Allocates memory for a sparse parallel matrix in
MATMPIBAIJ 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.
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 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 it 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 (possibly different for each block row) or NULL.
If the *_nnz parameter is given then the *_nz parameter is ignored
Options Database Keys#
-mat_block_size - size of the blocks to use
-set hash table factor
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).
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.
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.