create a cubic spline interpolation of a set of (x,y) pairsThis is one of the main reasons for c2_function objects to exist. More...

#include <c2_function.hh>

Inheritance diagram for interpolating_function_p< float_type >:

Collaboration diagram for interpolating_function_p< float_type >:

Public Member Functions
	interpolating_function_p ()
	an empty linear-linear cubic-spline interpolating_function_p More...

	interpolating_function_p (const c2_function_transformation< float_type > &transform)
	an empty cubic-spline interpolating_function_p with a specific transform More...

interpolating_function_p < float_type > &	load (const std::vector< float_type > &x, const std::vector< float_type > &f, bool lowerSlopeNatural, float_type lowerSlope, bool upperSlopeNatural, float_type upperSlope, bool splined=true) throw (c2_exception)
	do the dirty work of constructing the spline from a function. More...

interpolating_function_p < float_type > &	load_pairs (std::vector< std::pair< float_type, float_type > > &data, bool lowerSlopeNatural, float_type lowerSlope, bool upperSlopeNatural, float_type upperSlope, bool splined=true) throw (c2_exception)
	do the dirty work of constructing the spline from a function. More...

interpolating_function_p < float_type > &	sample_function (const c2_function< float_type > &func, float_type amin, float_type amax, float_type abs_tol, float_type rel_tol, bool lowerSlopeNatural, float_type lowerSlope, bool upperSlopeNatural, float_type upperSlope) throw (c2_exception)
	do the dirty work of constructing the spline from a function. More...

interpolating_function_p < float_type > &	load_random_generator_function (const std::vector< float_type > &bincenters, const c2_function< float_type > &binheights) throw (c2_exception)
	initialize from a grid of points and a c2_function (un-normalized) to an interpolator which, when evaluated with a uniform random variate on [0,1] returns random numbers distributed as the input function. More...

interpolating_function_p < float_type > &	load_random_generator_bins (const std::vector< float_type > &bins, const std::vector< float_type > &binheights, bool splined=true) throw (c2_exception)

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...

virtual	~interpolating_function_p ()
	destructor More...

virtual interpolating_function_p < float_type > &	clone () const throw (c2_exception)

void	get_data (std::vector< float_type > &xvals, std::vector< float_type > &yvals) const throw ()

void	get_internal_data (std::vector< float_type > &xvals, std::vector< float_type > &yvals, std::vector< float_type > &y2vals) const

void	set_lower_extrapolation (float_type bound)

void	set_upper_extrapolation (float_type bound)

interpolating_function_p < float_type > &	unary_operator (const c2_function< float_type > &source) const

interpolating_function_p < float_type > &	binary_operator (const c2_function< float_type > &rhs, const c2_binary_function< float_type > *combining_stub) const

interpolating_function_p < float_type > &	add_pointwise (const c2_function< float_type > &rhs) const

interpolating_function_p < float_type > &	subtract_pointwise (const c2_function< float_type > &rhs) const

interpolating_function_p < float_type > &	multiply_pointwise (const c2_function< float_type > &rhs) const

interpolating_function_p < float_type > &	divide_pointwise (const c2_function< float_type > &rhs) const

void	clone_data (const interpolating_function_p< float_type > &rhs)

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...

Public Attributes
const c2_function_transformation < float_type > &	fTransform

Protected Member Functions
void	spline (bool lowerSlopeNatural, float_type lowerSlope, bool upperSlopeNatural, float_type upperSlope) throw (c2_exception)
	create the spline coefficients 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)

Static Protected Member Functions
static bool	comp_pair (std::pair< float_type, float_type > const &i, std::pair< float_type, float_type > const &j)

Protected Attributes
std::vector< float_type >	Xraw

std::vector< float_type >	X

std::vector< float_type >	F

std::vector< float_type >	y2

c2_const_ptr< float_type >	sampler_function

bool	xInverted

size_t	lastKLow

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 interpolating_function_p< float_type >

create a cubic spline interpolation of a set of (x,y) pairs

This is one of the main reasons for c2_function objects to exist.

