/* nag_dgelsy (f08bac) 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>

int main(void)
{
  /* Scalars */
  double        rcond;
  Integer       exit_status = 0, i, j, m, n, nrhs, rank, pda, pdb;
  /* Arrays */
  double        *a = 0, *b = 0;
  Integer       *jpvt = 0;
  /* Nag Types */
  Nag_OrderType order;
  NagError      fail;

#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_dgelsy (f08bac) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%ld%ld%ld%*[^\n]", &m, &n, &nrhs);

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

#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = m;
#else
  pda = n;
  pdb = nrhs;
#endif

  /* Read A and 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 <= m; ++i)
    for (j = 1; j <= nrhs; ++j)
      scanf("%lf", &B(i, j));
  scanf("%*[^\n]");
  
  /* nag_iload (f16dbc).
   * Initialize jpvt to be zero so that all columns are free.
   */
  nag_iload(n, 0, jpvt, 1, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_iload (f16dbc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

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

  /* nag_dgelsy (f08bac).
   * Solve the least squares problem min( norm2(b - Ax) ) for the x
   * of minimum norm. 
   */
  nag_dgelsy(order, m, n, nrhs, a, pda, b, pdb, jpvt, rcond, &rank, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgelsy (f08bac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print solution */
  printf("Least squares solution\n");
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= nrhs; ++j)
      printf("%11.4f%s", B(i,j), j%7 == 0?"\n":" ");
    printf("\n");
  }

  /* Print the effective rank of A */
  printf("\nTolerance used to estimate the rank of A\n");
  printf("%11.2e\n", rcond);
  printf("Estimated rank of A\n%6ld\n", rank);

 END:
  if (a) NAG_FREE(a);
  if (b) NAG_FREE(b);
  if (jpvt) NAG_FREE(jpvt);

  return exit_status;
}
#undef A
#undef B