Delete .venv directory
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"""
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``numpy.linalg``
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================
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The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient
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low level implementations of standard linear algebra algorithms. Those
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libraries may be provided by NumPy itself using C versions of a subset of their
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reference implementations but, when possible, highly optimized libraries that
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take advantage of specialized processor functionality are preferred. Examples
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of such libraries are OpenBLAS, MKL (TM), and ATLAS. Because those libraries
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are multithreaded and processor dependent, environmental variables and external
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packages such as threadpoolctl may be needed to control the number of threads
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or specify the processor architecture.
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- OpenBLAS: https://www.openblas.net/
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- threadpoolctl: https://github.com/joblib/threadpoolctl
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Please note that the most-used linear algebra functions in NumPy are present in
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the main ``numpy`` namespace rather than in ``numpy.linalg``. There are:
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``dot``, ``vdot``, ``inner``, ``outer``, ``matmul``, ``tensordot``, ``einsum``,
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``einsum_path`` and ``kron``.
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Functions present in numpy.linalg are listed below.
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Matrix and vector products
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--------------------------
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multi_dot
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matrix_power
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Decompositions
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--------------
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cholesky
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qr
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svd
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Matrix eigenvalues
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------------------
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eig
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eigh
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eigvals
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eigvalsh
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Norms and other numbers
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-----------------------
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norm
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cond
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det
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matrix_rank
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slogdet
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Solving equations and inverting matrices
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----------------------------------------
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solve
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tensorsolve
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lstsq
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inv
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pinv
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tensorinv
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Exceptions
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----------
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LinAlgError
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"""
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# To get sub-modules
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from . import linalg
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from .linalg import *
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__all__ = linalg.__all__.copy()
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from numpy._pytesttester import PytestTester
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test = PytestTester(__name__)
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del PytestTester
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@@ -1,26 +0,0 @@
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from typing import Any, List
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__all__: List[str]
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class LinAlgError(Exception): ...
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def tensorsolve(a, b, axes=...): ...
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def solve(a, b): ...
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def tensorinv(a, ind=...): ...
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def inv(a): ...
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def matrix_power(a, n): ...
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def cholesky(a): ...
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def qr(a, mode=...): ...
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def eigvals(a): ...
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def eigvalsh(a, UPLO=...): ...
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def eig(a): ...
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def eigh(a, UPLO=...): ...
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def svd(a, full_matrices=..., compute_uv=..., hermitian=...): ...
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def cond(x, p=...): ...
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def matrix_rank(M, tol=..., hermitian=...): ...
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def pinv(a, rcond=..., hermitian=...): ...
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def slogdet(a): ...
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def det(a): ...
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def lstsq(a, b, rcond=...): ...
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def norm(x, ord=..., axis=..., keepdims=...): ...
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def multi_dot(arrays, *, out=...): ...
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@@ -1,83 +0,0 @@
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import os
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import sys
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def configuration(parent_package='', top_path=None):
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from numpy.distutils.misc_util import Configuration
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from numpy.distutils.system_info import (
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get_info, system_info, lapack_opt_info, blas_opt_info)
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config = Configuration('linalg', parent_package, top_path)
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config.add_subpackage('tests')
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# Configure lapack_lite
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src_dir = 'lapack_lite'
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lapack_lite_src = [
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os.path.join(src_dir, 'python_xerbla.c'),
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os.path.join(src_dir, 'f2c_z_lapack.c'),
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os.path.join(src_dir, 'f2c_c_lapack.c'),
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os.path.join(src_dir, 'f2c_d_lapack.c'),
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os.path.join(src_dir, 'f2c_s_lapack.c'),
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os.path.join(src_dir, 'f2c_lapack.c'),
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os.path.join(src_dir, 'f2c_blas.c'),
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os.path.join(src_dir, 'f2c_config.c'),
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os.path.join(src_dir, 'f2c.c'),
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]
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all_sources = config.paths(lapack_lite_src)
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if os.environ.get('NPY_USE_BLAS_ILP64', "0") != "0":
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lapack_info = get_info('lapack_ilp64_opt', 2)
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else:
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lapack_info = get_info('lapack_opt', 0) # and {}
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use_lapack_lite = not lapack_info
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if use_lapack_lite:
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# This makes numpy.distutils write the fact that lapack_lite
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# is being used to numpy.__config__
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class numpy_linalg_lapack_lite(system_info):
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def calc_info(self):
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info = {'language': 'c'}
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if sys.maxsize > 2**32:
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# Build lapack-lite in 64-bit integer mode.
