.. meta::
  :description: rocSOLVER LAPACK-like functions API documentation
  :keywords: rocSOLVER, ROCm, API, documentation, LAPACK-like functions

.. _lapack-like:

********************************
rocSOLVER LAPACK-like functions
********************************

Other LAPACK-like routines are provided by rocSOLVER. They are divided into the following subcategories:

* :ref:`liketriangular`: Based on Gaussian elimination.
* :ref:`likelinears`: Based on triangular factorizations.
* :ref:`likeeigens`: Eigenproblems for symmetric matrices.
* :ref:`likesvds`: Singular values and related problems for general matrices.

.. note::
   
   The API descriptions use the following notations:

   *  ``i``, ``j``, and ``k`` are used as general purpose indices. In some legacy LAPACK APIs, ``k`` can be
      a parameter indicating some problem or matrix dimension.
   *  Depending on the context, when it is necessary to index rows, columns, and blocks or submatrices,
      ``i`` is assigned to rows, ``j`` to columns, and ``k`` to blocks. ``l`` is always used to index
      matrices or problems in a batch.
   *  ``x[i]`` stands for the i-th element of vector x, while ``A[i,j]`` represents the element
      in the i-th row and j-th column of matrix ``A``. Indices are 1-based, for instance, ``x[1]`` is the first
      element of ``x``.
   *  To identify a block in a matrix or a matrix in the batch, ``k`` and ``l`` are used as sub-indices
   *  ``x_i`` :math:`=x_i`. Both notations are used, :math:`x_i` when displaying mathematical
      equations and ``x_i`` in the text describing the function parameters.
   *  If ``X`` is a real vector or matrix, :math:`X^T` indicates its transpose. If ``X`` is complex, then
      :math:`X^H` represents its conjugate transpose. When ``X`` could be real or complex, the descriptions use ``X'`` to
      indicate ``X`` transposed or ``X`` conjugate transposed, accordingly.
   *  When a matrix ``A`` is formed as the product of several matrices, the following notation is used:
      ``A=M(1)M(2)...M(t)``.



.. _liketriangular:

Triangular factorizations
===========================

.. contents:: List of LAPACK-like triangular factorizations
   :local:
   :backlinks: top

.. _getf2_npvt:

rocsolver_<type>getf2_npvt()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetf2_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_cgetf2_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_dgetf2_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_sgetf2_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_zgetf2_npvt
   :outline:
.. doxygenfunction:: rocsolver_cgetf2_npvt
   :outline:
.. doxygenfunction:: rocsolver_dgetf2_npvt
   :outline:
.. doxygenfunction:: rocsolver_sgetf2_npvt

rocsolver_<type>getf2_npvt_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetf2_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_cgetf2_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_dgetf2_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_sgetf2_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_zgetf2_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetf2_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetf2_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetf2_npvt_batched

rocsolver_<type>getf2_npvt_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetf2_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_cgetf2_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_dgetf2_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_sgetf2_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_zgetf2_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetf2_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetf2_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetf2_npvt_strided_batched

.. _getrf_npvt:

rocsolver_<type>getrf_npvt()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetrf_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_cgetrf_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_dgetrf_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_sgetrf_npvt_64
   :outline:
.. doxygenfunction:: rocsolver_zgetrf_npvt
   :outline:
.. doxygenfunction:: rocsolver_cgetrf_npvt
   :outline:
.. doxygenfunction:: rocsolver_dgetrf_npvt
   :outline:
.. doxygenfunction:: rocsolver_sgetrf_npvt

rocsolver_<type>getrf_npvt_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetrf_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_cgetrf_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_dgetrf_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_sgetrf_npvt_batched_64
   :outline:
.. doxygenfunction:: rocsolver_zgetrf_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetrf_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetrf_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetrf_npvt_batched

rocsolver_<type>getrf_npvt_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetrf_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_cgetrf_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_dgetrf_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_sgetrf_npvt_strided_batched_64
   :outline:
.. doxygenfunction:: rocsolver_zgetrf_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetrf_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetrf_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetrf_npvt_strided_batched

.. _geblttrf_npvt:

rocsolver_<type>geblttrf_npvt()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrf_npvt
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrf_npvt
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrf_npvt
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrf_npvt

rocsolver_<type>geblttrf_npvt_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrf_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrf_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrf_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrf_npvt_batched

rocsolver_<type>geblttrf_npvt_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrf_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrf_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrf_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrf_npvt_strided_batched

rocsolver_<type>geblttrf_npvt_interleaved_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrf_npvt_interleaved_batched
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrf_npvt_interleaved_batched
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrf_npvt_interleaved_batched
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrf_npvt_interleaved_batched



