/* nag_lapackeig_dgejsv (f08khc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.0, 2023.
 */

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

int main(void) {
  /* Scalars */
  double eps, serrbd;
  Integer exit_status = 0;
  Integer pda, pdu, pdv;
  Integer i, j, m, n, n_uvecs, n_vvecs;
  /* Arrays */
  double *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *u = 0, *v = 0;
  double work[7];
  Integer iwork[3];
  char nag_enum_arg[40];

  /* Nag Types */
  Nag_OrderType order;
  Nag_Preprocess joba;
  Nag_LeftVecsType jobu;
  Nag_RightVecsType jobv;
  Nag_ZeroCols jobr;
  Nag_TransType jobt;
  Nag_Perturb jobp;
  NagError fail;

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_dgejsv (f08khc) Example Program Results\n\n");

  /* Skip heading in data file */
  scanf("%*[^\n]");
  scanf("%" NAG_IFMT "%" NAG_IFMT "%*[^\n]", &m, &n);

  if (n < 0 || m < n) {
    printf("Invalid n or nrhs\n");
    exit_status = 1;
    goto END;
    ;
  }

  /* Read Nag type arguments by name and convert to value */
  scanf(" %39s%*[^\n]", nag_enum_arg);
  /* nag_enum_name_to_value (x04nac).
   * Converts NAG enum member name to value
   */
  joba = (Nag_Preprocess)nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  jobu = (Nag_LeftVecsType)nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  jobv = (Nag_RightVecsType)nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  jobr = (Nag_ZeroCols)nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  jobt = (Nag_TransType)nag_enum_name_to_value(nag_enum_arg);
  scanf(" %39s%*[^\n]", nag_enum_arg);
  jobp = (Nag_Perturb)nag_enum_name_to_value(nag_enum_arg);

  /* Size of u and v depends on some of the above Nag type arguments. */
  n_uvecs = 1;
  if (jobu == Nag_LeftVecs) {
    n_uvecs = m;
  } else if (jobu == Nag_LeftSpan) {
    n_uvecs = n;
  } else if (jobu == Nag_NotLeftWork && jobv == Nag_RightVecs &&
             jobt == Nag_Trans && m == n) {
    n_uvecs = m;
  }
  if (jobv == Nag_NotRightVecs) {
    n_vvecs = 1;
  } else {
    n_vvecs = n;
  }
#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdu = m;
  pdv = n;
#else
  pda = n;
  pdu = n_uvecs;
  pdv = n_vvecs;
#endif

  if (!(a = NAG_ALLOC(m * n, double)) || !(rcondu = NAG_ALLOC(m, double)) ||
      !(rcondv = NAG_ALLOC(m, double)) || !(s = NAG_ALLOC(n, double)) ||
      !(u = NAG_ALLOC(m * n_uvecs, double)) ||
      !(v = NAG_ALLOC(n_vvecs * n_vvecs, double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* 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_dgejsv (f08khc)
   * Compute the singular values and left and right singular vectors
   * of A (A = U*S*V^T, m>=n).
   */
  nag_lapackeig_dgejsv(order, joba, jobu, jobv, jobr, jobt, jobp, m, n, a, pda,
                       s, u, pdu, v, pdv, work, iwork, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgejsv (f08khc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* Get the machine precision, eps and compute the approximate
   * error bound for the computed singular values. Note that for
   * the 2-norm, s[0] = norm(A).
   */
  eps = nag_machine_precision;
  serrbd = eps * s[0];

  /* Print (possibly scaled) singular values. */
  if (fabs(work[0] - work[1]) < 2.0 * eps) {
    /* No scaling required */
    printf("Singular values\n");
    for (j = 0; j < n; j++)
      printf("%8.4f", s[j]);
  } else {
    printf("Scaled singular values\n");
    for (j = 0; j < n; j++)
      printf("%8.4f", s[j]);
    printf("\nFor true singular values, multiply by a/b,\n");
    printf("where a = %f and b = %f", work[0], work[1]);
  }
  printf("\n\n");

  /* Print left and right (spanning) singular vectors, if requested.  using
   * nag_file_print_matrix_real_gen (x04cac)
   * Print real general matrix (easy-to-use)
   */
  if (jobu == Nag_LeftVecs || jobu == Nag_LeftSpan) {
    fflush(stdout);
    nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
                                   n, 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;
    }
  }
  if (jobv == Nag_RightVecs || jobv == Nag_RightVecsJRots) {
    printf("\n");
    fflush(stdout);
    nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                   n, v, pdv, "Right 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;
    }
  }

  /* nag_lapackeig_ddisna (f08flc)
   * Estimate reciprocal condition numbers for the singular vectors.
   */
  nag_lapackeig_ddisna(Nag_LeftSingVecs, m, n, s, rcondu, &fail);
  if (fail.code == NE_NOERROR)
    nag_lapackeig_ddisna(Nag_RightSingVecs, m, n, s, rcondv, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_ddisna (f08flc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  if (joba == Nag_ColpivRrankCond || joba == Nag_FullpivRrankCond) {
    printf("\n\nEstimate of the condition number of column equilibrated A\n");
    printf("%11.1e", work[2]);
  }

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

  printf("\n\nError estimates for left singular vectors\n");
  for (i = 0; i < n; i++)
    printf("%11.1e", serrbd / rcondu[i]);

  printf("\n\nError estimates for right singular vectors\n");
  for (i = 0; i < n; i++)
    printf("%11.1e", serrbd / rcondv[i]);
  printf("\n");

END:
  NAG_FREE(a);
  NAG_FREE(rcondu);
  NAG_FREE(rcondv);
  NAG_FREE(s);
  NAG_FREE(u);
  NAG_FREE(v);

  return exit_status;
}