### 41.13 Examples

The following example program builds a 5-by-4 sparse matrix and prints it in triplet, compressed column, and compressed row format. The matrix which is constructed is The output of the program is

    printing all matrix elements:
    A(0,0) = 0
    A(0,1) = 0
    A(0,2) = 3.1
    A(0,3) = 4.6
    A(1,0) = 1
    .
    .
    .
    A(4,0) = 4.1
    A(4,1) = 0
    A(4,2) = 0
    A(4,3) = 0
    matrix in triplet format (i,j,Aij):
    (0, 2, 3.1)
    (0, 3, 4.6)
    (1, 0, 1.0)
    (1, 2, 7.2)
    (3, 0, 2.1)
    (3, 1, 2.9)
    (3, 3, 8.5)
    (4, 0, 4.1)
    matrix in compressed column format:
    i = [ 1, 3, 4, 3, 0, 1, 0, 3, ]
    p = [ 0, 3, 4, 6, 8, ]
    d = [ 1, 2.1, 4.1, 2.9, 3.1, 7.2, 4.6, 8.5, ]
    matrix in compressed row format:
    i = [ 2, 3, 0, 2, 0, 1, 3, 0, ]
    p = [ 0, 2, 4, 4, 7, 8, ]
    d = [ 3.1, 4.6, 1, 7.2, 2.1, 2.9, 8.5, 4.1, ]

We see in the compressed column output, the data array stores each column contiguously, the array i stores the row index of the corresponding data element, and the array p stores the index of the start of each column in the data array. Similarly, for the compressed row output, the data array stores each row contiguously, the array i stores the column index of the corresponding data element, and the p array stores the index of the start of each row in the data array.

    #include <stdio.h>
    #include <stdlib.h>

    #include <gsl/gsl_spmatrix.h>

    int
    main()
    {
      gsl_spmatrix *A = gsl_spmatrix_alloc(5, 4); /* triplet format */
      gsl_spmatrix *B, *C;
      size_t i, j;

      /* build the sparse matrix */
      gsl_spmatrix_set(A, 0, 2, 3.1);
      gsl_spmatrix_set(A, 0, 3, 4.6);
      gsl_spmatrix_set(A, 1, 0, 1.0);
      gsl_spmatrix_set(A, 1, 2, 7.2);
      gsl_spmatrix_set(A, 3, 0, 2.1);
      gsl_spmatrix_set(A, 3, 1, 2.9);
      gsl_spmatrix_set(A, 3, 3, 8.5);
      gsl_spmatrix_set(A, 4, 0, 4.1);

      printf("printing all matrix elements:\n");
      for (i = 0; i < 5; ++i)
        for (j = 0; j < 4; ++j)
          printf("A(%zu,%zu) = %g\n", i, j,
                 gsl_spmatrix_get(A, i, j));

      /* print out elements in triplet format */
      printf("matrix in triplet format (i,j,Aij):\n");
      gsl_spmatrix_fprintf(stdout, A, "%.1f");

      /* convert to compressed column format */
      B = gsl_spmatrix_ccs(A);

      printf("matrix in compressed column format:\n");
      printf("i = [ ");
      for (i = 0; i < B->nz; ++i)
        printf("%zu, ", B->i[i]);
      printf("]\n");

      printf("p = [ ");
      for (i = 0; i < B->size2 + 1; ++i)
        printf("%zu, ", B->p[i]);
      printf("]\n");

      printf("d = [ ");
      for (i = 0; i < B->nz; ++i)
        printf("%g, ", B->data[i]);
      printf("]\n");

      /* convert to compressed row format */
      C = gsl_spmatrix_crs(A);

      printf("matrix in compressed row format:\n");
      printf("i = [ ");
      for (i = 0; i < C->nz; ++i)
        printf("%zu, ", C->i[i]);
      printf("]\n");

      printf("p = [ ");
      for (i = 0; i < C->size1 + 1; ++i)
        printf("%zu, ", C->p[i]);
      printf("]\n");

      printf("d = [ ");
      for (i = 0; i < C->nz; ++i)
        printf("%g, ", C->data[i]);
      printf("]\n");

      gsl_spmatrix_free(A);
      gsl_spmatrix_free(B);
      gsl_spmatrix_free(C);

      return 0;
    }