/* nag_dopmtr (f08ggc) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf08.h>
#include <nagx04.h>

int main(void)
{
  /* Scalars */
  Integer       ap_len, i, j, m, n, nsplit, pdz, d_len, e_len;
  Integer       tau_len;
  Integer       exit_status = 0;
  double        vl = 0.0, vu = 0.0;
  NagError      fail;
  Nag_UploType  uplo;
  Nag_OrderType order;
  /* Arrays */
  char          nag_enum_arg[40];
  Integer       *iblock = 0, *ifailv = 0, *isplit = 0;
  double        *ap = 0, *d = 0, *e = 0, *tau = 0, *w = 0, *z = 0;
  
#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 Z(I, J) z[(J - 1) * pdz + I - 1]
  order = Nag_ColMajor;
#else
#define A_LOWER(I, J) ap[I * (I - 1) / 2 + J - 1]
#define A_UPPER(I, J) ap[(2 * n - I) * (I - 1) / 2 + J - 1]
#define Z(I, J) z[(I - 1) * pdz + J - 1]
  order = Nag_RowMajor;
#endif
  
  INIT_FAIL(fail);
  
  printf("nag_dopmtr (f08ggc) Example Program Results\n\n");
  
  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%ld%*[^\n] ", &n);
  pdz = n;
  
  ap_len = n*(n+1)/2;
  tau_len = n-1;
  d_len = n;
  e_len = n-1;
  /* Allocate memory */
  if (!(ap = NAG_ALLOC(ap_len, double)) ||
      !(d = NAG_ALLOC(d_len, double)) ||
      !(e = NAG_ALLOC(e_len, double)) ||
      !(iblock = NAG_ALLOC(n, Integer)) ||
      !(ifailv = NAG_ALLOC(n, Integer)) ||
      !(isplit = NAG_ALLOC(n, Integer)) ||
      !(w = NAG_ALLOC(n, double)) ||
      !(tau = NAG_ALLOC(tau_len, double)) ||
      !(z = NAG_ALLOC(n * n, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
  
  /* Read A from data file */
  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);
  if (uplo == Nag_Upper)
    {
      for (i = 1; i <= n; ++i)
        {
          for (j = i; j <= n; ++j)
            scanf("%lf", &A_UPPER(i, j));
        }
      scanf("%*[^\n] ");
    }
  else
    {
      for (i = 1; i <= n; ++i)
        {
          for (j = 1; j <= i; ++j)
            scanf("%lf", &A_LOWER(i, j));
        }
      scanf("%*[^\n] ");
    }
  
  /* Reduce A to tridiagonal form T = (Q**T)*A*Q */
  /* nag_dsptrd (f08gec).
   * Orthogonal reduction of real symmetric matrix to
   * symmetric tridiagonal form, packed storage
   */
  nag_dsptrd(order, uplo, n, ap, d, e, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dsptrd (f08gec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* Calculate the two smallest eigenvalues of T (same as A) */
  /* nag_dstebz (f08jjc).
   * Selected eigenvalues of real symmetric tridiagonal matrix
   * by bisection
   */
  nag_dstebz(Nag_Indices, Nag_ByBlock, n, vl, vu, 1, 2, 0.0,
             d, e, &m, &nsplit, w, iblock, isplit, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dstebz (f08jjc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* Print eigenvalues */
  printf("Eigenvalues\n");
  for (i = 0; i < m; ++i)
    printf("%8.4f%s", w[i], (i+1)%8 == 0?"\n":" ");
  printf("\n\n");
  /* Calculate the eigenvectors of T storing the result in Z */
  /* nag_dstein (f08jkc).
   * Selected eigenvectors of real symmetric tridiagonal
   * matrix by inverse iteration, storing eigenvectors in real
   * array
   */
  nag_dstein(order, n, d, e, m, w, iblock, isplit, z, pdz, ifailv,
             &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dstein (f08jkc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* Calculate all the eigenvectors of A = Q*(eigenvectors of T) */
  /* nag_dopmtr (f08ggc).
   * Apply orthogonal transformation determined by nag_dsptrd
   * (f08gec)
   */
  nag_dopmtr(order, Nag_LeftSide, uplo, Nag_NoTrans, n, m, ap,
             tau, z, pdz, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dopmtr (f08ggc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* Normalize the eigenvectors */
  for(j=1; j<=m; j++)
    {
      for(i=n; i>=1; i--)
        {
          Z(i, j) = Z(i, j) / Z(1,j);
        }
    }  
  /* Print eigenvectors */
  /* nag_gen_real_mat_print (x04cac).
   * Print real general matrix (easy-to-use)
   */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, m, z,
                         pdz, "Eigenvectors", 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }
 END:
  if (ap) NAG_FREE(ap);
  if (d) NAG_FREE(d);
  if (e) NAG_FREE(e);
  if (iblock) NAG_FREE(iblock);
  if (ifailv) NAG_FREE(ifailv);
  if (isplit) NAG_FREE(isplit);
  if (tau) NAG_FREE(tau);
  if (w) NAG_FREE(w);
  if (z) NAG_FREE(z);
  
  return exit_status;
}