/* nag_dormbr (f08kgc) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

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

int main(void)
{
  /* Scalars */
  Integer  i, ic, j, m, n, pda, pdpt, pdu;
  Integer  d_len, e_len, tau_len, tauq_len, taup_len;
  Integer  exit_status=0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  double *a=0, *d=0, *e=0, *pt=0, *tau=0, *taup=0, *tauq=0, *u=0;

#ifdef NAG_COLUMN_MAJOR
#define A(I,J) a[(J-1)*pda + I - 1]
#define U(I,J) u[(J-1)*pdu + I - 1]
#define PT(I,J) pt[(J-1)*pdpt + I - 1]
  order = Nag_ColMajor;
#else
#define A(I,J) a[(I-1)*pda + J - 1]
#define U(I,J) u[(I-1)*pdu + J - 1]
#define PT(I,J) pt[(I-1)*pdpt + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);
  Vprintf("nag_dormbr (f08kgc) Example Program Results\n");

  /* Skip heading in data file */
  Vscanf("%*[^\n] ");
  for (ic = 1; ic <= 2; ++ic)
    {
      Vscanf("%ld%ld%*[^\n] ", &m, &n);

#ifdef NAG_COLUMN_MAJOR
      pda = m;
      pdu = m;
      pdpt = n;
      taup_len = n;
      tauq_len = n;
      tau_len = n;
      d_len =  n;
      e_len =  n-1;
#else
      pda = n;
      pdu = m;
      pdpt = n;
      taup_len = n;
      tauq_len = n;
      tau_len = n;
      d_len =  n;
      e_len =  n-1;
#endif

