Class for first type Chebyshev-Gauss quadrature rule for one-dimensional functions. More...

#include <1DQuadrature.h>

Inheritance diagram for QUESO::WignerInverseChebyshev1st1DQuadrature:

Collaboration diagram for QUESO::WignerInverseChebyshev1st1DQuadrature:

Public Member Functions
Constructor/Destructor methods
	WignerInverseChebyshev1st1DQuadrature (double minDomainValue, double maxDomainValue, unsigned int order)
	TODO: Default constructor. More...

	~WignerInverseChebyshev1st1DQuadrature ()
	Destructor. More...

Mathematical methods
void	dumbRoutine () const
	A bogus method. More...

Public Member Functions inherited from QUESO::Base1DQuadrature
	Base1DQuadrature (double minDomainValue, double maxDomainValue, unsigned int order)
	Default constructor. More...

virtual	~Base1DQuadrature ()
	Virtual destructor. More...

double	minDomainValue () const
	Returns the minimum value of the domain of the (one-dimensional) function. More...

double	maxDomainValue () const
	Returns the maximum value of the domain of the (one-dimensional) function. More...

unsigned int	order () const
	Returns the order of the quadrature rule. More...

const std::vector< double > &	positions () const
	Array of the positions for the numerical integration. More...

const std::vector< double > &	weights () const
	Array of the weights used in the numerical integration. More...

Additional Inherited Members
Protected Attributes inherited from QUESO::Base1DQuadrature
double	m_minDomainValue

double	m_maxDomainValue

unsigned int	m_order

std::vector< double >	m_positions

std::vector< double >	m_weights

Detailed Description

Class for first type Chebyshev-Gauss quadrature rule for one-dimensional functions.

Chebyshev-Gauss quadrature, also called Chebyshev Type 1 quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function $W(x)=\frac{1}{\sqrt{1-x^2}}$ .
The abscissas for quadrature order $ n $ are given by the roots of the Chebyshev polynomial of the first kind $ T_n(x) $ , which occur symmetrically about 0.

The abscissas are given explicitly by $x_i=\cos[\frac{(2i-1)\pi}{2n}]$ and the weights are $w_i=\frac{\pi}{n}.$

See Also: Weisstein, Eric W. "Chebyshev-Gauss Quadrature." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/Chebyshev-GaussQuadrature.html.; http://en.wikipedia.org/wiki/Chebyshev-Gauss_quadrature.

Definition at line 267 of file 1DQuadrature.h.

Constructor & Destructor Documentation

QUESO::WignerInverseChebyshev1st1DQuadrature::WignerInverseChebyshev1st1DQuadrature	(	double	minDomainValue,
		double	maxDomainValue,
		unsigned int	order
	)

TODO: Default constructor.

Todo:: Constructs a Gaussian-Chebyshev quadrature (of first type) of order order, in the interval [minDomainValue,maxDomainValue]. This method scales the the abscissas (positions) of the quadrature from the interval [-1,1] to [minDomainValue,maxDomainValue].

Definition at line 678 of file 1DQuadrature.C.

References QUESO::Base1DQuadrature::m_maxDomainValue, QUESO::Base1DQuadrature::m_minDomainValue, QUESO::Base1DQuadrature::m_order, QUESO::Base1DQuadrature::m_positions, QUESO::Base1DQuadrature::m_weights, UQ_FATAL_TEST_MACRO, and QUESO::UQ_UNAVAILABLE_RANK.

   :
   Base1DQuadrature(minDomainValue,maxDomainValue,order)
 {
   m_positions.resize(m_order+1,0.); // Yes, '+1'
   m_weights.resize  (m_order+1,0.); // Yes, '+1'
 
   // http://en.wikipedia.org/wiki/Chebyshev-Gauss_quadrature
   switch (m_order) {
     default:
       UQ_FATAL_TEST_MACRO(true,
                           UQ_UNAVAILABLE_RANK,
                           "WignerInverseChebyshev1st1DQuadrature::constructor()",
                           "order not supported");
     break;
   }
 
   // Scale positions from the interval [-1, 1] to the interval [min,max]
   for (unsigned int j = 0; j < m_positions.size(); ++j) {
     m_positions[j] = .5*(m_maxDomainValue - m_minDomainValue)*m_positions[j] + .5*(m_maxDomainValue + m_minDomainValue);
     m_weights[j] *= .5*(m_maxDomainValue - m_minDomainValue);
   }
 }

QUESO::WignerInverseChebyshev1st1DQuadrature::~WignerInverseChebyshev1st1DQuadrature ( )

Destructor.

Definition at line 705 of file 1DQuadrature.C.

706 {

707 }

Member Function Documentation

void QUESO::WignerInverseChebyshev1st1DQuadrature::dumbRoutine ( ) const

virtual

A bogus method.

Implements QUESO::Base1DQuadrature.

Definition at line 710 of file 1DQuadrature.C.

 {
   return;
 }

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

src/misc/inc/1DQuadrature.h
src/misc/src/1DQuadrature.C

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation