/* nag_linsys_real_square_solve (f04bac) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {

  /* Scalars */
  double errbnd, rcond;
  Integer exit_status, i, j, n, nrhs, pda, pdb;

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

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

#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

  exit_status = 0;
  INIT_FAIL(fail);

  printf("nag_linsys_real_square_solve (f04bac) 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) {
    /* Allocate memory */
    if (!(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * nrhs, double)) ||
        !(ipiv = NAG_ALLOC(n, Integer))) {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
#ifdef NAG_COLUMN_MAJOR
    pda = n;
    pdb = n;
#else
    pda = n;
    pdb = nrhs;
#endif
  } else {
    printf("%s\n", "n and/or nrhs too small");
    exit_status = 1;
    return exit_status;
  }

  /* 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 */
  /* nag_linsys_real_square_solve (f04bac).
   * Computes the solution and error-bound to a real system of
   * linear equations
   */
  nag_linsys_real_square_solve(order, n, nrhs, a, pda, 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");
    printf("%s\n      %10.1e\n\n\n", "Estimate of condition number",
           1.0 / rcond);
    printf("%s\n      %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%s\n%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_gen (x04cac), see above. */
    fflush(stdout);
    nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                   n, a, pda, "Details of factorization", 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 pivot indices */
    printf("\n");
    printf("%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_square_solve (f04bac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(ipiv);
  return exit_status;
}