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# MatSolve
Solves A x = b, given a factored matrix. 
## Synopsis
```
#include "petscmat.h" 
PetscErrorCode MatSolve(Mat mat, Vec b, Vec x)
```
Neighbor-wise Collective


## Input Parameters

- ***mat -*** the factored matrix
- ***b -*** the right-hand-side vector



## Output Parameter

- ***x -*** the result vector





## Notes
The vectors `b` and `x` cannot be the same.  I.e., one cannot
call `MatSolve`(A,x,x).

Most users should employ the `KSP` interface for linear solvers
instead of working directly with matrix algebra routines such as this.
See, e.g., `KSPCreate()`.


## See Also
 [](ch_matrices), `Mat`, [Matrix Factorization](sec_matfactor), `MatGetFactor()`, `MatLUFactor()`, `MatSolveAdd()`, `MatSolveTranspose()`, `MatSolveTransposeAdd()`

## Level
developer

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

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/unconstrained/tutorials/eptorsion1.c.html">src/tao/unconstrained/tutorials/eptorsion1.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/unconstrained/tutorials/eptorsion3.c.html">src/tao/unconstrained/tutorials/eptorsion3.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/tao/unconstrained/tutorials/rosenbrock1.c.html">src/tao/unconstrained/tutorials/rosenbrock1.c</A><BR>

## Implementations

<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/mpi/clique/clique.cxx.html#MatSolve_SparseElemental">MatSolve_SparseElemental in src/mat/impls/aij/mpi/clique/clique.cxx</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/mpi/mumps/mumps.c.html#MatSolve_MUMPS">MatSolve_MUMPS in src/mat/impls/aij/mpi/mumps/mumps.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/mpi/pastix/pastix.c.html#MatSolve_PaStiX">MatSolve_PaStiX in src/mat/impls/aij/mpi/pastix/pastix.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/mpi/strumpack/strumpack.c.html#MatSolve_STRUMPACK">MatSolve_STRUMPACK in src/mat/impls/aij/mpi/strumpack/strumpack.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/aijfact.c.html#MatSolve_SeqAIJ">MatSolve_SeqAIJ in src/mat/impls/aij/seq/aijfact.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/essl/essl.c.html#MatSolve_Essl">MatSolve_Essl in src/mat/impls/aij/seq/essl/essl.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/klu/klu.c.html#MatSolve_KLU">MatSolve_KLU in src/mat/impls/aij/seq/klu/klu.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/kokkos/aijkok.kokkos.cxx.html#MatSolve_SeqAIJKokkos">MatSolve_SeqAIJKokkos in src/mat/impls/aij/seq/kokkos/aijkok.kokkos.cxx</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/lusol/lusol.c.html#MatSolve_LUSOL">MatSolve_LUSOL in src/mat/impls/aij/seq/lusol/lusol.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/matlab/aijmatlab.c.html#MatSolve_Matlab">MatSolve_Matlab in src/mat/impls/aij/seq/matlab/aijmatlab.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu.html#MatSolve_SeqAIJCUSPARSE">MatSolve_SeqAIJCUSPARSE in src/mat/impls/aij/seq/seqcusparse/aijcusparse.cu</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/seqcusparse/aijcusparseband.cu.html#MatSolve_SeqAIJCUSPARSEBAND">MatSolve_SeqAIJCUSPARSEBAND in src/mat/impls/aij/seq/seqcusparse/aijcusparseband.cu</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/seqhipsparse/aijhipsparse.hip.c.html#MatSolve_SeqAIJHIPSPARSE">MatSolve_SeqAIJHIPSPARSE in src/mat/impls/aij/seq/seqhipsparse/aijhipsparse.hip.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/seqhipsparse/aijhipsparseband.hip.c.html#MatSolve_SeqAIJHIPSPARSEBAND">MatSolve_SeqAIJHIPSPARSEBAND in src/mat/impls/aij/seq/seqhipsparse/aijhipsparseband.hip.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/spqr/aijspqr.c.html#MatSolve_SPQR">MatSolve_SPQR in src/mat/impls/aij/seq/spqr/aijspqr.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/superlu/superlu.c.html#MatSolve_SuperLU">MatSolve_SuperLU in src/mat/impls/aij/seq/superlu/superlu.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/umfpack/umfpack.c.html#MatSolve_UMFPACK">MatSolve_UMFPACK in src/mat/impls/aij/seq/umfpack/umfpack.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/elemental/matelem.cxx.html#MatSolve_Elemental">MatSolve_Elemental in src/mat/impls/elemental/matelem.cxx</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/sbaij/seq/cholmod/sbaijcholmod.c.html#MatSolve_CHOLMOD">MatSolve_CHOLMOD in src/mat/impls/sbaij/seq/cholmod/sbaijcholmod.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/scalapack/matscalapack.c.html#MatSolve_ScaLAPACK">MatSolve_ScaLAPACK in src/mat/impls/scalapack/matscalapack.c</A><BR>


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