create a c2_function which smoothly connects two other c2_functions.This takes two points and generates a polynomial which matches two c2_function arguments at those two points, with two derivatives at each point, and an arbitrary value at the center of the region. It is useful for splicing together functions over rough spots (0/0, for example). More...

#include <c2_function.hh>

Inheritance diagram for c2_connector_function_p< float_type >:

Collaboration diagram for c2_connector_function_p< float_type >:

Public Member Functions
	c2_connector_function_p (float_type x0, const c2_function< float_type > &f0, float_type x2, const c2_function< float_type > &f2, bool auto_center, float_type y1)
	construct the container from two functions More...

	c2_connector_function_p (float_type x0, float_type y0, float_type yp0, float_type ypp0, float_type x2, float_type y2, float_type yp2, float_type ypp2, bool auto_center, float_type y1)
	construct the container from numerical values More...

	c2_connector_function_p (const c2_fblock< float_type > &fb0, const c2_fblock< float_type > &fb2, bool auto_center, float_type y1)
	construct the container from c2_fblock<float_type> objects More...

virtual	~c2_connector_function_p ()
	destructor More...

virtual float_type	value_with_derivatives (float_type x, float_type yprime, float_type yprime2) const throw (c2_exception)
	get the value and derivatives. More...

Public Member Functions inherited from c2_function< float_type >
const std::string	cvs_header_vers () const
	get versioning information for the header file More...

const std::string	cvs_file_vers () const
	get versioning information for the source file More...

virtual	~c2_function ()
	destructor More...

float_type	operator() (float_type x) const throw (c2_exception)
	evaluate the function in the classic way, ignoring derivatives. More...

float_type	operator() (float_type x, float_type yprime, float_type yprime2) const throw (c2_exception)
	get the value and derivatives. More...

float_type	find_root (float_type lower_bracket, float_type upper_bracket, float_type start, float_type value, int error=0, float_type final_yprime=0, float_type *final_yprime2=0) const throw (c2_exception)
	solve f(x)==value very efficiently, with explicit knowledge of derivatives of the function More...

float_type	partial_integrals (std::vector< float_type > xgrid, std::vector< float_type > *partials=0, float_type abs_tol=1e-12, float_type rel_tol=1e-12, int derivs=2, bool adapt=true, bool extrapolate=true) const throw (c2_exception)
	solve f(x)=value partial_integrals uses a method with an error O(dx**10) with full information from the derivatives, and falls back to lower order methods if informed of incomplete derivatives. It uses exact midpoint splitting of the intervals for recursion, resulting in no recomputation of the function during recursive descent at previously computed points. More...

float_type	integral (float_type amin, float_type amax, std::vector< float_type > *partials=0, float_type abs_tol=1e-12, float_type rel_tol=1e-12, int derivs=2, bool adapt=true, bool extrapolate=true) const throw (c2_exception)
	a fully-automated integrator which uses the information provided by the get_sampling_grid() function to figure out what to do. More...

c2_piecewise_function_p < float_type > *	adaptively_sample (float_type amin, float_type amax, float_type abs_tol=1e-12, float_type rel_tol=1e-12, int derivs=2, std::vector< float_type > xvals=0, std::vector< float_type > yvals=0) const throw (c2_exception)
	create a c2_piecewise_function_p from c2_connector_function_p segments which is a representation of the parent function to the specified accuracy, but maybe much cheaper to evaluate More...

float_type	xmin () const

float_type	xmax () const

void	set_domain (float_type amin, float_type amax)

size_t	get_evaluations () const
	and sampler do increment it. More...

void	reset_evaluations () const
	reset the counter More...

void	increment_evaluations () const
	count evaluations More...

bool	check_monotonicity (const std::vector< float_type > &data, const char message[]) const throw (c2_exception)
	check that a vector is monotonic, throw an exception if not, and return a flag if it is reversed More...

