MathTL::Piecewise< C > Class Template Reference

#include <piecewise.h>

Inheritance diagram for MathTL::Piecewise< C >:

List of all members.

Public Types
typedef std::map< int, Polynomial< C > >	PiecesType
Public Member Functions
	Piecewise ()
	Piecewise (const Piecewise< C > &p)
	Piecewise (const int j)
	~Piecewise ()
Polynomial< C >	get_local_expansion (const int k) const
const PiecesType *	get_expansion () const
void	set_local_expansion (const int k, const Polynomial< C > &p)
int	get_granularity () const
void	clip_me (const int k1, const int k2)
Piecewise< C >	clip (const int k1, const int k2) const
void	split_me (const int jnew)
Piecewise	split (const int jnew) const
void	dilate_me (const int j)
Piecewise< C >	dilate (const int j) const
void	shift_me (const int k)
Piecewise< C >	shift (const int k) const
Piecewise< C >	differentiate () const
double	integrate (const bool quadrature=false) const
double	integrate (const int k1, const int k2, const bool quadrature=false) const
C	value (const C x) const
C	value (const Point< 1 > &x, const unsigned int component=0) const
void	vector_value (const Point< 1 > &p, Vector< C > &values) const
C	derivative (const C x) const
C	secondDerivative (const C x) const
Piecewise< C > &	scale (const C c)
Piecewise< C > &	add (const Polynomial< C > &p)
Piecewise< C > &	add (const Piecewise< C > &p)
C	inner_product (const Piecewise< C > &p) const
C	inner_product (const Polynomial< C > &p) const
Piecewise< C > &	operator= (const Piecewise< C > &p)
C	operator() (const C x) const
Piecewise< C > &	operator+= (const Polynomial< C > &p)
Piecewise< C > &	operator+= (const Piecewise< C > &p)
Piecewise< C > &	operator-= (const Polynomial< C > &p)
Piecewise< C > &	operator-= (const Piecewise< C > &p)
Piecewise< C > &	operator*= (const C c)
Piecewise< C > &	operator*= (const Polynomial< C > &p)
Piecewise< C > &	operator*= (const Piecewise< C > &p)
void	MatError (char *str) const
Protected Attributes
PiecesType	expansion
int	granularity

---

Detailed Description

template<class C>
class MathTL::Piecewise< C >

A template class for univariate compactly supported functions f which admit a piecewise polynomial representation.

The nodes of a piecewise function are assumed to take dyadic values 2^{-j}k, with

• supp(f) = [2^{-j}tmin, 2^{-j}tmax]
• f|[2^{-j}k,2^{-j}(k+1)] is a polynomial for each integer k

Note:

• the local polynomial degree may vary
• f may not be as regular as a spline

Piecewise polynomial functions may be

• constructed as B-splines
• evaluated
• added/subtracted
• multiplied with constants
• multiplied with polynomials
• multiplied with another piecewise function
• (symbolically) differentiated
• (symbolically) integrated, quadrature rules optional

We derive Piecewise<C> from the class Function<1>, as it is indeed one.

---

Constructor & Destructor Documentation

template<class C >

MathTL::Piecewise< C >::Piecewise

(

)

default constructor: yields the zero spline, granularity j=0

default constructor

template<class C >

MathTL::Piecewise< C >::Piecewise

(

const Piecewise< C > &

p

)

copy constructor

template<class C >

MathTL::Piecewise< C >::Piecewise

(

const int

j

)

constructor with predefined granularity j

constructor for predefined granularity

template<class C >

MathTL::Piecewise< C >::~Piecewise

(

)

destructor

---

Member Function Documentation

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::add

(

const Polynomial< C > &

p

)

add a polynomial to this piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::add

(

const Piecewise< C > &

p

)

add an other piecewise to this piecewise

template<class C >

Piecewise< C > MathTL::Piecewise< C >::clip	(	const int	k1,
		const int	k2
	)		const

clip to [2^{-j}k1,2^{-j}k2]

template<class C >

void MathTL::Piecewise< C >::clip_me	(	const int	k1,
		const int	k2
	)

clip this spline to [2^{-j}k1,2^{-j}k2]

clip

template<class C >

C MathTL::Piecewise< C >::derivative

(

const C

x

)

const

point evaluation of first derivative

template<class C >

Piecewise< C > MathTL::Piecewise< C >::differentiate

(

)

