# MatZeroRows
Zeros all entries (except possibly the main diagonal) of a set of rows of a matrix. 
## Synopsis
```
#include "petscmat.h" 
PetscErrorCode MatZeroRows(Mat mat, PetscInt numRows, const PetscInt rows[], PetscScalar diag, Vec x, Vec b)
```
Collective on mat


## Input Parameters

- ***mat -*** the matrix
- ***numRows -*** the number of rows to remove
- ***rows -*** the global row indices
- ***diag -*** value put in the diagonal of the eliminated rows
- ***x -*** optional vector of solutions for zeroed rows (other entries in vector are not used), these must be set before this call
- ***b -*** optional vector of right hand side, that will be adjusted by provided solution



## Notes
This routine, along with `MatZeroRowsColumns()`, is typically used to eliminate known Dirichlet boundary conditions from a linear system.

For each zeroed row, the value of the corresponding b is set to diag times the value of the corresponding x.

If the resulting linear system is to be solved with `KSP` then one can (but does not have to) call `KSPSetInitialGuessNonzero()` to allow the
Krylov method to take advantage of the known solution on the zeroed rows.

May be followed by using a `PC` of type `PCREDISTRIBUTE` to solve the reducing problem (after completely eliminating the zeroed rows and their corresponding columns)
from the matrix.

Unlike `MatZeroRowsColumns()` for the `MATAIJ` and `MATBAIJ` matrix formats this removes the old nonzero structure, from the eliminated rows of the matrix
but does not release memory.  Because of this removal matrix-vector products with the adjusted matrix will be a bit faster. For the dense and block diagonal
formats this does not alter the nonzero structure.

If the option `MatSetOption`(mat,`MAT_KEEP_NONZERO_PATTERN`,`PETSC_TRUE`) the nonzero structure
of the matrix is not changed the values are
merely zeroed.

The user can set a value in the diagonal entry (or for the `MATAIJ` format
formats can optionally remove the main diagonal entry from the
nonzero structure as well, by passing 0.0 as the final argument).

For the parallel case, all processes that share the matrix (i.e.,
those in the communicator used for matrix creation) MUST call this
routine, regardless of whether any rows being zeroed are owned by
them.

Each processor can indicate any rows in the entire matrix to be zeroed (i.e. each process does NOT have to
list only rows local to itself).

You can call `MatSetOption`(mat,`MAT_NO_OFF_PROC_ZERO_ROWS`,`PETSC_TRUE`) if each process indicates only rows it
owns that are to be zeroed. This saves a global synchronization in the implementation.




## See Also
 `Mat`, `MatZeroRowsIS()`, `MatZeroRowsColumns()`, `MatZeroRowsLocalIS()`, `MatZeroRowsStencil()`, `MatZeroEntries()`, `MatZeroRowsLocal()`, `MatSetOption()`,
`MatZeroRowsColumnsLocal()`, `MatZeroRowsColumnsLocalIS()`, `MatZeroRowsColumnsIS()`, `MatZeroRowsColumnsStencil()`, `PCREDISTRIBUTE`

## Level
intermediate

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

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex3.c.html">src/ksp/ksp/tutorials/ex3.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex49.c.html">src/ksp/ksp/tutorials/ex49.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex51.c.html">src/ksp/ksp/tutorials/ex51.c.html</A><BR>
<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/tutorials/ex3.c.html">src/tao/tutorials/ex3.c.html</A><BR>

## Implementations

<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/mpi/mpiaij.c.html#MatZeroRows_MPIAIJ">MatZeroRows_MPIAIJ in src/mat/impls/aij/mpi/mpiaij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/seq/aij.c.html#MatZeroRows_SeqAIJ">MatZeroRows_SeqAIJ in src/mat/impls/aij/seq/aij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/baij/mpi/mpibaij.c.html#MatZeroRows_MPIBAIJ">MatZeroRows_MPIBAIJ in src/mat/impls/baij/mpi/mpibaij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/baij/seq/baij.c.html#MatZeroRows_SeqBAIJ">MatZeroRows_SeqBAIJ in src/mat/impls/baij/seq/baij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/mpi/mpidense.c.html#MatZeroRows_MPIDense">MatZeroRows_MPIDense in src/mat/impls/dense/mpi/mpidense.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/seq/dense.c.html#MatZeroRows_SeqDense">MatZeroRows_SeqDense in src/mat/impls/dense/seq/dense.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/hypre/mhypre.c.html#MatZeroRows_HYPRE">MatZeroRows_HYPRE in src/mat/impls/hypre/mhypre.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/is/matis.c.html#MatZeroRows_IS">MatZeroRows_IS in src/mat/impls/is/matis.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/shell/shell.c.html#MatZeroRows_Shell">MatZeroRows_Shell in src/mat/impls/shell/shell.c</A><BR>


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