/* nag_lapackeig_dgesvj (f08kjc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */

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

int main(void) {
  /* Scalars */
  double eps, serrbd, ctol;
  Integer exit_status = 0;
  Integer i, j, lwork, m, mv, n, n_vrows, n_vcols, pda, pdv, ranka;

  /* Arrays */
  double *a = 0, *rcondu = 0, *rcondv = 0, *s = 0, *v = 0, *work = 0;
  char nag_enum_arg[40];

  /* Nag Types */
  Nag_OrderType order;
  Nag_MatrixType joba;
  Nag_LeftVecsType jobu;
  Nag_RightVecsType jobv;
  NagError fail;

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

  INIT_FAIL(fail);

  printf("nag_lapackeig_dgesvj (f08kjc) 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 m or n\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_MatrixType)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);

  n_vcols = n;
  n_vrows = n;
  mv = 0;
  if (jobv == Nag_RightVecsMV) {
    scanf("%" NAG_IFMT, &mv);
    n_vrows = mv;
  } else if (jobv == Nag_NotRightVecs) {
    n_vrows = 1;
    n_vcols = 1;
  }
  scanf("%*[^\n]");

#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdv = n_vrows;
#else
  pda = n;
  pdv = n_vcols;
#endif
  lwork = 6;

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

  /* Read the m by n matrix A from data file */
  if (joba == Nag_GeneralMatrix) {
    for (i = 1; i <= m; i++)
      for (j = 1; j <= n; j++)
        scanf("%lf", &A(i, j));
  } else if (joba == Nag_UpperMatrix) {
    for (i = 1; i <= m; i++)
      for (j = i; j <= n; j++)
        scanf("%lf", &A(i, j));
  } else {
    for (i = 1; i <= m; i++)
      for (j = 1; j <= i; j++)
        scanf("%lf", &A(i, j));
  }
  scanf("%*[^\n]");
  /* jobv==Nag_RightVecsMV means that the first mv rows of v must be set. */
  if (jobv == Nag_RightVecsMV) {
    for (i = 1; i <= mv; i++)
      for (j = 1; j <= n; j++)
        scanf("%lf", &V(i, j));
    scanf("%*[^\n]");
  }
  ctol = 10.0;
  /* nag_lapackeig_dgesvj (f08kjc)
   * Compute the singular values and left and right singular vectors
   * of A (A = U*S*V, m>=n).
   */
  nag_lapackeig_dgesvj(order, joba, jobu, jobv, m, n, a, pda, s, mv, v, pdv,
                       ctol, work, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgesvj (f08kjc).\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 solution */
  printf("Singular values\n   ");
  for (j = 0; j < n; j++)
    printf("%8.4f", s[j]);
  printf("\n\n");
  if (fabs(work[0] - 1.0) > eps)
    printf("Values need scaling by factor = %13.5e\n\n", work[0]);

  ranka = (Integer)work[1];
  printf("Rank of A = %5" NAG_IFMT "\n\n", ranka);
  if (jobu != Nag_NotLeftVecs) {
    /* 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, m,
                                   ranka, a, pda,
                                   "Left spanning 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) {
    printf("\n");
    fflush(stdout);
    nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, n,
                                   n, v, pdv, "Right singular vectors", 0,
                                   &fail);
  } else if (jobv == Nag_RightVecsMV) {
    printf("\n");
    fflush(stdout);
    nag_file_print_matrix_real_gen(
        order, Nag_GeneralMatrix, Nag_NonUnitDiag, mv, n, v, pdv,
        "Right singular vectors applied to input V", 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);
  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;
  }

  /* Print the approximate error bounds for the singular values and vectors. */
  printf("\nError estimate for the singular values\n");
  printf("%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(v);
  NAG_FREE(work);

  return exit_status;
}