Geant4  v4-10.4-release
accumulated_histogram< float_type > 클래스 템플릿 참조

An interpolating_function_p which is the cumulative integral of a histogram.Note than binedges should be one element longer than binheights, since the lower & upper edges are specified. Note that this is a malformed spline, since the second derivatives are all zero, so it has less continuity. Also, note that the bin edges can be given in backwards order to generate the reversed accumulation (starting at the high end) 더 자세히 ...

#include <c2_function.hh>

accumulated_histogram< float_type >에 대한 상속 다이어그램 :

## Public 멤버 함수

accumulated_histogram (const std::vector< float_type >binedges, const std::vector< float_type > binheights, bool normalize=false, bool inverse_function=false, bool drop_zeros=true)
Construct the integrated histogram. 더 자세히 ...

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)
do the dirty work of constructing the spline from a function. 더 자세히 ...

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)
do the dirty work of constructing the spline from a function. 더 자세히 ...

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)
do the dirty work of constructing the spline from a function. 더 자세히 ...

interpolating_function_p
< float_type > &
load_random_generator_function (const std::vector< float_type > &bincenters, const c2_function< float_type > &binheights)
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. 더 자세히 ...

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

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

virtual
interpolating_function_p
< float_type > &
clone () const

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

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)

get versioning information for the header file 더 자세히 ...

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

float_type operator() (float_type x) const
evaluate the function in the classic way, ignoring derivatives. 더 자세히 ...

float_type operator() (float_type x, float_type *yprime, float_type *yprime2) const
get the value and derivatives. 더 자세히 ...

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

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 더 자세히 ...

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. 더 자세히 ...

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 더 자세히 ...

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 더 자세히 ...

void increment_evaluations () const
count evaluations 더 자세히 ...

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 더 자세히 ...

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

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

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. 더 자세히 ...

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 더 자세히 ...

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 더 자세히 ...

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. 더 자세히 ...

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. 더 자세히 ...

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. 더 자세히 ...

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

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. 더 자세히 ...

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

size_t release_ownership_for_return () const
decrement our reference count. Do not destroy at zero. 더 자세히 ...

void release_ownership () const

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

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

## Public 속성

const
c2_function_transformation
< float_type > &
fTransform

## Protected 멤버 함수

void spline (bool lowerSlopeNatural, float_type lowerSlope, bool upperSlopeNatural, float_type upperSlope)
create the spline coefficients 더 자세히 ...

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

## 정적 Protected 멤버 함수

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

## Protected 속성

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

std::vector< float_type > * sampling_grid

bool no_overwrite_grid

float_type fXMin

float_type fXMax

size_t evaluations

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

## 상세한 설명

### template<typename float_type = double> class accumulated_histogram< float_type >

An interpolating_function_p which is the cumulative integral of a histogram.

Note than binedges should be one element longer than binheights, since the lower & upper edges are specified. Note that this is a malformed spline, since the second derivatives are all zero, so it has less continuity. Also, note that the bin edges can be given in backwards order to generate the reversed accumulation (starting at the high end)

c2_function.hh 파일의 2173 번째 라인에서 정의되었습니다.

## 생성자 & 소멸자 문서화

template<typename float_type = double>
 accumulated_histogram< float_type >::accumulated_histogram ( const std::vector< float_type > binedges, const std::vector< float_type > binheights, bool normalize = false, bool inverse_function = false, bool drop_zeros = true )

Construct the integrated histogram.

매개변수
 binedges the edges of the bins in binheights. It should have one more element than binheights binheights the number of counts in each bin. normalize if true, normalize integral to 1 inverse_function if true, drop zero channels, and return inverse function for random generation drop_zeros eliminate null bins before integrating, so integral is strictly monotonic.

## 멤버 함수 문서화

template<typename float_type = double>
 c2_piecewise_function_p* 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
inherited

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.

주의
the sampling_grid of the returned function matches the sampling_grid of its parent.
참고
매개변수
 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)
반환값
a new, sampled representation, if derivs is 2. A null pointer if derivs is 0 or 1.
template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::add_pointwise ( const c2_function< float_type > & rhs ) const
inlineinherited

c2_function.hh 파일의 1687 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::binary_operator ( const c2_function< float_type > & rhs, const c2_binary_function< float_type > * combining_stub ) const
inherited
template<typename float_type = double>
 bool c2_function< float_type >::check_monotonicity ( const std::vector< float_type > & data, const char message[] ) const
inherited

check that a vector is monotonic, throw an exception if not, and return a flag if it is reversed

매개변수
 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
반환값
true if in decreasing order, false if increasing
template<typename float_type = double>
 void c2_function< float_type >::claim_ownership ( ) const
inlineinherited

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

c2_function.hh 파일의 506 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 virtual interpolating_function_p& interpolating_function_p< float_type >::clone ( ) const
inlinevirtualinherited
template<typename float_type = double>
 void interpolating_function_p< float_type >::clone_data ( const interpolating_function_p< float_type > & rhs )
inlineinherited
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 )
inlinestaticprotectedinherited

c2_function.hh 파일의 1712 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 size_t c2_function< float_type >::count_owners ( ) const
inlineinherited

get the reference count, mostly for debugging

반환값
the count

c2_function.hh 파일의 524 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 const std::string c2_function< float_type >::cvs_file_vers ( ) const
inherited

get versioning information for the source file

반환값
the CVS Id string
template<typename float_type = double>
 const std::string c2_function< float_type >::cvs_header_vers ( ) const
inlineinherited

get versioning information for the header file

반환값
the CVS Id string

c2_function.hh 파일의 151 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::divide_pointwise ( const c2_function< float_type > & rhs ) const
inlineinherited

c2_function.hh 파일의 1696 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 void c2_function< float_type >::fill_fblock ( c2_fblock< float_type > & fb ) const
inlineinherited

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

매개변수
 [in,out] fb the block to fill in with information

c2_function.hh 파일의 556 번째 라인에서 정의되었습니다.

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
inherited

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.

매개변수
 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
반환값
the position of the root.
참고
Root finding sample
template<typename float_type = double>
 void interpolating_function_p< float_type >::get_data ( std::vector< float_type > & xvals, std::vector< float_type > & yvals ) const
inherited
template<typename float_type = double>
 size_t c2_function< float_type >::get_evaluations ( ) const
inlineinherited

and sampler do increment it.

반환값
number of evaluations logged since last reset.

c2_function.hh 파일의 395 번째 라인에서 정의되었습니다.

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
inlineinherited

c2_function.hh 파일의 1670 번째 라인에서 정의되었습니다.

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
virtualinherited
template<typename float_type = double>
 std::vector* c2_function< float_type >::get_sampling_grid_pointer ( ) const
inlineinherited

get the sampling grid, which may be a null pointer

반환값
pointer to the sampling grid

c2_function.hh 파일의 432 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 float_type c2_function< float_type >::get_trouble_point ( ) const
inlineinherited

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.

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

c2_function.hh 파일의 502 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 void c2_function< float_type >::increment_evaluations ( ) const
inlineinherited

count evaluations

c2_function.hh 파일의 399 번째 라인에서 정의되었습니다.

다음에 의해서 참조됨 : c2_function< G4double >::fill_fblock().

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
inherited

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()

매개변수
 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.
반환값
sum of partial integrals, which is the definite integral from the first value in xgrid to the last.
template<typename float_type = double>
 interpolating_function_p& 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 )
inherited

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

매개변수
 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.
반환값
the same interpolating function, filled
template<typename float_type = double>
 interpolating_function_p& 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 )
inherited

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

매개변수
 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.
반환값
the same interpolating function, filled
template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::load_random_generator_bins ( const std::vector< float_type > & bins, const std::vector< float_type > & binheights, bool splined = true )
inherited
template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::load_random_generator_function ( const std::vector< float_type > & bincenters, const c2_function< float_type > & binheights )
inherited

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.

참고
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.
매개변수
 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.
반환값
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& interpolating_function_p< float_type >::multiply_pointwise ( const c2_function< float_type > & rhs ) const
inlineinherited

c2_function.hh 파일의 1693 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_function& c2_function< float_type >::normalized_function ( float_type amin, float_type amax, float_type norm = 1.0 ) const
inherited

create a new c2_function from this one which is normalized on the interval

매개변수
 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
반환값
a new c2_function with the desired norm.
template<typename float_type = double>
 float_type c2_function< float_type >::operator() ( float_type x ) const
inlineinherited

evaluate the function in the classic way, ignoring derivatives.

매개변수
 x the point at which to evaluate
반환값
the value of the function

c2_function.hh 파일의 186 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 float_type c2_function< float_type >::operator() ( float_type x, float_type * yprime, float_type * yprime2 ) const
inlineinherited

get the value and derivatives.

매개변수
 [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)
반환값
the value of the function

c2_function.hh 파일의 195 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_composed_function_p& c2_function< float_type >::operator() ( const c2_function< float_type > & inner ) const
inlineinherited

compose this function outside another.

매개변수
 inner the inner function
반환값
the composed function

c2_function.hh 파일의 495 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_product_p& c2_function< float_type >::operator* ( const c2_function< float_type > & rhs ) const
inlineinherited

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

매개변수
 rhs the right-hand term of the product
반환값
a new c2_function

c2_function.hh 파일의 486 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_sum_p& c2_function< float_type >::operator+ ( const c2_function< float_type > & rhs ) const
inlineinherited

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

매개변수
 rhs the right-hand term of the sum
반환값
a new c2_function

c2_function.hh 파일의 473 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_diff_p& c2_function< float_type >::operator- ( const c2_function< float_type > & rhs ) const
inlineinherited

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

매개변수
 rhs the right-hand term of the difference
반환값
a new c2_function

c2_function.hh 파일의 479 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_ratio_p& c2_function< float_type >::operator/ ( const c2_function< float_type > & rhs ) const
inlineinherited

c2_function.hh 파일의 488 번째 라인에서 정의되었습니다.

