/* nag_dgeesx (f08pbc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <stdio.h>
#include <math.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagx02.h>
#include <nagf16.h>
#include <nagf08.h>
#include <nagx04.h>

#ifdef __cplusplus
extern "C" {
#endif
  static Nag_Boolean NAG_CALL sel(const double wr, const double wi);
#ifdef __cplusplus
}
#endif

int main(void)
{

  /* Scalars */
  double        alpha, anorm, beta, eps, norm, rconde, rcondv;
  Integer       exit_status = 0, i, j, n, pda, pdd, pdc, pdvs, sdim;

  /* Arrays */
  double        *a = 0, *d = 0, *c = 0, *vs = 0, *wi = 0, *wr = 0;

  /* Nag Types */
  NagError      fail;
  Nag_OrderType order;

#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_dgeesx (f08pbc) Example Program Results\n\n");
  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%*[^\n]", &n);
  if (n < 0)
    {
      printf("Invalid n\n");
      exit_status = 1;
      goto END;;
    }

  pda = n;
  pdc = n;
  pdd = pda;
  pdvs = n;
  /* Allocate memory */
  if (!(a  = NAG_ALLOC(n * n, double)) ||
      !(d  = NAG_ALLOC(n * n, double)) ||
      !(c  = NAG_ALLOC(n * n, double)) || 
      !(vs = NAG_ALLOC(n * n, double)) ||
      !(wi = NAG_ALLOC(n, double)) ||
      !(wr = NAG_ALLOC(n, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Read in the matrix A */
  for (i = 1; i <= n; ++i)
    for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j));
  scanf("%*[^\n]");

  /* Copy A to D: nag_dge_copy (f16qfc),
   * real valued general matrix copy.
   */
  nag_dge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dge_copy (f16qfc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* nag_gen_real_mat_print (x04cac): Print Matrix A. */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n, a,
			 pda, "Matrix A", 0, &fail);
  printf("\n");
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print (x04cac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* Find the Frobenius norms of A */
  nag_dge_norm(order, Nag_FrobeniusNorm, n, n, a, pda, &anorm, &fail);
  
/* Find the Schur factorization of A using nag_dgeesx (f08pbc). */
  nag_dgeesx(order, Nag_Schur, Nag_SortEigVals, sel, Nag_RCondBoth, n, a, pda,
	     &sdim, wr, wi, vs, pdvs, &rconde, &rcondv, &fail);

  if (fail.code != NE_NOERROR && fail.code != NE_SCHUR_REORDER_SELECT)
    {
      printf("Error from nag_dgeesx (f08pbc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Reconstruct A from Schur Factorization Z*T*Trans(Z) where T is upper
   * triangular and stored in A. This can be done using the following steps:
   * i.  C = Z*T (nag_dgemm, f16yac), 
   * ii. D = D-C*trans(Z) (nag_dgemm, f16yac).
   */
  alpha = 1.0;
  beta = 0.0;
  nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, alpha, vs, pdvs, a, pda,
	    beta, c, pdc, &fail);
  if (fail.code == NE_NOERROR)
    {
      alpha = -1.0;
      beta = 1.0;
      nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, alpha, c, pdc, vs, 
                pdvs, beta, d, pdd, &fail);
    }
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
 
  /* nag_dge_norm (f16rac): Find norm of matrix difference matrix D and 
   * print warning if it is too large relative to teh norm of A
   */
  nag_dge_norm(order, Nag_OneNorm, n, n, d, pdd, &norm, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* Get the machine precision, using nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  if (norm > pow(eps,0.8)*MAX(anorm,1.0))
    {
      printf("||A-(Z*T*Z^H)||/||A|| is larger than expected.\n"
	     "Schur factorization has failed.\n");
      exit_status = 1;
      goto END;
    }

  /* Print details on eigenvalues */
  printf("Number of eigenvalues for which SELECT is true = %4ld\n\n",
	 sdim);
  if (fail.code == NE_SCHUR_REORDER_SELECT) {
    printf(" ** Note that rounding errors mean that leading eigenvalues in the"
	   " Schur form\n    no longer satisfy sel(lambda) = Nag_TRUE\n\n");
  } else {
    printf("The selected eigenvaues are:\n");
    for (i=0;i<sdim;i++) 
      printf("%3ld (%11.4e, %11.4e)\n", i+1, wr[i], wi[i]);
  }

  /* Print out the reciprocal condition numbers */
  printf("\nReciprocal of projection norm onto the invariant subspace\n");
  printf("%26sfor the selected eigenvalues rconde = %8.1e\n\n", "", rconde);
  printf("Reciprocal condition number for the invariant subspace rcondv = "
	 "%8.1e\n\n", rcondv);
          
  /* Compute the approximate asymptotic error bound on the average absolute
   * error of the selected eigenvalues given by  eps*norm(A)/rconde.
   */
  printf("Approximate asymptotic error bound for selected eigenvalues   = "
	 "%8.1e\n\n", eps * anorm / rconde);
          
  /* Compute an approximate asymptotic bound on the maximum angular error in
   * the computed invariant subspace given by  eps*norm(A)/rcondv
   */       
  printf("Approximate asymptotic error bound for the invariant subspace = "
	 "%8.1e\n", eps * anorm / rcondv);

 END:
  if (a)  NAG_FREE(a);
  if (d)  NAG_FREE(d);
  if (c)  NAG_FREE(c);
  if (vs) NAG_FREE(vs);
  if (wi) NAG_FREE(wi);
  if (wr) NAG_FREE(wr);

  return exit_status;
}

static Nag_Boolean NAG_CALL sel(const double ar, const double ai)
{
  /* Boolean function sel for use with nag_dgees (f08pac)
   * Returns the value Nag_TRUE if the imaginary part of the eigenvalue
   * (ar + ai*i) is zero, i.e. the eigenvalue is real
   */

  return (ai==0.0?Nag_TRUE:Nag_FALSE);
}