SimplexCondNum< N, T > Class Template Reference

Implements the condition number quality metric. More...

#include <SimplexCondNum.h>

Inheritance diagram for SimplexCondNum< N, T >:

List of all members.

Public Types
typedef T	Number
	The number type.
typedef Base::Vertex	Vertex
	The class for a vertex.
typedef Base::Simplex	Simplex
	The simplex type.
typedef Base::Matrix	Matrix
	An NxN matrix.
Public Member Functions
Constructors etc.
	SimplexCondNum ()
	Default constructor. Un-initialized memory.
	SimplexCondNum (const SimplexCondNum &other)
	Copy constructor.
	SimplexCondNum (const Simplex &s)
	Construct from a simplex.
SimplexCondNum &	operator= (const SimplexCondNum &other)
	Assignment operator.
	~SimplexCondNum ()
	Trivial destructor.
Mathematical functions
Number	operator() () const
	Return the condition number (kappa) quality metric.
Number	operator() (const Simplex &simplex) const
	Return the condition number (kappa) quality metric.
void	computeGradient (Vertex *gradient) const
	Calculate the gradient of the condition number (kappa) quality metric.
Protected Member Functions
Number	computeFunction (Number snj, Number sna) const
	Return the quality metric given and .

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Detailed Description

template<int N, typename T = double>
class SimplexCondNum< N, T >

Implements the condition number quality metric.

Parameters:

	N	is the dimension.
	T	is the number type. By default it is double.

This class implements the condition number quality metric. Let be the Jacobian matrix, be its adjoint (scaled inverse), be the Jacobian determinant and be the Frobenius norm. The operator()() member function returns the condition number quality metric:

This quality metric is only defined for simplices with positive content. (The Jacobian determinant must be positive.)

computeGradient() calculates the gradient of the condition number metric.

Before evaluating the condition number metric, you must set the Jacobian matrix with setFunction() or set(). Before evaluating the gradient of the metric, you must set the Jacobian matrix and its gradient with set().

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Member Function Documentation

template<int N, typename T = double>

void SimplexCondNum< N, T >::computeGradient

(

Vertex *

gradient

)

const

Calculate the gradient of the condition number (kappa) quality metric.

Precondition:

The Jacobian determinant must be positive.

Let be the Jacobian matrix, be its scaled inverse, be the Jacobian determinant and be the Frobenius norm. The kappa function is

Reimplemented in SimplexModCondNum< N, T >.

template<int N, typename T = double>

Number SimplexCondNum< N, T >::operator()

(

const Simplex &

simplex

)

const [inline]

Return the condition number (kappa) quality metric.

Precondition:

The Jacobian determinant must be positive.

Returns:

Let be the Jacobian matrix, be its scaled inverse, be the Jacobian determinant and be the Frobenius norm. Return

Reimplemented in SimplexModCondNum< N, T >.

References SimplexCondNum< N, T >::operator()(), and SimplexAdjJacQF< N, T >::setFunction().

template<int N, typename T = double>

Number SimplexCondNum< N, T >::operator()

(

)

const

Return the condition number (kappa) quality metric.

Precondition:

The Jacobian determinant must be positive.

Returns:

Let be the Jacobian matrix, be its scaled inverse, be the Jacobian determinant and be the Frobenius norm. Return

Reimplemented in SimplexModCondNum< N, T >.

Referenced by SimplexCondNum< N, T >::operator()().

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

• SimplexCondNum.h