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Diffstat (limited to 'numpy/linalg/__init__.py')
| -rw-r--r-- | numpy/linalg/__init__.py | 110 |
1 files changed, 67 insertions, 43 deletions
diff --git a/numpy/linalg/__init__.py b/numpy/linalg/__init__.py index 4b696c883..55560815d 100644 --- a/numpy/linalg/__init__.py +++ b/numpy/linalg/__init__.py @@ -1,53 +1,77 @@ """ -Core Linear Algebra Tools -========================= - -=============== ========================================================== -Linear algebra basics -========================================================================== -norm Vector or matrix norm -inv Inverse of a square matrix -solve Solve a linear system of equations -det Determinant of a square matrix -slogdet Logarithm of the determinant of a square matrix -lstsq Solve linear least-squares problem -pinv Pseudo-inverse (Moore-Penrose) calculated using a singular - value decomposition -matrix_power Integer power of a square matrix -matrix_rank Calculate matrix rank using an SVD-based method -=============== ========================================================== - -=============== ========================================================== -Eigenvalues and decompositions -========================================================================== -eig Eigenvalues and vectors of a square matrix -eigh Eigenvalues and eigenvectors of a Hermitian matrix -eigvals Eigenvalues of a square matrix -eigvalsh Eigenvalues of a Hermitian matrix -qr QR decomposition of a matrix -svd Singular value decomposition of a matrix -cholesky Cholesky decomposition of a matrix -=============== ========================================================== - -=============== ========================================================== -Tensor operations -========================================================================== -tensorsolve Solve a linear tensor equation -tensorinv Calculate an inverse of a tensor -=============== ========================================================== - -=============== ========================================================== +``numpy.linalg`` +================ + +The NumPy linear algebra functions rely on BLAS and LAPACK to provide efficient +low level implementations of standard linear algebra algorithms. Those +libraries may be provided by NumPy itself using C versions of a subset of their +reference implementations but, when possible, highly optimized libraries that +take advantage of specialized processor functionality are preferred. Examples +of such libraries are OpenBLAS, MKL (TM), and ATLAS. Because those libraries +are multithreaded and processor dependent, environmental variables and external +packages such as threadpoolctl may be needed to control the number of threads +or specify the processor architecture. + +- OpenBLAS: https://www.openblas.net/ +- threadpoolctl: https://github.com/joblib/threadpoolctl + +Please note that the most-used linear algebra functions in NumPy are present in +the main ``numpy`` namespace rather than in ``numpy.linalg``. There are: +``dot``, ``vdot``, ``inner``, ``outer``, ``matmul``, ``tensordot``, ``einsum``, +``einsum_path`` and ``kron``. + +Functions present in numpy.linalg are listed below. + + +Matrix and vector products +-------------------------- + + multi_dot + matrix_power + +Decompositions +-------------- + + cholesky + qr + svd + +Matrix eigenvalues +------------------ + + eig + eigh + eigvals + eigvalsh + +Norms and other numbers +----------------------- + + norm + cond + det + matrix_rank + slogdet + +Solving equations and inverting matrices +---------------------------------------- + + solve + tensorsolve + lstsq + inv + pinv + tensorinv + Exceptions -========================================================================== -LinAlgError Indicates a failed linear algebra operation -=============== ========================================================== +---------- + + LinAlgError """ from __future__ import division, absolute_import, print_function # To get sub-modules -from .info import __doc__ - from .linalg import * from numpy._pytesttester import PytestTester |