/* nag_lapackeig_dgelqf (f08ahc) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {
  /* Scalars */
  Integer i, j, m, n, nrhs, pda, pdb, tau_len;
  Integer exit_status = 0;
  NagError fail;
  Nag_OrderType order;
  /* Arrays */
  double *a = 0, *b = 0, *tau = 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]
  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_lapackeig_dgelqf (f08ahc) 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 = n;
#else
  pda = n;
  pdb = nrhs;
#endif

  tau_len = MIN(m, n);

  /* Allocate memory */
  if (!(a = NAG_ALLOC(m * n, double)) || !(b = NAG_ALLOC(n * nrhs, double)) ||
      !(tau = NAG_ALLOC(tau_len, double))) {
    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] ");

  /* Compute the LQ factorization of A */
  /* nag_lapackeig_dgelqf (f08ahc).
   * LQ factorization of real general rectangular matrix
   */
  nag_lapackeig_dgelqf(order, m, n, a, pda, tau, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgelqf (f08ahc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }
  /* Solve L*Y = B, storing the result in B */
  /* nag_lapacklin_dtrtrs (f07tec).
   * Solution of real triangular system of linear equations,
   * multiple right-hand sides
   */
  nag_lapacklin_dtrtrs(order, Nag_Lower, Nag_NoTrans, Nag_NonUnitDiag, m, 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;
  }
  /* Set rows (M+1) to N of B to zero */
  if (m < n) {
    for (i = m + 1; i <= n; ++i) {
      for (j = 1; j <= nrhs; ++j)
        B(i, j) = 0.0;
    }
  }

  /* Compute minimum-norm solution X = (Q^T)*B in B */
  /* nag_lapackeig_dormlq (f08akc).
   * Apply orthogonal transformation determined by nag_lapackeig_dgelqf (f08ahc)
   */
  nag_lapackeig_dormlq(order, Nag_LeftSide, Nag_Trans, n, nrhs, m, a, pda, tau,
                       b, pdb, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dormlq (f08akc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print minimum-norm solution(s) */
  /* 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, b, pdb, "Minimum-norm solution(s)", 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);
  return exit_status;
}