Class for Legendre 1D polynomials computation. More...

#include <gcg.h>

Inheritance diagram for gcgLEGENDREBASIS1D< NUMTYPE >:

Public Member Functions
bool	setBasisDegree (unsigned int degree)
	Sets the maximum degree of the polynomials of the basis. The number of polynomials = maximum degree + 1. More...

bool	setNumberOfSamples (unsigned int nsamples)
	Sets the number of samples for the discretization of polynomial functions. Call it BEFORE using getDiscreteValue(), projectSignal(), reconstructSignal() or basisInformation(). This method computes all polynomial basis vectors which might be slow if current degree is big. More...

unsigned int	getNumberOfCoefficients ()
	Returns the number of coefficients used in 1D polynomial projection/reconstruction. More...

NUMTYPE	getPointValue (unsigned int idegree, NUMTYPE x)
	Computes the value of the polynomial of idegree degree at point x in [-1, 1]. More...

NUMTYPE	getIntegralValue (unsigned int idegree, NUMTYPE a, NUMTYPE b)
	Computes the integral of the polynomial of degree idegree in the interval [a, b]. More...

NUMTYPE	getDiscreteValue (unsigned int idegree, unsigned int i)
	Compute normalized i-th sample of the polynomial of degree idegree. Parameter i in [0, nsamples-1] is the i-th sample of a uniform discretization of the domain [-1,1] with nsamples samples. Call setNumberOfSamples() to set the number of samples to be used. More...

bool	projectSignal (int atX, gcgDISCRETE1D< float > vector, gcgDISCRETE1D< NUMTYPE > outputcoef)
	Computes the npolynomials coefficients of the projection of the vector (as 1D signal) on the discretized basis of current degree + 1 polynomials = npolynomials. Only nsamples elements starting at atX are used. The coefficients are stored in array outputcoef (as 1D signal) that is adjusted to have current degree + 1 elements. Call setNumberOfSamples() to set the number of samples to be used. More...

bool	reconstructSignal (int atX, gcgDISCRETE1D< NUMTYPE > inputcoef, gcgDISCRETE1D< float > outputvector)
	Computes up to nsamples components of a vector (as 1D signal), using the degree + 1 coefficients given in array inputcoef (as 1D signal). The components are stored in the array outputvector (as 1D signal) starting at position atX. Call setNumberOfSamples() to set the number of samples to be used. More...

bool	basisInformation (const char *filename)
	Output basis information with current degree for numerical analysis. Saves information of the orthogonality of the basis with nsamples elements. Call setNumberOfSamples() to set the number of samples to be used. More...

Public Member Functions inherited from gcgCLASS
void *	operator new (size_t size)
	Defines a new operator to be used by instatiations of GCGlib classes instead the global one. More...

void *	operator new (size_t size, const std::nothrow_t &) throw ()
	Defines a new operator to be used by instantiations of GCGlib classes instead the global one. Returns a NULL pointer instead of throwing an exception if an error occurs. More...

void *	operator new[] (size_t size)
	Defines a new operator to be used by GCGlib array allocations instead the global one. More...

void *	operator new[] (size_t size, const std::nothrow_t &) throw ()
	Defines a new operator to be used by vector allocations instead the global one. More...

void	operator delete (void *p)
	Defines a delete operator to free instances of GCGlib classes instead the global one. It is designed to match the new operator. More...

void	operator delete (void *p, const std::nothrow_t &) throw ()
	Defines a delete operator to free instances of GCGlib classes instead the global one. It is designed to match the new operator. More...

void	operator delete[] (void *p)
	Defines a delete operator to free instances of arrays for GCGlib classes instead the global one. It is designed to match the new[] operator. More...

void	operator delete[] (void *p, const std::nothrow_t &) throw ()
	Defines a delete operator to free instances of arrays for GCGlib classes instead the global one. It is designed to match the new[] operator. More...

Public Attributes
unsigned int	degree
	Degree of the polynomials = number of polynomials - 1. Read-only. See setBasisDegree().

unsigned int	nsamples
	Current number of samples of each discretized polynomial. Read-only. See setNumberOfSamples().

Detailed Description

template<>
class gcgLEGENDREBASIS1D< NUMTYPE >

Class for Legendre 1D polynomials computation.

Template Parameters

NUMTYPE Type of the samples representing the signal. Supported types: float or double.

Use gcgLEGENDREBASIS1D<float> for single precision and gcgLEGENDREBASIS1D<double> for double precision. Methods for projection and reconstruction are avalaible. The performance of the numeric methods can be verified by using the basisInformation() method.

Since: 0.01.6

Member Function Documentation

◆ basisInformation()

bool gcgLEGENDREBASIS1D< NUMTYPE >::basisInformation ( const char * filename )

Output basis information with current degree for numerical analysis. Saves information of the orthogonality of the basis with nsamples elements. Call setNumberOfSamples() to set the number of samples to be used.

Parameters

[in] filename name of output text file.

Returns: true if file creation was successful.

See also: setNumberOfSamples()

◆ getDiscreteValue()

NUMTYPE gcgLEGENDREBASIS1D< NUMTYPE >::getDiscreteValue	(	unsigned int	idegree,
		unsigned int	i
	)

Compute normalized i-th sample of the polynomial of degree idegree. Parameter i in [0, nsamples-1] is the i-th sample of a uniform discretization of the domain [-1,1] with nsamples samples. Call setNumberOfSamples() to set the number of samples to be used.

