/* nag_matop_complex_gen_matrix_cond_num (f01kbc) Example Program.
 *
 * Copyright 2022 Numerical Algorithms Group.
 *
 * Mark 28.3, 2022.
 */
#include <math.h>
#include <nag.h>

#ifdef __cplusplus
extern "C" {
#endif
static void NAG_CALL f(Integer *iflag, Integer nz, const Complex z[],
                       Complex fz[], Nag_Comm *comm);
#ifdef __cplusplus
}
#endif

#define A(I, J) a[J * pda + I]

int main(void) {

  /* Scalars */
  Integer exit_status = 0;
  Integer i, iflag, j, n, pda;
  double conda, cond_rel, eps, norma, normfa;
  /* Arrays */
  static double ruser[1] = {-1.0};
  Complex *a = 0;
  /* Nag Types */
  Nag_OrderType order = Nag_ColMajor;
  Nag_Comm comm;
  NagError fail;

  INIT_FAIL(fail);

  /* Output preamble */
  printf("nag_matop_complex_gen_matrix_cond_num (f01kbc) ");
  printf("Example Program Results\n\n");

  /* For communication with user-supplied functions: */
  comm.user = ruser;

  fflush(stdout);

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

  /* Read in the problem size */
  scanf("%" NAG_IFMT "%*[^\n]", &n);

  pda = n;
  if (!(a = NAG_ALLOC((pda) * (n), Complex))) {
    printf("Allocation failure\n");
    exit_status = -1;
    goto END;
  }

  /* Read in the matrix A from data file */
  for (i = 0; i < n; i++)
    for (j = 0; j < n; j++)
      scanf(" ( %lf , %lf ) ", &A(i, j).re, &A(i, j).im);
  scanf("%*[^\n] ");

  /* Print matrix A using nag_file_print_matrix_complex_gen (x04dac):
   *   Print complex general matrix (easy-to-use)
   */
  nag_file_print_matrix_complex_gen(order, Nag_GeneralMatrix, Nag_NonUnitDiag,
                                    n, n, a, pda, "A", NULL, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_file_print_matrix_complex_gen (x04dac)\n%s\n",
           fail.message);
    exit_status = 2;
    goto END;
  }

  /* Find absolute condition number estimate of f(A) for a complex matrix A
   * using ... nag_matop_complex_gen_matrix_cond_num (f01kbc):
   *   Condition number for general function of a complex matrix
   *   using numerical differentiation.
   */
  nag_matop_complex_gen_matrix_cond_num(n, a, pda, f, &comm, &iflag, &conda,
                                        &norma, &normfa, &fail);
  if (fail.code != NE_NOERROR) {
    printf("Error from nag_matop_complex_gen_matrix_cond_num (f01kbc)\n%s\n",
           fail.message);
    exit_status = 1;
    goto END;
  }

  /* Print absolute condition number estimate */
  printf("\nF(A) = sin(2A)\n");
  printf("Estimated absolute condition number is: %7.2f\n", conda);

  /* nag_machine_precision (x02ajc) The machine precision */
  eps = nag_machine_precision;

  /* Find relative condition number estimate */
  if (normfa > eps) {
    cond_rel = conda * norma / normfa;
    printf("Estimated relative condition number is: %7.2f\n", cond_rel);
  } else {
    printf("The estimated norm of f(A) is effectively zero");
    printf("and so the relative condition number is undefined.\n");
  }

END:
  NAG_FREE(a);
  return exit_status;
}

static void NAG_CALL f(Integer *iflag, Integer nz, const Complex z[],
                       Complex fz[], Nag_Comm *comm) {
  /* Scalars */
  Integer j;
#ifdef _OPENMP
#pragma omp master
#endif
  if (comm->user[0] == -1.0) {
    printf("(User-supplied callback f, first invocation.)\n");
    comm->user[0] = 0.0;
  }
  for (j = 0; j < nz; j++) {
    /* Complex representation of sin(2z). */
    fz[j].re = sin(2.0 * z[j].re) * cosh(2.0 * z[j].im);
    fz[j].im = cos(2.0 * z[j].re) * sinh(2.0 * z[j].im);
  }
  /* Set iflag nonzero to terminate execution for any reason. */
  *iflag = 0;
}