Summary of Matrix Types Available In PETSc#

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 \(A\); \(I \otimes S + A \otimes T\)

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

MATMFFD

MatCreateMFFD()

Provides only matrix-vector products

User-provided operations

MATSHELL

MatCreateShell()

Low-rank updates

MATLMVM, MATLMVMDFP, MATLMVMBFGS, MATLMVMSR1, …

MatCreateLMVM()

limited-memory BFGS style matrices

MATLRC

MatCreateLRC()

\(A + UCV^T\)

FFT

MATFFTW

MatCreateFFT()

FFTW

MATSEQCUFFT

MatCreateSeqCUFFT()

NVIDIA’s CuFFT

NVIDIA GPUs

Hierarchical

MATHTOOL

MatCreateHtoolFromKernel()

Htool

MATH2OPUS

MatCreateH2OpusFromMat()

\(\mathcal H^2\) matrices

Transpose, \(A^T\), virtual

MATTRANSPOSEVIRTUAL

MatCreateTranspose()

Hermitian Transpose, \(A^H\), virtual

MATHERMITIANTRANSPOSEVIRTUAL

MatCreateHermitianTranspose()

Normal, \(A^TA\), virtual

MATNORMAL

MatCreateNormal()

Hermitian Normal, \(A^HA\), 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()

\(I - \frac{1}{N}e e^T\), \(e=[1,\dots,1]^T\)

Block matrix

MATBLOCKMAT

MatCreateBlockMat()