def test_permutation_2sided_single_transform_umeyama_approx_trans_scale_zero_padding(
n, ncol, nrow):
r"""Test 2sided-perm single transf with "umeyama_approx" by arrays with translate, scaling."""
# define a random, symmetric matrix
array_a = np.random.uniform(-10.0, 10.0, (n, n))
array_a = (array_a + array_a.T) / 2.0
# check with all possible permutation matrices
perm = generate_random_permutation_matrix(n)
# Compute the translated, scaled matrix padded with zeros
array_b = np.dot(perm.T, np.dot(20 * array_a + 9, perm))
# pad the matrices with zeros
array_b = np.concatenate((array_b, np.zeros((n, ncol))), axis=1)
array_b = np.concatenate((array_b, np.zeros((nrow, n + ncol))), axis=0)
# Check
res = permutation_2sided(
array_a,
array_b,
single=True,
method="approx-umeyama",
unpad_col=True,
unpad_row=True,
translate=True,
scale=True,
)
assert_almost_equal(res.t, perm, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_2trans_regular():
r"""Test regular 2sided-perm by practical example."""
# Example taken from page 64 in parallel solution of
# svd-related problems, with applications
# vummath.ma.man.ac.uk/~higham/links/theses/papad93.pdf
b = np.array([
[32, 14, 3, 63, 50],
[24, 22, 1, 56, 4],
[94, 16, 28, 75, 81],
[19, 72, 42, 90, 54],
[71, 85, 10, 96, 58],
])
a = np.array([
[58, 96, 85, 10, 71],
[81, 75, 16, 28, 94],
[4, 56, 22, 1, 24],
[54, 90, 72, 42, 19],
[50, 63, 14, 3, 32],
])
p1 = np.array([[0, 0, 0, 0, 1], [0, 0, 1, 0, 0], [0, 1, 0, 0, 0],
[0, 0, 0, 1, 0], [1, 0, 0, 0, 0]])
p2 = np.array([[0, 0, 0, 0, 1], [0, 0, 0, 1, 0], [0, 1, 0, 0, 0],
[0, 0, 1, 0, 0], [1, 0, 0, 0, 0]])
result = permutation_2sided(a, b, single=False, method="flip-flop")
assert_almost_equal(result.s, p1, decimal=6)
assert_almost_equal(result.t, p2, decimal=6)
assert_almost_equal(result.error, 0.0, decimal=6)
def test_permutation_2sided_1trans_directed(n):
r"""Test 2sided-perm with single transform and directed."""
# A random array
a = np.random.uniform(-10.0, 10.0, (n, n))
p = generate_random_permutation_matrix(n)
b = np.dot(p.T, np.dot(a, p))
# Procrustes with no translate and scale
res = permutation_2sided(a, b, single=True, method="approx-umeyama")
res = permutation_2sided(res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t)
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.s, p.T, decimal=6)
assert_almost_equal(res.error, 0.0, decimal=6)
def test_permutation_2sided_1trans_small_matrices_umeyama_all_permutations(n):
r"""Test 2sided-perm single transform with Umeyama guess for all permutations."""
# define a random matrix
a = np.random.uniform(-10.0, 10.0, (n, n))
# check with all possible permutation matrices
for comb in itertools.permutations(np.arange(n)):
p = np.zeros((n, n))
p[np.arange(n), comb] = 1
# get array_b by permutation
b = np.dot(p.T, np.dot(a, p))
res = permutation_2sided(a, b, single=True, method="approx-umeyama")
res = permutation_2sided(res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t)
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_1trans_directed_all_permutations(n):
r"""Test 2sided-perm with "directed" over all permutations."""
# define a random matrix
a = np.random.uniform(-10.0, 10.0, (n, n))
# check with all possible permutation matrices
for comb in itertools.permutations(np.arange(n)):
perm = np.zeros((n, n))
perm[np.arange(n), comb] = 1
b = np.dot(perm.T, np.dot(a, perm))
res = permutation_2sided(a, b, single=True, method="approx-umeyama")
res = permutation_2sided(res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t)
assert_almost_equal(res.t, perm, decimal=6)
assert_almost_equal(res.s, perm.T, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_2trans_flipflop_rectangular():
r"""Test regular 2sided-perm by rectangular 4by2 random arrays."""
a = np.array([[6, 8], [10, 8], [5, 8], [5, 7]])
p = np.array([[0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, 1]])
q = np.array([[0, 1], [1, 0]])
b = np.linalg.multi_dot([p, a, q])
result = permutation_2sided(a, b, single=False, method="flip-flop")
assert_almost_equal(result.s, p, decimal=6)
assert_almost_equal(result.t, q, decimal=6)
assert_almost_equal(result.error, 0.0, decimal=6)
def test_permutation_2sided_regular_unsquared():
r"""Test regular 2sided-perm by unsquared 4by2 random arrays."""
