# MatShift
Computes Y =  Y + a I, where a is a PetscScalar and I is the identity matrix. 
## Synopsis
```
#include "petscmat.h"  
PetscErrorCode MatShift(Mat Y, PetscScalar a)
```
Neighbor-wise Collective


## Input Parameters

- ***Y -*** the matrices
- ***a -*** the PetscScalar





## Notes
If Y is a rectangular matrix, the shift is done on the main diagonal Y_{ii} of the matrix (https://en.wikipedia.org/wiki/Main_diagonal)

If the matrix Y is missing some diagonal entries this routine can be very slow. To make it fast one should initially
fill the matrix so that all diagonal entries have a value (with a value of zero for those locations that would not have an
entry). No operation is performed when a is zero.

To form Y = Y + diag(V) use MatDiagonalSet()


## See Also
 `MatDiagonalSet()`, `MatScale()`, `MatDiagonalScale()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/utils/axpy.c.html#MatShift">src/mat/utils/axpy.c</A>

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex1.c.html">src/ksp/ksp/tutorials/ex1.c.html</A><BR>
<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/ksp/ksp/tutorials/ex79.c.html">src/ksp/ksp/tutorials/ex79.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex81.c.html">src/ksp/ksp/tutorials/ex81.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex82.c.html">src/ksp/ksp/tutorials/ex82.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/snes/tutorials/ex20.c.html">src/snes/tutorials/ex20.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex16fwd.c.html">src/ts/tutorials/ex16fwd.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex20fwd.c.html">src/ts/tutorials/ex20fwd.c.html</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ts/tutorials/ex3.c.html">src/ts/tutorials/ex3.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/pde_constrained/tutorials/hyperbolic.c.html">src/tao/pde_constrained/tutorials/hyperbolic.c.html</A><BR>

## Implementations

<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/aij/mpi/mpiaij.c.html#MatShift_MPIAIJ">MatShift_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#MatShift_SeqAIJ">MatShift_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#MatShift_MPIBAIJ">MatShift_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#MatShift_SeqBAIJ">MatShift_SeqBAIJ in src/mat/impls/baij/seq/baij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/cdiagonal/cdiagonal.c.html#MatShift_ConstantDiagonal">MatShift_ConstantDiagonal in src/mat/impls/cdiagonal/cdiagonal.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/mpi/mpidense.c.html#MatShift_MPIDense">MatShift_MPIDense in src/mat/impls/dense/mpi/mpidense.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/mpi/mpidense.c.html#MatShift_MPIDenseCUDA">MatShift_MPIDenseCUDA in src/mat/impls/dense/mpi/mpidense.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/mpi/mpidense.c.html#MatShift_MPIDenseHIP">MatShift_MPIDenseHIP in src/mat/impls/dense/mpi/mpidense.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/seq/cuda/densecuda.cu.html#MatShift_SeqDenseCUDA">MatShift_SeqDenseCUDA in src/mat/impls/dense/seq/cuda/densecuda.cu</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/seq/dense.c.html#MatShift_SeqDense">MatShift_SeqDense in src/mat/impls/dense/seq/dense.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/dense/seq/hip/densehip.hip.c.html#MatShift_SeqDenseHIP">MatShift_SeqDenseHIP in src/mat/impls/dense/seq/hip/densehip.hip.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/is/matis.c.html#MatShift_IS">MatShift_IS in src/mat/impls/is/matis.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/nest/matnest.c.html#MatShift_Nest">MatShift_Nest in src/mat/impls/nest/matnest.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/sbaij/mpi/mpisbaij.c.html#MatShift_MPISBAIJ">MatShift_MPISBAIJ in src/mat/impls/sbaij/mpi/mpisbaij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/sbaij/seq/sbaij.c.html#MatShift_SeqSBAIJ">MatShift_SeqSBAIJ in src/mat/impls/sbaij/seq/sbaij.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/scalapack/matscalapack.c.html#MatShift_ScaLAPACK">MatShift_ScaLAPACK in src/mat/impls/scalapack/matscalapack.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/sell/mpi/mpisell.c.html#MatShift_MPISELL">MatShift_MPISELL in src/mat/impls/sell/mpi/mpisell.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/sell/seq/sell.c.html#MatShift_SeqSELL">MatShift_SeqSELL in src/mat/impls/sell/seq/sell.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/shell/shell.c.html#MatShift_Shell">MatShift_Shell in src/mat/impls/shell/shell.c</A><BR>
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/submat/submat.c.html#MatShift_SubMatrix">MatShift_SubMatrix in src/mat/impls/submat/submat.c</A><BR>


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