/* nag_zhpgv (f08tnc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <math.h>
#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx02.h>

int main(void)
{
  /* Scalars */
  double        anorm, bnorm, eps, rcond, rcondb, t1, t2;
  Integer       i, j, n;
  Integer       exit_status = 0;
  /* Arrays */
  Complex       *ap = 0, *bp = 0;
  Complex       dummy[1];
  double        *eerbnd = 0, *w = 0;
  char          nag_enum_arg[40];

  /* 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_UPPER(I, J) bp[J*(J-1)/2 + I - 1]
#define B_LOWER(I, J) bp[(2*n-J)*(J-1)/2 + I - 1]
  order = Nag_ColMajor;
#else
#define A_UPPER(I, J) ap[(2*n-I)*(I-1)/2 + J - 1]
#define A_LOWER(I, J) ap[I*(I-1)/2 + J - 1]
#define B_UPPER(I, J) bp[(2*n-I)*(I-1)/2 + J - 1]
#define B_LOWER(I, J) bp[I*(I-1)/2 + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);


  printf("nag_zhpgv (f08tnc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%*[^\n]", &n);
  scanf(" %s%*[^\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);

  /* Allocate memory */
  if (!(ap     = NAG_ALLOC(n*(n+1)/2, Complex)) ||
      !(bp     = NAG_ALLOC(n*(n+1)/2, Complex)) ||
      !(eerbnd = NAG_ALLOC(n, double)) ||
      !(w      = NAG_ALLOC(n, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Read the triangular parts of the matrices A and B from data file. */
  if (uplo == Nag_Upper)
    {
      for (i = 1; i <= n; ++i)
	for (j = i; j <= n; ++j)
	  scanf(" ( %lf , %lf )", &A_UPPER(i, j).re, &A_UPPER(i, j).im);
      scanf("%*[^\n]");
      for (i = 1; i <= n; ++i)
	for (j = i; j <= n; ++j)
	  scanf(" ( %lf , %lf )", &B_UPPER(i, j).re, &B_UPPER(i, j).im);
    }
  else if (uplo == Nag_Lower)
    {
      for (i = 1; i <= n; ++i)
	for (j = 1; j <= i; ++j)
	  scanf(" ( %lf , %lf )", &A_LOWER(i, j).re, &A_LOWER(i, j).im);
      scanf("%*[^\n]");
      for (i = 1; i <= n; ++i)
	for (j = 1; j <= i; ++j)
	  scanf(" ( %lf , %lf )", &B_LOWER(i, j).re, &B_LOWER(i, j).im);
    }
  scanf("%*[^\n]");

  /* Compute the one-norms of the symmetric matrices A and B 
  * using nag_zhp_norm (f16udc). */
  nag_zhp_norm(order, Nag_OneNorm, uplo, n, ap, &anorm, &fail);
  nag_zhp_norm(order, Nag_OneNorm, uplo, n, bp, &bnorm, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zhp_norm (f16udc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Solve the generalized symmetric eigenvalue problem
   * A*x = lambda*B*x (itype = 1)
   */
  nag_zhpgv(order, 1, Nag_EigVals, uplo, n, ap, bp, w, dummy, 1, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zhpgv (f08tnc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print eigensolution */
  printf("Eigenvalues\n  ");
  for (j = 0; j < n; ++j) printf(" %11.4f%s", w[j], j%6 == 5?"\n":"");
  printf("\n\n");

  /* Estimate the reciprocal condition  number of the Cholesky factor of B.
   * nag_ztpcon (f07uuc).
   * Note that: cond(B) = 1/rcond**2
   */
  nag_ztpcon(order, Nag_OneNorm, uplo, Nag_NonUnitDiag, n, bp, &rcond, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_ztpcon (f07uuc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print the reciprocal condition number of B */
  rcondb = rcond * rcond;
  printf("Estimate of reciprocal condition number for B\n    %11.1e\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;
    }

  t1 = eps / rcondb;
  t2 = anorm / bnorm;
  for (i = 0; i < n; ++i) eerbnd[i] = t1 * (t2 + fabs(w[i]));

  /* Print the approximate error bounds for the eigenvalues */
  printf("\nError estimates for the eigenvalues\n    ");
  for (i = 0; i < n; ++i) printf("%11.1e%s", eerbnd[i], i%6 == 5?"\n":"");
  printf("\n");

 END:
  if (ap)     NAG_FREE(ap);
  if (bp)     NAG_FREE(bp);
  if (eerbnd) NAG_FREE(eerbnd);
  if (w)      NAG_FREE(w);

  return exit_status;
}