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.. _doc_matrix:
==========================================
Summary of Matrix Types Available In PETSc
==========================================
.. list-table::
:widths: auto
:align: center
:header-rows: 1
* - Format
- Matrix Types
- Constructor
- External Packages
- Details
* - CSR
- ``MATAIJ``
- ``MatCreateAIJ()``
-
- Compressed sparse row
* -
- ``MATAIJMKL``
- ``MatCreateMPIAIJMKL()``
- Intel oneAPI MKL
- OpenMP support
* -
- ``MATAIJSELL``
- ``MatCreateMPIAIJSELL()``
-
- SIMD acceleration
* -
- ``MATAIJPERM``
- ``MatCreateMPIAIJPERM()``
-
- Vectorized version
* -
- ``MATAIJCUSPARSE``
- ``MatCreateAIJCUSPARSE()``
- NVIDIA cuSPARSE library
- NVIDIA GPU acceleration
* -
- ``MATAIJKOKKOS``
- ``MatCreateAIJKokkos()``
- Kokkos
- GPU acceleration
* - Constant row length
- ``MATAIJCRL``
- ``MatCreateMPIAIJCRL()``
-
- Vectorized version
* - Multiple applications of single ``MATAIJ``
- ``MATMAIJ``
- ``MatCreateMAIJ()``
-
- Commonly used for identical interpolations on each component of a multi-component vector
* - Kronecker product of sparse matrix :math:`A`; :math:`I \otimes S + A \otimes T`
- ``MATKAIJ``
- ``MatCreateKAIJ()``
-
-
* - Sliced Ellpack
- ``MATSELL``
- ``MatCreateSELL()``
-
- SIMD and GPU acceleration
* - Block CSR
- ``MATBAIJ``
- ``MatCreateBAIJ()``
-
- Block compressed sparse row
* - Symmetric Block CSR
- ``MATSBAIJ``
- ``MatCreateSBAIJ()``
-
- Upper triangular compressed sparse row
* - Dense
- ``MATDENSE``
- ``MatCreateDense()``
-
- Row oriented storage
* -
- ``MATELEMENTAL``
- ``MatCreateElemental()``
- Elemental by Jack Poulson
- Block cyclic storage
* -
- ``MATSCALAPACK``
- ``MatCreateScaLAPACK()``
- ScaLAPACK
- Block cyclic storage
* -
- ``MATDENSECUDA``
- ``MatCreateDenseCUDA()``
-
- NVIDIA GPU Acceleration
* - ``MatMult()`` via finite differencing of a function
- ``MATMFFD``, see :any:`sec_nlmatrixfree`
- ``MatCreateMFFD()``, see also ``MatCreateSNESMF()``
-
- Provides only matrix-vector products
* - User-provided operations
- ``MATSHELL``, see also :any:`sec_matrixfree`
- ``MatCreateShell()``
-
-
* - Low-rank updates
- ``MATLMVM``, ``MATLMVMDFP``, ``MATLMVMBFGS``, ``MATLMVMSR1``, ...
- ``MatCreateLMVM()``
-
- limited-memory BFGS style matrices
* -
- ``MATLRC``
- ``MatCreateLRC()``
-
- :math:`A + UCV^T`
* - FFT
- ``MATFFTW``
- ``MatCreateFFT()``
- FFTW
-
* -
- ``MATSEQCUFFT``
- ``MatCreateSeqCUFFT()``
- NVIDIA's CuFFT
- NVIDIA GPUs
* - Hierarchical
- ``MATHTOOL``
- ``MatCreateHtoolFromKernel()``
- Htool
-
* -
- ``MATH2OPUS``
- ``MatCreateH2OpusFromMat()``
- :math:`\mathcal H^2` matrices
-
* - Transpose, :math:`A^T`, virtual
- ``MATTRANSPOSEVIRTUAL``
- ``MatCreateTranspose()``
-
-
* - Hermitian Transpose, :math:`A^H`, virtual
- ``MATHERMITIANTRANSPOSEVIRTUAL``
- ``MatCreateHermitianTranspose()``
-
-
* - Normal, :math:`A^TA`, virtual
- ``MATNORMAL``
- ``MatCreateNormal()``
-
-
* - Hermitian Normal, :math:`A^HA`, virtual
- ``MATNORMALHERMITIAN``
- ``MatCreateNormalHermitian()``
-
-
* - Schur complement
- ``MATSCHURCOMPLEMENT``
- ``MatCreateSchurComplement()``, ``MatGetSchurComplement()``
-
-
* - Sub-matrix, virtual
- ``MATSUBMATRIX``
- ``MatCreateSubMatrixVirtual()``
-
- Provides ``MatMult()`` and similar operations
* -
- ``MATLOCALREF``
- ``MatCreateLocalRef()``
-
- For use in matrix assembly
* - Nested matrix
- ``MATNEST``
- ``MatCreateNest()``
-
-
* - Scatter operator
- ``MATSCATTER``
- ``MatCreateScatter()``
-
-
* - Centering operator
- ``MATCENTERING``
- ``MatCreateCentering()``
-
- :math:`I - \frac{1}{N}e e^T`, :math:`e=[1,\dots,1]^T`
* - Block matrix
- ``MATBLOCKMAT``
- ``MatCreateBlockMat()``
-
-
|
