matrix = initial_matrix.transpose()
assert expected_matrix == output_matrix
def test_eq_and_ne(self):
m = 3
m1 = Matrix.tridiagonal(m)
a = [2, -1, -1, 2, -1, -1, 2]
ia = [0, 2, 5, 7]
ja = [0, 1, 0, 1, 2, 1, 2]
m2 = Matrix(m, m, a, ia, ja)
assert m1 == m2
a = [1, 1, 1, 1, 1, 1, 1]
m3 = Matrix(m, m, a, ia, ja)
assert m2 != m3
def test_left_mult(self):
A = Matrix.tridiagonal(3)
a_inv = [0.75, 0.5, 0.25, 0.5, 1., 0.5, 0.25, 0.5, 0.75]
ia_inv = [0, 3, 6, 9]
ja_inv = [0, 1, 2, 0, 1, 2, 0, 1, 2]
a = [1.0, 1.0, 1.0]
ia = [0, 1, 2, 3]
ja = [0, 1, 2]
A_inv = Matrix(3, 3, a_inv, ia_inv, ja_inv)
I = Matrix(3, 3, a, ia, ja)
assert A * A_inv == I
def test_push_column_with_zeros(self):
m = 3
n = 2
a = [1, 2, 5, 3]
ia = [0, 1, 3, 4]
ja = [0, 0, 1, 0]
first_vector = numpy.matrix([[1], [2], [3]])
second_vector = numpy.matrix([[0], [5], [0]])
expected_matrix = Matrix(m, n, a, ia, ja)
output_matrix = Matrix.from_column_vector(first_vector)
output_matrix.push_column(second_vector)
assert expected_matrix == output_matrix
def test_push_column(self):
m = 3
n = 2
a = [1, 4, 2, 5, 3, 6]
ia = [0, 2, 4, 6]
ja = [0, 1, 0, 1, 0, 1]
first_vector = numpy.matrix([[1], [2], [3]])
second_vector = numpy.matrix([[4], [5], [6]])
expected_matrix = Matrix(m, n, a, ia, ja)
output_matrix = Matrix.from_column_vector(first_vector)
output_matrix.push_column(second_vector)
assert expected_matrix == output_matrix
def test_tridiagonal_generation(self):
m = 3
a = Matrix.tridiagonal(m)
assert len(a.ia) == m + 1
assert len(a) == 3 * m - 2
assert a.shape() == (m, m)
assert a.a == [2, -1, -1, 2, -1, -1, 2]
assert a.ia == [0, 2, 5, 7]
assert a.ja == [0, 1, 0, 1, 2, 1, 2]
def test_symmetric(self):
A = Matrix.tridiagonal(3)
print A.a
print A.ia
print A.ja
assert A.symmetric() == True
a = [1, 2, 1, 1]
ia = [0, 2, 3, 4]
ja = [0, 1, 0, 0]
A = Matrix(3, 3, a, ia, ja)
assert A.symmetric() == False
A = Matrix.from_mm_file('data/ash958.mtx')
assert A.symmetric() == False
def test_gmres_tridiagonal(self):
A = Matrix.tridiagonal(20)
b = numpy.ones((A.shape()[0], 1))
gmres = Gmres(A, b)
output_vector, error, metadata = gmres.solve()
assert error < Gmres.EPSILON
from gmrescrs import Gmres
from crsmatrix import Matrix
import numpy
max_matrix_size = 1000
max_iterations = 500
max_restart = 500
A = Matrix.tridiagonal(max_matrix_size)
b = numpy.ones((A.m, 1))
x, error, metadata = Gmres(A,
b,
max_iterations=max_iterations,
restart_after=max_restart).solve()
error_time_values = []
delta = metadata[1]
dur = metadata[2][1:] # discard the first to match siz of deltas
for i in range(0, metadata[0] - 1):
et = delta[i] / dur[i]
error_time_values.append(et)
handle = open('generated_data.csv', 'a')
handle.write(
'matrix_size,iteration_norm,error_delta_normed,duration,error_time\n')
for i in range(0, metadata[0] - 1):
iteration_norm = float(i + 1) / max_matrix_size
items = [
max_matrix_size, iteration_norm, delta[i], dur[i], error_time_values[i]
]
line = ','.join([str(s) for s in items]) + '\n'
def test_from_mm_file(self):
file_path = './data/ash958.mtx'
ash958 = Matrix.from_mm_file(file_path)
assert ash958.shape() == (958, 292)
assert len(ash958) == 1916
def test_mult_vect_right(self):
input_vector = numpy.matrix([1, 1, 1, 1, 1]).T
expected_vector = numpy.matrix([1, 0, 0, 0, 1]).T
test_matrix = Matrix.tridiagonal(5)
output_vector = test_matrix.mult_left_vector(input_vector)
assert (expected_vector == output_vector).all()
from gmrescrs import Gmres
from crsmatrix import Matrix
import numpy
from datetime import datetime
A = Matrix.from_mm_file('data/bcsstk18.mtx')
b = numpy.ones((A.shape()[0], 1))
gmres = Gmres(A, b)
x, error, metadata = gmres.solve()
print error
# times = 3
# durations = []
# for i in range(0, times):
# gmres = Gmres(A, b, max_iterations=100000, restart_after=75)
# print "starting"
# start = datetime.now()
# output_vector, error, metadata = gmres.solve()
# end = datetime.now()
# seconds = (end - start).seconds
# decimal = float((end - start).microseconds) / 1e6
# print "ending"
# durations.append(seconds + decimal)
#
#
# print error
# print "iterations: " + str(metadata[0])
# print "duration: " + str(sum(durations) / times) + " sec"