Class for Lagrange polynomial basis. More...

#include <1D1DFunction.h>

Inheritance diagram for QUESO::LagrangeBasis1D1DFunction:

Collaboration diagram for QUESO::LagrangeBasis1D1DFunction:

Public Member Functions
Constructor/Destructor methods
	LagrangeBasis1D1DFunction (const std::vector< double > &positionValues, unsigned int basisIndex)
	Default constructor. More...

	~LagrangeBasis1D1DFunction ()
	Destructor. More...

Mathematical methods
double	value (double domainValue) const
	Returns the value of the Lagrange basis at point `domainValue`. More...

double	deriv (double domainValue) const
	TODO: Returns the value of the derivative of the Lagrange basis at point `domainValue`. More...

Public Member Functions inherited from QUESO::Base1D1DFunction
	Base1D1DFunction (double minDomainValue, double maxDomainValue)
	Default constructor. More...

virtual	~Base1D1DFunction ()
	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...

virtual double	multiplyAndIntegrate (const Base1D1DFunction &func, unsigned int quadratureOrder, double *resultWithMultiplicationByTAsWell) const
	TODO: Multiplies `this` function with `function`, and integrates it numerically. See template specialization. More...

Protected Attributes
std::vector< double >	m_positionValues

unsigned int	m_basisIndex

Protected Attributes inherited from QUESO::Base1D1DFunction
double	m_minDomainValue

double	m_maxDomainValue

Detailed Description

Class for Lagrange polynomial basis.

Given a set of $ k+1 $ data points $(x_0, y_0),\ldots,(x_j, y_j),\ldots,(x_k, y_k)$ where no two $ x_j $ are the same, the interpolation polynomial in the Lagrange form is a linear combination

$L(x) = \sum_{j=0}^{k} y_j \ell_j(x)$

of Lagrange basis polynomials

$\ell_j(x) = \prod_{0\le m\le k;\, m\neq j} \frac{x-x_m}{x_j-x_m} = \frac{(x-x_0)}{(x_j-x_0)} \cdots \frac{(x-x_{j-1})}{(x_j-x_{j-1})} \frac{(x-x_{j+1})}{(x_j-x_{j+1})} \cdots \frac{(x-x_k)}{(x_j-x_k)},$

where $0\le j\le k$ .
This class implements the one-dimensional function (Lagrange basis) $\ell_j(x)$ . In this class, the array std::vector<double>& positionValues stores the points $ x_1, x_2, ... x_n $ and the index $ j $ is stored in basisIndex.

Definition at line 609 of file 1D1DFunction.h.

Constructor & Destructor Documentation

QUESO::LagrangeBasis1D1DFunction::LagrangeBasis1D1DFunction	(	const std::vector< double > &	positionValues,
		unsigned int	basisIndex
	)

Default constructor.

Definition at line 820 of file 1D1DFunction.C.

References m_basisIndex, m_positionValues, and queso_require_less_msg.

   :
   Base1D1DFunction(-INFINITY,INFINITY),
   m_positionValues(positionValues),
   m_basisIndex    (basisIndex)
 {
   queso_require_less_msg(m_basisIndex, m_positionValues.size(), "invalid input");
 }

QUESO::LagrangeBasis1D1DFunction::~LagrangeBasis1D1DFunction ( )

Destructor.

Definition at line 831 of file 1D1DFunction.C.

832 {

833 }

Member Function Documentation

double QUESO::LagrangeBasis1D1DFunction::deriv ( double domainValue ) const

virtual

TODO: Returns the value of the derivative of the Lagrange basis at point domainValue.

Todo:: This function checks if point domainValue belongs to the domain of this function, and in affirmative case, it returns the value of the derivative at such point.

Implements QUESO::Base1D1DFunction.

Definition at line 853 of file 1D1DFunction.C.

References QUESO::Base1D1DFunction::m_maxDomainValue, QUESO::Base1D1DFunction::m_minDomainValue, queso_not_implemented, queso_require_msg, and value().

 {
   double value = 0.;
 
   if ((domainValue < m_minDomainValue) || (domainValue > m_maxDomainValue)) {
     std::cerr << "In LagrangeBasis1D1DFunction::deriv()"
               << ": requested x ("            << domainValue
               << ") is out of the interval (" << m_minDomainValue
               << ", "                         << m_maxDomainValue
               << ")"
               << std::endl;
   }
 
   queso_require_msg(!((domainValue < m_minDomainValue) || (domainValue > m_maxDomainValue)), "x out of range");
 
   queso_not_implemented();
 
   return value;
 }

double QUESO::LagrangeBasis1D1DFunction::value ( double domainValue ) const

virtual

Returns the value of the Lagrange basis at point domainValue.

Implements QUESO::Base1D1DFunction.

Definition at line 836 of file 1D1DFunction.C.

References k, m_basisIndex, and m_positionValues.

Referenced by deriv().

 {
   double scaleFactor = 1.;
 
   unsigned int k = m_basisIndex;
   double posK = m_positionValues[k];
   for (unsigned int j = 0; j < m_positionValues.size(); ++j) {
     if (j != k) {
       double posJ = m_positionValues[j];
       scaleFactor *= (domainValue-posJ)/(posK-posJ);
     }
   }
 
   return scaleFactor;
 }

Member Data Documentation

unsigned int QUESO::LagrangeBasis1D1DFunction::m_basisIndex

protected

Definition at line 636 of file 1D1DFunction.h.

Referenced by LagrangeBasis1D1DFunction(), and value().

std::vector<double> QUESO::LagrangeBasis1D1DFunction::m_positionValues

protected

Definition at line 635 of file 1D1DFunction.h.

Referenced by LagrangeBasis1D1DFunction(), and value().

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

src/misc/inc/1D1DFunction.h
src/misc/src/1D1DFunction.C

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation