/* nag_lapackeig_dgesdd (f08kdc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */

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

int main(void) {

  /* Scalars */
  double eps, serrbd;
  Integer exit_status = 0, i, j, m, n, pda, pdu;

  /* Arrays */
  double *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *u = 0;
  double *uerrbd = 0, *verrbd = 0;
  double dummy[1];

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

#ifdef NAG_COLUMN_MAJOR
#define A(I, J) a[(J - 1) * pda + I - 1]
#define U(I, J) u[(J - 1) * pdu + I - 1]
  order = Nag_ColMajor;
#else
#define A(I, J) a[(I - 1) * pda + J - 1]
#define U(I, J) u[(I - 1) * pdu + J - 1]
  order = Nag_RowMajor;
#endif

  INIT_FAIL(fail);

  printf("nag_lapackeig_dgesdd (f08kdc) Example Program Results\n\n");

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

  /* Allocate memory */
  if (!(a = NAG_ALLOC(m * n, double)) || !(rcondu = NAG_ALLOC(m, double)) ||
      !(rcondv = NAG_ALLOC(m, double)) || !(s = NAG_ALLOC(MIN(m, n), double)) ||
      !(u = NAG_ALLOC(m * m, double)) || !(uerrbd = NAG_ALLOC(m, double)) ||
      !(verrbd = NAG_ALLOC(m, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdu = m;
#else
  pda = n;
  pdu = MIN(m, n);
#endif

  /* Read the m by n matrix A from data file */
  for (i = 1; i <= m; ++i)
    for (j = 1; j <= n; ++j)
      scanf("%lf", &A(i, j));
  scanf("%*[^\n]");

  /* nag_lapackeig_dgesdd (f08kdc).
   * Compute the singular values and left and right singular vectors
   * of A (A = U*S*(V^T), m.le.n)
   */
  nag_lapackeig_dgesdd(order, Nag_DoOverwrite, m, n, a, pda, s, u, pdu, dummy,
                       1, &fail);

  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgesdd (f08kdc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print singular values */
  printf("Singular values\n");
  for (i = 0; i < m; ++i)
    printf(" %7.4f%s", s[i], i % 8 == 7 ? "\n" : "");
  printf("\n\n");

  /*  Normalize so that first elements of singular vectors u >= 0 */
  for (i = 1; i <= m; ++i) {
    if (U(1, i) < 0.0) {
      for (j = 1; j <= m; ++j)
        U(j, i) = -U(j, i);
      for (j = 1; j <= n; ++j)
        A(i, j) = -A(i, j);
    }
  }
  /* Print left and right singular vectors using
   * nag_file_print_matrix_real_gen (x04cac).
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
                                 m, u, pdu, "Left singular vectors", 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;
  }
  printf("\n");

  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
                                 n, a, pda, "Right singular vectors by row", 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;
  }

  /* Get the machine precision, eps using nag_machine_precision (x02ajc). */
  eps = nag_machine_precision;

  /* compute the approximate error bound for the computed singular values.
   * Note that for the 2-norm, s[0] = ||A||
   */
  serrbd = eps * s[0];

  /* Call nag_lapackeig_ddisna (f08flc) to estimate reciprocal condition numbers
   * for the singular vectors.
   */
  nag_lapackeig_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail);
  nag_lapackeig_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail);

  /* Compute the error estimates for the singular vectors. */
  for (i = 0; i < m; ++i) {
    uerrbd[i] = serrbd / rcondu[i];
    verrbd[i] = serrbd / rcondv[i];
  }

  /* Print the approximate error bounds for the singular values and vectors */
  printf("\nError estimate for the singular values\n%11.1e\n", serrbd);

  printf("\nError estimates for the left singular vectors\n");
  for (i = 0; i < m; ++i)
    printf(" %10.1e%s", uerrbd[i], i % 6 == 5 ? "\n" : "");

  printf("\n\nError estimates for the right singular vectors\n");
  for (i = 0; i < m; ++i)
    printf(" %10.1e%s", verrbd[i], i % 6 == 5 ? "\n" : "");
  printf("\n");

END:
  NAG_FREE(a);
  NAG_FREE(rcondu);
  NAG_FREE(rcondv);
  NAG_FREE(s);
  NAG_FREE(u);
  NAG_FREE(uerrbd);
  NAG_FREE(verrbd);

  return exit_status;
}

#undef A