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"""Auxiliary, norm, reflector, rotation, and permutation correctness tests."""
from __future__ import annotations
import numpy as np
import pytest
from .helpers import assert_allclose_float64, general_band_storage, native_pivots
pytestmark = [pytest.mark.fortran_end_to_end, pytest.mark.real_library]
def test_dlamch_reports_float64_machine_epsilon(prik_lapack, scipy_lapack, f2py_lapack):
expected = np.finfo(np.float64).eps / 2.0
prik_value = prik_lapack.dlamch("E")
f2py_value = f2py_lapack.dlamch(b"E")
scipy_value = scipy_lapack.dlamch(b"E")
assert_allclose_float64(prik_value, expected)
assert_allclose_float64(f2py_value, expected)
assert_allclose_float64(scipy_value, expected)
def test_dlangb_computes_frobenius_norm_of_band_storage(prik_lapack, scipy_lapack, f2py_lapack):
matrix = np.array([[2.0, -1.0, 0.0], [3.0, 4.0, 5.0], [0.0, 6.0, -2.0]], dtype=np.float64)
expected = float(np.sqrt(sum(float(value * value) for value in matrix.flat)))
prik_ab = general_band_storage(matrix, 1, 1)
f2py_ab = prik_ab.copy(order="F")
scipy_ab = prik_ab.copy(order="F")
prik_result = prik_lapack.dlangb(
"F", np.int32(3), np.int32(1), np.int32(1), prik_ab, np.int32(3), np.empty(3, dtype=np.float64)
)
f2py_value = f2py_lapack.dlangb(b"F", 3, 1, 1, f2py_ab, np.empty(3, dtype=np.float64))
scipy_value = scipy_lapack.dlangb(b"F", 1, 1, scipy_ab)
assert prik_result[1:] == (3, 1, 1, 3)
assert_allclose_float64(prik_result[0], expected, operation_size=7)
assert_allclose_float64(f2py_value, expected, operation_size=7)
assert_allclose_float64(scipy_value, expected, operation_size=7)
def test_dlange_computes_one_norm(prik_lapack, scipy_lapack, f2py_lapack):
matrix = np.array([[1.0, -5.0], [3.0, 2.0], [-2.0, 4.0]], dtype=np.float64, order="F")
expected = 11.0
work = np.empty(3, dtype=np.float64)
prik_result = prik_lapack.dlange("1", np.int32(3), np.int32(2), matrix.copy(order="F"), np.int32(3), work.copy())
f2py_value = f2py_lapack.dlange(b"1", 3, 2, matrix.copy(order="F"), work.copy())
scipy_value = scipy_lapack.dlange(b"1", matrix.copy(order="F"))
assert prik_result[1:] == (3, 2, 3)
assert_allclose_float64(prik_result[0], expected, operation_size=3)
assert_allclose_float64(f2py_value, expected, operation_size=3)
assert_allclose_float64(scipy_value, expected, operation_size=3)
def test_dlantr_ignores_unused_triangle_and_unit_diagonal(prik_lapack, scipy_lapack, f2py_lapack):
stored = np.array([[np.nan, 2.0, -1.0], [np.nan, np.nan, 3.0], [np.nan, np.nan, np.nan]], order="F")
expected = float(np.sqrt(1.0 + 4.0 + 1.0 + 1.0 + 9.0 + 1.0))
work = np.empty(3, dtype=np.float64)
prik_result = prik_lapack.dlantr(
"F", "U", "U", np.int32(3), np.int32(3), stored.copy(order="F"), np.int32(3), work.copy()
)
f2py_value = f2py_lapack.dlantr(b"F", b"U", b"U", 3, 3, stored.copy(order="F"), work.copy())
scipy_value = scipy_lapack.dlantr(b"F", stored.copy(order="F"), uplo=b"U", diag=b"U")
assert prik_result[1:] == (3, 3, 3)
assert_allclose_float64(prik_result[0], expected, operation_size=6)
assert_allclose_float64(f2py_value, expected, operation_size=6)
assert_allclose_float64(scipy_value, expected, operation_size=6)
def test_dlarf_applies_householder_reflector_from_left(prik_lapack, scipy_lapack, f2py_lapack):
vector = np.array([1.0, 2.0], dtype=np.float64)
tau = 0.4
original = np.array([[1.0, 3.0], [2.0, -1.0]], dtype=np.float64)
reflector = np.eye(2, dtype=np.float64) - tau * np.outer(vector, vector)
expected = reflector @ original
prik_c, f2py_c = original.copy(order="F"), original.copy(order="F")
prik_scalars = prik_lapack.dlarf(
"L", np.int32(2), np.int32(2), vector, np.int32(1), np.float64(tau), prik_c, np.int32(2), np.empty(2)