It provides support for cubic spline interpolation of data provides from tables of x, y pairs. It supports automatic, transparent linearization of the data before storing in its tables (through subclasses such as log_lin_interpolating_function, lin_log_interpolating_function, and log_log_interpolating_function) to permit very high accuracy representations of data which have a suitable structure. It provides utility functions LinearInterpolatingGrid() and LogLogInterpolatingGrid() to create grids for mapping other functions onto a arithmetic or geometric grid.

In its simplest form, an untransformed cubic spline of a data set, using natural boundary conditions (vanishing second derivative), is created as:

    c2_ptr<double> c2p;
    c2_factory<double> c2;
std::vector<double> xvals(10), yvals(10); 
// < fill in xvals and yvals >
c2p myfunc=c2.interpolating_function().load(xvals, yvals,true,0,true,0);
// and it can be evaluated at a point for its value only by: 
double y=myfunc(x); 
// or it can be evaluated with its derivatives by
double yprime, yprime2; 
double y=myfunc(x,&yprime, &yprime2);

The factory function c2_factory::interpolating_function() creates *new interpolating_function_p()

Definition at line 1513 of file c2_function.hh.

Constructor & Destructor Documentation

template<typename float_type = double>

interpolating_function_p< float_type >::interpolating_function_p ( )

inline

an empty linear-linear cubic-spline interpolating_function_p

Definition at line 1518 of file c2_function.hh.

template<typename float_type = double>

interpolating_function_p< float_type >::interpolating_function_p ( const c2_function_transformation< float_type > & transform )

inline

an empty cubic-spline interpolating_function_p with a specific transform

Definition at line 1524 of file c2_function.hh.

template<typename float_type = double>

virtual interpolating_function_p< float_type >::~interpolating_function_p ( )

inlinevirtual

destructor

Definition at line 1661 of file c2_function.hh.

References interpolating_function_p< float_type >::fTransform.

Member Function Documentation

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::add_pointwise ( const c2_function< float_type > & rhs ) const

inline

Definition at line 1687 of file c2_function.hh.

References interpolating_function_p< float_type >::binary_operator().

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template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::binary_operator	(	const c2_function< float_type > &	rhs,
		const c2_binary_function< float_type > *	combining_stub
	)		const

Referenced by interpolating_function_p< float_type >::add_pointwise(), interpolating_function_p< float_type >::divide_pointwise(), interpolating_function_p< float_type >::multiply_pointwise(), and interpolating_function_p< float_type >::subtract_pointwise().

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template<typename float_type = double>

virtual interpolating_function_p<float_type>& interpolating_function_p< float_type >::clone	(		)	const
throw	(	c2_exception
	)

inlinevirtual

Reimplemented in arrhenius_interpolating_function_p< float_type >, log_log_interpolating_function_p< float_type >, lin_log_interpolating_function_p< float_type >, and log_lin_interpolating_function_p< float_type >.

Definition at line 1663 of file c2_function.hh.

template<typename float_type = double>

void interpolating_function_p< float_type >::clone_data ( const interpolating_function_p< float_type > & rhs )

inline

Definition at line 1698 of file c2_function.hh.

References interpolating_function_p< float_type >::F, c2_function< float_type >::set_sampling_grid_pointer(), interpolating_function_p< float_type >::X, interpolating_function_p< float_type >::Xraw, and interpolating_function_p< float_type >::y2.

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template<typename float_type = double>

static bool interpolating_function_p< float_type >::comp_pair	(	std::pair< float_type, float_type > const &	i,
		std::pair< float_type, float_type > const &	j
	)

inlinestaticprotected

Definition at line 1712 of file c2_function.hh.

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::divide_pointwise ( const c2_function< float_type > & rhs ) const

inline

Definition at line 1696 of file c2_function.hh.

References interpolating_function_p< float_type >::binary_operator().

