dg::DLT< real_type > Struct Template Reference

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

Static Public Member Functions
static std::vector< real_type >	abscissas (unsigned n)
	Return Gauss-Legendre nodes on the interval [-1,1].
static std::vector< real_type >	weights (unsigned n)
	Return Gauss-Legendre weights.
static std::vector< real_type >	backward (unsigned n)
	Return backward DLT trafo matrix.
static std::vector< real_type >	forward (unsigned n)
	Return forward DLT trafo matrix.
static std::vector< real_type >	backwardEQ (unsigned n)
	Return equidistant backward DLT trafo matrix.

Detailed Description

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

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

For n <= 20 we have tabulated values

Template Parameters

real_type

value type (double or float) of the coefficients

Member Function Documentation

abscissas()

template<class real_type >

static std::vector< real_type > dg::DLT< real_type >::abscissas ( unsigned n )

inlinestatic

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

Parameters

n	Number of polynomial coefficients n <= 20

Returns

n abscissas

backward()

template<class real_type >

static std::vector< real_type > dg::DLT< real_type >::backward ( unsigned n )

inlinestatic

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 >

static std::vector< real_type > dg::DLT< real_type >::backwardEQ ( unsigned n )

inlinestatic

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 >

static std::vector< real_type > dg::DLT< real_type >::forward ( unsigned n )

inlinestatic

Return forward DLT trafo matrix.

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

Returns

n*n forward transformation coefficients

weights()

template<class real_type >

static std::vector< real_type > dg::DLT< real_type >::weights ( unsigned n )

inlinestatic

Return Gauss-Legendre weights.

Parameters

n	Number of polynomial coefficients n <= 20

Returns

n weights

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

• topology/dlt.h