)
f2py_result = f2py_lapack.dlarf(b"L", 2, 2, vector, 1, tau, f2py_c, np.empty(2))
scipy_c = scipy_lapack.dlarf(vector, tau, original.copy(order="F"), np.empty(2), side=b"L")
assert prik_scalars == (2, 2, 1, tau, 2)
assert f2py_result is None
assert_allclose_float64(prik_c, expected, operation_size=2)
assert_allclose_float64(f2py_c, expected, operation_size=2)
assert_allclose_float64(scipy_c, expected, operation_size=2)
def test_dlarfg_constructs_a_valid_householder_reflector(prik_lapack, scipy_lapack, f2py_lapack):
alpha = 4.0
original_x = np.array([3.0, 0.0], dtype=np.float64)
prik_x, f2py_x = original_x.copy(), original_x.copy()
f2py_alpha = np.array(alpha, dtype=np.float64)
f2py_tau = np.array(0.0, dtype=np.float64)
prik_scalars = prik_lapack.dlarfg(np.int32(3), np.float64(alpha), prik_x, np.int32(1), np.float64(0.0))
f2py_result = f2py_lapack.dlarfg(3, f2py_alpha, f2py_x, 1, f2py_tau)
scipy_beta, scipy_x, scipy_tau = scipy_lapack.dlarfg(3, alpha, original_x.copy())
_, prik_beta, _, prik_tau = prik_scalars
prik_vector = np.concatenate(([1.0], prik_x))
f2py_vector = np.concatenate(([1.0], f2py_x))
original = np.concatenate(([alpha], original_x))
prik_expected = np.array([prik_beta, 0.0, 0.0], dtype=np.float64)
f2py_expected = np.array([f2py_alpha, 0.0, 0.0], dtype=np.float64)
assert f2py_result is None
assert_allclose_float64((np.eye(3) - prik_tau * np.outer(prik_vector, prik_vector)) @ original, prik_expected)
assert_allclose_float64((np.eye(3) - f2py_tau * np.outer(f2py_vector, f2py_vector)) @ original, f2py_expected)
assert_allclose_float64(prik_beta, scipy_beta)
assert_allclose_float64(f2py_alpha, scipy_beta)
assert_allclose_float64(prik_x, scipy_x)
assert_allclose_float64(f2py_x, scipy_x)
assert_allclose_float64(prik_tau, scipy_tau)
assert_allclose_float64(f2py_tau, scipy_tau)
def test_dlartg_constructs_a_givens_rotation(prik_lapack, scipy_lapack, f2py_lapack):
f, g = 3.0, 4.0
f2py_c = np.array(0.0, dtype=np.float64)
f2py_s = np.array(0.0, dtype=np.float64)
f2py_r = np.array(0.0, dtype=np.float64)
prik_scalars = prik_lapack.dlartg(np.float64(f), np.float64(g), np.float64(0.0), np.float64(0.0), np.float64(0.0))
f2py_result = f2py_lapack.dlartg(f, g, f2py_c, f2py_s, f2py_r)
scipy_c, scipy_s, scipy_r = scipy_lapack.dlartg(f, g)
_, _, prik_c, prik_s, prik_r = prik_scalars
assert f2py_result is None
assert_allclose_float64(prik_c * f + prik_s * g, prik_r)
assert_allclose_float64(-prik_s * f + prik_c * g, 0.0)
assert_allclose_float64(prik_c * prik_c + prik_s * prik_s, 1.0)
assert_allclose_float64([prik_c, prik_s, prik_r], [scipy_c, scipy_s, scipy_r])
assert_allclose_float64(f2py_c * f + f2py_s * g, f2py_r)
assert_allclose_float64(-f2py_s * f + f2py_c * g, 0.0)
assert_allclose_float64(f2py_c * f2py_c + f2py_s * f2py_s, 1.0)
assert_allclose_float64([f2py_c, f2py_s, f2py_r], [scipy_c, scipy_s, scipy_r])
def test_dlaswp_applies_native_one_based_row_pivots(prik_lapack, scipy_lapack, f2py_lapack):
original = np.array([[1.0, 10.0], [2.0, 20.0], [3.0, 30.0]], dtype=np.float64)
scipy_pivots = np.array([2, 2], dtype=np.int32)
native_ipiv = native_pivots(scipy_pivots)
expected = original[[2, 0, 1], :]
prik_a, f2py_a = original.copy(order="F"), original.copy(order="F")
prik_scalars = prik_lapack.dlaswp(
np.int32(2), prik_a, np.int32(3), np.int32(1), np.int32(2), native_ipiv, np.int32(1)
)
f2py_result = f2py_lapack.dlaswp(2, f2py_a, 1, 2, native_ipiv, 1)
scipy_a = scipy_lapack.dlaswp(original.copy(order="F"), scipy_pivots, k1=0, k2=1)
assert prik_scalars == (2, 3, 1, 2, 1)
assert f2py_result is None
assert_allclose_float64(prik_a, expected)
assert_allclose_float64(f2py_a, expected)
assert_allclose_float64(scipy_a, expected)