# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iomanip>
# include <iostream>

using namespace std;

# include "helmholtz_exact.hpp"

int main ( );
void helmholtz_exact_print ( int m, int n );
double *r8vec_linspace_new ( int n, double a, double b );
void timestamp ( );

//****************************************************************************80

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    helmholtz_exact_test() tests helmholtz_exact().
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2025
//
//  Author:
//
//    John Burkardt
//
{
  int m;
  int n;

  timestamp ( );
  cout << "\n";
  cout << "helmholtz_exact_test():\n";
  cout << "  C version\n";  
  cout << "  Test helmholtz_exact().\n";

  m = 1;
  n = 2;
  helmholtz_exact_print ( m, n );

  m = 2;
  n = 3;
  helmholtz_exact_print ( m, n );
//
//  Terminate.
//
  cout << "\n";
  cout << "helmholtz_exact_test():\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void helmholtz_exact_print ( int m, int n )

//****************************************************************************80
//
//  Purpose:
//
//    helmholtz_exact_print() tabulates a solution of the Helmholtz equation.
//
//  Discussion:
//
//    The solution is assumed to have a simple form depending on the n-th
//    J Bessel function and its m-th root.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    17 June 2025
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    integer m: the index of the root of the Bessel function J(n,x).
//
//    integer n: the index of the Bessel function.
//
{
  double a;
  double alpha;
  double beta;
  double gamma;
  int i;
  int j;
  int k;
  int nr;
  int nt;
  int nxy;
  double *r;
  double r8_pi = 3.141592653589793;
  double *t;
  double *X;
  double *Y;
  double *Z;

  a = 1.5;

  alpha = 4.0;
  beta = 3.0;
  gamma = 2.0;

  nt = 5;
  t = r8vec_linspace_new ( nt + 1, 0.0, 2.0 * r8_pi );

  nr = 5;
  r = r8vec_linspace_new ( nr, 0.0, 1.0 );
  for ( i = 0; i < nr; i++ )
  {
    r[i] = sqrt ( r[i] ) * a;
  }

  nxy = ( nr - 1 ) * nt + 1;
  X = new double[nxy];
  Y = new double[nxy];

  k = 0;
  for ( i = 0; i < nt; i++ )
  {
    for ( j = 0; j < nr; j++ )
    {
      if ( j == 0 && 0 < i )
      {
        continue;
      }
      else
      {
        X[k] = r[j] * cos ( t[i] );
        Y[k] = r[j] * sin ( t[i] );
        k = k + 1;
      }
    }
  }

  Z = helmholtz_exact ( a, m, n, alpha, beta, gamma, nxy, X, Y );

  cout << "\n";
  cout << "  Helmholtz exact solution with\n";
  cout << "  m = " << m << ", n = " << n << "\n";
  cout << "\n";
  cout << "  k   X(k)  Y(k)  Z(k)\n";
  cout << "\n";
  for ( k = 0; k < nxy; k++ )
  {
    cout << "  " << setw(2) << k
         << "  " << setw(10) << X[k]
         << "  " << setw(10) << Y[k]
         << "  " << setw(10) << Z[k] << "\n";
  }

  delete [] r;
  delete [] t;
  delete [] X;
  delete [] Y;
  delete [] Z;

  return;
}
//****************************************************************************80

double *r8vec_linspace_new ( int n, double a_first, double a_last )

//****************************************************************************80
//
//  Purpose:
//
//    r8vec_linspace_new() creates a vector of linearly spaced values.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12.
//
//    In other words, the interval is divided into N-1 even subintervals,
//    and the endpoints of intervals are used as the points.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    29 March 2011
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    int N, the number of entries in the vector.
//
//    double A_FIRST, A_LAST, the first and last entries.
//
//  Output:
//
//    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
//
{
  double *a;
  int i;

  a = new double[n];

  if ( n == 1 )
  {
    a[0] = ( a_first + a_last ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      a[i] = ( ( double ) ( n - 1 - i ) * a_first 
             + ( double ) (         i ) * a_last ) 
             / ( double ) ( n - 1     );
    }
  }
  return a;
}
//****************************************************************************80

void timestamp ( )

//****************************************************************************80
//
//  Purpose:
//
//    timestamp() prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    19 March 2018
//
//  Author:
//
//    John Burkardt
//
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct std::tm *tm_ptr;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}