/* nag_linsys_real_symm_solve (f04bhc) Example Program.
 *
 * Copyright 2019 Numerical Algorithms Group.
 *
 * Mark 27.0, 2019.
 */

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

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

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

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

#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_symm_solve (f04bhc) 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;
  }
  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);

  if (uplo == Nag_Upper) {
    /* Read the upper triangular part of A from data file */
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j) {
        scanf("%lf", &A(i, j));
      }
    }
    scanf("%*[^\n] ");
  }
  else {
    /* Read the lower triangular part of A from data file */
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j) {
        scanf("%lf", &A(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_solve (f04bhc).
   * Computes the solution and error-bound to a real symmetric
   * system of linear equations
   */
  nag_linsys_real_symm_solve(order, uplo, 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%s\n%6s%10.1e\n", "Estimate of condition number", "",
           1. / 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\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_UpperMatrix, 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%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_symm_solve (f04bhc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(ipiv);

  return exit_status;
}