/* nag_lapackeig_dgesvd (f08kbc) Example Program.
 *
 * Copyright 2023 Numerical Algorithms Group.
 *
 * Mark 29.2, 2023.
 */

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

int main(void) {

  /* Scalars */
  double alpha, beta, eps, norm, serrbd;
  Integer exit_status = 0, i, j, m, n, pda, pdd, pdu, pdvt;

  /* Arrays */
  double *a = 0, *d = 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;

#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_dgesvd (f08kbc) 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)) || !(d = 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(n * n, double)) ||
      !(work = NAG_ALLOC(MIN(m, n), double))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  pdu = m;
  pdvt = n;
#ifdef NAG_COLUMN_MAJOR
  pda = m;
  pdd = m;
#else
  pda = n;
  pdd = 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]");

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

  /* nag_lapackeig_dgesvd (f08kbc).
   * Compute the singular values and left and right singular vectors
   * of A (A = U*S*(V^T), m.ge.n)
   */
  nag_lapackeig_dgesvd(order, Nag_AllU, Nag_AllVT, m, n, a, 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;
  }

  /* U <- U*S */
  for (i = 1; i <= m; i++)
    for (j = 1; j <= n; j++)
      U(i, j) *= s[j - 1];

  /* nag_blast_dgemm (f16yac):
   * Compute D = D - U*S*V^T from the factorization of A
   * and store in d */
  alpha = -1.0;
  beta = 1.0;
  nag_blast_dgemm(order, Nag_NoTrans, Nag_NoTrans, m, n, n, alpha, u, pdu, vt,
                  pdvt, beta, d, pdd, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dgemm (f16yac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_blast_dge_norm (f16rac)
   * Find norm of matrix D and print warning if it is too large.
   */
  nag_blast_dge_norm(order, Nag_OneNorm, m, n, d, pdd, &norm, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_blast_dge_norm (f16rac).\n%s\n", fail.message);
    exit_status = 1;
    goto END;
  }

  /* nag_machine_precision (x02ajc): the machine precision. */
  eps = nag_machine_precision;
  if (norm > pow(eps, 0.8)) {
    printf("\nNorm of A-(U*S*V^T) is much greater than 0.\n"
           "Schur factorization has failed.\n");
    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).
   */
  serrbd = eps * s[0];

  /* Estimate reciprocal condition numbers for the singular vectors using
   * nag_lapackeig_ddisna (f08flc).
   */
  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 < n; ++i) {
    uerrbd[i] = serrbd / rcondu[i];
    verrbd[i] = serrbd / rcondv[i];
  }

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

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

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

  return exit_status;
}

#undef A
#undef U