virtual void	set_sampling_grid (const std::vector< float_type > &grid) throw (c2_exception)
	establish a grid of 'interesting' points on the function. More...

std::vector< float_type > *	get_sampling_grid_pointer () const
	get the sampling grid, which may be a null pointer More...

virtual void	get_sampling_grid (float_type amin, float_type amax, std::vector< float_type > &grid) const

void	preen_sampling_grid (std::vector< float_type > *result) const
	The grid is modified in place. More...

void	refine_sampling_grid (std::vector< float_type > &grid, size_t refinement) const

c2_function< float_type > &	normalized_function (float_type amin, float_type amax, float_type norm=1.0) const throw (c2_exception)
	create a new c2_function from this one which is normalized on the interval More...

c2_function< float_type > &	square_normalized_function (float_type amin, float_type amax, float_type norm=1.0) const throw (c2_exception)

c2_function< float_type > &	square_normalized_function (float_type amin, float_type amax, const c2_function< float_type > &weight, float_type norm=1.0) const throw (c2_exception)
	create a new c2_function from this one which is square-normalized with the provided weight on the interval More...

c2_sum_p< float_type > &	operator+ (const c2_function< float_type > &rhs) const
	factory function to create a c2_sum_p from a regular algebraic expression. More...

c2_diff_p< float_type > &	operator- (const c2_function< float_type > &rhs) const
	factory function to create a c2_diff_p from a regular algebraic expression. More...

c2_product_p< float_type > &	operator* (const c2_function< float_type > &rhs) const
	factory function to create a c2_product_p from a regular algebraic expression. More...

c2_ratio_p< float_type > &	operator/ (const c2_function< float_type > &rhs) const

c2_composed_function_p < float_type > &	operator() (const c2_function< float_type > &inner) const
	compose this function outside another. More...

float_type	get_trouble_point () const
	Find out where a calculation ran into trouble, if it got a nan. If the most recent computation did not return a nan, this is undefined. More...

void	claim_ownership () const
	increment our reference count. Destruction is only legal if the count is zero. More...

size_t	release_ownership_for_return () const throw (c2_exception)
	decrement our reference count. Do not destroy at zero. More...

void	release_ownership () const throw (c2_exception)

size_t	count_owners () const
	get the reference count, mostly for debugging More...

void	fill_fblock (c2_fblock< float_type > &fb) const throw (c2_exception)
	fill in a c2_fblock<float_type>... a shortcut for the integrator & sampler More...

Protected Member Functions
void	init (const c2_fblock< float_type > &fb0, const c2_fblock< float_type > &fb2, bool auto_center, float_type y1)
	fill container numerically More...

Protected Member Functions inherited from c2_function< float_type >
	c2_function (const c2_function< float_type > &src)

	c2_function ()

virtual void	set_sampling_grid_pointer (std::vector< float_type > &grid)

Protected Attributes
float_type	fhinv

float_type	fy1

float_type	fa

float_type	fb

float_type	fc

float_type	fd

float_type	fe

float_type	ff

Protected Attributes inherited from c2_function< float_type >
std::vector< float_type > *	sampling_grid

bool	no_overwrite_grid

float_type	fXMin

float_type	fXMax

size_t	evaluations

float_type	bad_x_point
	this point may be used to record where a calculation ran into trouble More...

Detailed Description

template<typename float_type = double>
class c2_connector_function_p< float_type >

create a c2_function which smoothly connects two other c2_functions.

This takes two points and generates a polynomial which matches two c2_function arguments at those two points, with two derivatives at each point, and an arbitrary value at the center of the region. It is useful for splicing together functions over rough spots (0/0, for example).

If auto_center is true, the value at the midpoint is computed so that the resulting polynomial is of order 5. If auto_center is false, the value y1 is used at the midpoint, resulting in a polynomial of order 6.

This is usually used in conjunction with c2_piecewise_function_p to assemble an apparently seamless function from a series of segments.

