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.
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

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
	)

Constructor.

Definition at line 57 of file GlobiPack_TestLagrPolyMeritFunc1D_def.hpp.

Member Function Documentation

template<typename Scalar >

bool GlobiPack::TestLagrPolyMeritFunc1D< Scalar >::supportsDerivEvals ( ) const [virtual]

Implements GlobiPack::MeritFunc1DBase< Scalar >.

Definition at line 71 of file GlobiPack_TestLagrPolyMeritFunc1D_def.hpp.

template<typename Scalar >

void GlobiPack::TestLagrPolyMeritFunc1D< Scalar >::eval	(	const Scalar &	alpha,
		const Ptr< Scalar > &	phi,
		const Ptr< Scalar > &	Dphi
	)		const `[virtual]`