dg::DLT< real_type > Class Template Reference

Struct holding coefficients for Discrete Legendre Transformation (DLT) related operations. More...

Public Member Functions
	DLT (unsigned n=3)
	Initialize coefficients. More...
unsigned	n () const
	# of polynomial coefficients More...
const std::vector< real_type > &	weights () const
	Return Gauss-Legendre weights. More...
const std::vector< real_type > &	abscissas () const
	Return Gauss-Legendre nodes on the interval [-1,1]. More...
const std::vector< real_type > &	forward () const
	Return forward DLT trafo matrix. More...
const std::vector< real_type > &	backward () const
	Return backward DLT trafo matrix. More...
const std::vector< real_type > &	backwardEQ () const
	Return equidistant backward DLT trafo matrix. More...

Detailed Description

template<class real_type>
class dg::DLT< real_type >

Struct holding coefficients for Discrete Legendre Transformation (DLT) related operations.

Template Parameters

real_type

value type (double or float)

Constructor & Destructor Documentation

DLT()

template<class real_type >

dg::DLT< real_type >::DLT

(

unsigned

n = 3

)

Initialize coefficients.

The constructor initializes internal data with tabulated values for the given number of polynomial coefficients.

Parameters

n	# of polynomial coefficients (0<n<21)

Member Function Documentation

abscissas()

template<class real_type >

const std::vector< real_type > & dg::DLT< real_type >::abscissas ( ) const

inline

Return Gauss-Legendre nodes on the interval [-1,1].

Returns

n nodes

backward()

template<class real_type >

const std::vector< real_type > & dg::DLT< real_type >::backward ( ) const

inline

Return backward DLT trafo matrix.

accesss elements in C-fashion: \( F_{ij} =\) backward()[i*n+j]

Returns

n*n backward transformation coefficients

backwardEQ()

template<class real_type >

const std::vector< real_type > & dg::DLT< real_type >::backwardEQ ( ) const

inline

Return equidistant backward DLT trafo matrix.

For vizualisation purposes it is useful to have the values of the DLT - expansion on an equidistant grid. accesss elements in C-fashion: \( F_{ij} = \) backwardEQ()[i*n+j]

Returns

n*n equidistant backward transformation coefficients

forward()

template<class real_type >

const std::vector< real_type > & dg::DLT< real_type >::forward ( ) const

inline

Return forward DLT trafo matrix.

accesss elements in C-fashion: \( F_{ij} = \) forward()[i*n+j]

Returns

n*n forward transformation coefficients

n()

template<class real_type >

unsigned dg::DLT< real_type >::n ( ) const

inline

# of polynomial coefficients

weights()

template<class real_type >

const std::vector< real_type > & dg::DLT< real_type >::weights ( ) const

inline

Return Gauss-Legendre weights.

Returns

n weights

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

• topology/dlt.h