Parameters

[in]	idegree	degree of the polynomial function.
[in]	i	index of the sample. Must be in the interval [0 nsamples - 1].

Returns: the value of the i-th sample.

See also: setBasisDegree(); setNumberOfSamples()

◆ getIntegralValue()

NUMTYPE gcgLEGENDREBASIS1D< NUMTYPE >::getIntegralValue	(	unsigned int	idegree,
		NUMTYPE	a,
		NUMTYPE	b
	)

Computes the integral of the polynomial of degree idegree in the interval [a, b].

Parameters

[in]	idegree	of the polynomial function.
[in]	a	inferior limit of the interval [a, b].
[in]	b	superior limit of the interval [a, b].

Returns: the value of the integral in the interval [a, b].

◆ getNumberOfCoefficients()

unsigned int gcgLEGENDREBASIS1D< NUMTYPE >::getNumberOfCoefficients ( )

virtual

Returns the number of coefficients used in 1D polynomial projection/reconstruction.

Returns: the number of polynomials of the basis = degree + 1.

Implements gcgBASIS1D< NUMTYPE >.

◆ getPointValue()

NUMTYPE gcgLEGENDREBASIS1D< NUMTYPE >::getPointValue	(	unsigned int	idegree,
		NUMTYPE	x
	)

Computes the value of the polynomial of idegree degree at point x in [-1, 1].

Parameters

[in]	idegree	degree of the polynomial function.
[in]	x	coordinate of the point to be evaluated. Must be in the interval [-1, 1]

Returns: the value of the polynomial at point x.

See also: getSampleValue(); getDiscreteValue()

◆ projectSignal()

bool gcgLEGENDREBASIS1D< NUMTYPE >::projectSignal	(	int	atX,
		gcgDISCRETE1D< float > *	vector,
		gcgDISCRETE1D< NUMTYPE > *	outputcoef
	)

virtual

Computes the npolynomials coefficients of the projection of the vector (as 1D signal) on the discretized basis of current degree + 1 polynomials = npolynomials. Only nsamples elements starting at atX are used. The coefficients are stored in array outputcoef (as 1D signal) that is adjusted to have current degree + 1 elements. Call setNumberOfSamples() to set the number of samples to be used.

Parameters

[in]	atX	origin of the signal for this projection (relative to vector).
[in]	vector	array (as 1D signal) containing components of the vector to be projected onto the basis.
[out]	outputcoef	array (as 1D signal) that receives the computed coefficients. It is adjusted to have degree + 1 elements.

Returns: true if projection is successful.

See also: setBasisDegree(); setNumberOfSamples(); reconstructSignal()

Implements gcgBASIS1D< NUMTYPE >.

◆ reconstructSignal()

bool gcgLEGENDREBASIS1D< NUMTYPE >::reconstructSignal	(	int	atX,
		gcgDISCRETE1D< NUMTYPE > *	inputcoef,
		gcgDISCRETE1D< float > *	outputvector
	)

virtual

Computes up to nsamples components of a vector (as 1D signal), using the degree + 1 coefficients given in array inputcoef (as 1D signal). The components are stored in the array outputvector (as 1D signal) starting at position atX. Call setNumberOfSamples() to set the number of samples to be used.

Parameters

[in]	atX	origin of the signal for this projection (relative to outputvector).
[in]	inputcoef	array (as 1D signal) of coefficients representing the vector to be reconstructed.
[out]	outputvector	array (as 1D signal) that receives the reconstructed vector.

Returns: true if reconstruction is successful.

See also: setBasisDegree(); setNumberOfSamples(); projectSignal()

Implements gcgBASIS1D< NUMTYPE >.

◆ setBasisDegree()

bool gcgLEGENDREBASIS1D< NUMTYPE >::setBasisDegree ( unsigned int degree )

Sets the maximum degree of the polynomials of the basis. The number of polynomials = maximum degree + 1.

Parameters

[in] degree maximum degree of the polynomial basis.

Returns: true if setup succeded

◆ setNumberOfSamples()

bool gcgLEGENDREBASIS1D< NUMTYPE >::setNumberOfSamples ( unsigned int nsamples )

virtual

Sets the number of samples for the discretization of polynomial functions. Call it BEFORE using getDiscreteValue(), projectSignal(), reconstructSignal() or basisInformation(). This method computes all polynomial basis vectors which might be slow if current degree is big.

Parameters

[in] nsamples number of samples of a discretization of poynomials domain [-1, 1].

Returns: true if discretized basis creation is successful.

See also: getDiscreteValue(); projectSignal(); reconstructSignal(); basisInformation()

Implements gcgBASIS1D< NUMTYPE >.

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

M:/Documentos/Projetos/Projetos/GCGlib/src/gcg.h

Public Member Functions

Public Attributes

Detailed Description

template<> class gcgLEGENDREBASIS1D< NUMTYPE >

Member Function Documentation

◆ basisInformation()

◆ getDiscreteValue()

◆ getIntegralValue()

◆ getNumberOfCoefficients()

◆ getPointValue()

◆ projectSignal()

◆ reconstructSignal()

◆ setBasisDegree()

◆ setNumberOfSamples()

template<>
class gcgLEGENDREBASIS1D< NUMTYPE >