Spectral Integral Suite in C++
Public Member Functions | Public Attributes | List of all members
sis::Chebfun< T > Class Template Reference

This is a chebfun analogue. Chebfun will represent both values in physical space or an array of Chebyshev-coefficients. Values can be in either space for calculations. To convert between physical values or Chebyshev coefficients, one can call Chebfun.c2p() and Chebfun.p2c(). More...

#include <sis.hpp>

Public Member Functions

 Chebfun ()
 Null constructor. More...
 
 Chebfun (const std::valarray< T > &in)
 constructor by an input valarray More...
 
 Chebfun (const Eigen::Array< T, Eigen::Dynamic, Eigen::Dynamic > &in)
 constructor by an input Eigen::Array<T,Eigen::Dynamic,1> More...
 
 Chebfun (const Chebfun &in)
 Copy conststructor. More...
 
void p2c ()
 Converts a Chebfun from values in physical-space to coefficients of Chebyshev polynomials. More...
 
void c2p ()
 Converts a Chebfun from Chebyshev coefficients to values in physical space. More...
 
Eigen::Array< T, Eigen::Dynamic, 1 > ev ()
 Returns property v in terms of Eigen::Array. More...
 
Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > MultMat ()
 This function returns the Toeplitz + almost Hankel matrix needed to express multiplication of two Chebyshev series. This is used in solving for nonconstant coefficients. More...
 
void operator= (T right)
 Equating the Chebfun to a constant. More...
 
void operator= (const Chebfun &right)
 To assign a Chebfun through another Chebfun. More...
 
void operator= (const Eigen::Matrix< T, Eigen::Dynamic, 1 > &right)
 To assign a Chebfun through a vector. More...
 
void operator= (const std::valarray< T > &right)
 To assign a Chebfun through a valarray. More...
 
void operator+= (const T &right)
 Adding constant to itself. More...
 
void operator+= (Chebfun right)
 Add a Chebfun to itself. If both are in same space, return will be in same space, else the lhs will retain space. More...
 
T operator() (const T &a)
 To assign a Chebfun through a Array. More...
 
Chebfun< T > cumsum ()
 Returns a Chebfun that represents the indefinite integral of the Chebfun. More...
 
T L2norm ()
 Returns the L2norm of the function. More...
 
bool isMachinePrecision ()
 
bool isMachinePrecisionHalf ()
 
T trunc ()
 Provides the truncation defined in terms of the abs(last + last_but_one)/2.0. More...
 

Public Attributes

int dct_flag
 
std::valarray< T > v
 Stores a flag to denote if function is in Cheb-space or physical space. More...
 

Detailed Description

template<class T>
class sis::Chebfun< T >

This is a chebfun analogue. Chebfun will represent both values in physical space or an array of Chebyshev-coefficients. Values can be in either space for calculations. To convert between physical values or Chebyshev coefficients, one can call Chebfun.c2p() and Chebfun.p2c().

Definition at line 1150 of file sis.hpp.

Constructor & Destructor Documentation

◆ Chebfun() [1/4]

template<class T>
sis::Chebfun< T >::Chebfun ( )
inline

Null constructor.

By default the function is f(y) =y, with values in physical space.

Definition at line 1160 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, sis::N, PI, SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ Chebfun() [2/4]

template<class T>
sis::Chebfun< T >::Chebfun ( const std::valarray< T > &  in)
inline

constructor by an input valarray

Definition at line 1167 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, sis::N, SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ Chebfun() [3/4]

template<class T>
sis::Chebfun< T >::Chebfun ( const Eigen::Array< T, Eigen::Dynamic, Eigen::Dynamic > &  in)
inline

constructor by an input Eigen::Array<T,Eigen::Dynamic,1>

Definition at line 1178 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, sis::N, SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ Chebfun() [4/4]

template<class T>
sis::Chebfun< T >::Chebfun ( const Chebfun< T > &  in)
inline

Copy conststructor.

Definition at line 1210 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, and sis::Chebfun< T >::v.

Member Function Documentation

◆ c2p()

template<class T>
void sis::Chebfun< T >::c2p ( )
inline

Converts a Chebfun from Chebyshev coefficients to values in physical space.

Definition at line 1257 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, sis::rev_half_shift(), SIS_CHEB_SPACE, SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

Referenced by sis::Chebfun< T >::cumsum(), sis::Chebfun< std::complex< T > >::cumsum(), sis::diff(), sis::Chebfun< T >::L2norm(), sis::Chebfun< std::complex< T > >::L2norm(), sis::Chebfun< T >::operator()(), sis::Chebfun< std::complex< T > >::operator()(), sis::operator*(), sis::operator+(), sis::Chebfun< T >::operator+=(), sis::Chebfun< std::complex< T > >::operator+=(), sis::Linop< T >::operator=(), and sis::Linop< std::complex< T > >::operator=().