.. _likelinears:

Linear-systems solvers
========================

.. contents:: List of LAPACK-like linear solvers
   :local:
   :backlinks: top

.. _getri_npvt:

rocsolver_<type>getri_npvt()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_npvt
   :outline:
.. doxygenfunction:: rocsolver_cgetri_npvt
   :outline:
.. doxygenfunction:: rocsolver_dgetri_npvt
   :outline:
.. doxygenfunction:: rocsolver_sgetri_npvt

rocsolver_<type>getri_npvt_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetri_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetri_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetri_npvt_batched

rocsolver_<type>getri_npvt_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetri_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetri_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetri_npvt_strided_batched

.. _getri_outofplace:

rocsolver_<type>getri_outofplace()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_outofplace
   :outline:
.. doxygenfunction:: rocsolver_cgetri_outofplace
   :outline:
.. doxygenfunction:: rocsolver_dgetri_outofplace
   :outline:
.. doxygenfunction:: rocsolver_sgetri_outofplace

rocsolver_<type>getri_outofplace_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_outofplace_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetri_outofplace_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetri_outofplace_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetri_outofplace_batched

rocsolver_<type>getri_outofplace_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_outofplace_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetri_outofplace_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetri_outofplace_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetri_outofplace_strided_batched

.. _getri_npvt_outofplace:

rocsolver_<type>getri_npvt_outofplace()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_npvt_outofplace
   :outline:
.. doxygenfunction:: rocsolver_cgetri_npvt_outofplace
   :outline:
.. doxygenfunction:: rocsolver_dgetri_npvt_outofplace
   :outline:
.. doxygenfunction:: rocsolver_sgetri_npvt_outofplace

rocsolver_<type>getri_npvt_outofplace_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_npvt_outofplace_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetri_npvt_outofplace_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetri_npvt_outofplace_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetri_npvt_outofplace_batched

rocsolver_<type>getri_npvt_outofplace_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgetri_npvt_outofplace_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgetri_npvt_outofplace_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgetri_npvt_outofplace_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgetri_npvt_outofplace_strided_batched

.. _geblttrs_npvt:

rocsolver_<type>geblttrs_npvt()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrs_npvt
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrs_npvt
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrs_npvt
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrs_npvt

rocsolver_<type>geblttrs_npvt_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrs_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrs_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrs_npvt_batched
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrs_npvt_batched

rocsolver_<type>geblttrs_npvt_strided_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrs_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrs_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrs_npvt_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrs_npvt_strided_batched

rocsolver_<type>geblttrs_npvt_interleaved_batched()
--------------------------------------------------------
.. doxygenfunction:: rocsolver_zgeblttrs_npvt_interleaved_batched
   :outline:
.. doxygenfunction:: rocsolver_cgeblttrs_npvt_interleaved_batched
   :outline:
.. doxygenfunction:: rocsolver_dgeblttrs_npvt_interleaved_batched
   :outline:
.. doxygenfunction:: rocsolver_sgeblttrs_npvt_interleaved_batched



.. _likeeigens:

Symmetric eigensolvers
================================

.. contents:: List of LAPACK-like symmetric eigensolvers
   :local:
   :backlinks: top

.. _syevj:

rocsolver_<type>syevj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevj
   :outline:
.. doxygenfunction:: rocsolver_ssyevj

rocsolver_<type>syevj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevj_batched
   :outline:
.. doxygenfunction:: rocsolver_ssyevj_batched

rocsolver_<type>syevj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_ssyevj_strided_batched

.. _heevj:

rocsolver_<type>heevj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevj
   :outline:
.. doxygenfunction:: rocsolver_cheevj

rocsolver_<type>heevj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevj_batched
   :outline:
.. doxygenfunction:: rocsolver_cheevj_batched

rocsolver_<type>heevj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cheevj_strided_batched

.. _sygvj:

rocsolver_<type>sygvj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvj
   :outline:
.. doxygenfunction:: rocsolver_ssygvj

rocsolver_<type>sygvj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvj_batched
   :outline:
.. doxygenfunction:: rocsolver_ssygvj_batched

rocsolver_<type>sygvj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_ssygvj_strided_batched