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
inherited

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.

매개변수
 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.
반환값
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
inherited

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
inherited
template<typename float_type = double>
 void c2_function< float_type >::release_ownership ( ) const
inlineinherited

c2_function.hh 파일의 519 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 size_t c2_function< float_type >::release_ownership_for_return ( ) const
inlineinherited

decrement our reference count. Do not destroy at zero.

반환값
final owner count, to check whether object should disappear.

c2_function.hh 파일의 509 번째 라인에서 정의되었습니다.

다음에 의해서 참조됨 : c2_function< G4double >::release_ownership().

template<typename float_type = double>
 void c2_function< float_type >::reset_evaluations ( ) const
inlineinherited

reset the counter

c2_function.hh 파일의 397 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 interpolating_function_p& 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 )
inherited

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

매개변수
 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
반환값
the same interpolating function, filled
주의
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 c2_function< float_type >::set_domain ( float_type amin, float_type amax )
inlineinherited
template<typename float_type = double>
 void interpolating_function_p< float_type >::set_lower_extrapolation ( float_type bound )
inherited
template<typename float_type = double>
 virtual void c2_function< float_type >::set_sampling_grid ( const std::vector< float_type > & grid )
virtualinherited

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.

매개변수
 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 )
inlineprotectedvirtualinherited

c2_function.hh 파일의 538 번째 라인에서 정의되었습니다.

다음에 의해서 참조됨 : interpolating_function_p< float_type >::clone_data().

template<typename float_type = double>
 void interpolating_function_p< float_type >::set_upper_extrapolation ( float_type bound )
inherited
template<typename float_type = double>
 void interpolating_function_p< float_type >::spline ( bool lowerSlopeNatural, float_type lowerSlope, bool upperSlopeNatural, float_type upperSlope )
protectedinherited

create the spline coefficients

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

create a new c2_function from this one which is square-normalized with the provided weight on the interval

매개변수
 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
반환값
a new c2_function with the desired norm.
template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::subtract_pointwise ( const c2_function< float_type > & rhs ) const
inlineinherited

c2_function.hh 파일의 1690 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 interpolating_function_p& interpolating_function_p< float_type >::unary_operator ( const c2_function< float_type > & source ) const
inherited
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
virtualinherited

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

매개변수
 [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)
반환값
the value of the function
template<typename float_type = double>
 float_type c2_function< float_type >::xmax ( ) const
inlineinherited
template<typename float_type = double>
 float_type c2_function< float_type >::xmin ( ) const
inlineinherited

## 멤버 데이타 문서화

template<typename float_type = double>
mutableprotectedinherited

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

c2_function.hh 파일의 551 번째 라인에서 정의되었습니다.

다음에 의해서 참조됨 : c2_function< G4double >::get_trouble_point().

template<typename float_type = double>
 size_t c2_function< float_type >::evaluations
mutableprotectedinherited

c2_function.hh 파일의 548 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 std::vector interpolating_function_p< float_type >::F
protectedinherited

c2_function.hh 파일의 1716 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 const c2_function_transformation& interpolating_function_p< float_type >::fTransform
inherited

c2_function.hh 파일의 1703 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 float_type c2_function< float_type >::fXMax
protectedinherited

c2_function.hh 파일의 547 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 float_type c2_function< float_type >::fXMin
protectedinherited

c2_function.hh 파일의 547 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 size_t interpolating_function_p< float_type >::lastKLow
mutableprotectedinherited

c2_function.hh 파일의 1719 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 bool c2_function< float_type >::no_overwrite_grid
protectedinherited

c2_function.hh 파일의 545 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_const_ptr interpolating_function_p< float_type >::sampler_function
protectedinherited

c2_function.hh 파일의 1717 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 std::vector* c2_function< float_type >::sampling_grid
protectedinherited
template<typename float_type = double>
 std::vector interpolating_function_p< float_type >::X
protectedinherited

c2_function.hh 파일의 1716 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 bool interpolating_function_p< float_type >::xInverted
protectedinherited

c2_function.hh 파일의 1718 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 std::vector interpolating_function_p< float_type >::Xraw
protectedinherited

c2_function.hh 파일의 1716 번째 라인에서 정의되었습니다.

다음에 의해서 참조됨 : interpolating_function_p< float_type >::clone_data().

template<typename float_type = double>
 std::vector interpolating_function_p< float_type >::y2
protectedinherited

c2_function.hh 파일의 1716 번째 라인에서 정의되었습니다.

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