◆ cumsum()

template<class T>
Chebfun<T> sis::Chebfun< T >::cumsum ( )
inline

Returns a Chebfun that represents the indefinite integral of the Chebfun.

Definition at line 1427 of file sis.hpp.

References sis::Chebfun< T >::c2p(), sis::Chebfun< T >::dct_flag, sis::integ(), sis::Chebfun< T >::p2c(), SIS_CHEB_SPACE, SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ ev()

template<class T>
Eigen::Array<T, Eigen::Dynamic, 1> sis::Chebfun< T >::ev ( )
inline

Returns property v in terms of Eigen::Array.

Definition at line 1297 of file sis.hpp.

References sis::Chebfun< T >::v.

◆ isMachinePrecision()

template<class T>
bool sis::Chebfun< T >::isMachinePrecision ( )
inline

Definition at line 1461 of file sis.hpp.

References sis::N, and sis::Chebfun< T >::v.

◆ isMachinePrecisionHalf()

template<class T>
bool sis::Chebfun< T >::isMachinePrecisionHalf ( )
inline

Definition at line 1468 of file sis.hpp.

References sis::N, and sis::Chebfun< T >::v.

◆ L2norm()

template<class T>
T sis::Chebfun< T >::L2norm ( )
inline

Returns the L2norm of the function.

Definition at line 1444 of file sis.hpp.

References sis::Chebfun< T >::c2p(), sis::Chebfun< T >::dct_flag, sis::integ(), sis::Chebfun< T >::p2c(), SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

Referenced by sis::EigenSorter< T >::compute().

◆ MultMat()

template<class T>
Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> sis::Chebfun< T >::MultMat ( )
inline

This function returns the Toeplitz + almost Hankel matrix needed to express multiplication of two Chebyshev series. This is used in solving for nonconstant coefficients.

To assign a Chebfun to a constant

Definition at line 1309 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, sis::N, sis::Chebfun< T >::p2c(), SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ operator()()

template<class T>
T sis::Chebfun< T >::operator() ( const T &  a)
inline

To assign a Chebfun through a Array.

Evaluate the Chebfun at a point in the domain, i.e., -1 to 1.

Definition at line 1402 of file sis.hpp.

References sis::Chebfun< T >::c2p(), sis::Chebfun< T >::dct_flag, sis::N, sis::Chebfun< T >::p2c(), SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ operator+=() [1/2]

template<class T>
void sis::Chebfun< T >::operator+= ( const T &  right)
inline

Adding constant to itself.

Definition at line 1372 of file sis.hpp.

References SIS_CHEB_SPACE, and sis::Chebfun< T >::v.

◆ operator+=() [2/2]

template<class T>
void sis::Chebfun< T >::operator+= ( Chebfun< T >  right)
inline

Add a Chebfun to itself. If both are in same space, return will be in same space, else the lhs will retain space.

Definition at line 1382 of file sis.hpp.

References sis::Chebfun< T >::c2p(), sis::Chebfun< T >::dct_flag, sis::Chebfun< T >::p2c(), SIS_PHYS_SPACE, and sis::Chebfun< T >::v.

◆ operator=() [1/4]

template<class T>
void sis::Chebfun< T >::operator= ( T  right)
inline

Equating the Chebfun to a constant.

Definition at line 1345 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, SIS_CHEB_SPACE, and sis::Chebfun< T >::v.

◆ operator=() [2/4]

template<class T>
void sis::Chebfun< T >::operator= ( const Chebfun< T > &  right)
inline

To assign a Chebfun through another Chebfun.

Definition at line 1355 of file sis.hpp.

References sis::Chebfun< T >::dct_flag, and sis::Chebfun< T >::v.

◆ operator=() [3/4]

template<class T>
void sis::Chebfun< T >::operator= ( const Eigen::Matrix< T, Eigen::Dynamic, 1 > &  right)
inline

To assign a Chebfun through a vector.

Definition at line 1361 of file sis.hpp.

References sis::N, and sis::Chebfun< T >::v.

◆ operator=() [4/4]

template<class T>
void sis::Chebfun< T >::operator= ( const std::valarray< T > &  right)
inline

To assign a Chebfun through a valarray.

Definition at line 1368 of file sis.hpp.

References sis::Chebfun< T >::v.

◆ p2c()

template<class T>
void sis::Chebfun< T >::p2c ( )
inline

Converts a Chebfun from values in physical-space to coefficients of Chebyshev polynomials.

