/* nag_rnla_svd_rowext_real (f10cac) Example Program.
 *
 * Copyright 2024 Numerical Algorithms Group.
 *
 * Mark 30.3, 2024.
 */

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

int main(void) {

  /* Scalars */
  Integer exit_status = 0, i, j, m, n, pda, pdu, pdvt;
  /* Arrays */
  double *a = 0, *a_copy = 0, *rcondu = 0, *rcondv = 0;
  double *s = 0, *u = 0, *uerrbd = 0, *verrbd = 0, *vt = 0, *work = 0;

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

  /* Declarations for randomised algorithm */
  Integer k = 5, r = 0;
  double rtol_abs, rtol_rel;
  char nag_enum_arg1[40];
  char nag_enum_arg2[40];
  Nag_ComputeUType jobu;
  Nag_ComputeVTType jobvt;

  /* Declarations for RNG */
  Integer lstate;
  Integer *state = 0;
  double *x = 0;
  Nag_BaseRNG genid = Nag_Basic;
  Integer subid = 0, lseed = 1;
  Integer seed[] = {1762543};

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

  INIT_FAIL(fail);

  printf("nag_rnla_svd_rowext_real (f10cac) 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)) || !(a_copy = NAG_ALLOC(m * n, double)) ||
      !(rcondu = NAG_ALLOC(n, double)) || !(rcondv = NAG_ALLOC(n, double)) ||
      !(s = NAG_ALLOC(MIN(m, n), double)) || !(u = NAG_ALLOC(m * m, double)) ||
      !(uerrbd = NAG_ALLOC(n, double)) || !(verrbd = NAG_ALLOC(n, double)) ||
      !(vt = NAG_ALLOC(m * n, double)) ||
      !(work = NAG_ALLOC(MIN(m, n), double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  pdu = m;
  pda = m;
  pdvt = n;

  /* 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]");
  /* Read in values for jobu, jobvt, k */
  scanf("%39s %39s %" NAG_IFMT "%*[^\n] ", nag_enum_arg1, nag_enum_arg2, &k);
  jobu = (Nag_ComputeUType)nag_enum_name_to_value(nag_enum_arg1);
  jobvt = (Nag_ComputeVTType)nag_enum_name_to_value(nag_enum_arg2);

  /* Copy a into a_copy */
  for (i = 0; i < m * n; i++)
    a_copy[i] = a[i];

  /* nag_file_print_matrix_real_gen (x04cac)
   * Print real general matrix A.
   */
  fflush(stdout);
  nag_file_print_matrix_real_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag, m,
                                 n, a, pda, "Matrix A", 0, &fail);
  printf("\n");
  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;
  }

  /* Perform deterministic SVD of A */

  /* nag_lapackeig_dgesvd (f08kbc).
   * Compute the singular values and left and right singular vectors
   * of A (A = U*S*(V^T), m >= n)
   */
  nag_lapackeig_dgesvd(order, Nag_AllU, Nag_AllVT, m, n, a_copy, pda, s, u, pdu,
                       vt, pdvt, work, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_lapackeig_dgesvd (f08kbc).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  printf(" Singular values of A using dgesvd: \n");
  for (i = 0; i < n; ++i)
    printf(" %10.1e\n", s[i]);
  printf("\n");

  /* Random number generation */

  /* Initialize the error structure */
  INIT_FAIL(fail);

  /* Get the length of the state array */
  lstate = -1;
  nag_rand_init_repeat(genid, subid, seed, lseed, state, &lstate, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
    exit_status = 2;
    goto END;
  }

  /* Allocate arrays */
  if (!(x = NAG_ALLOC(n, double)) || !(state = NAG_ALLOC(lstate, Integer))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Initialize the generator to a repeatable sequence */
  nag_rand_init_repeat(genid, subid, seed, lseed, state, &lstate, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rand_init_repeat (g05kfc).\n%s\n", fail.message);
    exit_status = 3;
    goto END;
  }

  /* Randomised SVD of A */

  rtol_abs = pow(X02AJC, 0.875);
  rtol_rel = rtol_abs;
  /* nag_rnla_svd_rowext_real (f10cac).
   * Compute the singular values and left and right singular vectors
   * of A (A = U*S*(V^T)
   */
  nag_rnla_svd_rowext_real(jobu, jobvt, m, n, a, pda, k, rtol_abs, rtol_rel,
                           state, s, u, pdu, vt, pdvt, &r, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_rnla_svd_rowext_real (f10cac).\n%s\n", fail.message);
    exit_status = 4;
    goto END;
  }

  printf(" Singular values of A using Randomized SVD:\n");
  for (i = 0; i < r; ++i)
    printf(" %10.1e\n", s[i]);

END:
  NAG_FREE(a);
  NAG_FREE(a_copy);
  NAG_FREE(rcondu);
  NAG_FREE(rcondv);
  NAG_FREE(s);
  NAG_FREE(u);
  NAG_FREE(uerrbd);
  NAG_FREE(verrbd);
  NAG_FREE(vt);
  NAG_FREE(work);
  NAG_FREE(x);
  NAG_FREE(state);

  return exit_status;
}

#undef A