# include <cmath>
# include <cstdlib>

using namespace std;

# include "biharmonic_exact.hpp"

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

double biharmonic_exact_r1 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g )

//****************************************************************************80
//
//  Purpose;
//
//    biharmonic_exact_r1() evaluates exact biharmonic residual for W(X,Y) #1.
//
//  Discussion:
//
//   Note the formula for W:
//
//   W = ( a     * cosh ( g * X ) 
//       + b     * sinh ( g * X ) 
//       + c * X * cosh ( g * X ) 
//       + d * X * sinh ( g * X ) ) 
//       * 
//       ( e * cos ( g * Y ) 
//       + f * sin ( g * Y ) )
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 August 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    real X, Y: the coordinates of the points.
//
//    real a, b, c, d, e, f, g: parameters.
//
//  Output:
//
//    real R: the residual evaluated at the points (X,Y).
//
{
  double R;
  double Wxxxx;
  double Wxxyy;
  double Wyyyy;

  Wxxxx =  
    pow ( g, 3 ) * ( e * cos ( g * Y ) + f * sin ( g * Y ) ) 
    * 
    (     a * g     * cosh ( g * X ) 
    +     b * g     * sinh ( g * X ) 
    +     c * g * X * cosh ( g * X ) 
    + 4 * c         * sinh ( g * X ) 
    +     d * g * X * sinh ( g * X ) 
    + 4 * d         * cosh ( g * X ) );

  Wxxyy = 
    - pow ( g, 3 ) * ( e * cos ( g * Y ) + f * sin ( g * Y ) ) 
    * 
    (     a * g     * cosh ( g * X ) 
    +     b * g     * sinh ( g * X )  
    +     c * g * X * cosh ( g * X )  
    + 2 * c         * sinh ( g * X )  
    +     d * g * X * sinh ( g * X )  
    + 2 * d         * cosh ( g * X ) );

  Wyyyy = 
    pow ( g, 4 ) * ( e * cos ( g * Y ) + f * sin ( g * Y ) ) 
    * 
    ( a     * cosh ( g * X ) 
    + b     * sinh ( g * X ) 
    + c * X * cosh ( g * X ) 
    + d * X * sinh ( g * X ) );

  R = Wxxxx + 2.0 * Wxxyy + Wyyyy;

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

double biharmonic_exact_r2 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g )

//****************************************************************************80
//
//  Purpose;
//
//    biharmonic_exact_r2() evaluates exact biharmonic residual for W(X,Y) #2.
//
//  Discussion:
//
//   Note the formula for W:
//
//  W = ( a     * cos ( g * X ) 
//      + b     * sin ( g * X ) 
//      + c * X * cos ( g * X ) 
//      + d * X * sin ( g * X ) )  
//      *
//      ( e * cosh ( g * Y ) 
//      + f * sinh ( g * Y ) )
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 August 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    real X, Y: the coordinates of the points.
//
//    real a, b, c, d, e, f, g: parameters.
//
//  Output:
//
//    real R: the residual evaluated at the points (X,Y).
//
{
  double R;
  double Wxxxx;
  double Wxxyy;
  double Wyyyy;

  Wxxxx = pow ( g, 3 ) * ( e * cosh ( g * Y ) + f * sinh ( g * Y ) ) 
    * 
    (     a * g     * cos ( g * X ) 
    +     b * g     * sin ( g * X ) 
    +     c * g * X * cos ( g * X ) 
    + 4 * c         * sin ( g * X ) 
    +     d * g * X * sin ( g * X ) 
    - 4 * d         * cos ( g * X ) );

  Wxxyy =  - pow ( g, 3 ) * ( e * cosh ( g * Y ) + f * sinh ( g * Y ) ) 
    * 
    (     a * g     * cos ( g * X ) 
    +     b * g     * sin ( g * X ) 
    +     c * g * X * cos ( g * X ) 
    + 2 * c         * sin ( g * X ) 
    +     d * g * X * sin ( g * X ) 
    - 2 * d         * cos ( g * X ) );

  Wyyyy = pow ( g, 4 ) * ( e * cosh ( g * Y ) + f * sinh ( g * Y ) ) 
    * 
    ( a     * cos ( g * X ) 
    + b     * sin ( g * X ) 
    + c * X * cos ( g * X ) 
    + d * X * sin ( g * X ) );

  R = Wxxxx + 2.0 * Wxxyy + Wyyyy;

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

double biharmonic_exact_r3 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f )

