/* nag_linsys_real_symm_packed_solve (f04bjc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.1, 2024.
 */

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

int main(void) {
  /* Scalars */
  double errbnd, rcond;
  Integer exit_status, i, j, n, nrhs, pdb;

  /* Arrays */
  char nag_enum_arg[40];
  double *ap = 0, *b = 0;
  Integer *ipiv = 0;

  /* Nag types */
  NagError fail;
  Nag_OrderType order;
  Nag_UploType uplo;

#ifdef NAG_COLUMN_MAJOR
#define A_UPPER(I, J) ap[J * (J - 1) / 2 + I - 1]
#define A_LOWER(I, J) ap[(2 * n - J) * (J - 1) / 2 + I - 1]
#define B(I, J) b[(J - 1) * pdb + I - 1]
  order = Nag_ColMajor;
#else
#define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1]
#define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + 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_symm_packed_solve (f04bjc) 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 (!(ap = NAG_ALLOC(n * (n + 1) / 2, 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
    pdb = n;
#else
    pdb = nrhs;
#endif
  } else {
    printf("%s\n", "n and/or nrhs too small");
    exit_status = 1;
    return exit_status;
  }
  scanf("%39s%*[^\n] ", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  uplo = (Nag_UploType)nag_enum_name_to_value(nag_enum_arg);

  /* Read the upper or lower triangular part of the matrix A from */
  /* data file */

  if (uplo == Nag_Upper) {
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j) {
        scanf("%lf", &A_UPPER(i, j));
      }
    }
    scanf("%*[^\n] ");
  } else {
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j) {
        scanf("%lf", &A_LOWER(i, j));
      }
    }
    scanf("%*[^\n] ");
  }

  /* Read B from data file */

  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_symm_packed_solve (f04bjc).
   * Computes the solution and error-bound to a real symmetric
   * system of linear equations, packed storage
   */
  nag_linsys_real_symm_packed_solve(order, uplo, n, nrhs, ap, 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%6s%10.1e\n", "Estimate of condition number", "", 1.0 / rcond);
    printf("\n\n");
    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", "Estimate of reciprocal of condition number",
           "", rcond);
    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,
                                   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_packed (x04ccc).
     * Print real packed triangular matrix (easy-to-use)
     */
    fflush(stdout);
    nag_file_print_matrix_real_packed(order, Nag_Upper, Nag_NonUnitDiag, n, ap,
                                      "Details of factorization", 0, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_file_print_matrix_real_packed (x04ccc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

    /* Print pivot indices */
    printf("\n");
    printf("%s\n%3s", "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_symm_packed_solve (f04bjc).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(ap);
  NAG_FREE(b);
  NAG_FREE(ipiv);

  return exit_status;
}