# MatMatMult#

Performs matrix-matrix multiplication C=A*B.

## Synopsis#

#include "petscmat.h"
PetscErrorCode MatMatMult(Mat A, Mat B, MatReuse scall, PetscReal fill, Mat *C)


Neighbor-wise Collective

## Input Parameters#

• A - the left matrix

• B - the right matrix

• scall - either MAT_INITIAL_MATRIX or MAT_REUSE_MATRIX

• fill - expected fill as ratio of nnz(C)/(nnz(A) + nnz(B)), use PETSC_DEFAULT if you do not have a good estimate if the result is a dense matrix this is irrelevant

## Output Parameter#

• C - the product matrix

## Notes#

Unless scall is MAT_REUSE_MATRIX C will be created.

MAT_REUSE_MATRIX can only be used if the matrices A and B have the same nonzero pattern as in the previous call and C was obtained from a previous call to this function with MAT_INITIAL_MATRIX.

To determine the correct fill value, run with -info and search for the string “Fill ratio” to see the value actually needed.

In the special case where matrix B (and hence C) are dense you can create the correctly sized matrix C yourself and then call this routine with MAT_REUSE_MATRIX, rather than first having MatMatMult() create it for you. You can NEVER do this if the matrix C is sparse.

## Example of Usage#

     MatProductCreate(A,B,NULL,&C);
MatProductSetType(C,MATPRODUCT_AB);
MatProductSymbolic(C);
MatProductNumeric(C); // compute C=A * B
MatProductReplaceMats(A1,B1,NULL,C); // compute C=A1 * B1
MatProductNumeric(C);
MatProductReplaceMats(A2,NULL,NULL,C); // compute C=A2 * B1
MatProductNumeric(C);


Matrices, Mat, MatProductType, MATPRODUCT_AB, MatTransposeMatMult(), MatMatTransposeMult(), MatPtAP(), MatProductCreate(), MatProductSymbolic(), MatProductReplaceMats(), MatProductNumeric()