N = np.array([[6, 8], [10, 8], [5, 8], [5, 7]])
perm_P = np.array([[0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, 1]])
perm_Q = np.array([[0, 1], [1, 0]])
M = np.linalg.multi_dot([perm_P, N, perm_Q])
new_M, new_N, new_P, new_Q, e_opt = permutation_2sided(
M, N, transform_mode='double', iteration=500)
assert_almost_equal(new_P, perm_P, decimal=6)
assert_almost_equal(new_Q, perm_Q, decimal=6)
assert_almost_equal(e_opt, 0, decimal=6)
def test_permutation_2sided_single_transform_normal2(n):
r"""Test 2sided-perm with "normal2"."""
# define a random, symmetric matrix
a = np.random.uniform(-10.0, 10.0, (n, n))
a = (a + a.T) / 2.0
# define b by permuting a
p = generate_random_permutation_matrix(n)
b = np.dot(p.T, np.dot(a, p))
res = permutation_2sided(a, b, single=True, method="approx-normal2")
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_1trans_umeyama(n):
r"""Test 2sided-permutation with single transform with umeyama guess."""
# define a random matrix
array_a = np.random.uniform(-10.0, 10.0, (n, n))
array_a = (array_a + array_a.T) / 2.0
# define array_b by permuting array_a
perm = generate_random_permutation_matrix(n)
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Check
res = permutation_2sided(array_a,
array_b,
single=True,
method="approx-umeyama")
res = permutation_2sided(res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t)
assert_almost_equal(res.t, perm, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_2trans_rectangular_negative():
r"""Test regular 2sided-perm by unsquared negative 6by4 random arrays."""
# build random matrix by seed 999
np.random.seed(999)
a = np.random.randint(-5, 6, size=(6, 4)).astype(float)
p1 = np.random.permutation(np.eye(6, 6))
p2 = np.random.permutation(np.eye(4, 4))
b = np.linalg.multi_dot([p1, a, p2])
result = permutation_2sided(b, a, single=False, method="flip-flop")
assert_almost_equal(result.s, p1, decimal=6)
assert_almost_equal(result.t, p2, decimal=6)
assert_almost_equal(result.error, 0.0, decimal=6)
def test_permutation_2sided_4by4_directed():
r"""Test 2sided-perm with "directed" by 4by4 arrays."""
# A random array
array_a = np.array([[29, 79, 95, 83], [37, 86, 67, 93], [72, 85, 15, 3],
[38, 39, 58, 24]])
# permutation
perm = np.array([[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0]])
# permuted array_b
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Procrustes with no translate and scale
result = permutation_2sided(array_a, array_b, transform_mode="single")
assert_almost_equal(result["array_u"], perm, decimal=6)
assert_almost_equal(result["error"], 0., decimal=6)
def test_permutation_2sided_regular_unsquared():
r"""Test regular 2sided-perm by unsquared 4by2 random arrays."""
array_n = np.array([[6, 8], [10, 8], [5, 8], [5, 7]])
perm_p = np.array([[0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0], [0, 0, 0, 1]])
perm_q = np.array([[0, 1], [1, 0]])
array_m = np.linalg.multi_dot([perm_p, array_n, perm_q])
result = permutation_2sided(array_m,
array_n,
transform_mode="double",
iteration=500)
assert_almost_equal(result[2], perm_p, decimal=6)
assert_almost_equal(result[3], perm_q, decimal=6)
assert_almost_equal(result[4], 0, decimal=6)
def test_permutation_2sided_4by4_directed_symmetric():
r"""Test 2sided-perm with "directed" by 4by4 symmetric arrays."""
