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()`