CppNoddy::FnQuadrature Class Reference

A quadrature class that takes a function pointer. More...

#include <FnQuadrature.h>

Inheritance diagram for CppNoddy::FnQuadrature:

Public Types
typedef void(*	fn_ptr) (const double &, double &)
	The function pointer associated with this instance. More...

Public Member Functions
	FnQuadrature (fn_ptr ptr_to_fn, const double &x1, const double &x2, const unsigned &num_of_regions)
	Constructor. More...
	FnQuadrature (fn_ptr ptr_to_fn, const double &x1, const double &x2, const DenseVector< double > &nodes)
	Constructor. More...
void	set_subintervals (const unsigned &n)
	A set method to define a UNIFORM number of sub intervals. More...
double	Gauss (const int &n)
	n-point Gauss rule inefficiently written! More...
double	sub_Gauss (const int &n)
	Evaluate the integral by applying an n-point Gauss rule on each of N sub-intervals. More...
double	trapezium ()
	Quick trapezium summation again for sanity checking. More...

Detailed Description

A quadrature class that takes a function pointer.

Definition at line 15 of file FnQuadrature.h.

Member Typedef Documentation

fn_ptr

typedef void(* CppNoddy::FnQuadrature::fn_ptr) (const double &, double &)

The function pointer associated with this instance.

Definition at line 20 of file FnQuadrature.h.

Constructor & Destructor Documentation

FnQuadrature() [1/2]

CppNoddy::FnQuadrature::FnQuadrature	(	fn_ptr	ptr_to_fn,
		const double &	x1,
		const double &	x2,
		const unsigned &	num_of_regions
	)

Constructor.

Parameters

ptr_to_fn	the function that defines the integrand.
x1	left hand boundary of the domain.
x2	right hand boundary of the domain.
num_of_regions	initial number of sub-regions to divide the domain into.

Definition at line 15 of file FnQuadrature.cpp.

                                                             :
    A(x1),
    B(x2),
    p_FN(ptr_to_fn) {
    NODES = Utility::uniform_node_vector(x1, x2, num_of_regions);
  }

References CppNoddy::Utility::uniform_node_vector().

FnQuadrature() [2/2]

CppNoddy::FnQuadrature::FnQuadrature	(	fn_ptr	ptr_to_fn,
		const double &	x1,
		const double &	x2,
		const DenseVector< double > &	nodes
	)

Constructor.

Parameters

ptr_to_fn	the function that defines the integrand.
x1	left hand boundary of the domain.
x2	right hand boundary of the domain.
nodes	A vector of nodal positions.

Definition at line 26 of file FnQuadrature.cpp.

                                                               :
    A(x1),
    B(x2),
    p_FN(ptr_to_fn) {
    NODES = nodes;
  }

Member Function Documentation

Gauss()

double CppNoddy::FnQuadrature::Gauss

(

const int &

n

)

n-point Gauss rule inefficiently written!

Parameters

n	The number of points.

Returns

Approximation to the integral

Definition at line 40 of file FnQuadrature.cpp.

                                         {
    DenseVector<double> t;    // evaluation points in [-1,1]
    DenseVector<double> w;    // respective weight values
    switch(n) {
    case 1:
      t.push_back(0.0);
      w.push_back(2.0);
      break;
    case 2:
      t.push_back(-1. / sqrt(3.));
      w.push_back(1.0);
      t.push_back(1. / sqrt(3.));
      w.push_back(1.0);
      break;
    case 3:
      t.push_back(0.0);
      w.push_back(8. / 9.);
      t.push_back(-0.774596669241483);
      w.push_back(5. / 9.);
      t.push_back(0.774596669241483);
      w.push_back(5. / 9.);
      break;
    default:
      std::string problem;
      problem = " The Quadrature.Gauss method is trying to apply \n";
      problem += " a Gauss rule with more points than 3. \n";
      problem += " Currenlty only n=1,2,3 are supported! \n";
      throw ExceptionRuntime(problem);
    }
 
    double sum = 0.0;
    double c = 0.5 * (B + A);
    double m = 0.5 * (B - A);
    double f, x;
    t.scale(m);
 
    for(unsigned i = 0; i < t.size(); ++i) {
      x = c + t[ i ];
      p_FN(x, f);
      sum += w[ i ] * f;
    }
 
    sum = sum * m;
 
    return sum;
  }

References f, m, CppNoddy::DenseVector< _Type >::push_back(), CppNoddy::DenseVector< _Type >::scale(), and CppNoddy::DenseVector< _Type >::size().

Referenced by sub_Gauss().

set_subintervals()

void CppNoddy::FnQuadrature::set_subintervals

(

const unsigned &

n

)

A set method to define a UNIFORM number of sub intervals.

Parameters

n	Number of sub intervals

Definition at line 36 of file FnQuadrature.cpp.

                                                       {
    NODES = Utility::uniform_node_vector(A, B, n);
  }

References CppNoddy::Utility::uniform_node_vector().

Referenced by main().

sub_Gauss()

double CppNoddy::FnQuadrature::sub_Gauss

(

const int &

n

)

Evaluate the integral by applying an n-point Gauss rule on each of N sub-intervals.

This is inefficient in terms of class instantiation for each sub-interval, but not currently an issue.

Parameters

n	The order of the Gauss rule.

Returns

Approximation to the integral.

Definition at line 88 of file FnQuadrature.cpp.

                                             {
    double x_left, x_right;
    double sum = 0.0;
    unsigned num = NODES.size();
    //    double h = ( B - A ) / num;
 
    for(unsigned i = 0; i < num - 1; ++i) {
      //x_left = A + i * h;
      x_left = NODES[ i ];
      //x_right = x_left + h;
      x_right = NODES[ i + 1 ];
      FnQuadrature I(p_FN, x_left, x_right, num);
      sum += I.Gauss(n);
    }
 
    return sum;
  }

References Gauss(), and CppNoddy::DenseVector< _Type >::size().

Referenced by main().

trapezium()

double CppNoddy::FnQuadrature::trapezium

(

)

Quick trapezium summation again for sanity checking.

Should be essentially equivalent to the 1-point Gauss rule.

Returns

An approximation to the integral.

Definition at line 106 of file FnQuadrature.cpp.

                                 {
    double sum = 0.0;
    unsigned num = NODES.size();
    double h = (B - A) / num;
    double x_left, x_right;
    double f_left, f_right;
 
    x_left = A;
    p_FN(x_left, f_left);
 
    for(unsigned i = 0; i < num; ++i) {
      x_right = A + (i + 1) * h;
      p_FN(x_right, f_right);
      sum += (f_left + f_right);
      f_left = f_right;
    }
    sum *= h / 2.;
    return sum;
  }

References h, and CppNoddy::DenseVector< _Type >::size().

Referenced by main().

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The documentation for this class was generated from the following files:

• include/FnQuadrature.h
• src/FnQuadrature.cpp