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Geant4
v4-10.4-release
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Geant4
v4-10.4-release
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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(). 더 자세히 ...
#include <c2_function.hh>
클래스 | |
| struct | c2_integrate_recur |
| structure used to pass information recursively in integrator. 더 자세히 ... | |
| struct | c2_root_info |
| structure used to hold root bracketing information 더 자세히 ... | |
| struct | c2_sample_recur |
| structure used to pass information recursively in sampler. 더 자세히 ... | |
| struct | recur_item |
| the data element for the internal recursion stack for the sampler and integrator 더 자세히 ... | |
Public 멤버 함수 | |
| const std::string | cvs_header_vers () const |
| 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 ... | |
| virtual | ~c2_function () |
| destructor 더 자세히 ... | |
| virtual float_type | value_with_derivatives (float_type x, float_type *yprime, float_type *yprime2) const =0 |
| get the value and derivatives. 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 ... | |
| 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 |
| c2_composed_function_p < float_type > & | operator() (const c2_function< float_type > &inner) const |
| compose this function outside another. 더 자세히 ... | |
| 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_function (const c2_function< float_type > &src) | |
| c2_function () | |
| 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 |
| float_type | bad_x_point |
| this point may be used to record where a calculation ran into trouble 더 자세히 ... | |
Private 멤버 함수 | |
| float_type | integrate_step (struct c2_integrate_recur &rb) const |
| Carry out the recursive subdivision and integration. 더 자세히 ... | |
| void | sample_step (struct c2_sample_recur &rb) const |
| Carry out the recursive subdivision for sampling. 더 자세히 ... | |
Private 속성 | |
| struct c2_root_info * | root_info |
| size_t | owner_count |
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
c2_function.hh 파일의 147 번째 라인에서 정의되었습니다.
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destructor
c2_function.hh 파일의 161 번째 라인에서 정의되었습니다.
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c2_function.hh 파일의 527 번째 라인에서 정의되었습니다.
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c2_function.hh 파일의 532 번째 라인에서 정의되었습니다.
| c2_piecewise_function_p<float_type>* c2_function< float_type >::adaptively_sample | ( | float_type | amin, |
| float_type | amax, | ||
| float_type | abs_tol = 1e-12, |
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| float_type | rel_tol = 1e-12, |
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| int | derivs = 2, |
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| std::vector< float_type > * | xvals = 0, |
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| std::vector< float_type > * | yvals = 0 |
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| ) | 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.
| 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) |
| 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
| 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 |
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increment our reference count. Destruction is only legal if the count is zero.
c2_function.hh 파일의 506 번째 라인에서 정의되었습니다.
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| const std::string c2_function< float_type >::cvs_file_vers | ( | ) | const |
get versioning information for the source file
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get versioning information for the header file
c2_function.hh 파일의 151 번째 라인에서 정의되었습니다.
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fill in a c2_fblock<float_type>... a shortcut for the integrator & sampler
| [in,out] | fb | the block to fill in with information |
c2_function.hh 파일의 556 번째 라인에서 정의되었습니다.
| 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, |
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| float_type * | final_yprime = 0, |
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| float_type * | final_yprime2 = 0 |
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| ) | 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.
| 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 |
다음에 의해서 참조됨 : G4ScreenedCoulombClassicalKinematics::DoScreeningComputation().
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and sampler do increment it.
c2_function.hh 파일의 395 번째 라인에서 정의되었습니다.
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get the sampling grid, which may be a null pointer
c2_function.hh 파일의 432 번째 라인에서 정의되었습니다.
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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.
c2_function.hh 파일의 502 번째 라인에서 정의되었습니다.
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count evaluations
c2_function.hh 파일의 399 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::fill_fblock().
| float_type c2_function< float_type >::integral | ( | float_type | amin, |
| float_type | amax, | ||
| std::vector< float_type > * | partials = 0, |
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| float_type | abs_tol = 1e-12, |
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| float_type | rel_tol = 1e-12, |
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| int | derivs = 2, |
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| bool | adapt = true, |
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| bool | extrapolate = true |
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| ) | 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()
| 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. |
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Carry out the recursive subdivision and integration.
This passes information recursively through the recur block pointer to allow very efficient recursion.
| rb | a pointer to the recur struct. |
| c2_function<float_type>& c2_function< float_type >::normalized_function | ( | float_type | amin, |
| float_type | amax, | ||
| float_type | norm = 1.0 |
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| ) | const |
create a new c2_function from this one which is normalized on the interval
| 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 |
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evaluate the function in the classic way, ignoring derivatives.
| x | the point at which to evaluate |
c2_function.hh 파일의 186 번째 라인에서 정의되었습니다.
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get the value and derivatives.
| [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) |
c2_function.hh 파일의 195 번째 라인에서 정의되었습니다.
