/* nag_lapackeig_dgeqpf (f08bec) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.1, 2023.
 */

#include <nag.h>
#include <stdio.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);

  printf("nag_lapackeig_dgeqpf (f08bec) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n] ");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\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))) {
    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", &A(i, j));
  }
  scanf("%*[^\n] ");
  for (i = 1; i <= m; ++i) {
    for (j = 1; j <= nrhs; ++j)
      scanf("%lf", &B(i, j));
  }
  scanf("%*[^\n] ");

  /* Initialize JPVT to be zero so that all columns are free */
  /* nag_blast_iload (f16dbc).
   * Broadcast scalar into integer vector
   */
  nag_blast_iload(n, 0, jpvt, 1, &fail);
  /* Compute the QR factorization of A */
  /* nag_lapackeig_dgeqpf (f08bec).
   * QR factorization of real general rectangular matrix with
   * column pivoting
   */
  nag_lapackeig_dgeqpf(order, m, n, a, pda, jpvt, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgeqpf (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 */

  /* nag_lapackeig_dormqr (f08agc).
   * Apply orthogonal transformation determined by nag_lapackeig_dgeqrf
   * (f08aec) or nag_lapackeig_dgeqpf (f08bec)
   */
  nag_lapackeig_dormqr(order, Nag_LeftSide, Nag_Trans, m, nrhs, n, a, pda, tau,
                       b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dormqr (f08agc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

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

  /* nag_lapacklin_dtrtrs (f07tec).
   * Solution of real triangular system of linear equations,
   * multiple right-hand sides
   */
  nag_lapacklin_dtrtrs(order, Nag_Upper, Nag_NoTrans, Nag_NonUnitDiag, k, nrhs,
                       a, pda, b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapacklin_dtrtrs (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 */
  /* nag_file_print_matrix_real_gen (x04cac).
   * Print real general matrix (easy-to-use)
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                 nrhs, x, pdx, "Least squares solution", 0,
                                 &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_real_gen (x04cac).\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }
END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(tau);
  NAG_FREE(x);
  NAG_FREE(jpvt);
  return exit_status;
}