c2_function< float_type > Class Template Reference

the parent class for all c2_functions.c2_functions know their value, first, and second derivative at almost every point. They can be efficiently combined with binary operators, via c2_binary_function, composed via c2_composed_function_, have their roots found via find_root(), and be adaptively integrated via partial_integrals() or integral(). They also can carry information with them about how to find 'interesting' points on the function. This information is set with set_sampling_grid() and extracted with get_sampling_grid(). More...

#include <c2_function.hh>

Inheritance diagram for c2_function< float_type >:

Collaboration diagram for c2_function< float_type >:

Public Member Functions
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...
virtual float_type	value_with_derivatives (float_type x, float_type *yprime, float_type *yprime2) const =0
	get the value and derivatives. 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_function (const c2_function< float_type > &src)
	c2_function ()
virtual void	set_sampling_grid_pointer (std::vector< float_type > &grid)

Protected Attributes
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_function< float_type >

the parent class for all c2_functions.

c2_functions know their value, first, and second derivative at almost every point. They can be efficiently combined with binary operators, via c2_binary_function, composed via c2_composed_function_, have their roots found via find_root(), and be adaptively integrated via partial_integrals() or integral(). They also can carry information with them about how to find 'interesting' points on the function. This information is set with set_sampling_grid() and extracted with get_sampling_grid().

Particularly important subclasses are the interpolating functions classes, interpolating_function , lin_log_interpolating_function, log_lin_interpolating_function, log_log_interpolating_function, and arrhenius_interpolating_function, as well as the template functions inverse_integrated_density_function().

For a discussion of memory management, see memory_management

Definition at line 147 of file c2_function.hh.

Constructor & Destructor Documentation

template<typename float_type = double>

virtual c2_function< float_type >::~c2_function ( )

inlinevirtual

destructor

Definition at line 161 of file c2_function.hh.

                         { 
    if(sampling_grid && !no_overwrite_grid) delete sampling_grid;         
    if(root_info) delete root_info; 
    if(owner_count) {
      std::ostringstream outstr;
      outstr << "attempt to delete an object with non-zero ownership in class";
      outstr << typeid(*this).name() << std::endl;
      //throw c2_exception(outstr.str().c_str());
    }
  }

template<typename float_type = double>

c2_function< float_type >::c2_function ( const c2_function< float_type > &  src )

inlineprotected

Definition at line 527 of file c2_function.hh.

  : sampling_grid(0),
    no_overwrite_grid(false),
    fXMin(src.fXMin), fXMax(src.fXMax), root_info(0), owner_count(0)
  {} // copy constructor only copies domain, and is only for internal use

template<typename float_type = double>

c2_function< float_type >::c2_function ( )

inlineprotected

Definition at line 532 of file c2_function.hh.

                : 
    sampling_grid(0), no_overwrite_grid(0), 
    fXMin(-std::numeric_limits<float_type>::max()), 
    fXMax(std::numeric_limits<float_type>::max()), root_info(0), owner_count(0)
  {}

Member Function Documentation

template<typename float_type = double>

c2_piecewise_function_p<float_type>* c2_function< 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

This method has three modes, depending on the derivs flag.

If derivs is 2, it computes a c2_piecewise_function_p representation of its parent function, which may be a much faster function to use in codes if the parent function is expensive. If xvals and yvals are non-null, it will also fill them in with the function values at each grid point the adaptive algorithm chooses.

If derivs is 1, this does not create the connectors, and returns an null pointer, but will fill in the xvals and yvals vectors with values of the function at points such that the linear interpolation error between the points is bounded by the tolerance values given. Because it uses derivative information from the function to manage the error control, it is almost completely free of issues with missing periods of oscillatory functions, even with no information provided in the sampling grid. This is typically useful for sampling a function for plotting.

If derivs is 0, this does something very like what it does if derivs = 1, but without derivatives. Instead, to compute the intermediate value of the function for error control, it just uses 3-point parabolic interpolation. This is useful amost exclusively for converting a non-c2_function, with no derivatives, but wrapped in a c2_classic_function wrapper, into a table of values to seed an interpolating_function_p. Note, however, that without derivatives, this is very susceptible to missing periods of oscillatory functions, so it is important to set a sampling grid which isn't too much coarser than the typical oscillations.

Note

the sampling_grid of the returned function matches the sampling_grid of its parent.