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compose this function outside another.
| inner | the inner function |
c2_function.hh 파일의 495 번째 라인에서 정의되었습니다.
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factory function to create a c2_product_p from a regular algebraic expression.
| rhs | the right-hand term of the product |
c2_function.hh 파일의 486 번째 라인에서 정의되었습니다.
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factory function to create a c2_sum_p from a regular algebraic expression.
| rhs | the right-hand term of the sum |
c2_function.hh 파일의 473 번째 라인에서 정의되었습니다.
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factory function to create a c2_diff_p from a regular algebraic expression.
| rhs | the right-hand term of the difference |
c2_function.hh 파일의 479 번째 라인에서 정의되었습니다.
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c2_function.hh 파일의 488 번째 라인에서 정의되었습니다.
| float_type c2_function< float_type >::partial_integrals | ( | std::vector< float_type > | xgrid, |
| std::vector< float_type > * | partials = 0, |
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| float_type | abs_tol = 1e-12, |
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| float_type | rel_tol = 1e-12, |
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| int | derivs = 2, |
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| bool | adapt = true, |
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| bool | extrapolate = true |
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| ) | 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.
| 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. |
| void c2_function< float_type >::preen_sampling_grid | ( | std::vector< float_type > * | result | ) | const |
The grid is modified in place.
| void c2_function< float_type >::refine_sampling_grid | ( | std::vector< float_type > & | grid, |
| size_t | refinement | ||
| ) | const |
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c2_function.hh 파일의 519 번째 라인에서 정의되었습니다.
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decrement our reference count. Do not destroy at zero.
c2_function.hh 파일의 509 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::release_ownership().
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reset the counter
c2_function.hh 파일의 397 번째 라인에서 정의되었습니다.
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Carry out the recursive subdivision for sampling.
This passes information recursively through the recur block pointer to allow very efficient recursion.
| rb | a pointer to the recur struct. |
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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.
| grid | a vector of abscissas. The contents is copied into an internal vector, so the grid can be discarded after passingin. |
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c2_function.hh 파일의 538 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : interpolating_function_p< float_type >::clone_data().
| c2_function<float_type>& c2_function< float_type >::square_normalized_function | ( | float_type | amin, |
| float_type | amax, | ||
| float_type | norm = 1.0 |
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| ) | const |
| 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 |
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| ) | const |
create a new c2_function from this one which is square-normalized with the provided weight on the interval
| 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 |
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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
| [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) |
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 >, c2_classic_function_p< float_type >에서 구현되었습니다.
다음에 의해서 참조됨 : c2_composed_function_p< float_type >::combine(), c2_sum_p< float_type >::combine(), c2_diff_p< float_type >::combine(), c2_product_p< float_type >::combine(), c2_ratio_p< float_type >::combine(), c2_function< G4double >::fill_fblock(), c2_function< G4double >::operator()().
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c2_function.hh 파일의 390 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : G4ScreenedCoulombCrossSection::BuildMFPTables(), c2_binary_function< float_type >::c2_binary_function(), c2_composed_function_p< float_type >::c2_composed_function_p(), G4ScreenedCoulombClassicalKinematics::DoScreeningComputation(), G4ScreenedNuclearRecoil::GetMeanFreePath(), LJZBLScreening(), G4NativeScreenedCoulombCrossSection::LoadData(), c2_plugin_function_p< G4double >::set_function().
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c2_function.hh 파일의 389 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : G4ScreenedCoulombCrossSection::BuildMFPTables(), c2_binary_function< float_type >::c2_binary_function(), c2_composed_function_p< float_type >::c2_composed_function_p(), G4ScreenedCoulombClassicalKinematics::DoScreeningComputation(), G4ScreenedNuclearRecoil::GetMeanFreePath(), LJZBLScreening(), c2_plugin_function_p< G4double >::set_function().
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mutableprotected |
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().
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mutableprotected |
c2_function.hh 파일의 548 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::get_evaluations(), c2_function< G4double >::increment_evaluations(), c2_function< G4double >::reset_evaluations().
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protected |
c2_function.hh 파일의 547 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::set_domain(), c2_function< G4double >::xmax().
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protected |
c2_function.hh 파일의 547 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::set_domain(), c2_function< G4double >::xmin().
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protected |
c2_function.hh 파일의 545 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::set_sampling_grid_pointer(), c2_function< G4double >::~c2_function().
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mutableprivate |
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private |
this carry a memory of the last root bracketing, to avoid the necessity of evaluating the function on the brackets every time if the brackets have not been changed. it is declared as a pointer, since many c2_functions may never need one allocated
c2_function.hh 파일의 628 번째 라인에서 정의되었습니다.
다음에 의해서 참조됨 : c2_function< G4double >::~c2_function().
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protected |
1.8.5
