/* nag_lapackeig_dsygst (f08sec) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.1, 2023.
 */

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

int main(void) {
  /* Scalars */
  Integer i, j, n, pda, pdb, d_len, e_len, tau_len;
  Integer exit_status = 0;
  NagError fail;
  Nag_UploType uplo;
  Nag_OrderType order;
  /* Arrays */
  char nag_enum_arg[40];
  double *a = 0, *b = 0, *d = 0, *e = 0, *tau = 0;

#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_lapackeig_dsygst (f08sec) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%*[^\n] ", &n);
#ifdef NAG_COLUMN_MAJOR
  pda = n;
  pdb = n;
#else
  pda = n;
  pdb = n;
#endif
  d_len = n;
  e_len = n - 1;
  tau_len = n - 1;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * n, double)) ||
      !(d = NAG_ALLOC(d_len, double)) || !(e = NAG_ALLOC(e_len, double)) ||
      !(tau = NAG_ALLOC(tau_len, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }
  /* Read A and B from data file */
  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) {
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j)
        scanf("%lf", &A(i, j));
    }
    scanf("%*[^\n] ");
    for (i = 1; i <= n; ++i) {
      for (j = i; j <= n; ++j)
        scanf("%lf", &B(i, j));
    }
    scanf("%*[^\n] ");
  } else {
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j)
        scanf("%lf", &A(i, j));
    }
    scanf("%*[^\n] ");
    for (i = 1; i <= n; ++i) {
      for (j = 1; j <= i; ++j)
        scanf("%lf", &B(i, j));
    }
    scanf("%*[^\n] ");
  }

  /* Compute the Cholesky factorization of B */
  /* nag_lapacklin_dpotrf (f07fdc).
   * Cholesky factorization of real symmetric
   * positive-definite matrix
   */
  nag_lapacklin_dpotrf(order, uplo, n, b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_dpotrf (f07fdc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Reduce the problem to standard form C*y = lambda*y, storing */
  /* the result in A */
  /* nag_lapackeig_dsygst (f08sec).
   * Reduction to standard form of real symmetric-definite
   * generalized eigenproblem Ax = lambda Bx, ABx = lambda x
   * or BAx = lambda x, B factorized by nag_lapacklin_dpotrf (f07fdc)
   */
  nag_lapackeig_dsygst(order, Nag_Compute_1, uplo, n, a, pda, b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsygst (f08sec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Reduce C to tridiagonal form T = (Q^T)*C*Q */
  /* nag_lapackeig_dsytrd (f08fec).
   * Orthogonal reduction of real symmetric matrix to
   * symmetric tridiagonal form
   */
  nag_lapackeig_dsytrd(order, uplo, n, a, pda, d, e, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsytrd (f08fec).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Calculate the eigenvalues of T (same as C) */
  /* nag_lapackeig_dsterf (f08jfc).
   * All eigenvalues of real symmetric tridiagonal matrix,
   * root-free variant of QL or QR
   */
  nag_lapackeig_dsterf(n, d, e, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsterf (f08jfc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Print eigenvalues */
  printf("Eigenvalues\n");
  for (i = 1; i <= n; ++i)
    printf("%8.4f%s", d[i - 1], i % 9 == 0 ? "\n" : " ");
  printf("\n");
END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(d);
  NAG_FREE(e);
  NAG_FREE(tau);

  return exit_status;
}