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# The suffix is arbitrary (lapack_lite symbols follow it),
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# but use the "64_" convention here.
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info['define_macros'] = [
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('HAVE_BLAS_ILP64', None),
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('BLAS_SYMBOL_SUFFIX', '64_')
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]
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self.set_info(**info)
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lapack_info = numpy_linalg_lapack_lite().get_info(2)
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def get_lapack_lite_sources(ext, build_dir):
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if use_lapack_lite:
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print("### Warning: Using unoptimized lapack ###")
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return all_sources
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else:
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if sys.platform == 'win32':
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print("### Warning: python_xerbla.c is disabled ###")
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return []
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return [all_sources[0]]
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config.add_extension(
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'lapack_lite',
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sources=['lapack_litemodule.c', get_lapack_lite_sources],
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depends=['lapack_lite/f2c.h'],
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extra_info=lapack_info,
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)
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# umath_linalg module
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config.add_extension(
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'_umath_linalg',
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sources=['umath_linalg.c.src', get_lapack_lite_sources],
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depends=['lapack_lite/f2c.h'],
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extra_info=lapack_info,
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libraries=['npymath'],
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)
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config.add_data_files('*.pyi')
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return config
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if __name__ == '__main__':
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from numpy.distutils.core import setup
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setup(configuration=configuration)
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from subprocess import PIPE, Popen
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import sys
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import re
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import pytest
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from numpy.linalg import lapack_lite
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from numpy.testing import assert_
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class FindDependenciesLdd:
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def __init__(self):
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self.cmd = ['ldd']
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try:
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p = Popen(self.cmd, stdout=PIPE, stderr=PIPE)
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stdout, stderr = p.communicate()
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except OSError as e:
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raise RuntimeError(f'command {self.cmd} cannot be run') from e
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def get_dependencies(self, lfile):
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p = Popen(self.cmd + [lfile], stdout=PIPE, stderr=PIPE)
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stdout, stderr = p.communicate()
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if not (p.returncode == 0):
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raise RuntimeError(f'failed dependencies check for {lfile}')
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return stdout
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def grep_dependencies(self, lfile, deps):
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stdout = self.get_dependencies(lfile)
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rdeps = dict([(dep, re.compile(dep)) for dep in deps])
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founds = []
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for l in stdout.splitlines():
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for k, v in rdeps.items():
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if v.search(l):
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founds.append(k)
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return founds
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class TestF77Mismatch:
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@pytest.mark.skipif(not(sys.platform[:5] == 'linux'),
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reason="no fortran compiler on non-Linux platform")
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def test_lapack(self):
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f = FindDependenciesLdd()
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deps = f.grep_dependencies(lapack_lite.__file__,
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[b'libg2c', b'libgfortran'])
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assert_(len(deps) <= 1,
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"""Both g77 and gfortran runtimes linked in lapack_lite ! This is likely to
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cause random crashes and wrong results. See numpy INSTALL.txt for more
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information.""")
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"""Test deprecation and future warnings.
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"""
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import numpy as np
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from numpy.testing import assert_warns
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def test_qr_mode_full_future_warning():
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"""Check mode='full' FutureWarning.
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In numpy 1.8 the mode options 'full' and 'economic' in linalg.qr were
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deprecated. The release date will probably be sometime in the summer
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of 2013.
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"""
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a = np.eye(2)
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assert_warns(DeprecationWarning, np.linalg.qr, a, mode='full')
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assert_warns(DeprecationWarning, np.linalg.qr, a, mode='f')
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assert_warns(DeprecationWarning, np.linalg.qr, a, mode='economic')
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assert_warns(DeprecationWarning, np.linalg.qr, a, mode='e')
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""" Test functions for linalg module
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"""
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import warnings
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import numpy as np
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from numpy import linalg, arange, float64, array, dot, transpose
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from numpy.testing import (
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assert_, assert_raises, assert_equal, assert_array_equal,
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assert_array_almost_equal, assert_array_less
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)
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class TestRegression:
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def test_eig_build(self):
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# Ticket #652
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rva = array([1.03221168e+02 + 0.j,
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-1.91843603e+01 + 0.j,
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-6.04004526e-01 + 15.84422474j,
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-6.04004526e-01 - 15.84422474j,
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-1.13692929e+01 + 0.j,
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-6.57612485e-01 + 10.41755503j,
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-6.57612485e-01 - 10.41755503j,
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1.82126812e+01 + 0.j,
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1.06011014e+01 + 0.j,
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7.80732773e+00 + 0.j,
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-7.65390898e-01 + 0.j,
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1.51971555e-15 + 0.j,
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-1.51308713e-15 + 0.j])
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a = arange(13 * 13, dtype=float64)
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a.shape = (13, 13)
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a = a % 17
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va, ve = linalg.eig(a)
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va.sort()
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rva.sort()
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assert_array_almost_equal(va, rva)
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def test_eigh_build(self):
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# Ticket 662.
