/* nag_zgeqp3 (f08btc) Example Program.
 *
 * Copyright 2011 Numerical Algorithms Group.
 *
 * Mark 23, 2011.
 */

#include <stdio.h>
#include <nag.h>
#include <nag_stdlib.h>
#include <naga02.h>
#include <nagf08.h>
#include <nagf16.h>
#include <nagx04.h>

int main(void)
{
  /* Scalars */
  Complex       one = { 1.0, 0.0 };
  Complex       zero = { 0.0, 0.0 };
  double        tol;
  Integer       i, j, k, m, n, nrhs, pda, pdb, pdw;
  Integer       exit_status = 0;
  /* Arrays */
  Complex       *a = 0, *b = 0, *tau = 0, *work = 0;
  double        *rnorm = 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_zgeqp3 (f08btc) Example Program Results\n\n");

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

#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = m;
  pdw = m;
#else
  pda = n;
  pdb = nrhs;
  pdw = 1;
#endif

  /* Allocate memory */
  if (!(a = NAG_ALLOC(m * n, Complex)) ||
      !(b = NAG_ALLOC(m * nrhs, Complex)) ||
      !(tau = NAG_ALLOC(n, Complex)) ||
      !(work = NAG_ALLOC(n, Complex)) ||
      !(rnorm = NAG_ALLOC(nrhs, double)) ||
      !(jpvt = NAG_ALLOC(n, Integer)))
    {
      printf("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)
      scanf(" ( %lf , %lf )", &A(i, j).re, &A(i, j).im);
  scanf("%*[^\n]");

  for (i = 1; i <= m; ++i)
    for (j = 1; j <= nrhs; ++j)
      scanf(" ( %lf , %lf )", &B(i, j).re, &B(i, j).im);
  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;
    }

  /* nag_zgeqp3 (f08btc).
   * Compute the QR factorization of A.
   */
  nag_zgeqp3(order, m, n, a, pda, jpvt, tau, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zgeqp3 (f08btc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
  
  /* nag_zunmqr (f08auc).
   * Compute C = (C1) = (Q**H)*B, storing the result in B.
   *             (C2)
   */
  nag_zunmqr(order, Nag_LeftSide, Nag_ConjTrans, m, nrhs, n, a, pda, tau,
             b, pdb, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zunmqr (f08auc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

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

  /* nag_complex_abs (a02dbc).
   * Determine and print the rank, k, of R relative to tol.
   */
  for (k = 1; k <= n; ++k)
    if (nag_complex_abs(A(k, k)) <= tol * nag_complex_abs(A(1, 1)))
      break;
  --k;

  printf("Tolerance used to estimate the rank of A\n");
  printf("%11.2e\n", tol);
  printf("Estimated rank of A\n");
  printf("%8ld\n\n", k);

  /* nag_ztrsm (f16zjc).
   * Compute least-squares solutions by backsubstitution in
   * R(1:k,1:k)*Y = C1, storing the result in B.
   */
  nag_ztrsm(order, Nag_LeftSide, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k,
            nrhs, one, a, pda, b, pdb, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_ztrsm (f16zjc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* nag_zge_norm (f16uac).
   * Compute estimates of the square roots of the residual sums of
   * squares (2-norm of each of the columns of C2).
   */
  for (j = 1; j <= nrhs; ++j) {
    nag_zge_norm(order, Nag_FrobeniusNorm, m - k, 1, &B(k + 1, j), pdb,
                 &rnorm[j - 1], &fail);
    if (fail.code != NE_NOERROR)
      {
        printf("Error from nag_zge_norm (f16uac).\n%s\n", fail.message);
        exit_status = 1;
        goto END;
      }
  }

  /* nag_zge_load (f16thc).
   * Set the remaining elements of the solutions to zero (to give
   * the basic solutions).
   */
  nag_zge_load(order, n - k, nrhs, zero, zero, &B(k + 1, 1), pdb, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_zge_load (f16thc).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }

  /* Permute the least-squares solutions stored in B to give X = P*Y */
  for (j = 1; j <= nrhs; ++j) {
    for (i = 1; i <= n; ++i) {
      work[jpvt[i - 1] - 1].re = B(i, j).re;
      work[jpvt[i - 1] - 1].im = B(i, j).im;
    }
    /* nag_zge_copy (f16tfc). 
     * Copy matrix.
     */
    nag_zge_copy(order, Nag_NoTrans, n, 1, work, pdw, &B(1, j), pdb, &fail);
    if (fail.code != NE_NOERROR)
      {
        printf("Error from nag_zge_copy (f16tfc).\n%s\n", fail.message);
        exit_status = 1;
        goto END;
      }
  }

  /* nag_gen_complx_mat_print_comp (x04dbc).
   * Print least-squares solutions.
   */
  fflush(stdout);
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                nrhs, b, pdb, Nag_BracketForm, "%7.4f",
                                "Least-squares solution(s)", Nag_IntegerLabels,
                                0, Nag_IntegerLabels, 0, 80, 0, 0, &fail);
  if (fail.code != NE_NOERROR)
    {
      printf("Error from nag_gen_complx_mat_print_comp (x04dbc).\n%s\n",
             fail.message);
      exit_status = 1;
      goto END;
    }

  /* Print the square roots of the residual sums of squares */
  printf("\nSquare root(s) of the residual sum(s) of squares\n");

  for (j = 0; j < nrhs; ++j)
    printf("%11.2e%s", rnorm[j], (j+1)%7 == 0?"\n":" ");
  
 END:
  if (a) NAG_FREE(a);
  if (b) NAG_FREE(b);
  if (tau) NAG_FREE(tau);
  if (work) NAG_FREE(work);
  if (rnorm) NAG_FREE(rnorm);
  if (jpvt) NAG_FREE(jpvt);

  return exit_status;
}

#undef A
#undef B