.. _hegvj:

rocsolver_<type>hegvj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvj
   :outline:
.. doxygenfunction:: rocsolver_chegvj

rocsolver_<type>hegvj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvj_batched
   :outline:
.. doxygenfunction:: rocsolver_chegvj_batched

rocsolver_<type>hegvj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_chegvj_strided_batched


.. _syevdj:

rocsolver_<type>syevdj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevdj
   :outline:
.. doxygenfunction:: rocsolver_ssyevdj

rocsolver_<type>syevdj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevdj_batched
   :outline:
.. doxygenfunction:: rocsolver_ssyevdj_batched

rocsolver_<type>syevdj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_ssyevdj_strided_batched

.. _heevdj:

rocsolver_<type>heevdj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevdj
   :outline:
.. doxygenfunction:: rocsolver_cheevdj

rocsolver_<type>heevdj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevdj_batched
   :outline:
.. doxygenfunction:: rocsolver_cheevdj_batched

rocsolver_<type>heevdj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cheevdj_strided_batched

.. _sygvdj:

rocsolver_<type>sygvdj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvdj
   :outline:
.. doxygenfunction:: rocsolver_ssygvdj

rocsolver_<type>sygvdj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvdj_batched
   :outline:
.. doxygenfunction:: rocsolver_ssygvdj_batched

rocsolver_<type>sygvdj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_ssygvdj_strided_batched

.. _hegvdj:

rocsolver_<type>hegvdj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvdj
   :outline:
.. doxygenfunction:: rocsolver_chegvdj

rocsolver_<type>hegvdj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvdj_batched
   :outline:
.. doxygenfunction:: rocsolver_chegvdj_batched

rocsolver_<type>hegvdj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_chegvdj_strided_batched


.. _syevdx:

rocsolver_<type>syevdx()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevdx
   :outline:
.. doxygenfunction:: rocsolver_ssyevdx

rocsolver_<type>syevdx_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevdx_batched
   :outline:
.. doxygenfunction:: rocsolver_ssyevdx_batched

rocsolver_<type>syevdx_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsyevdx_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_ssyevdx_strided_batched

.. _heevdx:

rocsolver_<type>heevdx()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevdx
   :outline:
.. doxygenfunction:: rocsolver_cheevdx

rocsolver_<type>heevdx_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevdx_batched
   :outline:
.. doxygenfunction:: rocsolver_cheevdx_batched

rocsolver_<type>heevdx_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zheevdx_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cheevdx_strided_batched

.. _sygvdx:

rocsolver_<type>sygvdx()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvdx
   :outline:
.. doxygenfunction:: rocsolver_ssygvdx

rocsolver_<type>sygvdx_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvdx_batched
   :outline:
.. doxygenfunction:: rocsolver_ssygvdx_batched

rocsolver_<type>sygvdx_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_dsygvdx_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_ssygvdx_strided_batched

.. _hegvdx:

rocsolver_<type>hegvdx()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvdx
   :outline:
.. doxygenfunction:: rocsolver_chegvdx

rocsolver_<type>hegvdx_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvdx_batched
   :outline:
.. doxygenfunction:: rocsolver_chegvdx_batched

rocsolver_<type>hegvdx_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zhegvdx_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_chegvdx_strided_batched




.. _likesvds:

Singular value decomposition
================================

.. contents:: List of LAPACK-like SVD-related functions
   :local:
   :backlinks: top

.. _gesvdj:

rocsolver_<type>gesvdj()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zgesvdj
   :outline:
.. doxygenfunction:: rocsolver_cgesvdj
   :outline:
.. doxygenfunction:: rocsolver_dgesvdj
   :outline:
.. doxygenfunction:: rocsolver_sgesvdj

rocsolver_<type>gesvdj_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zgesvdj_batched
   :outline:
.. doxygenfunction:: rocsolver_cgesvdj_batched
   :outline:
.. doxygenfunction:: rocsolver_dgesvdj_batched
   :outline:
.. doxygenfunction:: rocsolver_sgesvdj_batched

rocsolver_<type>gesvdj_strided_batched()
---------------------------------------------------
.. doxygenfunction:: rocsolver_zgesvdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_cgesvdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_dgesvdj_strided_batched
   :outline:
.. doxygenfunction:: rocsolver_sgesvdj_strided_batched