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

import os
import pytest

import numpy as np
from numpy.testing import assert_allclose
from pytest import raises as assert_raises
from scipy.sparse.linalg._svdp import _svdp
from scipy.sparse import csr_matrix, csc_matrix


# dtype_flavour to tolerance
TOLS = {
    np.float32: 1e-4,
    np.float64: 1e-8,
    np.complex64: 1e-4,
    np.complex128: 1e-8,
}


def is_complex_type(dtype):
    return np.dtype(dtype).kind == "c"


_dtypes = []
for dtype_flavour in TOLS.keys():
    marks = []
    if is_complex_type(dtype_flavour):
        marks = [pytest.mark.slow]
    _dtypes.append(pytest.param(dtype_flavour, marks=marks,
                                id=dtype_flavour.__name__))
_dtypes = tuple(_dtypes)  # type: ignore[assignment]


def generate_matrix(constructor, n, m, f,
                    dtype=float, rseed=0, **kwargs):
    """Generate a random sparse matrix"""
    rng = np.random.RandomState(rseed)
    if is_complex_type(dtype):
        M = (- 5 + 10 * rng.rand(n, m)
             - 5j + 10j * rng.rand(n, m)).astype(dtype)
    else:
        M = (-5 + 10 * rng.rand(n, m)).astype(dtype)
    M[M.real > 10 * f - 5] = 0
    return constructor(M, **kwargs)


def assert_orthogonal(u1, u2, rtol, atol):
    """Check that the first k rows of u1 and u2 are orthogonal"""
    A = abs(np.dot(u1.conj().T, u2))
    assert_allclose(A, np.eye(u1.shape[1], u2.shape[1]), rtol=rtol, atol=atol)


def check_svdp(n, m, constructor, dtype, k, irl_mode, which, f=0.8):
    tol = TOLS[dtype]

    M = generate_matrix(np.asarray, n, m, f, dtype)
    Msp = constructor(M)

    u1, sigma1, vt1 = np.linalg.svd(M, full_matrices=False)
    u2, sigma2, vt2, _ = _svdp(Msp, k=k, which=which, irl_mode=irl_mode,
                               tol=tol)

    # check the which
    if which.upper() == 'SM':
        u1 = np.roll(u1, k, 1)
        vt1 = np.roll(vt1, k, 0)
        sigma1 = np.roll(sigma1, k)

    # check that singular values agree
    assert_allclose(sigma1[:k], sigma2, rtol=tol, atol=tol)

    # check that singular vectors are orthogonal
    assert_orthogonal(u1, u2, rtol=tol, atol=tol)
    assert_orthogonal(vt1.T, vt2.T, rtol=tol, atol=tol)


@pytest.mark.parametrize('ctor', (np.array, csr_matrix, csc_matrix))
@pytest.mark.parametrize('dtype', _dtypes)
@pytest.mark.parametrize('irl', (True, False))
@pytest.mark.parametrize('which', ('LM', 'SM'))
def test_svdp(ctor, dtype, irl, which):
    np.random.seed(0)
    n, m, k = 10, 20, 3
    if which == 'SM' and not irl:
        message = "`which`='SM' requires irl_mode=True"
        with assert_raises(ValueError, match=message):
            check_svdp(n, m, ctor, dtype, k, irl, which)
    else:
        check_svdp(n, m, ctor, dtype, k, irl, which)


@pytest.mark.parametrize('dtype', _dtypes)
@pytest.mark.parametrize('irl', (False, True))
@pytest.mark.timeout(120)  # True, complex64 > 60 s: prerel deps cov 64bit blas
def test_examples(dtype, irl):
    # Note: atol for complex64 bumped from 1e-4 to 1e-3 due to test failures
    # with BLIS, Netlib, and MKL+AVX512 - see
    # https://github.com/conda-forge/scipy-feedstock/pull/198#issuecomment-999180432
    atol = {
        np.float32: 1.3e-4,
        np.float64: 1e-9,
        np.complex64: 1e-3,
        np.complex128: 1e-9,
    }[dtype]

    path_prefix = os.path.dirname(__file__)
    # Test matrices from `illc1850.coord` and `mhd1280b.cua` distributed with
    # PROPACK 2.1: http://sun.stanford.edu/~rmunk/PROPACK/
    relative_path = "propack_test_data.npz"
    filename = os.path.join(path_prefix, relative_path)
    with np.load(filename, allow_pickle=True) as data:
        if is_complex_type(dtype):
            A = data['A_complex'].item().astype(dtype)
        else:
            A = data['A_real'].item().astype(dtype)

    k = 200
    u, s, vh, _ = _svdp(A, k, irl_mode=irl, random_state=0)

    # complex example matrix has many repeated singular values, so check only
    # beginning non-repeated singular vectors to avoid permutations
    sv_check = 27 if is_complex_type(dtype) else k
    u = u[:, :sv_check]
    vh = vh[:sv_check, :]
    s = s[:sv_check]

    # Check orthogonality of singular vectors
    assert_allclose(np.eye(u.shape[1]), u.conj().T @ u, atol=atol)
    assert_allclose(np.eye(vh.shape[0]), vh @ vh.conj().T, atol=atol)

    # Ensure the norm of the difference between the np.linalg.svd and
    # PROPACK reconstructed matrices is small
    u3, s3, vh3 = np.linalg.svd(A.todense())
    u3 = u3[:, :sv_check]
    s3 = s3[:sv_check]
    vh3 = vh3[:sv_check, :]
    A3 = u3 @ np.diag(s3) @ vh3
    recon = u @ np.diag(s) @ vh
    assert_allclose(np.linalg.norm(A3 - recon), 0, atol=atol)


@pytest.mark.parametrize('shifts', (None, -10, 0, 1, 10, 70))
@pytest.mark.parametrize('dtype', _dtypes[:2])
def test_shifts(shifts, dtype):
    np.random.seed(0)
    n, k = 70, 10
    A = np.random.random((n, n))
    if shifts is not None and ((shifts < 0) or (k > min(n-1-shifts, n))):
        with pytest.raises(ValueError):
            _svdp(A, k, shifts=shifts, kmax=5*k, irl_mode=True)
    else:
        _svdp(A, k, shifts=shifts, kmax=5*k, irl_mode=True)


@pytest.mark.slow
@pytest.mark.xfail()
def test_shifts_accuracy():
    np.random.seed(0)
    n, k = 70, 10
    A = np.random.random((n, n)).astype(np.float64)
    u1, s1, vt1, _ = _svdp(A, k, shifts=None, which='SM', irl_mode=True)
    u2, s2, vt2, _ = _svdp(A, k, shifts=32, which='SM', irl_mode=True)
    # shifts <= 32 doesn't agree with shifts > 32
    # Does agree when which='LM' instead of 'SM'
    assert_allclose(s1, s2)