# MatRelax

Computes relaxation (SOR, Gauss-Seidel) sweeps.

### Synopsis

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

Collective on Mat and Vec

### 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 Parameters

x -the solution (can contain an initial 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_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 MatRelax() directly, but instead will employ the KSP/PC interface.

### Notes for Advanced Users

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.

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

See also, MatPBRelax(). This routine will automatically call the point block version if the point version is not available.

Level:developer
Location:src/mat/interface/matrix.c
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