/* nag_lapacklin_dgesvx (f07abc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.4, 2022.
 */

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

int main(void) {

  /* Scalars */
  double growth_factor, rcond;
  Integer exit_status = 0, i, j, n, nrhs, pda, pdaf, pdb, pdx;

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

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

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

  INIT_FAIL(fail);

  printf("nag_lapacklin_dgesvx (f07abc) Example Program Results\n\n");

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

  if (n < 0 || nrhs < 0) {
    printf("Invalid n or nrhs\n");
    exit_status = 1;
    return exit_status;
  }

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

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

  /* Read A and B from data file */

  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] ");

  /* Solve the equations AX = B for X using
   * nag_lapacklin_dgesvx (f07abc)
   */
  nag_lapacklin_dgesvx(order, Nag_EquilibrateAndFactor, Nag_NoTrans, n, nrhs, a,
                       pda, af, pdaf, ipiv, &equed, r, c, b, pdb, x, pdx,
                       &rcond, ferr, berr, &growth_factor, &fail);

  if (fail.code != NE_NOERROR && fail.code != NE_SINGULAR) {
    printf("Error from nag_lapacklin_dgesvx (f07abc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print solution using
   * nag_file_print_matrix_real_gen (x04cac)
   */
  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;
  }

  /* Print error bounds, condition number, the form of equilibration
   * and the pivot growth factor
   */
  printf("\nBackward errors (machine-dependent)\n");
  for (j = 1; j <= nrhs; ++j)
    printf("%11.1e%s", berr[j - 1], j % 7 == 0 || j == nrhs ? "\n" : " ");
  printf("\n\nEstimated forward error bounds (machine-dependent)\n");

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

  if (equed == Nag_NoEquilibration)
    printf("A has not been equilibrated\n");
  else if (equed == Nag_RowEquilibration)
    printf("A has been row scaled as diag(R)*A\n");
  else if (equed == Nag_ColumnEquilibration)
    printf("A has been column scaled as A*diag(C)\n");
  else if (equed == Nag_RowAndColumnEquilibration)
    printf("A has been row and column scaled as diag(R)*A*diag(C)\n");

  printf("\nReciprocal condition number estimate of scaled matrix\n");
  printf("%11.1e\n\n", rcond);

  printf("Estimate of reciprocal pivot growth factor\n");
  printf("%11.1e\n", growth_factor);

  if (fail.code == NE_SINGULAR) {
    printf("Error from nag_lapacklin_dgesvx (f07abc).\n%s\n", fail.message);
    exit_status = 1;
  }

END:
  NAG_FREE(a);
  NAG_FREE(af);
  NAG_FREE(b);
  NAG_FREE(berr);
  NAG_FREE(c);
  NAG_FREE(ferr);
  NAG_FREE(r);
  NAG_FREE(x);
  NAG_FREE(ipiv);

  return exit_status;
}

#undef B
#undef A