const

symbolic differentiation

template<class C >

Piecewise< C > MathTL::Piecewise< C >::dilate

(

const int

j

)

const

dilate by 2^{-j} (makes a copy)

template<class C >

void MathTL::Piecewise< C >::dilate_me

(

const int

j

)

dilate by 2^{-j} f(x) -> 2^{j/2} f(2^j x)

dilate

template<class C >

const Piecewise< C >::PiecesType * MathTL::Piecewise< C >::get_expansion

(

)

const

read access, all polynomials get all polynomial representations

reading access, all polynomials

template<class C>

int MathTL::Piecewise< C >::get_granularity

(

)

const [inline]

get the granularity j

template<class C >

Polynomial< C > MathTL::Piecewise< C >::get_local_expansion

(

const int

k

)

const

read access, local expansion get the local polynomial representation at interval k

reading access, local expansion on one subinterval

template<class C >

C MathTL::Piecewise< C >::inner_product

(

const Piecewise< C > &

p

)

const

inner product with another piecewise (don't use this extensively, since one copy has to be made!)

inner product with another piecewise

template<class C >

C MathTL::Piecewise< C >::inner_product

(

const Polynomial< C > &

p

)

const

inner product with another polynomial (don't use this extensively, since one copy has to be made!)

inner product with a polynomial

template<class C >

double MathTL::Piecewise< C >::integrate

(

const bool

quadrature = false

)

const

integration over entire support

integration, entire support

template<class C >

double MathTL::Piecewise< C >::integrate	(	const int	k1,
		const int	k2,
		const bool	quadrature = false
	)		const

integration over [2^{-j}k1,2^{-j}k2]

integration, specific support

template<class C >

void MathTL::Piecewise< C >::MatError

(

char *

str

)

const

Error output

template<class C >

C MathTL::Piecewise< C >::operator()

(

const C

x

)

const

point evaluation

point evaluation operator

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator*=

(

const C

c

)

scaling with a constant

in-place multiplication with a constant

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator*=

(

const Polynomial< C > &

p

)

pointwise multiplication with a polynomial

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator*=

(

const Piecewise< C > &

p

)

pointwise multiplication with another piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator+=

(

const Polynomial< C > &

p

)

in-place addition of a polynomial p

add a polynomial to this piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator+=

(

const Piecewise< C > &

p

)

in-place addition of a piecewise p

add an other piecewise to this piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator-=

(

const Polynomial< C > &

p

)

subtraction of a polynomial

subtract a polynomial from this piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator-=

(

const Piecewise< C > &

p

)

subtraction of another piecewise

subtract an other piecewise from this piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::operator=

(

const Piecewise< C > &

p

)

assignment of another piecewise

template<class C >

Piecewise< C > & MathTL::Piecewise< C >::scale

(

const C

c

)

in-place multiplication with a constant

template<class C >

C MathTL::Piecewise< C >::secondDerivative

(

const C

x

)

const

point evaluation of second derivative

template<class C >

void MathTL::Piecewise< C >::set_local_expansion	(	const int	k,
		const Polynomial< C > &	p
	)

write access, local expansion set the local polynomial representation at interval k

writing access, local expansion

template<class C >

Piecewise< C > MathTL::Piecewise< C >::shift

(

const int

k

)

const

shift by 2^{-j}k (makes a copy)

template<class C >

void MathTL::Piecewise< C >::shift_me

(

const int

k

)

shift by 2^{-j}k

shift

template<class C >

Piecewise< C > MathTL::Piecewise< C >::split

(

const int

jnew

)

const

increase granularity, jnew >= current granularity

template<class C >

void MathTL::Piecewise< C >::split_me

(

const int

jnew

)

increase granularity, jnew >= current granularity

increase granularity

template<class C >

C MathTL::Piecewise< C >::value

(

const C

x

)

const

point evaluation

template<class C >

C MathTL::Piecewise< C >::value	(	const Point< 1 > &	p,
		const unsigned int	component = 0
	)		const [inline]

point evaluation (calls the above value(const C)) needed as inheritance from Function<C>

point evaluation (calls above value(const C))

template<class C >

void MathTL::Piecewise< C >::vector_value	(	const Point< 1 > &	p,
		Vector< C > &	values
	)		const [inline]

point evaluation (calls the above value(const C)) needed as inheritance from Function<C>

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

• algebra/piecewise.h
• algebra/piecewise.cpp