/* nag_dggsvd (f08vac) Example Program.
 *
 * Copyright 2004 Numerical Algorithms Group.
 *
 * Mark 8, 2008.
 */

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

int main(int argc, char *argv[])
{
  FILE          *fpin, *fpout;
  char          *outfile = 0;

  /* System generated locals */
  double        d__1;


  /* Scalars */
  double        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;


#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
  /*#define a_ref(a_1,a_2) a[(a_2)*10 + a_1 - 11]
   #define b_ref(a_1,a_2) b[(a_2)*10 + a_1 - 11]
   */
  /* .. External Functions .. */

  INIT_FAIL(fail);

  /* Check for command-line IO options */
  fpin = nag_example_file_io(argc, argv, "-data", NULL);
  fpout = nag_example_file_io(argc, argv, "-results", NULL);
  (void) nag_example_file_io(argc, argv, "-nag_write", &outfile);
  fprintf(fpout, "nag_dggsvd (f08vac) Example Program Results\n\n");
  /* Skip heading in data file */
  fscanf(fpin, "%*[^\n] ");

  fscanf(fpin, "%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)))
        {
          fprintf(fpout, "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
    {
      fprintf(fpout, "%s\n", "MMAX and/or NMAX too small");
    }
  /* 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)
        {
          fscanf(fpin, "%lf", &A(i, j));
        }
    }
  fscanf(fpin, "%*[^\n] ");

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

  /* 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, &fail);
  if (fail.code == NE_NOERROR)
    {
      /* Print solution */
      irank = k + l;

      fprintf(fpout, "Number of infinite generalized singular values (K)\n");

      fprintf(fpout, "%5ld\n", k);

      fprintf(fpout, "\nNumber of finite generalized singular values (L)\n");

      fprintf(fpout, "%5ld\n", l);

      fprintf(fpout, "Numerical rank of (A**T B**T)**T (K+L)\n");

      fprintf(fpout, "%5ld\n", irank);

      fprintf(fpout, "\nFinite generalized singular values\n");

      for (j = k + 1; j <= irank; ++j)
        {
          d__1 = alpha[j - 1] / beta[j - 1];
          fprintf(fpout, "%13.4e%s", d__1, j%8 == 0 || j == irank?"\n":" ");
        }

      fprintf(fpout, "\n");
      if (outfile) fclose(fpout);
      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, outfile, &fail);
      if (outfile && !(fpout = fopen(outfile, "a")))
        {
          exit_status = 2;
          goto END;
        }
      if (fail.code != NE_NOERROR)
        {
          fprintf(fpout,
                  "Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      fprintf(fpout, "\n");
      if (outfile) fclose(fpout);
      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, outfile, &fail);
      if (outfile && !(fpout = fopen(outfile, "a")))
        {
          exit_status = 2;
          goto END;
        }
      if (fail.code != NE_NOERROR)
        {
          fprintf(fpout,
                  "Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      fprintf(fpout, "\n");
      if (outfile) fclose(fpout);
      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, outfile, &fail);
      if (outfile && !(fpout = fopen(outfile, "a")))
        {
          exit_status = 2;
          goto END;
        }
      if (fail.code != NE_NOERROR)
        {
          fprintf(fpout,
                  "Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      fprintf(fpout, "\n");
      if (outfile) fclose(fpout);
      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, outfile, &fail);
      if (outfile && !(fpout = fopen(outfile, "a")))
        {
          exit_status = 2;
          goto END;
        }
      if (fail.code != NE_NOERROR)
        {
          fprintf(fpout,
                  "Error from nag_gen_real_mat_print_comp (x04cbc).\n%s\n",
                  fail.message);
          exit_status = 1;
          goto END;
        }

      /* Call DTRCON (F07TGF) to 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)
        {
          fprintf(fpout, "Error from nag_dtrcon (f07tgc).\n%s\n", fail.message);
          exit_status = 1;
          goto END;
        }


      fprintf(fpout, "\nEstimate of reciprocal condition number for R\n");
      fprintf(fpout, "%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;

          fprintf(fpout, "Error estimate for the generalized singular values");

          fprintf(fpout, "\n%11.1e\n", serrbd);
        }
      else
        {
          fprintf(fpout, "(A**T B**T)**T is not of full rank\n");
        }
    }
  else
    {
      fprintf(fpout, "Failure in nag_dggsvd (f08vac)\n");
    }
 END:
  if (fpin != stdin) fclose(fpin);
  if (fpout != stdout) fclose(fpout);
  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);


  return exit_status;
}

#undef B
#undef A