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template<typename float_type = double>

void interpolating_function_p< float_type >::get_data	(	std::vector< float_type > &	xvals,
		std::vector< float_type > &	yvals
	)		const
throw	(
	)

template<typename float_type = double>

void interpolating_function_p< float_type >::get_internal_data	(	std::vector< float_type > &	xvals,
		std::vector< float_type > &	yvals,
		std::vector< float_type > &	y2vals
	)		const

inline

Definition at line 1670 of file c2_function.hh.

References interpolating_function_p< float_type >::F, interpolating_function_p< float_type >::X, and interpolating_function_p< float_type >::y2.

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::load	(	const std::vector< float_type > &	x,
		const std::vector< float_type > &	f,
		bool	lowerSlopeNatural,
		float_type	lowerSlope,
		bool	upperSlopeNatural,
		float_type	upperSlope,
		bool	splined = `true`
	)
throw	(	c2_exception
	)

do the dirty work of constructing the spline from a function.

Parameters

x	the list of abscissas. Must be either strictly increasing or strictly decreasing. Strictly increasing is preferred, as less memory is used since a copy is not required for the sampling grid.
f	the list of function values.
lowerSlopeNatural	if true, set y''(first point)=0, otherwise compute it from lowerSope
lowerSlope	derivative of the function at the lower bound, used only if lowerSlopeNatural is false
upperSlopeNatural	if true, set y''(last point)=0, otherwise compute it from upperSope
upperSlope	derivative of the function at the upper bound, used only if upperSlopeNatural is false
splined	if true (default), use cubic spline, if false, use linear interpolation.

Returns: the same interpolating function, filled

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::load_pairs	(	std::vector< std::pair< float_type, float_type > > &	data,
		bool	lowerSlopeNatural,
		float_type	lowerSlope,
		bool	upperSlopeNatural,
		float_type	upperSlope,
		bool	splined = `true`
	)
throw	(	c2_exception
	)

do the dirty work of constructing the spline from a function.

Parameters

data	std::vector of std::pairs of x,y. Will be sorted into x increasing order in place.
lowerSlopeNatural	if true, set y''(first point)=0, otherwise compute it from lowerSope
lowerSlope	derivative of the function at the lower bound, used only if lowerSlopeNatural is false
upperSlopeNatural	if true, set y''(last point)=0, otherwise compute it from upperSope
upperSlope	derivative of the function at the upper bound, used only if upperSlopeNatural is false
splined	if true (default), use cubic spline, if false, use linear interpolation.

Returns: the same interpolating function, filled

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::load_random_generator_bins	(	const std::vector< float_type > &	bins,
		const std::vector< float_type > &	binheights,
		bool	splined = `true`
	)
throw	(	c2_exception
	)

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::load_random_generator_function	(	const std::vector< float_type > &	bincenters,
		const c2_function< float_type > &	binheights
	)
throw	(	c2_exception
	)

initialize from a grid of points and a c2_function (un-normalized) to an interpolator which, when evaluated with a uniform random variate on [0,1] returns random numbers distributed as the input function.

See also: Arbitrary random generation inverse_integrated_density starts derivatives a probability density std::vector, generates the integral, and generates an interpolating_function_p of the inverse function which, when evaluated using a uniform random on [0,1] returns values derivatives a density distribution equal to the input distribution If the data are passed in reverse order (large X first), the integral is carried out from the big end.

Parameters

bincenters	the positions at which to sample the function binheights
binheights	a function which describes the density of the random number distribution to be produced.

Returns: an initialized interpolator, which if evaluated randomly with a uniform variate on [0,1] produces numbers distributed according to binheights

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::multiply_pointwise ( const c2_function< float_type > & rhs ) const

inline

Definition at line 1693 of file c2_function.hh.

References interpolating_function_p< float_type >::binary_operator().

