/* nag_dgges (f08xac) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

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

#ifdef __cplusplus
extern "C" {
#endif
  static Nag_Boolean NAG_CALL delctg(const double ar, const double ai,
				     const double b);
#ifdef __cplusplus
}
#endif

int main(void)
{
  /* Scalars */
  Integer           exit_status = 0;
  Integer           i, j, n, sdim, pda, pdb, pdc, pdd, pde, pdvsl, pdvsr;
  double            dg_a, dg_b, eps, small, norma, normb, normd, norme;
  /* Arrays */
  double            *a = 0, *alphai = 0, *alphar = 0, *b = 0, *beta = 0;
  double            *c = 0, *d = 0, *e = 0, *vsl = 0, *vsr = 0;
  char              nag_enum_arg[40];

  /* Nag Types */
  NagError          fail;
  Nag_OrderType     order;
  Nag_LeftVecsType  jobvsl;
  Nag_RightVecsType jobvsr;


#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_dgges (f08xac) 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;
    }
  scanf(" %s%*[^\n]", nag_enum_arg);
  /* nag_enum_name_to_value(x04nac).
   * Converts NAG enum member name to value
   */
  jobvsl = (Nag_LeftVecsType) nag_enum_name_to_value(nag_enum_arg);
  scanf(" %s%*[^\n]", nag_enum_arg);
  jobvsr = (Nag_RightVecsType) nag_enum_name_to_value(nag_enum_arg);

  pdvsl = (jobvsl==Nag_LeftVecs?n:1);
  pdvsr = (jobvsr==Nag_RightVecs?n:1);
  pda = n;
  pdb = n;
  pdc = n;
  pdd = pda;
  pde = pdb;
  /* Allocate memory */
  if (!(a =      NAG_ALLOC(n*n, double)) ||
      !(b =      NAG_ALLOC(n*n, double)) ||
      !(c =      NAG_ALLOC(n*n, double)) ||
      !(d =      NAG_ALLOC(n*n, double)) ||
      !(e =      NAG_ALLOC(n*n, double)) ||
      !(alphai = NAG_ALLOC(n, double)) ||
      !(alphar = NAG_ALLOC(n, double)) ||
      !(beta =   NAG_ALLOC(n, double)) ||
      !(vsl =    NAG_ALLOC(pdvsl*pdvsl, double)) ||
      !(vsr =    NAG_ALLOC(pdvsr*pdvsr, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

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

  /* nag_dge_norm (f16rac): Find norms of input matrices A and B. */
  nag_dge_norm(order, Nag_OneNorm, n, n, a, pda, &norma, &fail);
  nag_dge_norm(order, Nag_OneNorm, n, n, b, pdb, &normb, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Copy matrices A and B to matrices D and E using nag_dge_copy (f16qfc),
   * real valued general matrix copy.
   * The copies will be used as comparison against reconstructed matrices.
   */
  nag_dge_copy(order, Nag_NoTrans, n, n, a, pda, d, pdd, &fail);
  if (fail.code == NE_NOERROR) 
    {
      nag_dge_copy(order, Nag_NoTrans, n, n, b, pdb, e, pde, &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 Matrices A and B. */
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n,
			 a, pda, "Matrix A", 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;
    }
  printf("\n");
  fflush(stdout);
  nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, n,
			 b, pdb, "Matrix B", 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;
    }
  printf("\n");
  fflush(stdout);

  /* Find the generalized Schur form using nag_dgges (f08xac). */
  nag_dgges(order, jobvsl, jobvsr, Nag_SortEigVals, delctg, n, a, pda, b, pdb,
	    &sdim, alphar, alphai, beta, vsl, pdvsl, vsr, pdvsr, &fail);

  if (fail.code != NE_NOERROR && fail.code != NE_SCHUR_REORDER_SELECT)
    {
      printf("Error from nag_dgges (f08xac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  printf("Number of sorted eigenvalues = %4ld\n\n", sdim);

  /* nag_real_safe_small_number (x02amc), nag_machine_precision (x02ajc) */
  eps = nag_machine_precision;
  small = nag_real_safe_small_number;