See also: Sample Applications and Adaptive sampling

Definition at line 2215 of file c2_function.hh.

Constructor & Destructor Documentation

template<typename float_type = double>

c2_connector_function_p< float_type >::c2_connector_function_p	(	float_type	x0,
		const c2_function< float_type > &	f0,
		float_type	x2,
		const c2_function< float_type > &	f2,
		bool	auto_center,
		float_type	y1
	)

construct the container from two functions

Parameters

x0	the point at which to match f1 and its derivatives
f0	the function on the left side to be connected
x2	the point at which to match f2 and its derivatives
f2	the function on the right side to be connected
auto_center	if true, no midpoint value is specified. If false, match the value y1 at the midpoint
y1	the value to match at the midpoint, if auto_center is false

Returns: a c2_function with domain (x0,x2) which smoothly connects f0(x0) and f2(x2)

template<typename float_type = double>

c2_connector_function_p< float_type >::c2_connector_function_p	(	float_type	x0,
		float_type	y0,
		float_type	yp0,
		float_type	ypp0,
		float_type	x2,
		float_type	y2,
		float_type	yp2,
		float_type	ypp2,
		bool	auto_center,
		float_type	y1
	)

construct the container from numerical values

Parameters

x0	the position of the left edge
y0	the function derivative on the left boundary
yp0	the function second derivative on the left boundary
ypp0	the function value on the left boundary
x2	the position of the right edge
y2	the function derivative on the right boundary
yp2	the function second derivative on the right boundary
ypp2	the function value on the right boundary
auto_center	if true, no midpoint value is specified. If false, match the value y1 at the midpoint
y1	the value to match at the midpoint, if auto_center is false

Returns: a c2_function with domain (x0,x2) which smoothly connects the points described

template<typename float_type = double>

c2_connector_function_p< float_type >::c2_connector_function_p	(	const c2_fblock< float_type > &	fb0,
		const c2_fblock< float_type > &	fb2,
		bool	auto_center,
		float_type	y1
	)

construct the container from c2_fblock<float_type> objects

Parameters

fb0	the left edge
fb2	the right edge
auto_center	if true, no midpoint value is specified. If false, match the value y1 at the midpoint
y1	the value to match at the midpoint, if auto_center is false

Returns: a c2_function with domain (fb0.x,fb2.x) which smoothly connects fb0 and fb2

template<typename float_type = double>

virtual c2_connector_function_p< float_type >::~c2_connector_function_p ( )

virtual

destructor

Member Function Documentation

template<typename float_type = double>

void c2_connector_function_p< float_type >::init	(	const c2_fblock< float_type > &	fb0,
		const c2_fblock< float_type > &	fb2,
		bool	auto_center,
		float_type	y1
	)

protected

fill container numerically

template<typename float_type = double>

virtual float_type c2_connector_function_p< float_type >::value_with_derivatives	(	float_type	x,
		float_type *	yprime,
		float_type *	yprime2
	)		const
throw	(	c2_exception
	)

virtual

get the value and derivatives.

There is required checking for null pointers on the derivatives, and most implementations should operate faster if derivatives are not

Parameters

[in]	x	the point at which to evaluate the function
[out]	yprime	the first derivative (if pointer is non-null)
[out]	yprime2	the second derivative (if pointer is non-null)

Returns: the value of the function

Implements c2_function< float_type >.

Member Data Documentation

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fa

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fb

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fc

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fd

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fe

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::ff

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fhinv

protected

Definition at line 2275 of file c2_function.hh.

template<typename float_type = double>

float_type c2_connector_function_p< float_type >::fy1

protected

Definition at line 2275 of file c2_function.hh.

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

geant4.10.03/examples/extended/electromagnetic/TestEm7/include/c2_function.hh

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

template<typename float_type = double> class c2_connector_function_p< float_type >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename float_type = double>
class c2_connector_function_p< float_type >