/* nag_zheev (f08fnc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <math.h>
#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagx02.h>
#include <nagx04.h>

int main(void)
{  
  /* Scalars */
  double        eerrbd, eps;
  Integer       exit_status = 0, i, j, n, pda;
  /* Arrays */
  Complex       *a = 0;
  double        *rcondz = 0, *w = 0, *zerrbd = 0;
  /* Nag Types */
  Nag_OrderType order;
  NagError      fail;

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
  order = Nag_RowMajor;
#endif
  
  INIT_FAIL(fail);
  
  printf("nag_zheev (f08fnc) Example Program Results\n\n");
  
  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%*[^\n]", &n);
  
  /* Allocate memory */
  if (!(a = NAG_ALLOC(n*n, Complex)) ||
      !(rcondz = NAG_ALLOC(n, double)) ||
      !(w = NAG_ALLOC(n, double)) ||
      !(zerrbd = NAG_ALLOC(n, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
  
#ifdef NAG_COLUMN_MAJOR
  pda = n;
#else
  pda = n;
#endif
  
  /* Read the upper triangular part of the matrix A from data file */
  for (i = 1; i <= n; ++i)
    for (j = i; j <= n; ++j)
      scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
  scanf("%*[^\n]");
  
  /* nag_zheev (f08fnc).
   * Solve the Hermitian eigenvalue problem.
   */
  nag_zheev(order, Nag_DoBoth, Nag_Upper, n, a, pda, w, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zheev (f08fnc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* nag_complex_divide (a02cdc).
   * Normalize the eigenvectors.
   */
  for(j=1; j<=n; j++)
    for(i=n; i>=1; i--)
      A(i, j) = nag_complex_divide(A(i, j),A(1, j));
  
  /* Print solution */
  printf("Eigenvalues\n");
  for (j = 0; j < n; ++j)
    printf("%8.4f%s", w[j], (j+1)%8 == 0?"\n":" ");
  printf("\n\n");
 
  /* nag_gen_complx_mat_print (x04dac).
   * Print eigenvectors.
   */
  fflush(stdout);
  nag_gen_complx_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                           n, a, pda, "Eigenvectors", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_complx_mat_print (x04dac).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* Get the machine precision, eps, using nag_machine_precision (X02AJC)
   * and compute the approximate error bound for the computed eigenvalues. 
   * Note that for the 2-norm, ||A|| = max {|w[i]|, i=0..n-1}, and since    
   * the eigenvalues are in ascending order ||A|| = max( |w[0]|, |w[n-1]|).
   */
  eps = nag_machine_precision;
  eerrbd = eps * MAX(fabs(w[0]), fabs(w[n-1]));
  
  /* nag_ddisna (f08flc).
   * Estimate reciprocal condition numbers for the eigenvectors.
   */
  nag_ddisna(Nag_EigVecs, n, n, w, rcondz, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_ddisna (f08flc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* Compute the error estimates for the eigenvectors */
  for (i = 0; i < n; ++i)
    zerrbd[i] = eerrbd / rcondz[i];
  
  /* Print the approximate error bounds for the eigenvalues and vectors */
  printf("\nError estimate for the eigenvalues\n");
  printf("%11.1e\n\n", eerrbd);
  
  printf("Error estimates for the eigenvectors\n");
  for (i = 0; i < n; ++i)
    printf("%11.1e%s", zerrbd[i], (i+1)%6 == 0?"\n":" ");
  
 END:
  if (a) NAG_FREE(a);
  if (rcondz) NAG_FREE(rcondz);
  if (w) NAG_FREE(w);
  if (zerrbd) NAG_FREE(zerrbd);
  
  return exit_status;
}

#undef A