# MatMPIAIJSetPreallocation

Preallocates memory for a sparse parallel matrix in AIJ 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). By setting these parameters accurately, performance can be increased by more than a factor of 50.

### Synopsis

    PetscErrorCode PETSCMAT_DLLEXPORT MatMPIAIJSetPreallocation(Mat B,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt o_nnz[])

Collective on MPI_Comm

### Input Parameters

| A | - 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 PETSC_NULL, 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'. You must leave room for 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 PETSC_NULL, 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'.

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

The AIJ format (also called the Yale sparse matrix format or compressed row storage (CSR)), is fully compatible with standard Fortran 77 storage. The stored row and column indices begin with zero. See the users manual 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 r1-r2 of the global matrix, where r1 is the first row that belongs to the processor, and r2 is the last row belonging to the this processor. This is a square mxm matrix. The remaining portion of the local submatrix (mxN) constitute the OFF-DIAGONAL portion.

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

### Example 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 SeqAIJ matrices. for eg: proc1 will store [E] as a SeqAIJ matrix, ans [DF] as another SeqAIJ 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, coresponding 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.

### Keywords

matrix, aij, compressed row, sparse, parallel

### See Also

MatCreate(), MatCreateSeqAIJ(), MatSetValues(), MatCreateMPIAIJ(), MatMPIAIJSetPreallocationCSR(),
MPIAIJ

Level:intermediate
Location:src/mat/impls/aij/mpi/mpiaij.c
Index of all Mat routines
Table of Contents for all manual pages
Index of all manual pages

### Examples

src/mat/examples/tutorials/ex5.c.html
src/snes/examples/tutorials/ex26.c.html