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template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::sample_function	(	const c2_function< float_type > &	func,
		float_type	amin,
		float_type	amax,
		float_type	abs_tol,
		float_type	rel_tol,
		bool	lowerSlopeNatural,
		float_type	lowerSlope,
		bool	upperSlopeNatural,
		float_type	upperSlope
	)
throw	(	c2_exception
	)

do the dirty work of constructing the spline from a function.

Parameters

func	a function without any requirement of valid derivatives to sample into an interpolating function. Very probably a c2_classic_function.
amin	the lower bound of the region to sample
amax	the upper bound of the region to sample
abs_tol	the maximum absolute error permitted when linearly interpolating the points. the real error will be much smaller, since this uses cubic splines at the end.
rel_tol	the maximum relative error permitted when linearly interpolating the points. the real error will be much smaller, since this uses cubic splines at the end.
lowerSlopeNatural	if true, set y'(first point) from 3-point parabola, otherwise compute it from lowerSope
lowerSlope	derivative of the function at the lower bound, used only if lowerSlopeNatural is false
upperSlopeNatural	if true, set y'(last point) from 3-point parabola, otherwise compute it from upperSope
upperSlope	derivative of the function at the upper bound, used only if upperSlopeNatural is false

Returns: the same interpolating function, filled

Note: If the interpolator being filled has a log vertical axis, put the desired relative error in abs_tol, and 0 in rel_tol since the absolute error on the log of a function is the relative error on the function itself.

template<typename float_type = double>

void interpolating_function_p< float_type >::set_lower_extrapolation ( float_type bound )

template<typename float_type = double>

void interpolating_function_p< float_type >::set_upper_extrapolation ( float_type bound )

template<typename float_type = double>

void interpolating_function_p< float_type >::spline	(	bool	lowerSlopeNatural,
		float_type	lowerSlope,
		bool	upperSlopeNatural,
		float_type	upperSlope
	)
throw	(	c2_exception
	)

protected

create the spline coefficients

template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::subtract_pointwise ( const c2_function< float_type > & rhs ) const

inline

Definition at line 1690 of file c2_function.hh.

References interpolating_function_p< float_type >::binary_operator().

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template<typename float_type = double>

interpolating_function_p<float_type>& interpolating_function_p< float_type >::unary_operator ( const c2_function< float_type > & source ) const

template<typename float_type = double>

virtual float_type interpolating_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>

std::vector<float_type> interpolating_function_p< float_type >::F

protected

Definition at line 1716 of file c2_function.hh.

Referenced by interpolating_function_p< float_type >::clone_data(), and interpolating_function_p< float_type >::get_internal_data().

template<typename float_type = double>

const c2_function_transformation<float_type>& interpolating_function_p< float_type >::fTransform

Definition at line 1703 of file c2_function.hh.

Referenced by interpolating_function_p< float_type >::~interpolating_function_p().

template<typename float_type = double>

size_t interpolating_function_p< float_type >::lastKLow

mutableprotected

Definition at line 1719 of file c2_function.hh.

template<typename float_type = double>

c2_const_ptr<float_type> interpolating_function_p< float_type >::sampler_function

protected

Definition at line 1717 of file c2_function.hh.

template<typename float_type = double>

std::vector<float_type> interpolating_function_p< float_type >::X

protected

Definition at line 1716 of file c2_function.hh.

Referenced by interpolating_function_p< float_type >::clone_data(), and interpolating_function_p< float_type >::get_internal_data().

template<typename float_type = double>

bool interpolating_function_p< float_type >::xInverted

protected

Definition at line 1718 of file c2_function.hh.

template<typename float_type = double>

std::vector<float_type> interpolating_function_p< float_type >::Xraw

protected

Definition at line 1716 of file c2_function.hh.

Referenced by interpolating_function_p< float_type >::clone_data().

template<typename float_type = double>

std::vector<float_type> interpolating_function_p< float_type >::y2

protected

Definition at line 1716 of file c2_function.hh.

Referenced by interpolating_function_p< float_type >::clone_data(), and interpolating_function_p< float_type >::get_internal_data().

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

Public Attributes

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Detailed Description

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

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

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