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.. _routines.linalg:
.. module:: numpy.linalg
Linear algebra (:mod:`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
.. currentmodule:: numpy
Matrix and vector products
--------------------------
.. autosummary::
:toctree: generated/
dot
linalg.multi_dot
vdot
inner
outer
matmul
tensordot
einsum
einsum_path
linalg.matrix_power
kron
Decompositions
--------------
.. autosummary::
:toctree: generated/
linalg.cholesky
linalg.qr
linalg.svd
Matrix eigenvalues
------------------
.. autosummary::
:toctree: generated/
linalg.eig
linalg.eigh
linalg.eigvals
linalg.eigvalsh
Norms and other numbers
-----------------------
.. autosummary::
:toctree: generated/
linalg.norm
linalg.cond
linalg.det
linalg.matrix_rank
linalg.slogdet
trace
Solving equations and inverting matrices
----------------------------------------
.. autosummary::
:toctree: generated/
linalg.solve
linalg.tensorsolve
linalg.lstsq
linalg.inv
linalg.pinv
linalg.tensorinv
Exceptions
----------
.. autosummary::
:toctree: generated/
linalg.LinAlgError
.. _routines.linalg-broadcasting:
Linear algebra on several matrices at once
------------------------------------------
.. versionadded:: 1.8.0
Several of the linear algebra routines listed above are able to
compute results for several matrices at once, if they are stacked into
the same array.
This is indicated in the documentation via input parameter
specifications such as ``a : (..., M, M) array_like``. This means that
if for instance given an input array ``a.shape == (N, M, M)``, it is
interpreted as a "stack" of N matrices, each of size M-by-M. Similar
specification applies to return values, for instance the determinant
has ``det : (...)`` and will in this case return an array of shape
``det(a).shape == (N,)``. This generalizes to linear algebra
operations on higher-dimensional arrays: the last 1 or 2 dimensions of
a multidimensional array are interpreted as vectors or matrices, as
appropriate for each operation.
|