See Also

Adaptive Sampling Examples

Parameters

	amin	lower bound of the domain for sampling
	amax	upper bound of the domain for sampling
	abs_tol	the absolute error bound for each segment
	rel_tol	the fractional error bound for each segment.
	derivs	if 0 or 1, return a useless function, but fill in the xvals and yvals vectors (if non-null). Also, if 0 or 1, tolerances refer to linear interpolation, not high-order interpolation. If 2, return a full piecewise collection of c2_connector_function_p segments. See discussion above.
[in,out]	xvals	vector of abscissas at which the function was actually sampled (if non-null)
[in,out]	yvals	vector of function values corresponding to xvals (if non-null)

Returns

a new, sampled representation, if derivs is 2. A null pointer if derivs is 0 or 1.

template<typename float_type = double>

bool c2_function< float_type >::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

Parameters

data	a vector of data points which are expected to be monotonic.
message	an informative string to include in an exception if this throws c2_exception

Returns

true if in decreasing order, false if increasing

template<typename float_type = double>

void c2_function< float_type >::claim_ownership ( ) const

inline

increment our reference count. Destruction is only legal if the count is zero.

Definition at line 506 of file c2_function.hh.

{ owner_count++; }

template<typename float_type = double>

size_t c2_function< float_type >::count_owners ( ) const

inline

get the reference count, mostly for debugging

Returns

the count

Definition at line 524 of file c2_function.hh.

{ return owner_count; }

template<typename float_type = double>

const std::string c2_function< float_type >::cvs_file_vers

(

)

const

get versioning information for the source file

Returns

the CVS Id string

template<typename float_type = double>

const std::string c2_function< float_type >::cvs_header_vers ( ) const

inline

get versioning information for the header file

Returns

the CVS Id string

Definition at line 151 of file c2_function.hh.

                                                { return 
                "c2_function.hh 490 2012-04-10 19:05:40Z marcus ";
        }

template<typename float_type = double>

void c2_function< float_type >::fill_fblock ( c2_fblock< float_type > &  fb ) const

inline

fill in a c2_fblock<float_type>... a shortcut for the integrator & sampler

Parameters

[in,out]

fb

the block to fill in with information

Definition at line 556 of file c2_function.hh.

  {
    fb.y=value_with_derivatives(fb.x, &fb.yp, &fb.ypp);
    fb.ypbad=c2_isnan(fb.yp) || !c2_isfinite(fb.yp);
    fb.yppbad=c2_isnan(fb.ypp) || !c2_isfinite(fb.ypp);
    increment_evaluations();
  }

template<typename float_type = double>

float_type c2_function< 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

find_root solves by iterated inverse quadratic extrapolation for a solution to f(x)=y. It includes checks against bad convergence, so it should never be able to fail. Unlike typical secant method or fancier Brent's method finders, this does not depend in any strong wasy on the brackets, unless the finder has to resort to successive approximations to close in on a root. Often, it is possible to make the brackets equal to the domain of the function, if there is any clue as to where the root lies, as given by the parameter start.

Parameters

	lower_bracket	the lower bound for the search
	upper_bracket	the upper bound for the search. Function sign must be opposite to that at lower_bracket
	start	starting value for the search
	value	the value of the function being sought (solves f(x) = value)
[out]	error	If pointer is zero, errors raise exception. Otherwise, returns error here.
[out]	final_yprime	If pointer is not zero, return derivative of function at root
[out]	final_yprime2	If pointer is not zero, return second derivative of function at root

Returns

the position of the root.

See Also

Root finding sample

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template<typename float_type = double>

size_t c2_function< float_type >::get_evaluations ( ) const

inline

and sampler do increment it.

Returns

number of evaluations logged since last reset.

Definition at line 395 of file c2_function.hh.

{ return evaluations; }

template<typename float_type = double>

virtual void c2_function< float_type >::get_sampling_grid ( float_type  amin, float_type  amax, std::vector< float_type > &  grid  ) const

virtual

Reimplemented in c2_sin_p< float_type >, c2_plugin_function_p< float_type >, and c2_plugin_function_p< G4double >.

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template<typename float_type = double>

std::vector<float_type>* c2_function< float_type >::get_sampling_grid_pointer ( ) const

inline

get the sampling grid, which may be a null pointer

Returns

pointer to the sampling grid

Definition at line 432 of file c2_function.hh.

                                                           { 
    return sampling_grid; } 

template<typename float_type = double>

float_type c2_function< float_type >::get_trouble_point ( ) const

inline

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.

Returns

x value of point at which something went wrong, if integrator (or otherwise) returned a nan.

Definition at line 502 of file c2_function.hh.

{ return bad_x_point; }

template<typename float_type = double>

void c2_function< float_type >::increment_evaluations ( ) const

inline

count evaluations

Definition at line 399 of file c2_function.hh.

{ evaluations++; }

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template<typename float_type = double>

float_type c2_function< 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.

