ai-content-maker/.venv/Lib/site-packages/scipy/linalg/tests/test_decomp_lu.py

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2024-05-03 04:18:51 +03:00
import pytest
from pytest import raises as assert_raises
import numpy as np
from scipy.linalg import lu, lu_factor, lu_solve, get_lapack_funcs, solve
from numpy.testing import assert_allclose, assert_array_equal
class TestLU:
def setup_method(self):
self.rng = np.random.default_rng(1682281250228846)
def test_old_lu_smoke_tests(self):
"Tests from old fortran based lu test suite"
a = np.array([[1, 2, 3], [1, 2, 3], [2, 5, 6]])
p, l, u = lu(a)
result_lu = np.array([[2., 5., 6.], [0.5, -0.5, 0.], [0.5, 1., 0.]])
assert_allclose(p, np.rot90(np.eye(3)))
assert_allclose(l, np.tril(result_lu, k=-1)+np.eye(3))
assert_allclose(u, np.triu(result_lu))
a = np.array([[1, 2, 3], [1, 2, 3], [2, 5j, 6]])
p, l, u = lu(a)
result_lu = np.array([[2., 5.j, 6.], [0.5, 2-2.5j, 0.], [0.5, 1., 0.]])
assert_allclose(p, np.rot90(np.eye(3)))
assert_allclose(l, np.tril(result_lu, k=-1)+np.eye(3))
assert_allclose(u, np.triu(result_lu))
b = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
p, l, u = lu(b)
assert_allclose(p, np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]]))
assert_allclose(l, np.array([[1, 0, 0], [1/7, 1, 0], [4/7, 0.5, 1]]))
assert_allclose(u, np.array([[7, 8, 9], [0, 6/7, 12/7], [0, 0, 0]]),
rtol=0., atol=1e-14)
cb = np.array([[1.j, 2.j, 3.j], [4j, 5j, 6j], [7j, 8j, 9j]])
p, l, u = lu(cb)
assert_allclose(p, np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]]))
assert_allclose(l, np.array([[1, 0, 0], [1/7, 1, 0], [4/7, 0.5, 1]]))
assert_allclose(u, np.array([[7, 8, 9], [0, 6/7, 12/7], [0, 0, 0]])*1j,
rtol=0., atol=1e-14)
# Rectangular matrices
hrect = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 12, 12]])
p, l, u = lu(hrect)
assert_allclose(p, np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]]))
assert_allclose(l, np.array([[1, 0, 0], [1/9, 1, 0], [5/9, 0.5, 1]]))
assert_allclose(u, np.array([[9, 10, 12, 12], [0, 8/9, 15/9, 24/9],
[0, 0, -0.5, 0]]), rtol=0., atol=1e-14)
chrect = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 12, 12]])*1.j
p, l, u = lu(chrect)
assert_allclose(p, np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]]))
assert_allclose(l, np.array([[1, 0, 0], [1/9, 1, 0], [5/9, 0.5, 1]]))
assert_allclose(u, np.array([[9, 10, 12, 12], [0, 8/9, 15/9, 24/9],
[0, 0, -0.5, 0]])*1j, rtol=0., atol=1e-14)
vrect = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 12, 12]])
p, l, u = lu(vrect)
assert_allclose(p, np.eye(4)[[1, 3, 2, 0], :])
assert_allclose(l, np.array([[1., 0, 0], [0.1, 1, 0], [0.7, -0.5, 1],
[0.4, 0.25, 0.5]]))
assert_allclose(u, np.array([[10, 12, 12],
[0, 0.8, 1.8],
[0, 0, 1.5]]))
cvrect = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 12, 12]])*1j
p, l, u = lu(cvrect)
assert_allclose(p, np.eye(4)[[1, 3, 2, 0], :])
assert_allclose(l, np.array([[1., 0, 0],
[0.1, 1, 0],
[0.7, -0.5, 1],
[0.4, 0.25, 0.5]]))
assert_allclose(u, np.array([[10, 12, 12],
[0, 0.8, 1.8],
[0, 0, 1.5]])*1j)
@pytest.mark.parametrize('shape', [[2, 2], [2, 4], [4, 2], [20, 20],
