def passed_test(dtype, as_matrix, b_is_row, stride, uplo, trans_a, diag):
"""
Run one triangular solve test.
Arguments:
dtype: either 'float64' or 'float32', the NumPy dtype to test
as_matrix: True to test a NumPy matrix, False to test a NumPy ndarray
b_is_row: True to test a row vector as parameter b, False to test a column vector
stride: stride of x and y to test; if None, a random stride is assigned
uplo: BLASpy uplo parameter to test
trans_a: BLASpy trans parameter to test
diag: BLASpy diag parameter to test
Returns:
True if the expected result is within the margin of error of the actual result,
False otherwise.
"""
# generate random sizes for matrix/vector dimensions and vector stride (if necessary)
n = randint(N_MIN, N_MAX)
stride = randint(N_MIN, STRIDE_MAX) if stride is None else stride
n_A = n / stride + (n % stride > 0)
# create random vectors and matrices to test
b = random_vector(n, b_is_row, dtype, as_matrix)
A = random_triangular_matrix(n_A, dtype, as_matrix, uplo, diag)
A /= n_A # scale off-diagonal to avoid numerical issues
# fill diagonal with 1 if unit-triangular, else fill diagonal with values between 1 and 2
if diag == 'u':
fill_diagonal(A, 1)
else:
for i in range(n_A):
A[i, i] = uniform(1, 2)
# copy b for comparison later
expected = copy(b.T) if b_is_row else copy(b)
# solve for x
trsv(A, b, uplo, trans_a, diag, inc_b=stride)
b = b.T if b_is_row else b
# compute actual result
actual = gemv(A, b, zeros((n, 1), dtype=dtype), trans_a=trans_a, inc_x=stride, inc_y=stride)
if stride != 1:
for i in range(n):
if i % stride != 0: # zero out all non-relevant entries in expected vector
expected[i] = 0
# compare the actual result to the expected result and return result of the test
return allclose(actual, expected, RTOL, ATOL)
def test_row_as_ndarray(self):
A = array([[1., 2.],
[0., 3.]])
b = array([[5., 6.]])
expected = [[1., 2.]]
self.assertListEqual(trsv(A, b).tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_A_not_transposed_with_trans_a_n(self):
A = array([[1., 2.],
[0., 3.]])
b = array([[5.],
[6.]])
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b, trans_a='n').tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_upper_triangle_ignored_with_uplo_L(self):
A = array([[1., 55.],
[2., 3.]])
b = array([[1.],
[8.]])
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b, uplo='L').tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_lower_triangle_ignored_with_uplo_U(self):
A = array([[1., 2.],
[-100., 3.]])
b = array([[5.],
[6.]])
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b, uplo='U').tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_as_matrix_mixed(self):
A = asmatrix(array([[1., 2.],
[0., 3.]]))
b = array([[5.],
[6.]])
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b).tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_uplo_l_and_trans_a_t_and_diag_u(self):
A = array([[1., -100.],
[2., 3.]])
b = array([[5.],
[2.]])
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b, uplo='l', trans_a='t', diag='u').tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_A_unit_diag_with_diag_U(self):
A = array([[1., 2.],
[0., 3.]])
b = array([[5.],
[2.]])
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b, diag='U').tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_float64_dtype(self):
A = array([[1., 2.],
[0., 3.]], dtype='float64')
b = array([[5.],
[6.]], dtype='float64')
self.assertEqual(A.dtype, 'float64')
self.assertEqual(b.dtype, 'float64')
expected = [[1.],
[2.]]
self.assertListEqual(trsv(A, b).tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_stride_greater_than_length(self):
A = array([[1.]])
b = array([[5.],
[2.],
[3.],
[4.]])
expected = [[5.],
[2.],
[3.],
[4.]]
self.assertListEqual(trsv(A, b, inc_b=4).tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_stride_less_than_length(self):
A = array([[1., 2.],
[0., 3.]])
b = array([[5.],
[3.],
[6.],
[4.]])
expected = [[1.],
[3.],
[2.],
[4.]]
self.assertListEqual(trsv(A, b, inc_b=2).tolist(), expected)
self.assertListEqual(b.tolist(), expected)
def test_scalars_as_ndarray(self):
A = array([[1.]])
b = array([[2.]])
self.assertEqual(trsv(A, b), 2)
self.assertEqual(b, 2)
