# MatCreateKAIJ#

Creates a matrix of type MATKAIJ to be used for matrices of the following form:

## Synopsis#

#include "petscmat.h"
PetscErrorCode MatCreateKAIJ(Mat A, PetscInt p, PetscInt q, const PetscScalar S[], const PetscScalar T[], Mat *kaij)


[I \otimes S + A \otimes T]

where S is a dense (p \times q) matrix T is a dense (p \times q) matrix A is an MATAIJ (n \times n) matrix I is the identity matrix The resulting matrix is (np \times nq)

S and T are always stored independently on all processes as PetscScalar arrays in column-major format.

Collective

## Input Parameters#

• A - the MATAIJ matrix

• p - number of rows in S and T

• q - number of columns in S and T

• S - the S matrix (can be NULL), stored as a PetscScalar array (column-major)

• T - the T matrix (can be NULL), stored as a PetscScalar array (column-major)

## Output Parameter#

• kaij - the new MATKAIJ matrix

## Notes#

This function increases the reference count on the MATAIJ matrix, so the user is free to destroy the matrix if it is not needed.

Changes to the entries of the MATAIJ matrix will immediately affect the MATKAIJ matrix.

## Developer Note#

In the MATMPIKAIJ case, the internal ‘AIJ’ and ‘OAIJ’ sequential KAIJ matrices are kept up to date by tracking the object state of the AIJ matrix ‘A’ that describes the blockwise action of the MATMPIKAIJ matrix and, if the object state has changed, lazily rebuilding ‘AIJ’ and ‘OAIJ’ just before executing operations with the MATMPIKAIJ matrix. If new types of operations are added, routines implementing those must also ensure these are rebuilt when needed (by calling the internal MatKAIJ_build_AIJ_OAIJ() routine).

MatKAIJSetAIJ(), MatKAIJSetS(), MatKAIJSetT(), MatKAIJGetAIJ(), MatKAIJGetS(), MatKAIJGetT(), MATKAIJ