/* nag_dggsvd (f08vac) Example Program.
 *
 * Copyright 2004 Numerical Algorithms Group.
 *
 * Mark 9, 2009.
 */

#include <stdio.h>
#include <nag.h>
#include <nagf08.h>
#include <nagx04.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagx02.h>

int main(void)
{

  /* Scalars */
  double        d, eps, rcond, serrbd;
  Integer       exit_status = 0, i, irank, j, k, l, m, n, p,
                pda, pdb, pdq, pdu, pdv;
  NagError      fail;
  Nag_OrderType order;

  /* Arrays */
  double        *a = 0, *alpha = 0, *b = 0, *beta = 0, *q = 0, *u = 0, *v = 0;
  Integer       *iwork = 0;

#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_dggsvd (f08vac) Example Program Results\n\n");
  /* Skip heading in data file */
  scanf("%*[^\n] ");

  scanf("%ld%ld%ld%*[^\n] ", &m, &n, &p);
  if (m <= 10 && n <= 10 && p <= 10)
    {
      /* Allocate memory */
      if (!(a = NAG_ALLOC(m*n, double)) ||
          !(alpha = NAG_ALLOC(n, double)) ||
          !(b = NAG_ALLOC(p*n, double)) ||
          !(beta = NAG_ALLOC(n, double)) ||
          !(q = NAG_ALLOC(n*n, double)) ||
          !(u = NAG_ALLOC(m*m, double)) ||
          !(v = NAG_ALLOC(p*p, double)) ||
	  !(iwork = NAG_ALLOC(n, Integer)) )
        {
          printf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
#ifdef NAG_COLUMN_MAJOR
      pda = m;
      pdb = p;
      pdq = n;
      pdu = m;
      pdv = p;
#else
      pda = n;
      pdb = n;
      pdq = n;
      pdu = m;
      pdv = p;
#endif
    }
  else
    {
      printf("m and/or n too small\n");
      goto END;
    }
  /* Read the m by n matrix A and p by n matrix B from data file */
  for (i = 1; i <= m; ++i)
    for (j = 1; j <= n; ++j) scanf("%lf", &A(i, j));
  scanf("%*[^\n] ");

  for (i = 1; i <= p; ++i)
    for (j = 1; j <= n; ++j) scanf("%lf", &B(i, j));
  scanf("%*[^\n] ");

  /* nag_dggsvd (f08vac)
   * Compute the generalized singular value decomposition of (A, B)
   * (A = U*D1*(0 R)*(Q**T), B = V*D2*(0 R)*(Q**T), m.ge.n)
   */

  nag_dggsvd(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, n, p, &k, &l, a,
             pda, b, pdb, alpha, beta, u, pdu, v, pdv, q, pdq, iwork, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dggsvd (f08vac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  /* Print solution */
  irank = k + l;

  printf("Number of infinite generalized singular values (K)\n");
  printf("%5ld\n", k);
  printf("\nNumber of finite generalized singular values (L)\n");
  printf("%5ld\n", l);
  printf("Numerical rank of (A**T B**T)**T (K+L)\n");
  printf("%5ld\n", irank);

  printf("\nFinite generalized singular values\n");
  for (j = k; j < irank; ++j)
    {
      d = alpha[j] / beta[j];
      printf("%13.4e%s", d, (j+1)%8 == 0 || (j+1) == irank?"\n":" ");
    }
  
  printf("\n");
  fflush(stdout);
  nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
			      m, u, pdu, "%13.4e", "Orthogonal matrix U",
			      Nag_IntegerLabels, 0, Nag_IntegerLabels, 0,
			      80, 0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
	     fail.message);
      exit_status = 1;
      goto END;
    }

  printf("\n");
  fflush(stdout);
  nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, p,
			      p, v, pdv, "%13.4e", "Orthogonal matrix V",
			      Nag_IntegerLabels, 0, Nag_IntegerLabels, 0,
			      80, 0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
	     fail.message);
      exit_status = 1;
      goto END;
    }

  printf("\n");
  fflush(stdout);
  nag_gen_real_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
			      n, q, pdq, "%13.4e", "Orthogonal matrix Q",
			      Nag_IntegerLabels, 0, Nag_IntegerLabels, 0,
			      80, 0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
	     fail.message);
      exit_status = 1;
      goto END;
    }

  printf("\n");
  fflush(stdout);
  nag_gen_real_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag, irank,
			      irank, &A(1, n - irank + 1), pda, "%13.4e",
			      "Non singular upper triangular matrix R",
			      Nag_IntegerLabels, 0, Nag_IntegerLabels, 0,
			      80, 0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
	     fail.message);
      exit_status = 1;
      goto END;
    }

  /* nag_dtrcon (f07tgc)
   * estimate the reciprocal condition number of R
   */

  nag_dtrcon(order, Nag_InfNorm, Nag_Upper, Nag_NonUnitDiag, irank,
	     &A(1, n - irank + 1), pda, &rcond, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dtrcon (f07tgc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }


  printf("\nEstimate of reciprocal condition number for R\n");
  printf("%11.1e\n\n", rcond);

  /* So long as irank = n, get the machine precision, eps, and compute the
   * approximate error bound for the computed generalized singular values
   */
  if (irank == n)
    {
      eps = nag_machine_precision;
      serrbd = eps / rcond;
      printf("Error estimate for the generalized singular values");
      printf("\n%11.1e\n", serrbd);
    }
  else
    {
      printf("(A**T B**T)**T is not of full rank\n");
    }

 END:
  if (a) NAG_FREE(a);
  if (alpha) NAG_FREE(alpha);
  if (b) NAG_FREE(b);
  if (beta) NAG_FREE(beta);
  if (q) NAG_FREE(q);
  if (u) NAG_FREE(u);
  if (v) NAG_FREE(v);
  if (iwork) NAG_FREE(iwork);

  return exit_status;
}

#undef B
#undef A