MatMPIAIJSetPreallocation#

Preallocates memory for a sparse parallel matrix in MATMPIAIJ format (the default parallel PETSc format). 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).

Synopsis#

#include "petscmat.h" 
PetscErrorCode MatMPIAIJSetPreallocation(Mat B, PetscInt d_nz, const PetscInt d_nnz[], PetscInt o_nz, const PetscInt o_nnz[])

Collective

Input Parameters#

B - the matrix
d_nz - number of nonzeros per row in DIAGONAL portion of local submatrix (same value is used for all local rows)
d_nnz - array containing the number of nonzeros in the various rows of the DIAGONAL portion of the local submatrix (possibly different for each row) or NULL (PETSC_NULL_INTEGER in Fortran), if d_nz is used to specify the nonzero structure. The size of this array is equal to the number of local rows, i.e ‘m’. For matrices that will be factored, you must leave room for (and set) the diagonal entry even if it is zero.
o_nz - number of nonzeros per row in the OFF-DIAGONAL portion of local submatrix (same value is used for all local rows).
o_nnz - array containing the number of nonzeros in the various rows of the OFF-DIAGONAL portion of the local submatrix (possibly different for each row) or NULL (PETSC_NULL_INTEGER in Fortran), if o_nz is used to specify the nonzero structure. The size of this array is equal to the number of local rows, i.e ‘m’.

Usage#

Consider the following 8x8 matrix with 34 non-zero values, that is assembled across 3 processors. Lets assume that proc0 owns 3 rows, proc1 owns 3 rows, proc2 owns 2 rows. This division can be shown as follows

            1  2  0  |  0  3  0  |  0  4
    Proc0   0  5  6  |  7  0  0  |  8  0
            9  0 10  | 11  0  0  | 12  0
    -------------------------------------
           13  0 14  | 15 16 17  |  0  0
    Proc1   0 18  0  | 19 20 21  |  0  0
            0  0  0  | 22 23  0  | 24  0
    -------------------------------------
    Proc2  25 26 27  |  0  0 28  | 29  0
           30  0  0  | 31 32 33  |  0 34

This can be represented as a collection of submatrices as

      A B C
      D E F
      G H I

Where the submatrices A,B,C are owned by proc0, D,E,F are owned by proc1, G,H,I are owned by proc2.

The ‘m’ parameters for proc0,proc1,proc2 are 3,3,2 respectively. The ‘n’ parameters for proc0,proc1,proc2 are 3,3,2 respectively. The ‘M’,’N’ parameters are 8,8, and have the same values on all procs.

The DIAGONAL submatrices corresponding to proc0,proc1,proc2 are submatrices [A], [E], [I] respectively. The OFF-DIAGONAL submatrices corresponding to proc0,proc1,proc2 are [BC], [DF], [GH] respectively. Internally, each processor stores the DIAGONAL part, and the OFF-DIAGONAL part as MATSEQAIJ matrices. For example, proc1 will store [E] as a MATSEQAIJ matrix, ans [DF] as another MATSEQAIJ matrix.

When d_nz, o_nz parameters are specified, d_nz storage elements are allocated for every row of the local diagonal submatrix, and o_nz storage locations are allocated for every row of the OFF-DIAGONAL submat. One way to choose d_nz and o_nz is to use the max nonzerors per local rows for each of the local DIAGONAL, and the OFF-DIAGONAL submatrices. In this case, the values of d_nz, o_nz are

     proc0  dnz = 2, o_nz = 2
     proc1  dnz = 3, o_nz = 2
     proc2  dnz = 1, o_nz = 4

We are allocating m(d_nz+o_nz) storage locations for every proc. This translates to 3(2+2)=12 for proc0, 3*(3+2)=15 for proc1, 2*(1+4)=10 for proc3. i.e we are using 12+15+10=37 storage locations to store 34 values.

When d_nnz, o_nnz parameters are specified, the storage is specified for every row, corresponding to both DIAGONAL and OFF-DIAGONAL submatrices. In the above case the values for d_nnz, o_nnz are

     proc0 d_nnz = [2,2,2] and o_nnz = [2,2,2]
     proc1 d_nnz = [3,3,2] and o_nnz = [2,1,1]
     proc2 d_nnz = [1,1]   and o_nnz = [4,4]

Here the space allocated is sum of all the above values i.e 34, and hence pre-allocation is perfect.

Notes#

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

The MATAIJ format, also called compressed row storage (CSR), is compatible with standard Fortran storage. The stored row and column indices begin with zero. See Sparse Matrices for details.

The parallel matrix is partitioned such that the first m0 rows belong to process 0, the next m1 rows belong to process 1, the next m2 rows belong to process 2 etc.. where m0,m1,m2… are the input parameter ‘m’.

The DIAGONAL portion of the local submatrix of a processor can be defined as the submatrix which is obtained by extraction the part corresponding to the rows r1-r2 and columns c1-c2 of the global matrix, where r1 is the first row that belongs to the processor, r2 is the last row belonging to the this processor, and c1-c2 is range of indices of the local part of a vector suitable for applying the matrix to. This is an mxn matrix. In the common case of a square matrix, the row and column ranges are the same and the DIAGONAL part is also square. The remaining portion of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.

If o_nnz and d_nnz are specified, then o_nz and d_nz are ignored.

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.