# include <math.h>
# include <stdio.h>
# include <stdlib.h>
# include <time.h>

# include "helmholtz_exact.h"

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

/******************************************************************************/

int main ( )

/******************************************************************************/
/*
  Purpose:

    helmholtz_exact_test() tests helmholtz_exact().

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    16 June 2025

  Author:

    John Burkardt
*/
{
  int m;
  int n;

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

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

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

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

void helmholtz_exact_print ( int m, int n )

/******************************************************************************/
/*
  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:

    16 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 = ( double * ) malloc ( nxy * sizeof ( double ) );
  Y = ( double * ) malloc ( nxy * sizeof ( double ) );

  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 );

  printf ( "\n" );
  printf ( "  Helmholtz exact solution with\n" );
  printf ( "  m = %d, n = %d\n", m, n );
  printf ( "\n" );
  printf ( "  k   X(k)  Y(k)  Z(k)\n" );
  printf ( "\n" );
  for ( k = 0; k < nxy; k++ )
  {
    printf ( "  %2d  %10.4f  %10.4f  %14.6g\n", k, X[k], Y[k], Z[k] );
  }

  free ( r );
  free ( t );
  free ( X );
  free ( Y );
  free ( Z );

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

double *r8vec_linspace_new ( int n, double a, double b )

/******************************************************************************/
/*
  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, B, the first and last entries.

  Output:

    double R8VEC_LINSPACE_NEW[N], a vector of linearly spaced data.
*/
{
  int i;
  double *x;

  x = ( double * ) malloc ( n * sizeof ( double ) );

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

void timestamp ( )

/******************************************************************************/
/*
  Purpose:
 
    timestamp() prints the current YMDHMS date as a time stamp.

  Example:

    17 June 2014 09:45:54 AM

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    01 May 2021

  Author:

    John Burkardt
*/
{
# define TIME_SIZE 40

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

  now = time ( NULL );
  tm = localtime ( &now );

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

  printf ( "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}