QUESO::LagrangePolynomial1D1DFunction Class Reference

Class for one-dimensional Lagrange polynomials. More...

#include <1D1DFunction.h>

Inheritance diagram for QUESO::LagrangePolynomial1D1DFunction:

Public Member Functions
Constructor/Destructor methods
	LagrangePolynomial1D1DFunction (const std::vector< double > &positionValues, const std::vector< double > *functionValues)
	Default constructor. More...
	~LagrangePolynomial1D1DFunction ()
	Destructor. More...
Mathematical methods
double	value (double domainValue) const
	Returns the value of the Lagrange polynomial at point domainValue. More...
double	deriv (double domainValue) const
	TODO: Returns the value of the derivative of the Lagrange polynomial 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
std::vector< double >	m_functionValues
Protected Attributes inherited from QUESO::Base1D1DFunction
double	m_minDomainValue
double	m_maxDomainValue

Detailed Description

Class for one-dimensional Lagrange polynomials.

The Lagrange interpolating polynomial of a one-dimensional function \( f(x) = y \) is the polynomial \( P(x) \) of degree \( \leq n-1 \) that passes through the \( n \) points \( (x_1,y_1=f(x_1)), (x_2,y_2=f(x_2)), ..., (x_n,y_n=f(x_n))\), and is given by:

\[ P(x)=\sum_{j=1}^n \prod_{k=1; k\not=j}^n \frac{x-x_k}{x_j-x_k}.\]

Written explicitly,

\[ P(x)=\frac{(x-x_2)(x-x_3)...(x-x_n)}{(x_1-x_2)(x_1-x_3)...(x_1-x_n)}y_1+ \frac{(x-x_1)(x-x_3)...(x-x_n)}{(x_2-x_1)(x_2-x_3)...(x_2-x_n)}y_2+...+ \frac{(x-x_1)(x-x_2)...(x-x_(n-1))}{(x_n-x_1)(x_n-x_2)...(x_n-x_(n-1))}y_n.\]

In this class, the array std::vector<double>& positionValues stores the points \( x_1, x_2, ... x_n \) and the array std::vector<double>* functionValues stores the points \( y_1, y_2, ... y_n \) of the Lagrange polynomial.

See Also

Archer, Branden and Weisstein, Eric W. "Lagrange Interpolating Polynomial." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html.

Definition at line 558 of file 1D1DFunction.h.

Constructor & Destructor Documentation

QUESO::LagrangePolynomial1D1DFunction::LagrangePolynomial1D1DFunction	(	const std::vector< double > &	positionValues,
		const std::vector< double > *	functionValues
	)

Default constructor.

Definition at line 743 of file 1D1DFunction.C.

References m_functionValues, m_positionValues, and QUESO::queso_require_equal_to_msg.

  :
  Base1D1DFunction(-INFINITY,INFINITY),
  m_positionValues(positionValues),
  m_functionValues(positionValues.size(),1.)
{
  if (functionValues) {
    queso_require_equal_to_msg(m_positionValues.size(), functionValues->size(), "invalid input");
    m_functionValues = *functionValues;
  }
}

QUESO::LagrangePolynomial1D1DFunction::~LagrangePolynomial1D1DFunction

(

)

Destructor.

Definition at line 757 of file 1D1DFunction.C.

{
}

Member Function Documentation

double QUESO::LagrangePolynomial1D1DFunction::deriv ( double  domainValue ) const

virtual

TODO: Returns the value of the derivative of the Lagrange polynomial 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 797 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 LagrangePolynomial1D1DFunction::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::LagrangePolynomial1D1DFunction::value ( double  domainValue ) const

virtual

Returns the value of the Lagrange polynomial at point domainValue.

Implements QUESO::Base1D1DFunction.

Definition at line 762 of file 1D1DFunction.C.

References m_functionValues, and m_positionValues.

Referenced by deriv().

{
  double value = 0.;

  for (unsigned int k = 0; k < m_positionValues.size(); ++k) {
    double scaleFactor = 1.;
    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);
      }
    }

    //if (m_env.subDisplayFile()) {
    //  *m_env.subDisplayFile() << "In sddTG<K_V,K_M>::lagrange()"
    //                          << ": k = " << k
    //                          << ", scaleFactor = " << scaleFactor
    //                          << std::endl;
    //}

    value += scaleFactor * m_functionValues[k];

    //if (m_env.subDisplayFile()) {
    //  *m_env.subDisplayFile() << "In sddTG<K_V,K_M>::lagrange()"
    //                          << ": k = " << k
    //                          << ", value = " << value
    //                          << std::endl;
    //}
  }

  return value;
}

Member Data Documentation

std::vector<double> QUESO::LagrangePolynomial1D1DFunction::m_functionValues

protected

Definition at line 585 of file 1D1DFunction.h.

Referenced by LagrangePolynomial1D1DFunction(), and value().

std::vector<double> QUESO::LagrangePolynomial1D1DFunction::m_positionValues

protected

Definition at line 584 of file 1D1DFunction.h.

Referenced by LagrangePolynomial1D1DFunction(), 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