# MatTransposeMatMult
Performs matrix-matrix multiplication C=A^T*B. 
## Synopsis
```
#include "petscmat.h" 
PetscErrorCode MatTransposeMatMult(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 not known



## Output Parameters

- ***C -*** the product matrix



## Notes
C will be created if `MAT_INITIAL_MATRIX` and must be destroyed by the user with `MatDestroy()`.

`MAT_REUSE_MATRIX` can only be used if the matrices A and B have the same nonzero pattern as in the previous call.

This routine is shorthand for using `MatProductCreate()` with the `MatProductType` of `MATPRODUCT_AtB`

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

This routine is currently implemented for pairs of `MATAIJ` matrices and pairs of `MATSEQDENSE` matrices and classes
which inherit from `MATSEQAIJ`.  C will be of the same type as the input matrices.




## See Also
 `MatProductCreate()`, `MATPRODUCT_AtB`, `MatMatMult()`, `MatMatTransposeMult()`, `MatPtAP()`

## Level
intermediate

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

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex72.c.html">src/ksp/ksp/tutorials/ex72.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/constrained/tutorials/tomographyADMM.c.html">src/tao/constrained/tutorials/tomographyADMM.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/tutorials/ex4.c.html">src/tao/tutorials/ex4.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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