/* nag_ztpqrt (f08bpc) Example Program.
 *
 * Copyright 2014 Numerical Algorithms Group.
 *
 * Mark 24, 2013.
 */

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

int main(void)
{
  /* Scalars */
  double  rnorm;
  Integer exit_status = 0;
  Integer pda, pdb, pdt;
  Integer i, j, m, n, nb, nrhs;
  /* Arrays */
  Complex  *a = 0, *b = 0, *c = 0, *t = 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]
#define C(I,J) c[(J-1)*pdb + I-1]
#define T(I,J) t[(J-1)*pdt + 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 C(I,J) c[(I-1)*pdb + J-1]
#define T(I,J) t[(I-1)*pdt + J-1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_ztpqrt (f08bpc) Example Program Results\n\n");
  fflush(stdout);

  /* Skip heading in data file*/
  scanf("%*[^\n]");
  scanf("%ld%ld%ld%*[^\n]", &m, &n, &nrhs);
  nb = MIN(m, n);
  if (!(a = NAG_ALLOC(m*n, Complex))||
      !(b = NAG_ALLOC(m*nrhs, Complex))||
      !(c = NAG_ALLOC(m*nrhs, Complex))||
      !(t = NAG_ALLOC(nb*MIN(m, n), Complex)))
    {
      printf("Allocation failure\n");
      exit_status = -1;
      goto END;
    }
#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = m;
  pdt = nb;
#else
  pda = n;
  pdb = nrhs;
  pdt = MIN(m, n);
#endif

  /* 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]");

  for (i = 1; i <= m; ++i)
    for (j = 1; j <= nrhs; ++j)
      C(i, j) = B(i, j);

  /* nag_zgeqrt (f08apc).
   * Compute the QR factorization of first n rows of A by recursive algorithm.
   */
  nag_zgeqrt(order, n, n, nb, a, pda, t, pdt, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_zgeqrt (f08apc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_zgemqrt (f08aqc).
   * Compute C = (C1) = (Q^H)*B, storing the result in C
   *             (C2)
   * by applying Q^H from left.
   */
  nag_zgemqrt(order, Nag_LeftSide, Nag_ConjTrans, n, nrhs, n, nb, a, pda, t,
              pdt, c, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_zgemqrt (f08aqc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  for (i = 1; i <= n; ++i)
    for (j = 1; j <= nrhs; ++j)
      B(i, j) = C(i, j);

  /* nag_ztrtrs (f07tsc).
   * Compute least-squares solutions for first n rows
   * by backsubstitution in R*X = C1.
   */ 
  nag_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs, a, pda,
             c, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ztrtrs (f07tsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_gen_complx_mat_print_comp (x04dbc).
   * Print least-squares solutions using first n rows.
   */
  nag_gen_complx_mat_print_comp(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                nrhs, c, pdb, Nag_BracketForm, "%7.4f",
                                "Solution(s) for n rows", 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;
  }

  /* nag_ztpqrt (f08bpc).
   * Now add the remaining rows and perform QR update.
   */
  nag_ztpqrt(order, m - n, n, 0, nb, a, pda, &A(n + 1, 1), pda, t, pdt, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ztpqrt (f08bpc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_ztpmqrt (f08bqc).
   * Apply orthogonal transformations to C.
   */
  nag_ztpmqrt(order, Nag_LeftSide, Nag_ConjTrans, m - n, nrhs, n, 0, nb,
              &A(n + 1, 1), pda, t, pdt, b, pdb, &B(5, 1),pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ztpmqrt (f08bqc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_ztrtrs (f07tsc).
   * Compute least-squares solutions for first n rows
   * by backsubstitution in R*X = C1.
   */ 
  nag_ztrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, n, nrhs, a, pda,
             b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_ztrtrs (f07tsc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_gen_complx_mat_print_comp (x04dbc).
   * Print least-squares solutions.
   */
  printf("\n");
  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) for all rows",
                                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;
  }

  printf("\n Square root(s) of the residual sum(s) of squares\n");
  for ( j=1; j<=nrhs; j++) {
    /* nag_zge_norm (f16uac).
     * Compute and print estimate of the square root of the residual
     * sum of squares. 
     */
    nag_zge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1,j), pdb, &rnorm, 
                 &fail);
    if (fail.code != NE_NOERROR) {
      printf("\nError from nag_zge_norm (f16uac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
    printf("  %11.2e ", rnorm);
  }
  printf("\n");

 END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(c);
  NAG_FREE(t);

return exit_status;
}