# 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 on A


## 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 Parameters

- ***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
```none
     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);
```





## See Also
 `MatProductType`, `MATPRODUCT_AB`, `MatTransposeMatMult()`, `MatMatTransposeMult()`, `MatPtAP()`, `MatProductCreate()`, `MatProductSymbolic()`, `MatProductReplaceMats()`, `MatProductNumeric()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/interface/matrix.c.html#MatMatMult">src/mat/interface/matrix.c</A>

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex27.c.html">src/ksp/ksp/tutorials/ex27.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/snes/tutorials/ex70.c.html">src/snes/tutorials/ex70.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/pde_constrained/tutorials/elliptic.c.html">src/tao/pde_constrained/tutorials/elliptic.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/pde_constrained/tutorials/parabolic.c.html">src/tao/pde_constrained/tutorials/parabolic.c.html</A><BR>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/mat/interface/matrix.c)


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