  /* Print the eigenvalues */
  printf("     Eigenvalues\n");
  for (j = 0; j < n; ++j)
    {
      printf("%2ld ", j+1);
      if ((fabs(alphar[j]) + fabs(alphai[j])) * small >= fabs(beta[j]))
	printf("  infinite or undetermined, alpha = (%11.4e, %11.4e), "
	       "beta = %11.4e\n", alphar[j], alphai[j], beta[j]);
      else if (alphai[j] == 0.0)
	printf("  %12.4e\n", alphar[j]/beta[j]);
      else
	printf("  (%11.4e, %11.4e)\n", alphar[j]/beta[j], alphai[j]/beta[j]);
    }

  /* Check generalized Schur Form by reconstruction of Schur vectors are
   * available.
   */
  if (jobvsl==Nag_NotLeftVecs || jobvsr==Nag_NotRightVecs)
    {
      /* Cannot check factorization by reconstruction Schur vectors. */
      goto END;
    }

  /* Reconstruct A as Q*S*Z^T and subtract from original (D) using the steps
   * C = Q*S (Q in vsl, S in a) using nag_dgemm (f16yac).
   *         Note: not nag_dtrmm since S may not be strictly triangular.
   * D = D - C*Z^T (Z in vsr) using nag_dgemm (f16yac).
   */
  dg_a = 1.0;
  dg_b = 0.0;
  nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, dg_a, vsl, pdvsl, a, pda,
	    dg_b, c, pdc, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgemm (f16yac).\n%s\n",  fail.message);
      exit_status = 1;
      goto END;
    }
  dg_a = -1.0;
  dg_b = 1.0;
  nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, dg_a, c, pdc, vsr, pdvsr,
	    dg_b, d, pdd, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Reconstruct B as Q*T*Z^T and subtract from original (E) using the steps
   * C = Q*T (Q in vsl, T in b) using nag_dgemm (f16yac).
   * E = E - C*Z^T (Z in vsr) using nag_dgemm (f16yac).
   */
  dg_a = 1.0;
  dg_b = 0.0;
  nag_dgemm(order, Nag_NoTrans, Nag_NoTrans, n, n, n, dg_a, vsl, pdvsl, b, pdb,
	    dg_b, c, pdc, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgemm (f16yac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  dg_a = -1.0;
  dg_b = 1.0;
  nag_dgemm(order, Nag_NoTrans, Nag_Trans, n, n, n, dg_a, c, pdc, vsr, pdvsr,
	    dg_b, e, pde, &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 norms of difference matrices D and E. */
  nag_dge_norm(order, Nag_OneNorm, n, n, d, pdd, &normd, &fail);
  nag_dge_norm(order, Nag_OneNorm, n, n, e, pde, &norme, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dge_norm (f16rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  if (MAX(normd,norme) > pow(eps,0.8)*MAX(norma,normb))
    {
      printf("The norm of the error in the reconstructed matrices is greater "
	     "than expected.\nThe Schur factorization has failed.\n");
      exit_status = 1;
      goto END;
    }
  if (fail.code == NE_SCHUR_REORDER_SELECT)
    printf("*** Note that rounding errors mean that leading eigenvalues in the"
	   " generalized\n    Schur form no longer satisfy delctg = Nag_TRUE\n\n");
 END:
  if (a)      NAG_FREE(a);
  if (b)      NAG_FREE(b);
  if (c)      NAG_FREE(c);
  if (d)      NAG_FREE(d);
  if (e)      NAG_FREE(e);
  if (alphai) NAG_FREE(alphai);
  if (alphar) NAG_FREE(alphar);
  if (beta)   NAG_FREE(beta);
  if (vsl)    NAG_FREE(vsl);
  if (vsr)    NAG_FREE(vsr);

  return exit_status;
}

#undef B
#undef A


static Nag_Boolean NAG_CALL delctg(const double ar, const double ai,
				   const double b)
{
  /* Logical function delctg for use with nag_dgges (f08xac).
   *
   * Returns the value Nag_TRUE if the eigenvalue is real.
   */

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