# A random array
array_a = np.array([[4, 5, 3, 3], [5, 7, 3, 5], [3, 3, 2, 2], [3, 5, 2,
5]])
# permutation
perm = np.array([[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0]])
# permuted array_b
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Procrustes with no translate and scale
result = permutation_2sided(array_a, array_b, transform_mode="single")
assert_almost_equal(result["array_u"], perm, decimal=6)
assert_almost_equal(result["error"], 0., decimal=6)
def test_permutation_2sided_1trans_umeyama_approx(n):
r"""Test 2sided-perm, single transform with "umeyama_approx" mode."""
# define a random, symmetric matrix
array_a = np.random.uniform(-10.0, 10.0, (n, n))
array_a = (array_a + array_a.T) / 2.0
# define array_b by permuting array_a
perm = generate_random_permutation_matrix(n)
array_b = np.dot(perm.T, np.dot(array_a, perm))
res = permutation_2sided(array_a,
array_b,
single=True,
method="approx-umeyama-svd")
assert_almost_equal(res.t, perm, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_regular_unsquared_negative():
r"""Test regular 2sided-perm by unsquared negative 6by4 random arrays."""
# build random matrix by seed 999
np.random.seed(999)
N = np.random.randint(-5, 6, size=(6, 4))
N = np.float_(N)
perm_P = np.random.permutation(np.eye(6, 6))
perm_Q = np.random.permutation(np.eye(4, 4))
M = np.linalg.multi_dot([perm_P, N, perm_Q])
new_M, new_N, new_P, new_Q, e_opt = permutation_2sided(
M, N, transform_mode='double', iteration=500)
assert_almost_equal(new_P, perm_P, decimal=6)
assert_almost_equal(new_Q, perm_Q, decimal=6)
assert_almost_equal(e_opt, 0, decimal=6)
def test_permutation_2sided_1trans_normal1_translate_scale(n):
r"""Test 2sided-perm with "normal1" with translation and scaling."""
# define a random, symmetric matrix
a = np.random.uniform(-10.0, 10.0, (n, n))
a = np.dot(a, a.T)
p = generate_random_permutation_matrix(n)
b = np.dot(p.T, np.dot((14.7 * a + 3.14), p))
res = permutation_2sided(a,
b,
single=True,
method="approx-umeyama",
translate=True,
scale=True)
res = permutation_2sided(res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t,
translate=True,
scale=True)
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.s, p.T, decimal=6)
assert_almost_equal(res.error, 0.0, decimal=6)
def test_permutation_2sided_1trans_normal1_loop(n):
r"""Test 2sided-perm with "normal1" by small arrays with all permutations."""
# define a random matrix & symmetrize it
a = np.random.uniform(-10.0, 10.0, (n, n))
a = (a + a.T) / 2.0
# check with all possible permutation matrices
for comb in itertools.permutations(np.arange(n)):
p = np.zeros((n, n))
p[np.arange(n), comb] = 1
b = np.dot(p.T, np.dot(a, p))
res = permutation_2sided(a, b, single=True, method="approx-normal1")
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.s, p.T, decimal=6)
assert_almost_equal(res.error, 0.0, decimal=6)
def test_permutation_2sided_4by4_directed():
r"""Test 2sided-perm with 'directed' by 4by4 arrays."""
# A random array
array_a = np.array([[29, 79, 95, 83], [37, 86, 67, 93], [72, 85, 15, 3],
[38, 39, 58, 24]])
# permutation
perm = np.array([[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0]])
# permuted array_b
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Procrustes with no translate and scale
new_a, new_b, U, e_opt = permutation_2sided(
array_a, array_b, transform_mode='single_directed')
assert_almost_equal(U, perm, decimal=6)
assert_almost_equal(e_opt, 0., decimal=6)
def test_permutation_2sided_4by4_directed_symmetric():
r"""Test 2sided-perm with 'directed' by 4by4 symmetric arrays."""
# A random array
array_a = np.array([[4, 5, 3, 3], [5, 7, 3, 5], [3, 3, 2, 2], [3, 5, 2,
5]])
# permutation
perm = np.array([[0, 0, 0, 1], [0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0]])
# permuted array_b
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Procrustes with no translate and scale
new_a, new_b, U, e_opt = permutation_2sided(
array_a, array_b, transform_mode='single_directed')
assert_almost_equal(U, perm, decimal=6)
assert_almost_equal(e_opt, 0., decimal=6)
def test_permutation_2sided_1trans_umeyama_nmf_translate_scale(n):
r"""Test 2sided-perm single transform with "normal2" with translation and scaling."""
# generate random symmetric matrix.
a = np.random.uniform(-10.0, 10.0, (n, n))
a = np.dot(a, a.T) / 2.0
# define array_b by scale-translate array_a and permuting
p = generate_random_permutation_matrix(n)
shift = np.random.uniform(-10.0, 10.0, n)
b = np.dot(p.T, np.dot((14.7 * a + shift), p))
res = permutation_2sided(a,
b,
single=True,
method="approx-umeyama",
translate=True,
scale=True)
res = permutation_2sided(res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t)
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.s, p.T, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_4by4_normal2():
r"""Test 2sided-perm with "normal2" by 4by4 arrays."""
# define a random matrix
array_a = np.array([[4, 5, 3, 3], [5, 7, 3, 5], [3, 3, 2, 2], [3, 5, 2,
5]])
# define array_b by permuting array_a
perm = np.array([[0., 0., 1., 0.], [1., 0., 0., 0.], [0., 0., 0., 1.],
[0., 1., 0., 0.]])
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Check
_, _, array_u, e_opt = permutation_2sided(
array_a, array_b, transform_mode="single_undirected", mode="normal2")
assert_almost_equal(array_u, perm, decimal=6)
assert_almost_equal(e_opt, 0, decimal=6)
def test_permutation_2sided_4by4_umeyama():
r"""Test 2sided-perm with umeyama guess by 4by4 arrays."""
# define a random matrix
array_a = np.array([[4, 5, 3, 3], [5, 7, 3, 5], [3, 3, 2, 2], [3, 5, 2,
5]])
# define array_b by permuting array_a
perm = np.array([[0., 0., 1., 0.], [1., 0., 0., 0.], [0., 0., 0., 1.],
[0., 1., 0., 0.]])
array_b = np.dot(perm.T, np.dot(array_a, perm))
# Check
new_a, new_b, U, e_opt = permutation_2sided(
array_a, array_b, transform_mode='single_undirected', mode='umeyama')
assert_almost_equal(U, perm, decimal=6)
assert_almost_equal(e_opt, 0, decimal=6)
def test_permutation_2sided_2trans_kopt(n):
r"""Test regular 2sided permutation with kopt."""
a = np.random.uniform(-10.0, 10.0, (n, n))
p1 = generate_random_permutation_matrix(n)
p2 = generate_random_permutation_matrix(n)
b = p2.dot(a.dot(p1))
result = permutation_2sided(b,
a,
single=False,
method="k-opt",
options={"k": n})
assert_almost_equal(result.s, p2, decimal=6)
assert_almost_equal(result.t, p1.T, decimal=6)
assert_almost_equal(result.error, 0, decimal=6)
def test_permutation_2sided_1trans_umeyama_nmf_translate_scale_pad(
n, ncol, nrow, ncol2, nrow2):
r"""Test "normal1" by arrays by translation and scaling and zero padding."""
# define a random matrix & symmetrize it
a = np.random.uniform(-10.0, 10.0, (n, n))
a = (a + a.T) / 2.0
p = generate_random_permutation_matrix(n)
b = np.dot(p.T, np.dot(a, p))
# pad the matrices with zeros
a = np.concatenate((a, np.zeros((n, ncol))), axis=1)
a = np.concatenate((a, np.zeros((nrow, n + ncol))), axis=0)
b = np.concatenate((b, np.zeros((n, ncol2))), axis=1)
b = np.concatenate((b, np.zeros((nrow2, n + ncol2))), axis=0)
res = permutation_2sided(
a,
b,
single=True,
method="approx-umeyama",
unpad_col=True,
unpad_row=True,
translate=True,
scale=True,
)
res = permutation_2sided(
res.new_a,
res.new_b,
single=True,
method="nmf",
guess_p2=res.t,
unpad_col=True,
unpad_row=True,
translate=True,
scale=True,
)
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.s, p.T, decimal=6)
assert_almost_equal(res.error, 0, decimal=6)
def test_permutation_2sided_4by4_directed_netative_loop():
r"""Test 2sided-perm with "directed" by negative 4by4 arrays with all permutations."""