Definition at line 1217 of file sis.hpp.

References sis::conj(), sis::Chebfun< T >::dct_flag, sis::fft(), sis::half_shift(), std::real(), SIS_CHEB_SPACE, SIS_PHYS_SPACE, sis::Chebfun< T >::v, and sis::y().

Referenced by sis::Discretize< std::complex< T > >::ChebDiff(), sis::Chebfun< T >::cumsum(), sis::Chebfun< std::complex< T > >::cumsum(), sis::diff(), sis::Chebfun< T >::L2norm(), sis::Chebfun< std::complex< T > >::L2norm(), sis::Chebfun< T >::MultMat(), sis::Chebfun< std::complex< T > >::MultMat(), sis::Chebfun< T >::operator()(), sis::Chebfun< std::complex< T > >::operator()(), sis::operator*(), sis::operator+(), sis::Chebfun< T >::operator+=(), sis::Chebfun< std::complex< T > >::operator+=(), sis::Linop< T >::operator=(), and sis::Linop< std::complex< T > >::operator=().

◆ trunc()

template<class T>
T sis::Chebfun< T >::trunc ( )
inline

Provides the truncation defined in terms of the abs(last + last_but_one)/2.0.

Definition at line 1478 of file sis.hpp.

References sis::N, and sis::Chebfun< T >::v.

Member Data Documentation

◆ dct_flag

template<class T>
int sis::Chebfun< T >::dct_flag

Definition at line 1153 of file sis.hpp.

Referenced by sis::Chebfun< T >::c2p(), sis::Chebfun< std::complex< T > >::c2p(), sis::Chebfun< T >::Chebfun(), sis::Chebfun< std::complex< T > >::Chebfun(), sis::EigenSorter< T >::compute(), sis::Chebfun< T >::cumsum(), sis::Chebfun< std::complex< T > >::cumsum(), sis::diff(), sis::Chebfun< std::complex< T > >::imag(), sis::Chebfun< T >::L2norm(), sis::Chebfun< std::complex< T > >::L2norm(), sis::Chebfun< T >::MultMat(), sis::Chebfun< std::complex< T > >::MultMat(), sis::Chebfun< T >::operator()(), sis::Chebfun< std::complex< T > >::operator()(), sis::operator*(), sis::operator+(), sis::Chebfun< T >::operator+=(), sis::Chebfun< std::complex< T > >::operator+=(), sis::Chebfun< T >::operator=(), sis::Chebfun< std::complex< T > >::operator=(), sis::Linop< T >::operator=(), sis::Linop< std::complex< T > >::operator=(), sis::Chebfun< T >::p2c(), sis::Chebfun< std::complex< T > >::p2c(), and sis::Chebfun< std::complex< T > >::real().

◆ v

template<class T>
std::valarray<T> sis::Chebfun< T >::v

Stores a flag to denote if function is in Cheb-space or physical space.

Definition at line 1156 of file sis.hpp.

Referenced by sis::Chebfun< T >::c2p(), sis::Chebfun< std::complex< T > >::c2p(), sis::Chebfun< T >::Chebfun(), sis::Chebfun< std::complex< T > >::Chebfun(), sis::Chebfun< T >::cumsum(), sis::Chebfun< std::complex< T > >::cumsum(), sis::diff(), sis::Chebfun< T >::ev(), sis::Chebfun< std::complex< T > >::evc(), sis::Chebfun< std::complex< T > >::evi(), sis::Chebfun< std::complex< T > >::evr(), sis::Chebfun< std::complex< T > >::imag(), sis::Chebfun< T >::isMachinePrecision(), sis::Chebfun< T >::isMachinePrecisionHalf(), sis::Chebfun< T >::L2norm(), sis::Chebfun< std::complex< T > >::L2norm(), sis::Chebfun< T >::MultMat(), sis::Chebfun< std::complex< T > >::MultMat(), sis::Chebfun< T >::operator()(), sis::Chebfun< std::complex< T > >::operator()(), sis::Linop< T >::operator()(), sis::Linop< std::complex< T > >::operator()(), sis::operator*(), sis::operator+(), sis::Chebfun< T >::operator+=(), sis::Chebfun< std::complex< T > >::operator+=(), sis::operator-(), sis::Chebfun< T >::operator=(), sis::Chebfun< std::complex< T > >::operator=(), sis::Linop< T >::operator=(), sis::Linop< std::complex< T > >::operator=(), sis::Chebfun< T >::p2c(), sis::Chebfun< std::complex< T > >::p2c(), sis::Chebfun< std::complex< T > >::real(), sis::Chebfun< T >::trunc(), and sis::Chebfun< std::complex< T > >::trunc().

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