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rvals = [68.60568999, 89.57756725, 106.67185574]
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cov = array([[77.70273908, 3.51489954, 15.64602427],
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[3.51489954, 88.97013878, -1.07431931],
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[15.64602427, -1.07431931, 98.18223512]])
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vals, vecs = linalg.eigh(cov)
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assert_array_almost_equal(vals, rvals)
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def test_svd_build(self):
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# Ticket 627.
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a = array([[0., 1.], [1., 1.], [2., 1.], [3., 1.]])
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m, n = a.shape
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u, s, vh = linalg.svd(a)
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b = dot(transpose(u[:, n:]), a)
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assert_array_almost_equal(b, np.zeros((2, 2)))
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def test_norm_vector_badarg(self):
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# Regression for #786: Frobenius norm for vectors raises
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# ValueError.
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assert_raises(ValueError, linalg.norm, array([1., 2., 3.]), 'fro')
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def test_lapack_endian(self):
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# For bug #1482
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a = array([[5.7998084, -2.1825367],
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[-2.1825367, 9.85910595]], dtype='>f8')
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b = array(a, dtype='<f8')
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ap = linalg.cholesky(a)
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bp = linalg.cholesky(b)
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assert_array_equal(ap, bp)
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def test_large_svd_32bit(self):
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# See gh-4442, 64bit would require very large/slow matrices.
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x = np.eye(1000, 66)
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np.linalg.svd(x)
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def test_svd_no_uv(self):
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# gh-4733
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for shape in (3, 4), (4, 4), (4, 3):
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for t in float, complex:
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a = np.ones(shape, dtype=t)
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w = linalg.svd(a, compute_uv=False)
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c = np.count_nonzero(np.absolute(w) > 0.5)
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assert_equal(c, 1)
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assert_equal(np.linalg.matrix_rank(a), 1)
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assert_array_less(1, np.linalg.norm(a, ord=2))
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def test_norm_object_array(self):
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# gh-7575
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testvector = np.array([np.array([0, 1]), 0, 0], dtype=object)
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norm = linalg.norm(testvector)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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norm = linalg.norm(testvector, ord=1)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype != np.dtype('float64'))
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norm = linalg.norm(testvector, ord=2)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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assert_raises(ValueError, linalg.norm, testvector, ord='fro')
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assert_raises(ValueError, linalg.norm, testvector, ord='nuc')
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assert_raises(ValueError, linalg.norm, testvector, ord=np.inf)
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assert_raises(ValueError, linalg.norm, testvector, ord=-np.inf)
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with warnings.catch_warnings():
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warnings.simplefilter("error", DeprecationWarning)
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assert_raises((AttributeError, DeprecationWarning),
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linalg.norm, testvector, ord=0)
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assert_raises(ValueError, linalg.norm, testvector, ord=-1)
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assert_raises(ValueError, linalg.norm, testvector, ord=-2)
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testmatrix = np.array([[np.array([0, 1]), 0, 0],
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[0, 0, 0]], dtype=object)
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norm = linalg.norm(testmatrix)
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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norm = linalg.norm(testmatrix, ord='fro')
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assert_array_equal(norm, [0, 1])
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assert_(norm.dtype == np.dtype('float64'))
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assert_raises(TypeError, linalg.norm, testmatrix, ord='nuc')
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assert_raises(ValueError, linalg.norm, testmatrix, ord=np.inf)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=-np.inf)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=0)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=1)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=-1)
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assert_raises(TypeError, linalg.norm, testmatrix, ord=2)
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assert_raises(TypeError, linalg.norm, testmatrix, ord=-2)
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assert_raises(ValueError, linalg.norm, testmatrix, ord=3)
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def test_lstsq_complex_larger_rhs(self):
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# gh-9891
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size = 20
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n_rhs = 70
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G = np.random.randn(size, size) + 1j * np.random.randn(size, size)
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u = np.random.randn(size, n_rhs) + 1j * np.random.randn(size, n_rhs)
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b = G.dot(u)
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# This should work without segmentation fault.
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u_lstsq, res, rank, sv = linalg.lstsq(G, b, rcond=None)
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# check results just in case
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assert_array_almost_equal(u_lstsq, u)
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