# MatReorderForNonzeroDiagonal

Changes matrix ordering to remove zeros from diagonal. This may help in the LU factorization to prevent a zero pivot.

### Synopsis

    #include "petscmat.h"
    PetscErrorCode PETSCMAT_DLLEXPORT MatReorderForNonzeroDiagonal(Mat mat,PetscReal abstol,IS ris,IS cis)

Collective on Mat

### Input Parameters

| mat | - matrix to reorder
| rmap,cmap | - row and column permutations. Usually obtained from MatGetOrdering().

### Notes

This is not intended as a replacement for pivoting for matrices that have ``bad'' structure. It is only a stop-gap measure. Should be called after a call to MatGetOrdering(), this routine changes the column ordering defined in cis.

Only works for SeqAIJ matrices

### Options Database Keys (When using KSP)

| -pc_ilu_nonzeros_along_diagonal | - - -pc_lu_nonzeros_along_diagonal

### Algorithm Notes

Column pivoting is used.

1) Choice of column is made by looking at the non-zero elements in the troublesome row for columns that are not yet included (moving from left to right).

2) If (1) fails we check all the columns to the left of the current row and see if one of them has could be swapped. It can be swapped if its corresponding row has a non-zero in the column it is being swapped with; to make sure the previous nonzero diagonal remains nonzero

Level:intermediate
Location:src/mat/utils/zerodiag.c
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