.. _lapack-routines:

LAPACK Routines
===============


|IONE-MKL| implements routines from the
LAPACK package that are used for solving systems of linear equations,
linear least squares problems, eigenvalue and singular value problems,
and performing a number of related computational tasks. The library
includes LAPACK routines for both real and complex data. Routines are
supported for systems of equations with the following types of matrices:

-  General

-  Banded

-  Symmetric or Hermitian positive-definite (full, packed, and rectangular full packed (RFP) storage)

-  Symmetric or Hermitian positive-definite banded

-  Symmetric or Hermitian indefinite (both full and packed storage)

-  Symmetric or Hermitian indefinite banded

-  Triangular (full, packed, and RFP storage)

-  Triangular banded

-  Tridiagonal

-  Diagonally dominant tridiagonal.


.. note::
   Different arrays used as parameters to |O-MKL| LAPACK routines must not overlap.


.. warning::
   LAPACK routines assume that input matrices do not contain IEEE 754 special values such as INF or NaN values. Using these special values may cause LAPACK to return unexpected results or become unstable.

.. toctree::
   :maxdepth: 1
   :hidden:

   gebrd
   gebrd-usm-version
   gebrd_scratchpad_size
   geqrf
   geqrf-usm-version
   geqrf_batch-buffer-strided-version
   geqrf_batch-group-version
   geqrf_batch-usm-strided-version
   geqrf_batch_scratchpad_size-group-version
   geqrf_batch_scratchpad_size-strided-version
   geqrf_scratchpad_size
   gerqf
   gerqf-usm-version
   gerqf_scratchpad_size
   gesvd
   gesvd-usm-version
   gesvd_scratchpad_size
   getrf
   getrf-usm-version
   getrf_batch-buffer-strided-version
   getrf_batch-group-version
   getrf_batch-usm-strided-version
   getrf_batch_scratchpad_size-group-version
   getrf_batch_scratchpad_size-strided-version
   getrf_scratchpad_size
   getri
   getri-usm-version
   getri_batch-group-version
   getri_batch-usm-strided-version
   getri_batch_scratchpad_size-group-version
   getri_batch_scratchpad_size-strided-version
   getri_scratchpad_size
   getrs
   getrs-usm-version
   getrs_batch-buffer-strided-version
   getrs_batch-group-version
   getrs_batch-usm-strided-version
   getrs_batch_scratchpad_size-group-version
   getrs_batch_scratchpad_size-strided-version
   getrs_scratchpad_size
   heevd
   heevd-usm-version
   heevd_scratchpad_size
   hegvd
   hegvd-usm-version
   hegvd_scratchpad_size
   hetrd
   hetrd-usm-version
   hetrd_scratchpad_size
   hetrf
   hetrf-usm-version
   hetrf_scratchpad_size
   orgbr
   orgbr-usm-version
   orgbr_scratchpad_size
   orgqr
   orgqr-usm-version
   orgqr_batch-buffer-strided-version
   orgqr_batch-group-version
   orgqr_batch-usm-strided-version
   orgqr_batch_scratchpad_size-group-version
   orgqr_batch_scratchpad_size-strided-version
   orgqr_scratchpad_size
   orgtr
   orgtr-usm-version
   orgtr_scratchpad_size
   ormqr
   ormqr-usm-version
   ormqr_scratchpad_size
   ormrq
   ormrq-usm-version
   ormrq_scratchpad_size
   ormtr
   ormtr-usm-version
   ormtr_scratchpad_size
   potrf
   potrf-usm-version
   potrf_batch-buffer-strided-version
   potrf_batch-group-version
   potrf_batch-usm-strided-version
   potrf_batch_scratchpad_size-group-version
   potrf_batch_scratchpad_size-strided-version
   potrf_scratchpad_size
   potri
   potri-usm-version
   potri_scratchpad_size
   potrs
   potrs-usm-version
   potrs_batch-buffer-strided-version
   potrs_batch-group-version
   potrs_batch-usm-strided-version
   potrs_batch_scratchpad_size-group-version
   potrs_batch_scratchpad_size-strided-version
   potrs_scratchpad_size
   syevd
   syevd-usm-version
   syevd_scratchpad_size
   sygvd
   sygvd-usm-version
   sygvd_scratchpad_size
   sytrd
   sytrd-usm-version
   sytrd_scratchpad_size
   sytrf
   sytrf-usm-version
   sytrf_scratchpad_size
   trtrs
   trtrs-usm-version
   trtrs_scratchpad_size
   ungbr
   ungbr-usm-version
   ungbr_scratchpad_size
   ungqr
   ungqr-usm-version
   ungqr_batch-buffer-strided-version
   ungqr_batch-group-version
   ungqr_batch-usm-strided-version
   ungqr_batch_scratchpad_size-group-version
   ungqr_batch_scratchpad_size-strided-version
   ungqr_scratchpad_size
   ungtr
   ungtr-usm-version
   ungtr_scratchpad_size
   unmqr
   unmqr-usm-version
   unmqr_scratchpad_size
   unmrq
   unmrq-usm-version
   unmrq_scratchpad_size
   unmtr
   unmtr-usm-version
   unmtr_scratchpad_size