      /* Allocate memory */
      if ( !(a = NAG_ALLOC(m * n, double)) ||
           !(d = NAG_ALLOC(d_len, double)) ||
           !(e = NAG_ALLOC(e_len, double)) ||
           !(pt = NAG_ALLOC(n * n, double)) ||
           !(tau = NAG_ALLOC(tau_len, double)) ||
           !(taup = NAG_ALLOC(taup_len, double)) ||
           !(tauq = NAG_ALLOC(tauq_len, double)) ||
           !(u = NAG_ALLOC(m * m, double)) )
        {
          Vprintf("Allocation failure\n");
          exit_status = -1;
          goto END;
        }
      /* Read A from data file */
      for (i = 1; i <= m; ++i)
        {
          for (j = 1; j <= n; ++j)
            Vscanf("%lf", &A(i,j));
        }
      Vscanf("%*[^\n] ");
      if (m >= n)
        {
          /* Compute the QR factorization of A */
          /* nag_dgeqrf (f08aec).
           * QR factorization of real general rectangular matrix
           */
          nag_dgeqrf(order, m, n, a, pda, tau, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dgeqrf (f08aec).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Copy A to U */
          for (i = 1; i <= m; ++i)
            {
              for (j = 1; j <= MIN(i,n); ++j)
                U(i,j) = A(i,j);
            }
          /* Form Q explicitly, storing the result in U */
          /* nag_dorgqr (f08afc).
           * Form all or part of orthogonal Q from QR factorization
           * determined by nag_dgeqrf (f08aec) or nag_dgeqpf (f08bec)
           */
          nag_dorgqr(order, m, m, n, u, pdu, tau, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("order=%d\n", order);
              Vprintf("Error from nag_dorgqr (f08afc).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Copy R to PT (used as workspace) */
          for (i = 1; i <= n; ++i)
            {
              for (j = i; j <= n; ++j)
                PT(i,j) = A(i,j);
            }
          /* Set the strictly lower triangular part of R to zero */
          for (i = 2; i <= n; ++i)
            {
              for (j = 1; j <= MIN(i-1,n-1); ++j)
                PT(i,j) = 0.0;
            }
          /* Bidiagonalize R */
          /* nag_dgebrd (f08kec).
           * Orthogonal reduction of real general rectangular matrix
           * to bidiagonal form
           */
          nag_dgebrd(order, n, n, pt, pdpt, d, e, tauq, taup, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Update Q, storing the result in U */
          /* nag_dormbr (f08kgc).
           * Apply orthogonal transformations from reduction to
           * bidiagonal form determined by nag_dgebrd (f08kec)
           */
          nag_dormbr(order, Nag_FormQ, Nag_RightSide, Nag_NoTrans,
                     m, n, n, pt, pdpt, tauq, u, pdu, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dormbr (f08kgc).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Print bidiagonal form and matrix Q */
          Vprintf("\nExample 1: bidiagonal matrix B\nDiagonal\n");
          for (i = 1; i <= n; ++i)
            Vprintf("%8.4f%s", d[i-1], i%8==0 ?"\n":" ");
          Vprintf("\nSuper-diagonal\n");
          for (i = 1; i <= n - 1; ++i)
            Vprintf("%8.4f%s", e[i-1], i%8 == 0 ?"\n":" ");
          Vprintf("\n\n");
          /* nag_gen_real_mat_print (x04cac).
           * Print real general matrix (easy-to-use)
           */
          nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                 m, n, u, pdu, "Example 1: matrix Q", 0, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
                      fail.message);
              exit_status = 1;
              goto END;
            }
        }
      else
        {
          /* Compute the LQ factorization of A */
          /* nag_dgelqf (f08ahc).
           * LQ factorization of real general rectangular matrix
           */
          nag_dgelqf(order, m, n, a, pda, tau, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dgelqf (f08ahc).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Copy A to PT */
          for (i = 1; i <= m; ++i)
            {
              for (j = i; j <= n; ++j)
                PT(i,j) = A(i,j);
            }
          /* Form Q explicitly, storing the result in PT */
          /* nag_dorglq (f08ajc).
           * Form all or part of orthogonal Q from LQ factorization
           * determined by nag_dgelqf (f08ahc)
           */
          nag_dorglq(order, n, n, m, pt, pdpt, tau, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dorglq (f08ajc).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Copy L to U (used as workspace) */
          for (i = 1; i <= m; ++i)
            {
              for (j = 1; j <= i; ++j)
                U(i,j) = A(i,j);
            }
          /* Set the strictly upper triangular part of L to zero */
          for (i = 1; i <= m-1; ++i)
            {
              for (j = i+1; j <= m; ++j)
                U(i,j) = 0.0;
            }
          /* Bidiagonalize L */
          /* nag_dgebrd (f08kec), see above. */
          nag_dgebrd(order, m, m, u, pdu, d, e, tauq, taup, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dgebrd (f08kec).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }
          /* Update P**T, storing the result in PT */
          /* nag_dormbr (f08kgc), see above. */
          nag_dormbr(order, Nag_FormP, Nag_LeftSide, Nag_Trans,
                     m, n, m, u, pdu, taup, pt, pdpt, &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_dormbr (f08kgc).\n%s\n", fail.message);
              exit_status = 1;
              goto END;
            }

          /* Print bidiagonal form and matrix P**T */
          Vprintf("\nExample 2: bidiagonal matrix B\n%s\n",
                  "Diagonal");
          for (i = 1; i <= m; ++i)
            Vprintf("%8.4f%s", d[i-1], i%8==0 ?"\n":" ");
          Vprintf("\nSuper-diagonal\n");
          for (i = 1; i <= m - 1; ++i)
            Vprintf("%8.4f%s", e[i-1], i%8==0 ?"\n":" ");
          Vprintf("\n\n");
          /* nag_gen_real_mat_print (x04cac), see above. */
          nag_gen_real_mat_print(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                 m, n, pt, pdpt, "Example 2: matrix P**T", 0,
                                 &fail);
          if (fail.code != NE_NOERROR)
            {
              Vprintf("Error from nag_gen_real_mat_print (x04cac).\n%s\n",
                      fail.message);
              exit_status = 1;
              goto END;
            }
        }
    END:
      if (a) NAG_FREE(a);
      if (d) NAG_FREE(d);
      if (e) NAG_FREE(e);
      if (pt) NAG_FREE(pt);
      if (tau) NAG_FREE(tau);
      if (taup) NAG_FREE(taup);
      if (tauq) NAG_FREE(tauq);
      if (u) NAG_FREE(u);
    }
  return exit_status;
}