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

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_DECIDE to have calculated if m is given)
N - number of global columns (or PETSC_DECIDE to have calculated if n is given)
d_nz - number of block nonzeros per block row in diagonal portion of local submatrix (same for all local rows)
d_nzz - array containing the number of block nonzeros 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 block nonzeros per block row in the off-diagonal portion of local submatrix (same for all local rows).
o_nzz - array containing the number of nonzeros 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

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

Storage Information

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

The user can specify preallocated storage for the diagonal part ofthe local submatrix with either d_nz or d_nnz (not both). Setd_nz=PETSC_DEFAULT and d_nnz=PETSC_NULL for PETSc to control dynamicmemory allocation. Likewise, specify preallocated storage for theoff-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. Inthe 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 theo (off-diagonal) submatrix. Note that the d and the o submatrices arestored 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 memoryor you will get TERRIBLE performance; see the users' manual chapter onmatrices.

Keywords

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

See Also

MatCreate(), MatCreateSeqBAIJ(), MatSetValues(), MatCreateMPIAIJ()

Location: src/mat/impls/baij/mpi/mpibaij.c
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