//****************************************************************************80
//
//  Purpose;
//
//    biharmonic_exact_r3() evaluates exact biharmonic residual for W(X,Y) #3.
//
//  Discussion:
//
//   Note the formula for W:
//
//   R = sqrt ( ( X - e )**2 + ( Y - f )**2 )
//
//   W =   a * R**2 * log ( R ) 
//       + b * R**2 
//       + c * log ( R ) 
//       + d
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 August 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    real X, Y: the coordinates of the points.
//
//    real a, b, c, d, e, f: parameters.
//
//  Output:
//
//    real R: the residual evaluated at the points (X,Y).
//
{
  double R;
  double S;
  double Wxxxx;
  double Wxxyy;
  double Wyyyy;

  S = pow ( e - X, 2 ) + pow ( f - Y, 2 );

  Wxxxx =  2 * ( 8 * a * pow ( e - X, 4 )
    / pow ( S, 2 ) - 12 * a * pow ( e - X, 2 ) 
    / S            +  3 * a - 24 * c * pow ( e - X, 4 )
    / pow ( S, 3 ) + 24 * c * pow ( e - X, 2 ) 
    / pow ( S, 2 ) -  3 * c 
    / S ) 
    / S;

  Wxxyy =  2 * ( 8 * a * pow ( e - X, 2 ) * pow ( f - Y, 2 ) 
    / pow ( S, 2 ) - 2 * a * pow ( e - X, 2 )
    / S            - 2 * a * pow ( f - Y, 2 ) 
    / S            + a - 24 * c * pow ( e - X, 2 ) * pow ( f - Y, 2 )
    / pow ( S, 3 ) + 4 * c * pow ( e - X, 2 )
    / pow ( S, 2 ) + 4 * c * pow ( f - Y, 2 )
    / pow ( S, 2 ) - c 
    / S ) 
    / S;

  Wyyyy =  2 * ( 8 * a * pow ( f - Y, 4 )
    / pow ( S, 2 ) - 12 * a * pow ( f - Y, 2 )
    / S            +  3 * a - 24 * c * pow ( f - Y, 4 )
    / pow ( S, 3 ) + 24 * c * pow ( f - Y, 2 ) 
    / pow ( S, 2 )  - 3 * c 
    / S ) 
    / S;

  R = Wxxxx + 2.0 * Wxxyy + Wyyyy;

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

double biharmonic_exact_w1 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g )

//****************************************************************************80
//
//  Purpose;
//
//    biharmonic_exact1() evaluates exact biharmonic solution W(X,Y) #1.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 August 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    real X, Y: the coordinates of the points.
//
//    real a, b, c, d, e, f, g: parameters.
//
//  Output:
//
//    real W: the solution evaluated at the points (X,Y).
//
{
  double W;

  W = ( a     * cosh ( g * X )
      + b     * sinh ( g * X )
      + c * X * cosh ( g * X )
      + d * X * sinh ( g * X ) )  
      * 
      ( e * cos ( g * Y ) 
      + f * sin ( g * Y ) );

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

double biharmonic_exact_w2 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f, double g )

//****************************************************************************80
//
//  Purpose;
//
//    biharmonic_exact_w2() evaluates exact biharmonic solution W(X,Y) #2.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 August 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    real X, Y: the coordinates of the points.
//
//    real a, b, c, d, e, f, g: parameters.
//
//  Output:
//
//    real W: the solution evaluated at the points (X,Y).
//
{
  double W;

  W = ( a     * cos ( g * X ) 
      + b     * sin ( g * X ) 
      + c * X * cos ( g * X ) 
      + d * X * sin ( g * X ) )  
      * 
      ( e * cosh ( g * Y ) 
      + f * sinh ( g * Y ) );

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

double biharmonic_exact_w3 ( double X, double Y, double a, double b, double c, 
  double d, double e, double f )

//****************************************************************************80
//
//  Purpose;
//
//    biharmonic_exact_w3() evaluates exact biharmonic solution W(X,Y) #3.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    02 August 2024
//
//  Author:
//
//    John Burkardt
//
//  Input:
//
//    real X, Y: the coordinates of the points.
//
//    real a, b, c, d, e, f: parameters.
//
//  Output:
//
//    real W: the solution evaluated at the points (X,Y).
//
{
  double R;
  double W;

  R = sqrt ( pow ( X - e, 2 ) + pow ( Y - f, 2 ) );

  W =   a * R * R * log ( R ) 
      + b * R * R 
      + c * log ( R ) 
      + d;

  return W;
}