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# MatSOR

Computes relaxation (SOR, Gauss-Seidel) sweeps.

## Synopsis

    #include "petscmat.h"
    PetscErrorCode MatSOR(Mat mat, Vec b, PetscReal omega, MatSORType flag, PetscReal shift, PetscInt its, PetscInt lits, Vec x)

Neighbor-wise Collective

## Input Parameters

- mat - the matrix

- b - the right-hand side

- omega - the relaxation factor

- flag - flag indicating the type of SOR (see below)

- shift - diagonal shift

- its - the number of iterations

- lits - the number of local iterations

## Output Parameter

- x - the solution (can contain an initial guess, use option `SOR_ZERO_INITIAL_GUESS` to indicate no guess)

## SOR Flags

- `SOR_FORWARD_SWEEP` - forward SOR

- `SOR_BACKWARD_SWEEP` - backward SOR

- `SOR_SYMMETRIC_SWEEP` - SSOR (symmetric SOR)

- `SOR_LOCAL_FORWARD_SWEEP` - local forward SOR

- `SOR_LOCAL_BACKWARD_SWEEP` - local forward SOR

- `SOR_LOCAL_SYMMETRIC_SWEEP` - local SSOR

- `SOR_EISENSTAT` - SOR with Eisenstat trick

- `SOR_APPLY_UPPER`, `SOR_APPLY_LOWER` - applies upper/lower triangular part of matrix to vector (with `omega`)

- `SOR_ZERO_INITIAL_GUESS` - zero initial guess

## Notes

`SOR_LOCAL_FORWARD_SWEEP`, `SOR_LOCAL_BACKWARD_SWEEP`, and `SOR_LOCAL_SYMMETRIC_SWEEP` perform separate independent smoothings on each processor.

Application programmers will not generally use `MatSOR()` directly, but instead will employ `PCSOR` or `PCEISENSTAT`

For `MATBAIJ`, `MATSBAIJ`, and `MATAIJ` matrices with inodes, this does a block SOR smoothing, otherwise it does a pointwise smoothing. For `MATAIJ` matrices with inodes, the block sizes are determined by the inode sizes, not the block size set with `MatSetBlockSize()`

Vectors `x` and `b` CANNOT be the same

The flags are implemented as bitwise inclusive or operations. For example, use (`SOR_ZERO_INITIAL_GUESS` | `SOR_SYMMETRIC_SWEEP`) to specify a zero initial guess for SSOR.

## Developer Note

We should add block SOR support for `MATAIJ` matrices with block size set to greater than one and no inodes

## See Also

Matrices, `Mat`, `MatMult()`, `KSP`, `PC`, `MatGetFactor()`

## Level

developer

## Location

src/mat/interface/matrix.c

## Examples

src/tao/pde_constrained/tutorials/parabolic.c
src/tao/pde_constrained/tutorials/hyperbolic.c

## Implementations

MatSOR_MPIAIJ() in src/mat/impls/aij/mpi/mpiaij.c
MatSOR_SeqAIJ() in src/mat/impls/aij/seq/aij.c
MatSOR_SeqAIJSELL() in src/mat/impls/aij/seq/aijsell/aijsell.c
MatSOR_MPIBAIJ() in src/mat/impls/baij/mpi/mpibaij.c
MatSOR_SeqBAIJ() in src/mat/impls/baij/seq/baij.c
MatSOR_BlockMat() in src/mat/impls/blockmat/seq/blockmat.c
MatSOR_ConstantDiagonal() in src/mat/impls/cdiagonal/cdiagonal.c
MatSOR_SeqDense() in src/mat/impls/dense/seq/dense.c
MatSOR_SeqKAIJ() in src/mat/impls/kaij/kaij.c
MatSOR_MPISBAIJ() in src/mat/impls/sbaij/mpi/mpisbaij.c
MatSOR_SeqSBAIJ() in src/mat/impls/sbaij/seq/relax.h
MatSOR_MPISELL() in src/mat/impls/sell/mpi/mpisell.c
MatSOR_SeqSELL() in src/mat/impls/sell/seq/sell.c

Index of all Mat routines
Table of Contents for all manual pages
Index of all manual pages