MatMPISBAIJSetPreallocation#

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" 
PetscErrorCode MatMPISBAIJSetPreallocation(Mat B, PetscInt bs, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])

Collective

Input Parameters#

B - the matrix
bs - size of block, the blocks are ALWAYS square. One can use MatSetBlockSizes() to set a different row and column blocksize but the row blocksize always defines the size of the blocks. The column blocksize sets the blocksize of the vectors obtained with MatCreateVecs()
d_nz - number of block nonzeros per block row in diagonal portion of local submatrix (same for all local rows)
d_nnz - array containing the number of block nonzeros in the various block rows in the upper triangular and diagonal part of the in diagonal portion of the local (possibly different for each block row) or NULL. If you plan to factor the matrix you must leave room for the diagonal entry and set a value 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_nnz - array containing the number of nonzeros in the various block rows of the off-diagonal portion of the local submatrix that is right of the diagonal (possibly different for each block row) or NULL.

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#

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.

If the *_nnz parameter is given then the *_nz parameter is ignored

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 = 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).

You can call MatGetInfo() to get information on how effective the preallocation was; for example the fields mallocs,nz_allocated,nz_used,nz_unneeded; You can also run with the option -info and look for messages with the string malloc in them to see if additional memory allocation was needed.

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  |. . . d d d o o o o  o  o
   row 4  |. . . d d d o o o o  o  o
   row 5  |. . . 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 matrix is stored in MATSEQSBAIJ format and the o submatrix in MATSEQBAIJ format.

Now d_nz should indicate the number of block nonzeros per row in the upper triangular plus the diagonal part of 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.