MatCreateMPIBAIJ

Creates a sparse parallel matrix in block AIJ format (block compressed row). For good matrix assembly performance the user should preallocate the matrix storage by setting the parameters d_nz (or d_nnz) and o_nz (or o_nnz). By setting these parameters accurately, performance can be increased by more than a factor of 50.

Synopsis

#include "petscmat.h"  
int MatCreateMPIBAIJ(MPI_Comm comm,int bs,int m,int n,int M,int N,int d_nz,int *d_nnz,int o_nz,int *o_nnz,Mat *A)

Collective on MPI_Comm

Input Parameters

	comm	- MPI communicator
	bs	- size of blockk
	m	- number of local rows (or PETSC_DECIDE to have calculated if M is given) This value should be the same as the local size used in creating the y vector for the matrix-vector product y = Ax.
	n	- number of local columns (or PETSC_DECIDE to have calculated if N is given) This value should be the same as the local size used in creating the x vector for the matrix-vector product y = Ax.
	M	- number of global rows (or PETSC_DETERMINE to have calculated if m is given)
	N	- number of global columns (or PETSC_DETERMINE to have calculated if n is given)
	d_nz	- number of nonzero blocks per block row in diagonal portion of local submatrix (same for all local rows)
	d_nnz	- array containing the number of nonzero blocks in the various block rows of the in diagonal portion of the local (possibly different for each block row) or PETSC_NULL. You must leave room for the diagonal entry even if it is zero.
	o_nz	- number of nonzero blocks per block row in the off-diagonal portion of local submatrix (same for all local rows).
	o_nnz	- array containing the number of nonzero blocks in the various block rows of the off-diagonal portion of the local submatrix (possibly different for each block row) or PETSC_NULL.

Output Parameter

A -the matrix

Options Database Keys

-mat_no_unroll -uses code that does not unroll the loops in the block calculations (much slower)

-mat_block_size -size of the blocks to use

Notes

A nonzero block is any block that as 1 or more nonzeros in it

The user MUST specify either the local or global matrix dimensions (possibly both).

If PETSC_DECIDE or PETSC_DETERMINE is used for a particular argument on one processor than it must be used on all processors that share the object for that argument.

Storage Information

For a square global matrix we define each processor's diagonal portion to be its local rows and the corresponding columns (a square submatrix); each processor's off-diagonal portion encompasses the remainder of the local matrix (a rectangular submatrix).

The user can specify preallocated storage for the diagonal part of the local submatrix with either d_nz or d_nnz (not both). Set d_nz=PETSC_DEFAULT and d_nnz=PETSC_NULL for PETSc to control dynamic memory allocation. Likewise, specify preallocated storage for the off-diagonal part of the local submatrix with o_nz or o_nnz (not both).

Consider a processor that owns rows 3, 4 and 5 of a parallel matrix. In the figure below we depict these three local rows and all columns (0-11).

           0 1 2 3 4 5 6 7 8 9 10 11
          -------------------
   row 3  |  o o o d d d o o o o o o
   row 4  |  o o o d d d o o o o o o
   row 5  |  o o o d d d o o o o o o
          -------------------

Thus, any entries in the d locations are stored in the d (diagonal) submatrix, and any entries in the o locations are stored in the o (off-diagonal) submatrix. Note that the d and the o submatrices are stored simply in the MATSEQBAIJ format for compressed row storage.

Now d_nz should indicate the number of block nonzeros per row in the d matrix, and o_nz should indicate the number of block nonzeros per row in the o matrix. In general, for PDE problems in which most nonzeros are near the diagonal, one expects d_nz >> o_nz. For large problems you MUST preallocate memory or you will get TERRIBLE performance; see the users' manual chapter on matrices.

Keywords

matrix, block, aij, compressed row, sparse, parallel

Examples

src/sles/examples/tutorials/ex2.c.html
src/sles/examples/tutorials/ex23.c.html