/* nag_linsys_real_band_solve (f04bbc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.3, 2023.
 */

#include <nag.h>
#include <stdio.h>

int main(void) {

  /* Scalars */
  double errbnd, rcond;
  Integer exit_status, i, j, kl, ku, n, nrhs, pdab, pdb;

  /* Arrays */
  double *ab = 0, *b = 0;
  Integer *ipiv = 0;

  /* Nag Types */
  NagError fail;
  Nag_OrderType order;

#ifdef NAG_COLUMN_MAJOR
#define AB(I, J) ab[(J - 1) * pdab + kl + ku + I - J]
#define B(I, J) b[(J - 1) * pdb + I - 1]
  order = Nag_ColMajor;
#else
#define AB(I, J) ab[(I - 1) * pdab + kl + J - I]
#define B(I, J) b[(I - 1) * pdb + J - 1]
  order = Nag_RowMajor;
#endif

  exit_status = 0;
  INIT_FAIL(fail);

  printf("nag_linsys_real_band_solve (f04bbc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &kl,
        &ku, &nrhs);
  if (n >= 0 && kl >= 0 && ku >= 0 && nrhs >= 0) {
    /* Allocate memory */
    if (!(ab = NAG_ALLOC((2 * kl + ku + 1) * n, double)) ||
        !(b = NAG_ALLOC(n * nrhs, double)) || !(ipiv = NAG_ALLOC(n, Integer))) {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
    pdab = 2 * kl + ku + 1;
#ifdef NAG_COLUMN_MAJOR
    pdb = n;
#else
    pdb = nrhs;
#endif
  } else {
    printf("%s\n", "One or more of nmax, kl, ku or nrhs is"
                   " too small");
    exit_status = 1;
    return exit_status;
  }
  /* Read A and B from data file */
  for (i = 1; i <= n; ++i) {
    for (j = MAX(i - kl, 1); j <= MIN(i + ku, n); ++j) {
      scanf("%lf", &AB(i, j));
    }
  }
  scanf("%*[^\n] ");

  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= nrhs; ++j) {
      scanf("%lf", &B(i, j));
    }
  }
  scanf("%*[^\n] ");

  /* Solve the equations AX = B for X */
  /* nag_linsys_real_band_solve (f04bbc).
   * Computes the solution and error-bound to a real banded
   * system of linear equations
   */
  nag_linsys_real_band_solve(order, n, kl, ku, nrhs, ab, pdab, ipiv, b, pdb,
                             &rcond, &errbnd, &fail);
  if (fail.code == NE_NOERROR) {
    /* Print solution, estimate of condition number and approximate */
    /* error bound */

    /* nag_file_print_matrix_real_gen (x04cac).
     * Print real general matrix (easy-to-use)
     */
    fflush(stdout);
    nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                   nrhs, b, pdb, "Solution", 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    printf("\n%s\n%6s%10.1e\n\n\n", "Estimate of condition number", "",
           1.0 / rcond);

    printf("%s\n%6s%10.1e\n\n",
           "Estimate of error bound for computed solutions", "", errbnd);
  } else if (fail.code == NE_RCOND) {
    /* Matrix A is numerically singular.  Print estimate of */
    /* reciprocal of condition number and solution */
    printf("\n");
    printf("%s\n%6s%10.1e\n\n\n", "Estimate of reciprocal of condition number",
           "", rcond);
    /* nag_file_print_matrix_real_gen (x04cac), see above. */
    fflush(stdout);
    nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                   nrhs, b, pdb, "Solution", 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
  } else if (fail.code == NE_SINGULAR) {
    /* The upper triangular matrix U is exactly singular.  Print */
    /* details of factorization */
    printf("\n");
    /* nag_file_print_matrix_real_band (x04cec).
     * Print real packed banded matrix (easy-to-use)
     */
    fflush(stdout);
    nag_file_print_matrix_real_band(order, n, n, kl, kl + ku, ab, pdab,
                                    "Details of factorization", 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_file_print_matrix_real_band (x04cec).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    /* Print pivot indices */
    printf("\n%s\n", "Pivot indices");
    for (i = 1; i <= n; ++i) {
      printf("%11" NAG_IFMT "%s", ipiv[i - 1],
             i % 7 == 0 || i == n ? "\n" : " ");
    }
    printf("\n");
  } else {
    printf("Error from nag_linsys_real_band_solve (f04bbc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

END:
  NAG_FREE(ab);
  NAG_FREE(b);
  NAG_FREE(ipiv);

  return exit_status;
}