Lagrange Polynomial Merit Function used in testing. More...

#include <GlobiPack_TestLagrPolyMeritFunc1D_decl.hpp>

Inheritance diagram for GlobiPack::TestLagrPolyMeritFunc1D< Scalar >:

Public Member Functions
	TestLagrPolyMeritFunc1D (const ArrayView< const Scalar > &alpha, const ArrayView< const Scalar > &phi)
	Constructor. More...

Public Member Functions inherited from Teuchos::Describable
DescribableStreamManipulatorState	describe (const Describable &describable, const EVerbosityLevel verbLevel=Describable::verbLevel_default)

std::ostream &	operator<< (std::ostream &os, const DescribableStreamManipulatorState &d)

virtual std::string	description () const

virtual void	describe (FancyOStream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

void	describe (std::ostream &out, const EVerbosityLevel verbLevel=verbLevel_default) const

virtual	~Describable ()

	LabeledObject ()

virtual	~LabeledObject ()

virtual void	setObjectLabel (const std::string &objectLabel)

virtual std::string	getObjectLabel () const

Private Attributes
Array< Scalar >	alpha_

Array< Scalar >	phi_

Overridden from MeritFunc1DBase
virtual bool	supportsDerivEvals () const

virtual void	eval (const Scalar &alpha, const Ptr< Scalar > &phi, const Ptr< Scalar > &Dphi) const

Additional Inherited Members
Static Public Attributes inherited from Teuchos::Describable
static const EVerbosityLevel	verbLevel_default

Related Functions inherited from GlobiPack::MeritFunc1DBase< Scalar >
template<typename Scalar >
ScalarTraits< Scalar > ::magnitudeType	computeValue (const MeritFunc1DBase< Scalar > &phi, const Scalar &alpha)
	Compute the value of the merit function `phi(alpha)`. More...

template<typename Scalar >
PointEval1D< Scalar >	computePoint (const MeritFunc1DBase< Scalar > &phi, const Scalar &alpha, const bool compute_phi=true, const bool compute_Dphi=false)
	Compute a point as an object. More...

Detailed Description

template<typename Scalar>
class GlobiPack::TestLagrPolyMeritFunc1D< Scalar >

Lagrange Polynomial Merit Function used in testing.

This test class implements an arbitrary order polynomial specified as a set points.

Let the order-n polynomial approximation be:

  phi(alpha) =
    sum( phi_k * L(n,k)(alpha), k = 0...n-1 )

where L(n,k)(alpha) are the nth order Lagrange polynomials:


  L(n,k)(alpha) =
    product( (alpha - alpha[i]) / (alpha[k] - alpha[i]), i=0...n-1, i!=k )

The derivative of phi(alpha) with respect to alpha Dphi is given by:


  Dphi(alpha) =
    sum( phi_k * DL(n,k)(alpha), k = 0...n-1 )

where:


  DL(n,k)(alpha) = sum(
      1/(alpha-alpha[j])
        * product( (alpha-alpha[i])/(alpha[k]-alpha[i]), i=0...n-1, i!=k, i!=j ),
      j=0...n-1, j!=k
      )

Above, DL(n,k)(alpha) is derived using the simple product rule.

Definition at line 104 of file GlobiPack_TestLagrPolyMeritFunc1D_decl.hpp.

Constructor & Destructor Documentation

template<typename Scalar >

GlobiPack::TestLagrPolyMeritFunc1D< Scalar >::TestLagrPolyMeritFunc1D	(	const ArrayView< const Scalar > &	alpha,
		const ArrayView< const Scalar > &	phi
	)