create the formal inverse function of another functionfor example, given a c2_function f More...

#include <c2_function.hh>

Inheritance diagram for c2_inverse_function_p< float_type >:

Collaboration diagram for c2_inverse_function_p< float_type >:

Public Member Functions
	c2_inverse_function_p (const c2_function< float_type > &source)
	Construct the operator. More...

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

void	set_start_hint (float_type hint) const
	give the function a hint as to where to look for its inverse More...

virtual float_type	get_start_hint (float_type x) const

void	set_hinting_function (const c2_function< float_type > *hint_func)
	set or unset the approximate function used to start the root finder More...

void	set_hinting_function (const c2_const_ptr< float_type > hint_func)
	set the hinting function from a pointer. 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
	evaluate the function in the classic way, ignoring derivatives. More...

float_type	operator() (float_type x, float_type yprime, float_type yprime2) const
	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
	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

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
	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
	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

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
	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)
	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
	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

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
	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
	decrement our reference count. Do not destroy at zero. More...

void	release_ownership () const

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

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

Protected Member Functions
	c2_inverse_function_p ()

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	start_hint

const c2_const_ptr< float_type >	func

c2_const_ptr< float_type >	hinting_function

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_inverse_function_p< float_type >

create the formal inverse function of another function

for example, given a c2_function f

c2_inverse_function<double> inv(f);
a=f(x);
x1=inv(a);

will return x1=x to machine precision. The important part of this is that the resulting function is a first-class c2_function, so it knows its derivatives, too, unlike the case of a simple root-finding inverse. This means it can be integrated (for example) quite efficiently.

See Also: combined_inversion_hinting_sampling

Definition at line 2101 of file c2_function.hh.

Constructor & Destructor Documentation

template<typename float_type = double>

c2_inverse_function_p< float_type >::c2_inverse_function_p ( const c2_function< float_type > & source )

Construct the operator.

Parameters

source the function to be inverted

template<typename float_type = double>

c2_inverse_function_p< float_type >::c2_inverse_function_p ( )

inlineprotected

Definition at line 2154 of file c2_function.hh.

2154 {}

Member Function Documentation

template<typename float_type = double>

virtual float_type c2_inverse_function_p< float_type >::get_start_hint ( float_type x ) const

inlinevirtual

Definition at line 2116 of file c2_function.hh.

2117 { return hinting_function.valid()? hinting_function(x) : start_hint; }

test.x

tuple x

Definition: test.py:50

c2_inverse_function_p::start_hint

float_type start_hint

Definition: c2_function.hh:2155

c2_inverse_function_p::hinting_function

c2_const_ptr< float_type > hinting_function

Definition: c2_function.hh:2157

template<typename float_type = double>

void c2_inverse_function_p< float_type >::set_hinting_function ( const c2_function< float_type > * hint_func )

inline

set or unset the approximate function used to start the root finder

A hinting function is mostly useful if the evaluation of this inverse is going to be carried out in very non-local order, so the root finder has to start over for each step. If most evaluations are going to be made in fairly localized clusters (scanning through the function, for example), the default mechanism used (which just remembers the last point) is almost certainly faster.

Typically, the hinting function is likely to be set up by creating the inverse function, and then adaptively sampling an interpolating function from it, and then using the result to hint it. Another way, if the parent function is already an interpolating function, is just to create a version of the parent with the x & y coordinates reversed.

See Also: combined_inversion_hinting_sampling

Parameters

hint_func the function that is an approximate inverse of the parent of this inverse_function

Definition at line 2144 of file c2_function.hh.

2145 { hinting_function.set_function(hint_func); }

c2_inverse_function_p::hinting_function

c2_const_ptr< float_type > hinting_function

Definition: c2_function.hh:2157

template<typename float_type = double>

void c2_inverse_function_p< float_type >::set_hinting_function ( const c2_const_ptr< float_type > hint_func )

inline

set the hinting function from a pointer.

See discussion

Parameters

hint_func the container holding the function

Definition at line 2150 of file c2_function.hh.

2151 { hinting_function=hint_func; }

c2_inverse_function_p::hinting_function

c2_const_ptr< float_type > hinting_function

Definition: c2_function.hh:2157

template<typename float_type = double>

void c2_inverse_function_p< float_type >::set_start_hint ( float_type hint ) const

inline

give the function a hint as to where to look for its inverse

Parameters

hint	the likely value of the inverse, which defaults to whatever the evaluation returned.

Definition at line 2114 of file c2_function.hh.

2114 { start_hint=hint; }

c2_inverse_function_p::start_hint

float_type start_hint

Definition: c2_function.hh:2155

template<typename float_type = double>

virtual float_type c2_inverse_function_p< float_type >::value_with_derivatives	(	float_type	x,
		float_type *	yprime,
		float_type *	yprime2
	)		const

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>

const c2_const_ptr<float_type> c2_inverse_function_p< float_type >::func

protected

Definition at line 2156 of file c2_function.hh.

template<typename float_type = double>

c2_const_ptr<float_type> c2_inverse_function_p< float_type >::hinting_function

protected

Definition at line 2157 of file c2_function.hh.

template<typename float_type = double>

float_type c2_inverse_function_p< float_type >::start_hint

mutableprotected

Definition at line 2155 of file c2_function.hh.

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

source/geant4.10.03.p02/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_inverse_function_p< float_type >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<typename float_type = double>
class c2_inverse_function_p< float_type >