# MatCreateBAIJ
Creates a sparse parallel matrix in `MATBAIJ` format (block compressed row). 
## Synopsis
```
#include "petscmat.h"  
PetscErrorCode MatCreateBAIJ(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


## Input Parameters

- ***comm -*** MPI communicator
- ***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()`
- ***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 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 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 NULL.



## Output Parameter

- ***A -*** the matrix



## Options Database Keys

- ***-mat_block_size -*** size of the blocks to use
- ***-mat_use_hash_table <fact> -*** set hash table factor





## Notes
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.

It is recommended that one use the `MatCreate()`, `MatSetType()` and/or `MatSetFromOptions()`,
MatXXXXSetPreallocation() paradigm instead of this routine directly.
[MatXXXXSetPreallocation() is, for example, `MatSeqBAIJSetPreallocation()`]

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` = `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).

```none
           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.


## See Also
 `Mat`, `MatCreate()`, `MatCreateSeqBAIJ()`, `MatSetValues()`, `MatCreateBAIJ()`, `MatMPIBAIJSetPreallocation()`, `MatMPIBAIJSetPreallocationCSR()`

## Level
intermediate

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/impls/baij/mpi/mpibaij.c.html#MatCreateBAIJ">src/mat/impls/baij/mpi/mpibaij.c</A>

## Examples
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/ksp/ksp/tutorials/ex81.c.html">src/ksp/ksp/tutorials/ex81.c.html</A><BR>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/mat/impls/baij/mpi/mpibaij.c)


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