def test_skew_symmetrize_handles_blocksizes(blocksize):
dim = 3 # decides when to transpose
vector = np.random.randn(dim, blocksize)
input_matrix = skew_symmetrize(vector)
test_matrix = _skew_symmetrize(vector)
assert_allclose(input_matrix, test_matrix)
def test_skew_symmetrize_transposes_for_two_dimensions():
dim = 3
blocksize = 32
in_vector = np.random.randn(blocksize, dim) # switched order
vector = in_vector.T
input_matrix = skew_symmetrize(in_vector)
test_matrix = _skew_symmetrize(vector)
assert_allclose(input_matrix, test_matrix)
def test_inv_skew_symmetrize_correctness(blocksize):
dim = 3
vector = np.random.randn(dim, blocksize)
input_matrix = _skew_symmetrize(vector)
# reshape and squeeze because we are testing a single vector
test_vector = _inv_skew_symmetrize(input_matrix)
assert test_vector.shape == (3, blocksize)
assert_allclose(test_vector, vector)
def test_skew_symmetrize_sq_correctness_in_three_dimensions(blocksize):
dim = 3
vector = np.random.randn(dim, blocksize)
correct_matrix = _skew_symmetrize(vector).reshape(dim, dim, -1)
correct_matrix = np.einsum("ijk,jlk->ilk", correct_matrix, correct_matrix)
# reshape and squeeze because we are testing a single vector
test_matrix = _skew_symmetrize_sq(vector)
assert test_matrix.shape == (3, 3, blocksize)
assert_allclose(test_matrix, correct_matrix)
def test_skew_symmetrize_correctness_in_two_dimensions():
dim = 3
vector = np.hstack((np.random.randn(2), 1))
test_matrix = _skew_symmetrize(vector[:, np.newaxis])
# Reshape for checking correctness and drop the last dimension
test_matrix = test_matrix.reshape(dim, dim, -1)
test_matrix = test_matrix[:-1, :-1, 0]
correct_matrix = np.array([[0.0, -1.0], [1.0, 0.0]])
assert_allclose(test_matrix, correct_matrix)
def test_skew_symmetrize_against_input_shapes(ndim):
dim = 3
blocksize = 32
if ndim == 1:
in_vector = np.random.randn(dim)
vector = in_vector.reshape(dim, 1)
elif ndim == 2:
in_vector = np.random.randn(dim, blocksize)
vector = in_vector
input_matrix = skew_symmetrize(in_vector)
test_matrix = _skew_symmetrize(vector)
assert_allclose(input_matrix, test_matrix)
def test_skew_symmetrize_correctness_in_three_dimensions(blocksize):
dim = 3
vector = np.random.randn(dim, blocksize)
correct_matrix = np.zeros((dim * dim, blocksize))
correct_matrix[1] = -vector[2]
correct_matrix[2] = vector[1]
correct_matrix[3] = vector[2]
correct_matrix[5] = -vector[0]
correct_matrix[6] = -vector[1]
correct_matrix[7] = vector[0]
correct_matrix = correct_matrix.reshape(dim, dim, -1)
# reshape and squeeze because we are testing a single vector
test_matrix = _skew_symmetrize(vector)
assert test_matrix.shape == (3, 3, blocksize)
assert_allclose(test_matrix, correct_matrix)
def test_inv_skew_symmetrize_against_input_shapes(ndim):
dim = 3
# First generate a skew-symmetric matrix from vector
if ndim == 1:
blocksize = 1
else:
blocksize = 16
input_vector = np.random.randn(dim, blocksize)
input_matrix = _skew_symmetrize(input_vector)
if ndim == 1:
input_matrix = input_matrix.reshape(dim ** 2)
elif ndim == 2:
input_matrix = input_matrix.reshape(dim ** 2, blocksize)
elif ndim == 3:
input_matrix = input_matrix.reshape(dim, dim, blocksize)
test_vector = inv_skew_symmetrize(input_matrix)
assert_allclose(test_vector, input_vector)
def skew_symmetrize(vector):
vector = format_vector_shape(vector)
return _skew_symmetrize(vector)