It returns the integral of the function over the domain requested with error tolerances as specified. It is just a front-end to partial_integrals()

Parameters

amin	lower bound of the domain for integration
amax	upper bound of the domain for integration
partials	if non-NULL, a vector in which to receive the partial integrals. It will automatically be sized appropriately, if provided, to contain n - 1 elements where n is the length of xgrid
abs_tol	the absolute error bound for each segment
rel_tol	the fractional error bound for each segment. If the error is smaller than either the relative or absolute tolerance, the integration step is finished.
derivs	number of derivatives to trust, which sets the order of the integrator. The order is 3*derivs + 4. derivs can be 0, 1, or 2.
adapt	if true, use recursive adaptation, otherwise do simple evaluation on the grid provided with no error checking.
extrapolate	if true, use simple Richardson extrapolation on the final 2 steps to reduce the error.

Returns

sum of partial integrals, which is the definite integral from the first value in xgrid to the last.

template<typename float_type = double>

c2_function<float_type>& 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

Parameters

amin	lower bound of the domain for integration
amax	upper bound of the domain for integration
norm	the desired integral for the function over the region

Returns

a new c2_function with the desired norm.

template<typename float_type = double>

float_type c2_function< float_type >::operator() ( float_type  x ) const

inline

evaluate the function in the classic way, ignoring derivatives.

Parameters

x	the point at which to evaluate

Returns

the value of the function

Definition at line 186 of file c2_function.hh.

        { return value_with_derivatives(x, (float_type *)0, (float_type *)0); } 

template<typename float_type = double>

float_type c2_function< float_type >::operator() ( float_type  x, float_type *  yprime, float_type *  yprime2  ) const

inline

get the value and derivatives.

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

Definition at line 195 of file c2_function.hh.

        { return value_with_derivatives(x, yprime, yprime2); } 

template<typename float_type = double>

c2_composed_function_p<float_type>& c2_function< float_type >::operator() ( const c2_function< float_type > &  inner ) const

inline

compose this function outside another.

Parameters

inner

the inner function

Returns

the composed function

Definition at line 495 of file c2_function.hh.

  { return *new c2_composed_function_p<float_type>((*this), inner); }

template<typename float_type = double>

c2_product_p<float_type>& c2_function< float_type >::operator* ( const c2_function< float_type > &  rhs ) const

inline

factory function to create a c2_product_p from a regular algebraic expression.

Parameters

rhs	the right-hand term of the product

Returns

a new c2_function

Definition at line 486 of file c2_function.hh.

  { return *new c2_product_p<float_type>(*this, rhs); }

template<typename float_type = double>

c2_sum_p<float_type>& c2_function< float_type >::operator+ ( const c2_function< float_type > &  rhs ) const

inline

factory function to create a c2_sum_p from a regular algebraic expression.

Parameters

rhs	the right-hand term of the sum

Returns

a new c2_function

Definition at line 473 of file c2_function.hh.

  { return *new c2_sum_p<float_type>(*this, rhs); }

template<typename float_type = double>

c2_diff_p<float_type>& c2_function< float_type >::operator- ( const c2_function< float_type > &  rhs ) const

inline

factory function to create a c2_diff_p from a regular algebraic expression.

Parameters

rhs	the right-hand term of the difference

Returns

a new c2_function

Definition at line 479 of file c2_function.hh.

  { return *new c2_diff_p<float_type>(*this, rhs); }

template<typename float_type = double>

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

inline

Definition at line 488 of file c2_function.hh.

  { return *new c2_ratio_p<float_type>(*this, rhs); }

template<typename float_type = double>

float_type c2_function< 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

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.

Parameters

xgrid	points between which to evaluate definite integrals.
partials	if non-NULL, a vector in which to receive the partial integrals. It will automatically be sized apprpropriately, if provided, to contain n - 1 elements where n is the length of xgrid
abs_tol	the absolute error bound for each segment
rel_tol	the fractional error bound for each segment. If the error is smaller than either the relative or absolute tolerance, the integration step is finished.
derivs	number of derivatives to trust, which sets the order of the integrator. The order is 3*derivs + 4. derivs can be 0, 1, or 2.
adapt	if true, use recursive adaptation, otherwise do simple evaluation on the grid provided with no error checking.
extrapolate	if true, use simple Richardson extrapolation on the final 2 steps to reduce the error.

Returns

sum of partial integrals, which is the definite integral from the first value in xgrid to the last.

template<typename float_type = double>

void c2_function< float_type >::preen_sampling_grid

(

std::vector< float_type > *

result

)

const

The grid is modified in place.

template<typename float_type = double>

void c2_function< float_type >::refine_sampling_grid	(	std::vector< float_type > &	grid,
		size_t	refinement
	)		const

template<typename float_type = double>

void c2_function< float_type >::release_ownership ( ) const

inline

Definition at line 519 of file c2_function.hh.

