/* nag_dggsvp (f08vec) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

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

int main(void)
{
  /* Scalars */
  double        eps, norm, tola, tolb;
  Integer       i, irank, j, k, l, m, n, nrows, p, pda, pdb, pdq, pdu, pdv;
  Integer       exit_status = 0;
  /* Arrays */
  double        *a = 0, *b = 0, *q = 0, *u = 0, *v = 0;

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

#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_dggsvp (f08vec) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%ld%ld%*[^\n]", &m, &n, &p);
  if (n < 0 || m < 0 || p < 0)
    {
      printf("Invalid n, m or p\n");
      exit_status = 1;
      goto END;
    }

#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = p;
  pdv = p;
#else
  pda = n;
  pdb = n;
  pdv = m;
#endif
  pdq = n;
  pdu = m;

  /* Allocate memory */
  if (!(a = NAG_ALLOC(m*n, double)) ||
      !(b = NAG_ALLOC(p*n, double)) ||
      !(q = NAG_ALLOC(n*n, double)) ||
      !(u = NAG_ALLOC(m*m, double)) ||
      !(v = NAG_ALLOC(p*m, double)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      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]");

  /* get norms of A and B using nag_dge_norm (f16rac). */
  nag_dge_norm(order, Nag_OneNorm, m, n, a, pda, &norm, &fail);
  nag_dge_norm(order, Nag_OneNorm, p, n, b, pdb, &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;

  tola = MAX(m, n) * norm  * eps;
  tolb = MAX(p, n) * norm  * eps;

  /* Compute the factorization of (A, B) (A = U*S*(Q**T), B = V*T*(Q**T))
   * using nag_dggsvp (f08vec).
   */
  nag_dggsvp(order, Nag_AllU, Nag_ComputeV, Nag_ComputeQ, m, p, n, a, pda, b,
             pdb, tola, tolb, &k, &l, u, pdu, v, pdv, q, pdq, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dggsvp (f08vec).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print details of the generalizeed SVD */
  irank = k + l;
  printf("Numerical rank of (A**T B**T)**T (K+L)\n%5ld\n\n", irank);
  nrows = MIN(m,irank);
  fflush(stdout);
  nag_gen_real_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag, nrows,
			      irank, &A(1, n - irank + 1), pda, "%13.4e",
			      "Matrix S", Nag_IntegerLabels, 0,
			      Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  if (fail.code != NE_NOERROR) goto FAIL;
  printf("\n");
  fflush(stdout);
  nag_gen_real_mat_print_comp(order, Nag_UpperMatrix, Nag_NonUnitDiag, l, l,
			      &B(1, n - l + 1), pdb, "%13.4e",
			      "Upper triangular matrix T", Nag_IntegerLabels,
			      0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  if (fail.code != NE_NOERROR) goto FAIL;
  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) goto FAIL;
  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) goto FAIL;
  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);
 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;
    }

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

  return exit_status;
}