/* nag_dgeqpf (f08bec) Example Program.
 *
 * Copyright 2001 Numerical Algorithms Group.
 *
 * Mark 7, 2001.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <nagf07.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx04.h>

int main(void)
{
  /* Scalars */
  double   tol;
  Integer  i, j, jpvt_len, k, m, n, nrhs;
  Integer  pda, pdb, pdx, tau_len;
  Integer  exit_status=0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  double  *a=0, *b=0, *tau=0, *x=0;
  Integer *jpvt=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]
#define X(I,J) x[(J-1)*pdx + 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]
#define X(I,J) x[(I-1)*pdx + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);
  Vprintf("f08bec Example Program Results\n\n");

  /* Skip heading in data file */
  Vscanf("%*[^\n] ");
  Vscanf("%ld%ld%ld%*[^\n] ", &m, &n, &nrhs);
#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = m;
  pdx = m;
#else
  pda = n;
  pdb = nrhs;
  pdx = nrhs;
#endif
  tau_len = MIN(m,n);
  jpvt_len = n;

  /* Allocate memory */
  if ( !(a = NAG_ALLOC(m * n, double)) ||
       !(b = NAG_ALLOC(m * nrhs, double)) ||
       !(tau = NAG_ALLOC(tau_len, double)) ||
       !(x = NAG_ALLOC(m * nrhs, double)) ||
       !(jpvt = NAG_ALLOC(jpvt_len, Integer)) )
    {
      Vprintf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }

  /* Read A and B from data file */
  for (i = 1; i <= m; ++i)
    {
      for (j = 1; j <= n; ++j)
        Vscanf("%lf", &A(i,j));
    }
  Vscanf("%*[^\n] ");
  for (i = 1; i <= m; ++i)
    {
      for (j = 1; j <= nrhs; ++j)
        Vscanf("%lf", &B(i,j));
    }
  Vscanf("%*[^\n] ");

  /* Initialize JPVT to be zero so that all columns are free */
  f16dbc(n, 0, jpvt, 1, &fail);
  /* Compute the QR factorization of A */
  f08bec(order, m, n, a, pda, jpvt, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from f08bec.\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Choose TOL to reflect the relative accuracy of the input data */
  tol = 0.01;

  /* Determine which columns of R to use */
  for (k = 1; k <= n; ++k)
    {
      if (ABS(A(k, k)) <= tol * ABS(A(1, 1)) )
        break;
    }
  --k;

  /* Compute C = (Q**T)*B, storing the result in B */

  f08agc(order, Nag_LeftSide, Nag_Trans, m, nrhs, n, a, pda,
         tau, b, pdb, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from f08agc.\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Compute least-squares solution by backsubstitution in R*B = C */

  f07tec(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k, nrhs,
          a, pda, b, pdb, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from f07tec.\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  for (i = k + 1; i <= n; ++i)
    {
      for (j = 1; j <= nrhs; ++j)
        B(i,j) = 0.0;
    }

  /* Unscramble the least-squares solution stored in B */
  for (i = 1; i <= n; ++i)
    {
      for (j = 1; j <= nrhs; ++j)
        X(jpvt[i - 1], j) = B(i, j);
    }

  /* Print least-squares solution */
  x04cac(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n, nrhs, x, pdx,
         "Least-squares solution",  0, &fail);
  if (fail.code != NE_NOERROR)
    {
      Vprintf("Error from x04cac.\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
 END:
  if (a) NAG_FREE(a);
  if (b) NAG_FREE(b);
  if (tau) NAG_FREE(tau);
  if (x) NAG_FREE(x);
  if (jpvt) NAG_FREE(jpvt);
  return exit_status;
}