                                   { 
    if(!release_ownership_for_return()) delete this;
  }

template<typename float_type = double>

size_t c2_function< float_type >::release_ownership_for_return ( ) const

inline

decrement our reference count. Do not destroy at zero.

Returns

final owner count, to check whether object should disappear.

Definition at line 509 of file c2_function.hh.

                                                { 
    if(!owner_count) {
      std::ostringstream outstr;
      outstr << "attempt to release ownership of an unowned function in class ";
      outstr << typeid(*this).name() << std::endl;
      throw c2_exception(outstr.str().c_str());
    }
    owner_count--; 
    return owner_count;
  }

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template<typename float_type = double>

void c2_function< float_type >::reset_evaluations ( ) const

inline

reset the counter

Definition at line 397 of file c2_function.hh.

{ evaluations=0; } 

template<typename float_type = double>

void c2_function< float_type >::set_domain ( float_type  amin, float_type  amax  )

inline

Definition at line 391 of file c2_function.hh.

{ fXMin=amin; fXMax=amax; }

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template<typename float_type = double>

virtual void c2_function< float_type >::set_sampling_grid ( const std::vector< float_type > &  grid )

virtual

establish a grid of 'interesting' points on the function.

The sampling grid describes a reasonable initial set of points to look at the function. this should generally be set at a scale which is quite coarse, and sufficient for initializing adaptive integration or possibly root bracketing. For sampling a function to build a new interpolating function, one may want to refine this for accuracy. However, interpolating_functions themselves return their original X grid by default, so refining the grid in this case might be a bad idea.

Parameters

grid	a vector of abscissas. The contents is copied into an internal vector, so the grid can be discarded after passingin.

template<typename float_type = double>

virtual void c2_function< float_type >::set_sampling_grid_pointer ( std::vector< float_type > &  grid )

inlineprotectedvirtual

Definition at line 538 of file c2_function.hh.

  { 
    if (sampling_grid && !no_overwrite_grid) delete sampling_grid; 
    sampling_grid=&grid; no_overwrite_grid=1; 
  }

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template<typename float_type = double>

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

template<typename float_type = double>

c2_function<float_type>& 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

Parameters

amin	lower bound of the domain for integration
amax	upper bound of the domain for integration
weight	a c2_function providing the weight
norm	the desired integral for the function over the region

Returns

a new c2_function with the desired norm.

template<typename float_type = double>

virtual float_type c2_function< float_type >::value_with_derivatives ( float_type  x, float_type *  yprime, float_type *  yprime2  ) const

pure 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

Implemented in c2_piecewise_function_p< float_type >, c2_connector_function_p< float_type >, c2_inverse_function_p< float_type >, c2_power_law_p< float_type >, c2_quadratic_p< float_type >, c2_linear_p< float_type >, c2_linear_p< G4double >, c2_identity_p< float_type >, c2_recip_p< float_type >, c2_sqrt_p< float_type >, c2_exp_p< float_type >, c2_log_p< float_type >, c2_tan_p< float_type >, c2_cos_p< float_type >, c2_sin_p< float_type >, interpolating_function_p< float_type >, c2_constant_p< float_type >, c2_cached_function_p< float_type >, c2_scaled_function_p< float_type >, c2_binary_function< float_type >, c2_plugin_function_p< float_type >, c2_plugin_function_p< G4double >, and c2_classic_function_p< float_type >.

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template<typename float_type = double>

float_type c2_function< float_type >::xmax ( ) const

inline

Definition at line 390 of file c2_function.hh.

{ return fXMax; }

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template<typename float_type = double>

float_type c2_function< float_type >::xmin ( ) const

inline

Definition at line 389 of file c2_function.hh.

{ return fXMin; }

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Member Data Documentation

template<typename float_type = double>

float_type c2_function< float_type >::bad_x_point

mutableprotected

this point may be used to record where a calculation ran into trouble

Definition at line 551 of file c2_function.hh.

template<typename float_type = double>

size_t c2_function< float_type >::evaluations

mutableprotected

Definition at line 548 of file c2_function.hh.

template<typename float_type = double>

float_type c2_function< float_type >::fXMax

protected

Definition at line 547 of file c2_function.hh.

template<typename float_type = double>

float_type c2_function< float_type >::fXMin

protected

Definition at line 547 of file c2_function.hh.

template<typename float_type = double>

bool c2_function< float_type >::no_overwrite_grid

protected

Definition at line 545 of file c2_function.hh.

template<typename float_type = double>

std::vector<float_type>* c2_function< float_type >::sampling_grid

protected

Definition at line 544 of file c2_function.hh.

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

• source/geant4.10.03.p02/examples/extended/electromagnetic/TestEm7/include/c2_function.hh