Matrix conversion

  The Petsc structure for distributed matrices precludes such an easy solution for matrices as was possible for vectors. The only way to form a Petsc matrix out of a user-supplied matrix is to go through the following steps on every processor.

• Declare the matrix structure:

  Mat mat; /* The Petsc matrix structure */
  MatCreateMPIAIJ( <mpi context> ,
      n_local_rows, n_local_columns,
      n_global_rows,n_global_cols, 0,0,0,0, &mat);
  

  The local sizes need to be specified, the global sizes can be left unspecified by substituting PETSC_DECIDE; see the Petsc manual for the meaning of the zero parameters.
• Declare the matrix elements. This is done through repeated calls to

  int m,n;
  int *row_idxs, *col_idxs;
  Scalar *v;
  MatSetValues(mat, m,row_idxs, n,col_idxs, v,INSERT_VALUES);
  

  This inserts an $m\times n$ dense block of values into the matrix structure. Choosing the values m=n=1 will insert a single value.

  Matrix values can be declared by arbitrary processors. Eg, it is allowed to have one processor declare all values while other processors declare none. This has no relevance to the final distribution of the matrix, which had already been declared with the Create call above.

• Assembling the matrix.

  MatAssemblyBegin(mat,FINAL_ASSEMBLY);
  MatAssemblyEnd(mat,FINAL_ASSEMBLY);
  

  These calls will properly distribute values over the processors and set up communication structures for distributed matrix operations.