/* nag_lapacklin_dgerfs (f07ahc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {
  /* Scalars */
  Integer berr_len, i, ipiv_len, ferr_len, j, n, nrhs;
  Integer pda, pdaf, pdb, pdx;
  Integer exit_status = 0;
  NagError fail;
  Nag_OrderType order;

  /* Arrays */
  double *a = 0, *af = 0, *b = 0, *berr = 0, *ferr = 0, *x = 0;
  Integer *ipiv = 0;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define AF(I, J) af[(J - 1) * pdaf + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
#define X(I, J) x[(J - 1) * pdx + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define AF(I, J) af[(I - 1) * pdaf + J - 1]
#define B(I, J) b[(I - 1) * pdb + J - 1]
#define X(I, J) x[(I - 1) * pdx + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapacklin_dgerfs (f07ahc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n] ", &n, &nrhs);

#ifdef NAG_COLUMN_MAJOR
  pda = n;
  pdaf = n;
  pdb = n;
  pdx = n;
#else
  pda = n;
  pdaf = n;
  pdb = nrhs;
  pdx = nrhs;
#endif
  berr_len = nrhs;
  ferr_len = nrhs;
  ipiv_len = n;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(af = NAG_ALLOC(n * n, double)) ||
      !(b = NAG_ALLOC(n * nrhs, double)) ||
      !(berr = NAG_ALLOC(berr_len, double)) ||
      !(ferr = NAG_ALLOC(ferr_len, double)) ||
      !(x = NAG_ALLOC(n * nrhs, double)) ||
      !(ipiv = NAG_ALLOC(ipiv_len, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read A and B from data file, and copy A to AF and B to X */
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j)
      scanf("%lf", &A(i, j));
  }
  scanf("%*[^\n] ");
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= nrhs; ++j)
      scanf("%lf", &B(i, j));
  }
  scanf("%*[^\n] ");

  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= n; ++j)
      AF(i, j) = A(i, j);
  }
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= nrhs; ++j)
      X(i, j) = B(i, j);
  }

  /* Factorize A in the array AF */
  /* nag_lapacklin_dgetrf (f07adc).
   * LU factorization of real m by n matrix
   */
  nag_lapacklin_dgetrf(order, n, n, af, pdaf, ipiv, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_dgetrf (f07adc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  printf("\n");
  /* Compute solution in the array X */
  /* nag_lapacklin_dgetrs (f07aec).
   * Solution of real system of linear equations, multiple
   * right-hand sides, matrix already factorized by nag_lapacklin_dgetrf
   * (f07adc)
   */
  nag_lapacklin_dgetrs(order, Nag_NoTrans, n, nrhs, af, pdaf, ipiv, x, pdx,
                       &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_dgetrs (f07aec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Improve solution, and compute backward errors and */
  /* estimated bounds on the forward errors */
  /* nag_lapacklin_dgerfs (f07ahc).
   * Refined solution with error bounds of real system of
   * linear equations, multiple right-hand sides
   */
  nag_lapacklin_dgerfs(order, Nag_NoTrans, n, nrhs, a, pda, af, pdaf, ipiv, b,
                       pdb, x, pdx, ferr, berr, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_dgerfs (f07ahc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print solution */
  /* 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, x, pdx, "Solution(s)", 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("\nBackward errors (machine-dependent)\n");

  for (j = 1; j <= nrhs; ++j)
    printf("%11.1e%s", berr[j - 1], j % 7 == 0 ? "\n" : " ");

  printf("\nEstimated forward error bounds (machine-dependent)\n");

  for (j = 1; j <= nrhs; ++j)
    printf("%11.1e%s", ferr[j - 1], j % 7 == 0 ? "\n" : " ");
  printf("\n");
END:
  NAG_FREE(a);
  NAG_FREE(af);
  NAG_FREE(b);
  NAG_FREE(berr);
  NAG_FREE(ferr);
  NAG_FREE(x);
  NAG_FREE(ipiv);
  return exit_status;
}