Geant4  v4-10.4-release
c2_linear_p< float_type > 클래스 템플릿 참조

create a linear mapping of another functionfor example, given a c2_function f 더 자세히 ...

#include <c2_function.hh>

c2_linear_p< float_type >에 대한 상속 다이어그램 :

## Public 멤버 함수

c2_linear_p (float_type x0, float_type y0, float_type slope)
Construct the operator f=y0 + slope * (x-x0) 더 자세히 ...

void reset (float_type x0, float_type y0, float_type slope)
Change the slope and intercepts after construction. 더 자세히 ...

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

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 ...

## Protected 멤버 함수

c2_linear_p ()

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

## Protected 속성

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 ...

## Private 속성

float_type xint

float_type intercept

float_type m

## 상세한 설명

### template<typename float_type = double> class c2_linear_p< float_type >

create a linear mapping of another function

for example, given a c2_function f

c2_function<double> &F=c2_linear<double>(1.2, 2.0, 3.0)(f);

produces a new c2_function F=2.0+3.0*(f - 1.2)

The factory function c2_factory::linear() creates *new c2_linear_p

c2_function.hh 파일의 1972 번째 라인에서 정의되었습니다.

## 생성자 & 소멸자 문서화

template<typename float_type = double>
 c2_linear_p< float_type >::c2_linear_p ( float_type x0, float_type y0, float_type slope )
inline

Construct the operator f=y0 + slope * (x-x0)

매개변수
 x0 the x offset y0 the y-intercept i.e. f(x0) slope the slope of the mapping

c2_function.hh 파일의 1979 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 c2_linear_p< float_type >::c2_linear_p ( )
inlineprotected

c2_function.hh 파일의 1997 번째 라인에서 정의되었습니다.

## 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>
 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>
 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>
 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>
 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>
 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>
 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_linear_p< float_type >::reset ( float_type x0, float_type y0, float_type slope )
inline

Change the slope and intercepts after construction.

매개변수
 x0 the x offset y0 the y-intercept slope the slope of the mapping

c2_function.hh 파일의 1985 번째 라인에서 정의되었습니다.

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>
 void c2_function< float_type >::set_domain ( float_type amin, float_type amax )
inlineinherited
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>
 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>
 virtual float_type c2_linear_p< float_type >::value_with_derivatives ( float_type x, float_type * yprime, float_type * yprime2 ) const
inlinevirtual

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

c2_function.hh 파일의 1987 번째 라인에서 정의되었습니다.

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>
 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>
 float_type c2_linear_p< float_type >::intercept
private

c2_function.hh 파일의 1995 번째 라인에서 정의되었습니다.

template<typename float_type = double>
 float_type c2_linear_p< float_type >::m
private

c2_function.hh 파일의 1995 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>
 std::vector* c2_function< float_type >::sampling_grid
protectedinherited
template<typename float_type = double>
 float_type c2_linear_p< float_type >::xint
private

c2_function.hh 파일의 1995 번째 라인에서 정의되었습니다.

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