the parent class for all c2_functions. More...
#include <c2_function.hh>
Inheritance diagram for c2_function< float_type >: Collaboration diagram for c2_function< float_type >:Classes | |
| struct | c2_integrate_recur |
| structure used to pass information recursively in integrator. More... | |
| struct | c2_root_info |
| structure used to hold root bracketing information More... | |
| struct | c2_sample_recur |
| structure used to pass information recursively in sampler. More... | |
| struct | recur_item |
| the data element for the internal recursion stack for the sampler and integrator More... | |
Public Member Functions | |
| const std::string | cvs_header_vers () const |
| get versioning information for the header file More... | |
| const std::string | cvs_file_vers () const |
| get versioning information for the source file More... | |
| virtual | ~c2_function () |
| destructor More... | |
| virtual float_type | value_with_derivatives (float_type x, float_type *yprime, float_type *yprime2) const =0 throw (c2_exception) |
| get the value and derivatives. 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... | |
Protected Member Functions | |
| c2_function (const c2_function< float_type > &src) | |
| c2_function () | |
| virtual void | set_sampling_grid_pointer (std::vector< float_type > &grid) |
Protected Attributes | |
| std::vector< float_type > * | sampling_grid |
| bool | no_overwrite_grid |
| float_type | fXMin |
| float_type | fXMax |
| size_t | evaluations |
| float_type | bad_x_point |
| this point may be used to record where a calculation ran into trouble More... | |
Private Member Functions | |
| float_type | integrate_step (struct c2_integrate_recur &rb) const throw (c2_exception) |
| Carry out the recursive subdivision and integration. More... | |
| void | sample_step (struct c2_sample_recur &rb) const throw (c2_exception) |
| Carry out the recursive subdivision for sampling. More... | |
Private Attributes | |
| struct c2_root_info * | root_info |
| 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 More... | |
| size_t | owner_count |
Detailed Description
template<typename float_type = double>
class c2_function< float_type >
the parent class for all c2_functions.
c2_functions know their value, first, and second derivative at almost every point. They can be efficiently combined with binary operators, via c2_binary_function, composed via c2_composed_function_, have their roots found via find_root(), and be adaptively integrated via partial_integrals() or integral(). They also can carry information with them about how to find 'interesting' points on the function. This information is set with set_sampling_grid() and extracted with get_sampling_grid().
Particularly important subclasses are the interpolating functions classes, interpolating_function , lin_log_interpolating_function, log_lin_interpolating_function, log_log_interpolating_function, and arrhenius_interpolating_function, as well as the template functions inverse_integrated_density_function().
For a discussion of memory management, see memory_management
Definition at line 147 of file c2_function.hh.
Constructor & Destructor Documentation
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destructor
Definition at line 161 of file c2_function.hh.
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Definition at line 527 of file c2_function.hh.
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Definition at line 532 of file c2_function.hh.
Member Function Documentation
| 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 | ||
| 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
This method has three modes, depending on the derivs flag.
If derivs is 2, it computes a c2_piecewise_function_p representation of its parent function, which may be a much faster function to use in codes if the parent function is expensive. If xvals and yvals are non-null, it will also fill them in with the function values at each grid point the adaptive algorithm chooses.
If derivs is 1, this does not create the connectors, and returns an null pointer, but will fill in the xvals and yvals vectors with values of the function at points such that the linear interpolation error between the points is bounded by the tolerance values given. Because it uses derivative information from the function to manage the error control, it is almost completely free of issues with missing periods of oscillatory functions, even with no information provided in the sampling grid. This is typically useful for sampling a function for plotting.
If derivs is 0, this does something very like what it does if derivs = 1, but without derivatives. Instead, to compute the intermediate value of the function for error control, it just uses 3-point parabolic interpolation. This is useful amost exclusively for converting a non-c2_function, with no derivatives, but wrapped in a c2_classic_function wrapper, into a table of values to seed an interpolating_function_p. Note, however, that without derivatives, this is very susceptible to missing periods of oscillatory functions, so it is important to set a sampling grid which isn't too much coarser than the typical oscillations.
- Note
- the sampling_grid of the returned function matches the sampling_grid of its parent.
- See also
- Adaptive Sampling Examples
- Parameters
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amin lower bound of the domain for sampling amax upper bound of the domain for sampling abs_tol the absolute error bound for each segment rel_tol the fractional error bound for each segment. derivs if 0 or 1, return a useless function, but fill in the xvals and yvals vectors (if non-null). Also, if 0 or 1, tolerances refer to linear interpolation, not high-order interpolation. If 2, return a full piecewise collection of c2_connector_function_p segments. See discussion above. [in,out] xvals vector of abscissas at which the function was actually sampled (if non-null) [in,out] yvals vector of function values corresponding to xvals (if non-null)
- Returns
- a new, sampled representation, if derivs is 2. A null pointer if derivs is 0 or 1.
| bool c2_function< float_type >::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
- Parameters
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data a vector of data points which are expected to be monotonic. message an informative string to include in an exception if this throws c2_exception
- Returns
- true if in decreasing order, false if increasing
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increment our reference count. Destruction is only legal if the count is zero.
Definition at line 506 of file c2_function.hh.
