def test_row_row_as_ndarray_no_A(self):
x = array([[1., 2.]])
y = array([[3., 4.]])
expected = [[6., 10.],
[0., 16.]]
self.assertListEqual(syr2(x, y).tolist(), expected)
def test_matrix_col_col_as_ndarray_no_A(self):
x = array([[1.],
[2.]])
y = array([[3.],
[4.]])
expected = [[6., 10.],
[0., 16.]]
self.assertListEqual(syr2(x, y).tolist(), expected)
def test_as_matrix_mixed_no_A(self):
x = asmatrix(array([[1.],
[2.]]))
y = array([[3.],
[4.]])
expected = [[6., 10.],
[0., 16.]]
self.assertListEqual(syr2(x, y).tolist(), expected)
def test_row_row_as_ndarray_provide_A(self):
A = array([[1., 2.],
[2., 3.]])
x = array([[1., 2.]])
y = array([[3., 4.]])
expected = [[7., 12.],
[2., 19.]]
self.assertListEqual(syr2(x, y, A).tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def passed_test(dtype, as_matrix, x_is_row, y_is_row, provide_A, stride, uplo):
"""
Run one symmetric rank-2 update 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
x_is_row: True to test a row vector as parameter x, False to test a column vector
y_is_row: True to test a row vector as parameter y, False to test a column vector
provide_A: True if A is to be provided to the BLASpy function, False otherwise
stride: stride of x and y to test; if None, a random stride is assigned
uplo: BLASpy uplo 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 scalars, vectors, and matrices to test
alpha = uniform(SCAL_MIN, SCAL_MAX)
x = random_vector(n, x_is_row, dtype, as_matrix)
y = random_vector(n, y_is_row, dtype, as_matrix)
A = random_symmetric_matrix(n_A, dtype, as_matrix) if provide_A else None
# create copies/views of A, x, and y that can be used to calculate the expected result
x_2 = x.T if x_is_row else x
y_2 = y.T if y_is_row else y
A_2 = zeros((n_A, n_A)) if A is None else copy(A)
# compute the expected result
if stride == 1:
A_2 += alpha * dot(x_2, y_2.T)
A_2 += alpha * dot(y_2, x_2.T)
else:
for i in range(0, n_A):
for j in range(0, n_A):
A_2[i, j] += alpha * (x_2[i * stride, 0] * y_2[j * stride, 0])
A_2[i, j] += alpha * (y_2[i * stride, 0] * x_2[j * stride, 0])
# get the actual result
A = syr2(x, y, A, uplo, alpha, inc_x=stride, inc_y=stride)
# make A and A_2 triangular so that they can be compared
A = triu(A) if uplo == 'u' else tril(A)
A_2 = triu(A_2) if uplo == 'u' else tril(A_2)
# compare the actual result to the expected result and return result of the test
return allclose(A, A_2, RTOL, ATOL)
def test_lower_triangle_ignored_with_uplo_u(self):
A = array([[1., 2.],
[-100., 3.]])
x = array([[1.],
[2.]])
y = array([[3.],
[4.]])
expected = [[7., 12.],
[-100., 19.]]
self.assertListEqual(syr2(x, y, A, uplo='u').tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_upper_triangle_ignored_with_uplo_L(self):
A = array([[1., 55.],
[2., 3.]])
x = array([[1.],
[2.]])
y = array([[3.],
[4.]])
expected = [[7., 55.],
[12., 19.]]
self.assertListEqual(syr2(x, y, A, uplo='L').tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_strides_less_than_length_no_A(self):
x = array([[1.],
[2.],
[3.],
[4.]])
y = array([[3.],
[4.],
[5.],
[6.]])
expected = [[6., 14.],
[0., 30.]]
self.assertListEqual(syr2(x, y, inc_x=2, inc_y=2).tolist(), expected)
def test_alpha(self):
A = array([[1., 2.],
[2., 3.]])
x = array([[1.],
[2.]])
y = array([[3.],
[4.]])
alpha = 2.5
expected = [[16., 27.],
[2., 43.]]
self.assertListEqual(syr2(x, y, A, alpha=alpha).tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_unequal_strides(self):
A = array([[1., 2.],
[2., 3.]])
x = array([[1.],
[2.],
[3.],
[4.]])
y = array([[3.],
[5.]])
expected = [[7., 16.],
[2., 33.]]
self.assertListEqual(syr2(x, y, A, inc_x=2, inc_y=1).tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_strides_greater_than_length_provide_A(self):
A = array([[3.]])
x = array([[1.],
[2.],
[3.],
[4.]])
y = array([[3.],
[4.],
[5.],
[6.]])
expected = [[9.]]
self.assertListEqual(syr2(x, y, A, inc_x=4, inc_y=4).tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_float64_dtype(self):
A = array([[1., 2.],
[2., 3.]], dtype='float64')
x = array([[1.],
[2.]], dtype='float64')
y = array([[3.],
[4.]], dtype='float64')
self.assertEqual(A.dtype, 'float64')
self.assertEqual(x.dtype, 'float64')
self.assertEqual(y.dtype, 'float64')
expected = [[7., 12.],
[2., 19.]]
self.assertListEqual(syr2(x, y, A).tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_strides_less_than_length_provide_A(self):
A = array([[1., 2.],
[2., 3.]])
x = array([[1.],
[2.],
[3.],
[4.]])
y = array([[3.],
[4.],
[5.],
[6.]])
expected = [[7., 16.],
[2., 33.]]
self.assertListEqual(syr2(x, y, A, inc_x=2, inc_y=2).tolist(), expected)
self.assertListEqual(A.tolist(), expected)
def test_scalars_as_ndarray_no_A(self):
x = array([[2.]])
y = array([[3.]])
self.assertEqual(syr2(x, y), 12)
def test_scalars_as_ndarray_provide_A(self):
A = array([[1.]])
x = array([[2.]])
y = array([[3.]])
self.assertEqual(syr2(x, y, A), 13)
self.assertEqual(A, 13)