QUESO::LagrangeBasis1D1DFunction Class Reference

Class for Lagrange polynomial basis. More...

#include <1D1DFunction.h>

Inheritance 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, and m_positionValues.

  :
  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.

{
}

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, 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 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().

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

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