# define a random matrix
array_a = np.array([[29, 79, 95, 83], [37, -86, 67, 93], [72, 85, 15, 3],
[38, 39, -58, 24]])
# check with all possible permutation matrices
for comb in itertools.permutations(np.arange(4)):
perm = np.zeros((4, 4))
perm[np.arange(4), comb] = 1
# get array_b by permutation
array_b = np.dot(perm.T, np.dot(array_a, perm))
# check
result = permutation_2sided(array_a, array_b, transform_mode="single")
assert_almost_equal(result["array_u"], perm, decimal=6)
assert_almost_equal(result["error"], 0, decimal=6)
def test_permutation_2sided_regular2():
r"""Test regular 2sided-perm by 4by4 random arrays."""
# define a random matrix
array_n = np.array([[0.74163916, 0.82661152, 0.26856538, 0.23777467],
[0.06530971, 0.28429819, 0.44244327, 0.79478503],
[0.83645105, 0.49704302, 0.34292989, 0.01406331],
[0.04351473, 0.85459821, 0.00663386, 0.62464223]])
array_p = np.array([[0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0,
1]])
array_q = array_p.T
array_m = np.dot(np.dot(array_p, array_n), array_q)
result = permutation_2sided(array_m, array_n, transform_mode="double")
assert_almost_equal(result[2], array_p, decimal=6)
assert_almost_equal(result[3], array_q, decimal=6)
assert_almost_equal(result[4], 0, decimal=6)
def test_permutation_2sided_regular2():
r"""Test regular 2sided-perm by 4by4 random arrays."""
# define a random matrix
N = np.array([[0.74163916, 0.82661152, 0.26856538, 0.23777467],
[0.06530971, 0.28429819, 0.44244327, 0.79478503],
[0.83645105, 0.49704302, 0.34292989, 0.01406331],
[0.04351473, 0.85459821, 0.00663386, 0.62464223]])
P = np.array([[0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
Q = P.T
M = np.dot(np.dot(P, N), Q)
new_M, new_N, new_P, new_Q, e_opt = permutation_2sided(
M, N, transform_mode='double')
assert_almost_equal(new_P, P, decimal=6)
assert_almost_equal(new_Q, Q, decimal=6)
assert_almost_equal(e_opt, 0, decimal=6)
def test_permutation_2sided_2trans_flipflop():
r"""Test regular 2sided-perm by 4by4 random arrays."""
# define a random matrix
a = np.array([
[0.74163916, 0.82661152, 0.26856538, 0.23777467],
[0.06530971, 0.28429819, 0.44244327, 0.79478503],
[0.83645105, 0.49704302, 0.34292989, 0.01406331],
[0.04351473, 0.85459821, 0.00663386, 0.62464223],
])
p = np.array([[0, 0, 1, 0], [1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1]])
b = np.dot(np.dot(p, a), p.T)
result = permutation_2sided(b, a, single=False, method="flip-flop")
assert_almost_equal(result.s, p.T, decimal=6)
assert_almost_equal(result.t, p, decimal=6)
assert_almost_equal(result.error, 0.0, decimal=6)
def test_permutation_2sided_1trans_directed_translate_scale(n):
r"""Test 2sided-perm single transform with "directed" and translation, and scaling."""
a = np.random.uniform(-10.0, 10.0, (n, n))
p = generate_random_permutation_matrix(n)
b = np.dot(p.T, np.dot(15.3 * a + 5.45, p))
res = permutation_2sided(a,
b,
single=True,
method="approx-umeyama",
translate=True,
scale=True)
# res = permutation_2sided(res.new_a, res.new_b, single=True, method="nmf", guess_p2=res.t,
# translate=True, scale=True)
assert_almost_equal(res.t, p, decimal=6)
assert_almost_equal(res.s, p.T, decimal=6)
assert_almost_equal(res.error, 0.0, decimal=6)
def test_permutation_2sided_regular_unsquared_negative():
r"""Test regular 2sided-perm by unsquared negative 6by4 random arrays."""
# build random matrix by seed 999
np.random.seed(999)
array_n = np.random.randint(-5, 6, size=(6, 4))
array_n = np.float_(array_n)
perm_p = np.random.permutation(np.eye(6, 6))
perm_q = np.random.permutation(np.eye(4, 4))
array_m = np.linalg.multi_dot([perm_p, array_n, perm_q])
result = permutation_2sided(array_m,
array_n,
transform_mode="double",
iteration=500)
assert_almost_equal(result[2], perm_p, decimal=6)
assert_almost_equal(result[3], perm_q, decimal=6)
assert_almost_equal(result[4], 0, decimal=6)