# 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

    #include "petscmat.h"
    PetscErrorCode PETSCMAT_DLLEXPORT MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt d_nz,const PetscInt d_nnz[],PetscInt o_nz,const PetscInt 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_DETERMINE to have calculated if m is given)
| N | - number of global columns (or PETSC_DETERMINE to have calculated if n is given)
| d_nz | - number of nonzero blocks per block row in diagonal portion of local submatrix (same for all local rows)
| d_nnz | - array containing the number of nonzero blocks 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 nonzero blocks per block row in the off-diagonal portion of local submatrix (same for all local rows).
| o_nnz | - array containing the number of nonzero blocks 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_block_size | - size of the blocks to use
| -mat_use_hash_table <fact> | - Notes: If the *_nnz parameter is given then the *_nz parameter is ignored

A nonzero block is any block that as 1 or more nonzeros in it

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

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.

### 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=PETSC_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.

### Keywords

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

### C++ variants

| MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *A) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,0,PETSC_NULL,0,PETSC_NULL,A)
| MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt nnz[],const PetscInt onz[],Mat *A) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,0,nnz,0,onz,A)
| MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt nz,PetscInt nnz,Mat *A) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,nz,PETSC_NULL,nnz,PETSC_NULL,A)
| Mat MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,0,PETSC_NULL,0,PETSC_NULL,&A); return A;
| Mat MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt nnz[],const PetscInt onz[]) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,0,nnz,0,onz,&A); return A;
| Mat MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt nz,PetscInt nnz) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,nz,PETSC_NULL,nnz,PETSC_NULL,&A); return A;
| Mat MatCreateMPIBAIJ(PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt nz,const PetscInt nnz[],PetscInt onz,const PetscInt onnz[]) |  | -> |  | MatCreateMPIBAIJ(PETSC_COMM_WORLD,bs,m,n,M,N,nz,nnz,onz,onnz,&A); return A;
| MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,Mat *A) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,0,PETSC_NULL,0,PETSC_NULL,A)
| MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt nnz[],const PetscInt onz[],Mat *A) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,0,nnz,0,onz,A)
| MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt nz,PetscInt nnz,Mat *A) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,nz,PETSC_NULL,nnz,PETSC_NULL,A)
| Mat MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,0,PETSC_NULL,0,PETSC_NULL,&A); return A;
| Mat MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,const PetscInt nnz[],const PetscInt onz[]) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,0,nnz,0,onz,&A); return A;
| Mat MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt nz,PetscInt nnz) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,nz,PETSC_NULL,nnz,PETSC_NULL,&A); return A;
| Mat MatCreateMPIBAIJ(MPI_Comm comm,PetscInt bs,PetscInt m,PetscInt n,PetscInt M,PetscInt N,PetscInt nz,const PetscInt nnz[],PetscInt onz,const PetscInt onnz[]) |  | -> |  | MatCreateMPIBAIJ(comm,bs,m,n,M,N,nz,nnz,onz,onnz,&A); return A;

### See Also

MatCreate(), MatCreateSeqBAIJ(), MatSetValues(), MatCreateMPIBAIJ(), MatMPIBAIJSetPreallocation(), MatMPIBAIJSetPreallocationCSR()

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