/* nag_lapackeig_dgelss (f08kac) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {

  /* Scalars */
  double rcond, rnorm;
  Integer exit_status = 0, i, j, m, n, nrhs, rank, pda, pdb;

  /* Arrays */
  double *a = 0, *b = 0, *s = 0;

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

#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_dgelss (f08kac) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n, &nrhs);
  if (m < 0 || n < 0 || nrhs < 0) {
    printf("Invalid m, n or nrhs\n");
    exit_status = 1;
    goto END;
  }

#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdb = m;
#else
  pda = n;
  pdb = nrhs;
#endif
  /* Allocate memory */
  if (!(a = NAG_ALLOC(m * n, double)) ||
      !(b = NAG_ALLOC(MAX(m, n) * nrhs, double)) ||
      !(s = NAG_ALLOC(MIN(m, n), 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]");

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

  /* Solve the least squares problem min( norm2(b - Ax) ) for the x
   * of minimum norm using nag_lapackeig_dgelss (f08kac).
   */
  nag_lapackeig_dgelss(order, m, n, nrhs, a, pda, b, pdb, s, rcond, &rank,
                       &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgelss (f08kac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf("Least squares solution\n");
  for (i = 1; i <= n; ++i) {
    for (j = 1; j <= nrhs; ++j)
      printf(" %10.4f%s", B(i, j), j % 7 == 0 ? "\n" : "");
    printf("\n");
  }

  /* Print the effective rank of A */
  printf("\nTolerance used to estimate the rank of A\n%11.2e\n", rcond);
  printf("\nEstimated rank of A\n%6" NAG_IFMT "\n", rank);

  /* Print singular values of A */
  printf("\nSingular values of A\n");
  for (i = 0; i < n; ++i)
    printf(" %10.4f%s", s[i], i % 7 == 6 ? "\n" : "");
  printf("\n");

  /* Compute and print estimate of the square root of the
   * residual sum of squares using nag_blast_dge_norm (f16rac).
   */
  if (rank == n) {
    nag_blast_dge_norm(order, Nag_FrobeniusNorm, m - n, 1, &B(n + 1, 1), pdb,
                       &rnorm, &fail);
    if (fail.code != NE_NOERROR) {
      printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
      exit_status = 1;
      goto END;
    }
    printf("\nSquare root of the residual sum of squares\n%11.2e\n", rnorm);
  }

END:
  NAG_FREE(a);
  NAG_FREE(b);
  NAG_FREE(s);

  return exit_status;
}

#undef A
#undef B