/* nag_lapackeig_dsygv (f08sac) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.2, 2023.
 */

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

int main(void) {

  /* Scalars */
  double anorm, bnorm, eps, rcond, rcondb, t1, t2, t3;
  Integer exit_status = 0, i, j, n, pda, pdb;

  /* Arrays */
  double *a = 0, *b = 0, *eerbnd = 0, *rcondz = 0, *w = 0, *zerbnd = 0;
  char nag_enum_arg[40];

  /* 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

  INIT_FAIL(fail);

  printf("nag_lapackeig_dsygv (f08sac) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%*[^\n]", &n);
  if (n < 0) {
    printf("Invalid n\n");
    exit_status = 1;
    goto END;
    ;
  }
  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);

  pda = n;
  pdb = n;
  /* Allocate memory */
  if (!(a = NAG_ALLOC(n * n, double)) || !(b = NAG_ALLOC(n * n, double)) ||
      !(eerbnd = NAG_ALLOC(n, double)) || !(rcondz = NAG_ALLOC(n, double)) ||
      !(w = NAG_ALLOC(n, double)) || !(zerbnd = NAG_ALLOC(n, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read the triangular parts of the matrices A and B */
  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));
  } 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 one-norms of the symmetric matrices A and B */
  nag_blast_dsy_norm(order, Nag_OneNorm, uplo, n, a, pda, &anorm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dsy_norm (f16rcc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  nag_blast_dsy_norm(order, Nag_OneNorm, uplo, n, b, pdb, &bnorm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dsy_norm (f16rcc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Solve the generalized symmetric eigenvalue problem  A*x = lambda*B*x
   * using nag_lapackeig_dsygv (f08sac).
   */
  nag_lapackeig_dsygv(order, 1, Nag_DoBoth, uplo, n, a, pda, b, pdb, w, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dsygv (f08sac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Normalize the eigenvectors */
  for (j = 1; j <= n; j++)
    for (i = n; i >= 1; i--)
      A(i, j) = A(i, j) / A(1, j);

  /* Print eigensolution */
  printf(" Eigenvalues\n   ");
  for (j = 0; j < n; ++j)
    printf(" %10.4f%s", w[j], j % 6 == 5 ? "\n" : "");
  printf("\n\n");

  /* Print the normalized eigenvectors using nag_file_print_matrix_real_gen
   * (x04cac). */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 n, a, pda, "Eigenvectors", 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;
  }

  /* Estimate the reciprocal condition number of the Cholesky factor of B.
   * nag_lapacklin_dtrcon (f07tgc)
   * Note that: cond(B) = 1.0/(rcond*rcond)
   */
  nag_lapacklin_dtrcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, b, pdb,
                       &rcond, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_dtrcon (f07tgc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  rcondb = rcond * rcond;
  printf("\nEstimate of reciprocal condition number for B\n%15.1e\n", rcondb);

  /* Get the machine precision, using nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  if (rcond < eps) {
    printf("\nB is very ill-conditioned, error estimates have not been "
           "computed\n");
    goto END;
  }

  /* Estimate reciprocal condition numbers for the eigenvectors of A-lambda*B
   * nag_lapackeig_ddisna (f08flc).
   */
  nag_lapackeig_ddisna(Nag_EigVecs, n, n, w, rcondz, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_ddisna (f08flc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Compute the error estimates for the eigenvalues and eigenvectors */
  t1 = eps / rcondb;
  t2 = anorm / bnorm;
  t3 = t2 / rcond;
  for (i = 0; i < n; ++i) {
    eerbnd[i] = t1 * (t2 + fabs(w[i]));
    zerbnd[i] = t1 * (t3 + fabs(w[i])) / rcondz[i];
  }

  /* Print the approximate error bounds for the eigenvalues and vectors */
  printf("\nError estimates for the eigenvalues\n    ");
  for (i = 0; i < n; ++i)
    printf(" %10.1e%s", eerbnd[i], i % 6 == 5 ? "\n" : "");

  printf("\n\nError estimates for the eigenvectors\n    ");
  for (i = 0; i < n; ++i)
    printf(" %10.1e%s", zerbnd[i], i % 6 == 5 ? "\n" : "");
  printf("\n");

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(eerbnd);
  NAG_FREE(rcondz);
  NAG_FREE(w);
  NAG_FREE(zerbnd);

  return exit_status;
}