from numpy.testing import assert_array_almost_equal, assert_allclose, assert_ from numpy import (array, eye, zeros, empty_like, empty, tril_indices_from, tril, triu_indices_from, spacing, float32, float64, complex64, complex128) from numpy.random import rand, randint, seed from scipy.linalg import ldl import pytest from pytest import raises as assert_raises, warns from numpy import ComplexWarning def test_args(): A = eye(3) # Nonsquare array assert_raises(ValueError, ldl, A[:, :2]) # Complex matrix with imaginary diagonal entries with "hermitian=True" with warns(ComplexWarning): ldl(A*1j) def test_empty_array(): a = empty((0, 0), dtype=complex) l, d, p = ldl(empty((0, 0))) assert_array_almost_equal(l, empty_like(a)) assert_array_almost_equal(d, empty_like(a)) assert_array_almost_equal(p, array([], dtype=int)) def test_simple(): a = array([[-0.39-0.71j, 5.14-0.64j, -7.86-2.96j, 3.80+0.92j], [5.14-0.64j, 8.86+1.81j, -3.52+0.58j, 5.32-1.59j], [-7.86-2.96j, -3.52+0.58j, -2.83-0.03j, -1.54-2.86j], [3.80+0.92j, 5.32-1.59j, -1.54-2.86j, -0.56+0.12j]]) b = array([[5., 10, 1, 18], [10., 2, 11, 1], [1., 11, 19, 9], [18., 1, 9, 0]]) c = array([[52., 97, 112, 107, 50], [97., 114, 89, 98, 13], [112., 89, 64, 33, 6], [107., 98, 33, 60, 73], [50., 13, 6, 73, 77]]) d = array([[2., 2, -4, 0, 4], [2., -2, -2, 10, -8], [-4., -2, 6, -8, -4], [0., 10, -8, 6, -6], [4., -8, -4, -6, 10]]) e = array([[-1.36+0.00j, 0+0j, 0+0j, 0+0j], [1.58-0.90j, -8.87+0j, 0+0j, 0+0j], [2.21+0.21j, -1.84+0.03j, -4.63+0j, 0+0j], [3.91-1.50j, -1.78-1.18j, 0.11-0.11j, -1.84+0.00j]]) for x in (b, c, d): l, d, p = ldl(x) assert_allclose(l.dot(d).dot(l.T), x, atol=spacing(1000.), rtol=0) u, d, p = ldl(x, lower=False) assert_allclose(u.dot(d).dot(u.T), x, atol=spacing(1000.), rtol=0) l, d, p = ldl(a, hermitian=False) assert_allclose(l.dot(d).dot(l.T), a, atol=spacing(1000.), rtol=0) u, d, p = ldl(a, lower=False, hermitian=False) assert_allclose(u.dot(d).dot(u.T), a, atol=spacing(1000.), rtol=0) # Use upper part for the computation and use the lower part for comparison l, d, p = ldl(e.conj().T, lower=0) assert_allclose(tril(l.dot(d).dot(l.conj().T)-e), zeros((4, 4)), atol=spacing(1000.), rtol=0) def test_permutations(): seed(1234) for _ in range(10): n = randint(1, 100) # Random real/complex array x = rand(n, n) if randint(2) else rand(n, n) + rand(n, n)*1j x = x + x.conj().T x += eye(n)*randint(5, 1e6) l_ind = tril_indices_from(x, k=-1) u_ind = triu_indices_from(x, k=1) # Test whether permutations lead to a triangular array u, d, p = ldl(x, lower=0) # lower part should be zero assert_(not any(u[p, :][l_ind]), 'Spin {} failed'.format(_)) l, d, p = ldl(x, lower=1) # upper part should be zero assert_(not any(l[p, :][u_ind]), 'Spin {} failed'.format(_)) @pytest.mark.parametrize("dtype", [float32, float64]) @pytest.mark.parametrize("n", [30, 150]) def test_ldl_type_size_combinations_real(n, dtype): seed(1234) msg = ("Failed for size: {}, dtype: {}".format(n, dtype)) x = rand(n, n).astype(dtype) x = x + x.T x += eye(n, dtype=dtype)*dtype(randint(5, 1e6)) l, d1, p = ldl(x) u, d2, p = ldl(x, lower=0) rtol = 1e-4 if dtype is float32 else 1e-10 assert_allclose(l.dot(d1).dot(l.T), x, rtol=rtol, err_msg=msg) assert_allclose(u.dot(d2).dot(u.T), x, rtol=rtol, err_msg=msg) @pytest.mark.parametrize("dtype", [complex64, complex128]) @pytest.mark.parametrize("n", [30, 150]) def test_ldl_type_size_combinations_complex(n, dtype): seed(1234) msg1 = ("Her failed for size: {}, dtype: {}".format(n, dtype)) msg2 = ("Sym failed for size: {}, dtype: {}".format(n, dtype)) # Complex hermitian upper/lower x = (rand(n, n)+1j*rand(n, n)).astype(dtype) x = x+x.conj().T x += eye(n, dtype=dtype)*dtype(randint(5, 1e6)) l, d1, p = ldl(x) u, d2, p = ldl(x, lower=0) rtol = 1e-4 if dtype is complex64 else 1e-10 assert_allclose(l.dot(d1).dot(l.conj().T), x, rtol=rtol, err_msg=msg1) assert_allclose(u.dot(d2).dot(u.conj().T), x, rtol=rtol, err_msg=msg1) # Complex symmetric upper/lower x = (rand(n, n)+1j*rand(n, n)).astype(dtype) x = x+x.T x += eye(n, dtype=dtype)*dtype(randint(5, 1e6)) l, d1, p = ldl(x, hermitian=0) u, d2, p = ldl(x, lower=0, hermitian=0) assert_allclose(l.dot(d1).dot(l.T), x, rtol=rtol, err_msg=msg2) assert_allclose(u.dot(d2).dot(u.T), x, rtol=rtol, err_msg=msg2)