/* nag_linsys_real_gen_norm_rcomm (f04ydc) Example Program.
 *
 * Copyright 2014 Numerical Algorithms Group.
 *
 * Mark 23, 2013.
 */

#include <nag.h>
#include <math.h>
#include <nag_stdlib.h>
#include <nagf04.h>
#include <nagf07.h>
#include <nagf16.h>

int main(void)
{

  /* Scalars */
  Integer       exit_status = 0, irevcm = 0, seed = 354;
  Integer       i, j, m, n, pda, pdx, pdy, t;
  double        cond = 0.0, nrma = 0.0, nrminv = 0.0;

  /* Local Arrays */
  Integer       *icomm = 0, *ipiv = 0;
  double        *a = 0, *work = 0, *x = 0, *y = 0;

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

  INIT_FAIL(fail);

#define A(I, J) a[(J-1)*pda + I-1]

  order = Nag_ColMajor;

  /* Output preamble */
  printf("nag_linsys_real_gen_norm_rcomm (f04ydc) ");
  printf("Example Program Results\n\n");
  fflush(stdout);

  /* Skip heading in data file */
  scanf("%*[^\n] ");

  /* Read in the problem size and the value of the parameter t */
  scanf("%ld %ld %ld %*[^\n] ", &m, &n, &t);

  pda = n;
  pdx = n;
  pdy = m;

  if (!(a = NAG_ALLOC(m*n, double)) ||
      !(x = NAG_ALLOC(n*t, double)) ||
      !(y = NAG_ALLOC(m*t, double)) ||
      !(work = NAG_ALLOC(m*t, double))||
      !(ipiv = NAG_ALLOC(n, Integer)) ||
      !(icomm = NAG_ALLOC(2*n+5*t+20, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read in the matrix a from data file */
  for (i = 1; i <= m; i++)
    for (j = 1; j <= n; j++) scanf(" %lf ", &A(i, j));
  scanf("%*[^\n]");

  /* Compute the 1-norm of A */
  nag_dge_norm(order, Nag_OneNorm, m, n, a, pda, &nrma, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dge_norm\n%s\n",fail.message);
      exit_status = 1;
      goto END;
    }
  printf("Estimated norm of A is: %7.2f\n\n",nrma);

  /* 
   * Estimate the norm of A^(-1) without explicitly forming A^(-1) 
   */

  /* Compute an LU factorization of A using nag_dgetrf (f07adc) */
  nag_dgetrf(order, m, n, a, pda, ipiv, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_dgetrf\n%s\n",fail.message);
      exit_status = 2;
      goto END;
    }

  /* Estimate the norm of A^(-1) using the LU factors of A
   * nag_linsys_real_gen_norm_rcomm (f04ydc)
   * Estimate of the 1-norm of a real matrix
   */
  do {
    nag_linsys_real_gen_norm_rcomm(&irevcm, m, n, x, pdx, y, pdy,
                                   &nrminv, t, seed, work, icomm, &fail);
    if (irevcm == 1)
      {
        /* Compute y = inv(A)*x by solving Ay = x */
        trans = Nag_NoTrans;
        nag_dgetrs(order, trans, n, t, a, pda, ipiv, x, pdx, &fail);
        if (fail.code != NE_NOERROR)
          {
            printf("Error from nag_dgetrs\n%s\n",fail.message);
            exit_status = 3;
            goto END;
          }
        for (i = 0; i < n*t; i++) y[i] = x[i];
      }

    else if (irevcm == 2)
      {
        /* Compute x = inv(A)^T y by solving A^T x = y */
        trans = Nag_Trans;
        nag_dgetrs(order, trans, n, t, a, pda, ipiv, y, pdy, &fail);
        if (fail.code != NE_NOERROR)
          {
            printf("Error from nag_dgetrs\n%s\n",fail.message);
            exit_status = 4;
            goto END;
          }
        for (i = 0; i < n*t; i++) x[i] = y[i];
      }
    } while (irevcm != 0);


  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_linsys_real_gen_norm_rcomm (f04ydc)\n%s\n",
             fail.message);
      exit_status = 5;
      goto END;
    }

  printf("Estimated norm of inverse of A is: %7.2f\n\n",nrminv);

  /* Compute and print the estimated condition number */
  cond = nrma*nrminv;

  printf("Estimated condition number of A is: %7.2f\n",cond);

 END:
  NAG_FREE(a);
  NAG_FREE(x);
  NAG_FREE(y);
  NAG_FREE(work);
  NAG_FREE(icomm);
  NAG_FREE(ipiv);
  return exit_status;
}