[20, 4], [4, 20], [3, 2, 9, 9],
[2, 2, 17, 5], [2, 2, 11, 7]])
def test_simple_lu_shapes_real_complex(self, shape):
a = self.rng.uniform(-10., 10., size=shape)
p, l, u = lu(a)
assert_allclose(a, p @ l @ u)
pl, u = lu(a, permute_l=True)
assert_allclose(a, pl @ u)
b = self.rng.uniform(-10., 10., size=shape)*1j
b += self.rng.uniform(-10, 10, size=shape)
pl, u = lu(b, permute_l=True)
assert_allclose(b, pl @ u)
@pytest.mark.parametrize('shape', [[2, 2], [2, 4], [4, 2], [20, 20],
[20, 4], [4, 20]])
def test_simple_lu_shapes_real_complex_2d_indices(self, shape):
a = self.rng.uniform(-10., 10., size=shape)
p, l, u = lu(a, p_indices=True)
assert_allclose(a, l[p, :] @ u)
def test_1by1_input_output(self):
a = self.rng.random([4, 5, 1, 1], dtype=np.float32)
p, l, u = lu(a, p_indices=True)
assert_allclose(p, np.zeros(shape=(4, 5, 1), dtype=int))
assert_allclose(l, np.ones(shape=(4, 5, 1, 1), dtype=np.float32))
assert_allclose(u, a)
a = self.rng.random([4, 5, 1, 1], dtype=np.float32)
p, l, u = lu(a)
assert_allclose(p, np.ones(shape=(4, 5, 1, 1), dtype=np.float32))
assert_allclose(l, np.ones(shape=(4, 5, 1, 1), dtype=np.float32))
assert_allclose(u, a)
pl, u = lu(a, permute_l=True)
assert_allclose(pl, np.ones(shape=(4, 5, 1, 1), dtype=np.float32))
assert_allclose(u, a)
a = self.rng.random([4, 5, 1, 1], dtype=np.float32)*np.complex64(1.j)
p, l, u = lu(a)
assert_allclose(p, np.ones(shape=(4, 5, 1, 1), dtype=np.complex64))
assert_allclose(l, np.ones(shape=(4, 5, 1, 1), dtype=np.complex64))
assert_allclose(u, a)
def test_empty_edge_cases(self):
a = np.empty([0, 0])
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(0, 0), dtype=np.float64))
assert_allclose(l, np.empty(shape=(0, 0), dtype=np.float64))
assert_allclose(u, np.empty(shape=(0, 0), dtype=np.float64))
a = np.empty([0, 3], dtype=np.float16)
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(0, 0), dtype=np.float32))
assert_allclose(l, np.empty(shape=(0, 0), dtype=np.float32))
assert_allclose(u, np.empty(shape=(0, 3), dtype=np.float32))
a = np.empty([3, 0], dtype=np.complex64)
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(0, 0), dtype=np.float32))
assert_allclose(l, np.empty(shape=(3, 0), dtype=np.complex64))
assert_allclose(u, np.empty(shape=(0, 0), dtype=np.complex64))
p, l, u = lu(a, p_indices=True)
assert_allclose(p, np.empty(shape=(0,), dtype=int))
assert_allclose(l, np.empty(shape=(3, 0), dtype=np.complex64))
assert_allclose(u, np.empty(shape=(0, 0), dtype=np.complex64))
pl, u = lu(a, permute_l=True)
assert_allclose(pl, np.empty(shape=(3, 0), dtype=np.complex64))
assert_allclose(u, np.empty(shape=(0, 0), dtype=np.complex64))
a = np.empty([3, 0, 0], dtype=np.complex64)
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(3, 0, 0), dtype=np.float32))
assert_allclose(l, np.empty(shape=(3, 0, 0), dtype=np.complex64))
assert_allclose(u, np.empty(shape=(3, 0, 0), dtype=np.complex64))
a = np.empty([0, 0, 3])
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(0, 0, 0)))
assert_allclose(l, np.empty(shape=(0, 0, 0)))
assert_allclose(u, np.empty(shape=(0, 0, 3)))
