def householder_test(self):
"""Test the householder transformation to get a matrix in bidiagonalization."""
# set up test
c = [
[4, 3, 0],
[2, 1, 2],
[4, 4, 0]
]
matrix = Matrix(3, 3)
matrix.initialize(c, rowBased=True)
# execute householder transformation
u, bidiag, v = matrix.householder()
# expect, that multiplication works correctly.
res = u * bidiag * v
# res should be equal with c (except some rounding errors)
for row in range(res.get_height()):
for col in range(res.get_width()):
self.assertAlmostEqual(res.get_value(col, row), c[row][col], PRECISION)
# bidiag matrix should have 0 values below the diagonal
self.assertAlmostEqual(bidiag.get_value(0, 1), 0, PRECISION)
self.assertAlmostEqual(bidiag.get_value(0, 2), 0, PRECISION)
self.assertAlmostEqual(bidiag.get_value(1, 2), 0, PRECISION)
self.assertAlmostEqual(bidiag.get_value(2, 0), 0, PRECISION)
def householder_with_zero_column_test(self):
"""Test the householder transformation of a Matrix with a 0 column
All values of the 2nd column are 0."""
# set up test
c = [[3, 0, 3, 2], [0, 0, 5, 6], [4, 0, 4, 7], [8, 0, 3, 9]]
matrix = Matrix(4, 4)
matrix.initialize(c, rowBased=True)
# execute householder transformation
u, bidiag, v = matrix.householder()
# expect, that multiplication works correctly.
res = u * bidiag * v
# res should be equal with c (except some rounding errors)
for row in range(res.get_height()):
for col in range(res.get_width()):
self.assertAlmostEqual(res.get_value(col, row), c[row][col],
PRECISION)
def householder_with_zero_column_test(self):
"""Test the householder transformation of a Matrix with a 0 column
All values of the 2nd column are 0."""
# set up test
c = [
[3, 0, 3, 2],
[0, 0, 5, 6],
[4, 0, 4, 7],
[8, 0, 3, 9]
]
matrix = Matrix(4, 4)
matrix.initialize(c, rowBased=True)
# execute householder transformation
u, bidiag, v = matrix.householder()
# expect, that multiplication works correctly.
res = u * bidiag * v
# res should be equal with c (except some rounding errors)
for row in range(res.get_height()):
for col in range(res.get_width()):
self.assertAlmostEqual(res.get_value(col, row), c[row][col], PRECISION)
def householder_test(self):
"""Test the householder transformation to get a matrix in bidiagonalization."""
# set up test
c = [[4, 3, 0], [2, 1, 2], [4, 4, 0]]
matrix = Matrix(3, 3)
matrix.initialize(c, rowBased=True)
# execute householder transformation
u, bidiag, v = matrix.householder()
# expect, that multiplication works correctly.
res = u * bidiag * v
# res should be equal with c (except some rounding errors)
for row in range(res.get_height()):
for col in range(res.get_width()):
self.assertAlmostEqual(res.get_value(col, row), c[row][col],
PRECISION)
# bidiag matrix should have 0 values below the diagonal
self.assertAlmostEqual(bidiag.get_value(0, 1), 0, PRECISION)
self.assertAlmostEqual(bidiag.get_value(0, 2), 0, PRECISION)
self.assertAlmostEqual(bidiag.get_value(1, 2), 0, PRECISION)
self.assertAlmostEqual(bidiag.get_value(2, 0), 0, PRECISION)