with assert_raises(ValueError, match='at least two-dimensional'):
lu(np.array([]))
a = np.array([[]])
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(0, 0)))
assert_allclose(l, np.empty(shape=(1, 0)))
assert_allclose(u, np.empty(shape=(0, 0)))
a = np.array([[[]]])
p, l, u = lu(a)
assert_allclose(p, np.empty(shape=(1, 0, 0)))
assert_allclose(l, np.empty(shape=(1, 1, 0)))
assert_allclose(u, np.empty(shape=(1, 0, 0)))
class TestLUFactor:
def setup_method(self):
self.rng = np.random.default_rng(1682281250228846)
self.a = np.array([[1, 2, 3], [1, 2, 3], [2, 5, 6]])
self.ca = np.array([[1, 2, 3], [1, 2, 3], [2, 5j, 6]])
# Those matrices are more robust to detect problems in permutation
# matrices than the ones above
self.b = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
self.cb = np.array([[1j, 2j, 3j], [4j, 5j, 6j], [7j, 8j, 9j]])
# Reectangular matrices
self.hrect = np.array([[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 12, 12]])
self.chrect = np.array([[1, 2, 3, 4], [5, 6, 7, 8],
[9, 10, 12, 12]]) * 1.j
self.vrect = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 12, 12]])
self.cvrect = 1.j * np.array([[1, 2, 3],
[4, 5, 6],
[7, 8, 9],
[10, 12, 12]])
# Medium sizes matrices
self.med = self.rng.random((30, 40))
self.cmed = self.rng.random((30, 40)) + 1.j*self.rng.random((30, 40))
def _test_common_lu_factor(self, data):
l_and_u1, piv1 = lu_factor(data)
(getrf,) = get_lapack_funcs(("getrf",), (data,))
l_and_u2, piv2, _ = getrf(data, overwrite_a=False)
assert_allclose(l_and_u1, l_and_u2)
assert_allclose(piv1, piv2)
# Simple tests.
# For lu_factor gives a LinAlgWarning because these matrices are singular
def test_hrectangular(self):
self._test_common_lu_factor(self.hrect)
def test_vrectangular(self):
self._test_common_lu_factor(self.vrect)
def test_hrectangular_complex(self):
self._test_common_lu_factor(self.chrect)
def test_vrectangular_complex(self):
self._test_common_lu_factor(self.cvrect)
# Bigger matrices
def test_medium1(self):
"""Check lu decomposition on medium size, rectangular matrix."""
self._test_common_lu_factor(self.med)
def test_medium1_complex(self):
"""Check lu decomposition on medium size, rectangular matrix."""
self._test_common_lu_factor(self.cmed)
def test_check_finite(self):
p, l, u = lu(self.a, check_finite=False)
assert_allclose(p @ l @ u, self.a)
def test_simple_known(self):
# Ticket #1458
for order in ['C', 'F']:
A = np.array([[2, 1], [0, 1.]], order=order)
LU, P = lu_factor(A)
assert_allclose(LU, np.array([[2, 1], [0, 1]]))
assert_array_equal(P, np.array([0, 1]))
class TestLUSolve:
def setup_method(self):
self.rng = np.random.default_rng(1682281250228846)
def test_lu(self):
a0 = self.rng.random((10, 10))
b = self.rng.random((10,))
for order in ['C', 'F']:
a = np.array(a0, order=order)
x1 = solve(a, b)
lu_a = lu_factor(a)
x2 = lu_solve(lu_a, b)
assert_allclose(x1, x2)
def test_check_finite(self):
a = self.rng.random((10, 10))
b = self.rng.random((10,))
x1 = solve(a, b)
lu_a = lu_factor(a, check_finite=False)
x2 = lu_solve(lu_a, b, check_finite=False)
assert_allclose(x1, x2)