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get the reference count, mostly for debugging
- Returns
- the count
Definition at line 524 of file c2_function.hh.
| const std::string c2_function< float_type >::cvs_file_vers | ( | ) | const |
get versioning information for the source file
- Returns
- the CVS Id string
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get versioning information for the header file
- Returns
- the CVS Id string
Definition at line 151 of file c2_function.hh.
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fill in a c2_fblock<float_type>... a shortcut for the integrator & sampler
- Parameters
-
[in,out] fb the block to fill in with information
Definition at line 556 of file c2_function.hh.
| 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 | ||
| throw | ( | c2_exception | |
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solve f(x)==value very efficiently, with explicit knowledge of derivatives of the function
find_root solves by iterated inverse quadratic extrapolation for a solution to f(x)=y. It includes checks against bad convergence, so it should never be able to fail. Unlike typical secant method or fancier Brent's method finders, this does not depend in any strong wasy on the brackets, unless the finder has to resort to successive approximations to close in on a root. Often, it is possible to make the brackets equal to the domain of the function, if there is any clue as to where the root lies, as given by the parameter start.
- Parameters
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lower_bracket the lower bound for the search upper_bracket the upper bound for the search. Function sign must be opposite to that at lower_bracket start starting value for the search value the value of the function being sought (solves f(x) = value) [out] error If pointer is zero, errors raise exception. Otherwise, returns error here. [out] final_yprime If pointer is not zero, return derivative of function at root [out] final_yprime2 If pointer is not zero, return second derivative of function at root
- Returns
- the position of the root.
- See also
- Root finding sample
Referenced by G4ScreenedCoulombClassicalKinematics::DoScreeningComputation().
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and sampler do increment it.
- Returns
- number of evaluations logged since last reset.
Definition at line 395 of file c2_function.hh.
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Reimplemented in c2_sin_p< float_type >, c2_plugin_function_p< float_type >, and c2_plugin_function_p< G4double >.
Referenced by c2_plugin_function_p< G4double >::get_sampling_grid().
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get the sampling grid, which may be a null pointer
- Returns
- pointer to the sampling grid
Definition at line 432 of file c2_function.hh.
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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.
- Returns
- x value of point at which something went wrong, if integrator (or otherwise) returned a nan.
Definition at line 502 of file c2_function.hh.
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count evaluations
Definition at line 399 of file c2_function.hh.
Referenced by c2_function< G4double >::fill_fblock().
Here is the caller graph for this function:| 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 | ||
| throw | ( | c2_exception | |
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a fully-automated integrator which uses the information provided by the get_sampling_grid() function to figure out what to do.
It returns the integral of the function over the domain requested with error tolerances as specified. It is just a front-end to partial_integrals()
- Parameters
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amin lower bound of the domain for integration amax upper bound of the domain for integration partials if non-NULL, a vector in which to receive the partial integrals. It will automatically be sized appropriately, if provided, to contain n - 1 elements where n is the length of xgrid abs_tol the absolute error bound for each segment rel_tol the fractional error bound for each segment. If the error is smaller than either the relative or absolute tolerance, the integration step is finished. derivs number of derivatives to trust, which sets the order of the integrator. The order is 3*derivs + 4. derivs can be 0, 1, or 2. adapt if true, use recursive adaptation, otherwise do simple evaluation on the grid provided with no error checking. extrapolate if true, use simple Richardson extrapolation on the final 2 steps to reduce the error.
- Returns
- sum of partial integrals, which is the definite integral from the first value in xgrid to the last.
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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.
- Parameters
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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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| throw | ( | c2_exception | |
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create a new c2_function from this one which is normalized on the interval
- Parameters
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amin lower bound of the domain for integration amax upper bound of the domain for integration norm the desired integral for the function over the region
- Returns
- a new c2_function with the desired norm.
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evaluate the function in the classic way, ignoring derivatives.
- Parameters
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x the point at which to evaluate
- Returns
- the value of the function
Definition at line 186 of file c2_function.hh.
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get the value and derivatives.
- Parameters
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[in] x the point at which to evaluate the function [out] yprime the first derivative (if pointer is non-null) [out] yprime2 the second derivative (if pointer is non-null)
- Returns
- the value of the function
Definition at line 195 of file c2_function.hh.
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compose this function outside another.
- Parameters
-
inner the inner function
Definition at line 495 of file c2_function.hh.
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factory function to create a c2_product_p from a regular algebraic expression.
- Parameters
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rhs the right-hand term of the product
- Returns
- a new c2_function
Definition at line 486 of file c2_function.hh.
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factory function to create a c2_sum_p from a regular algebraic expression.
- Parameters
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rhs the right-hand term of the sum
- Returns
- a new c2_function
Definition at line 473 of file c2_function.hh.
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factory function to create a c2_diff_p from a regular algebraic expression.
- Parameters
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rhs the right-hand term of the difference
- Returns
- a new c2_function
Definition at line 479 of file c2_function.hh.
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Definition at line 488 of file c2_function.hh.
| 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 | ||
| throw | ( | c2_exception | |
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solve f(x)=value partial_integrals uses a method with an error O(dx**10) with full information from the derivatives, and falls back to lower order methods if informed of incomplete derivatives. It uses exact midpoint splitting of the intervals for recursion, resulting in no recomputation of the function during recursive descent at previously computed points.
- Parameters
-
xgrid points between which to evaluate definite integrals. partials if non-NULL, a vector in which to receive the partial integrals. It will automatically be sized apprpropriately, if provided, to contain n - 1 elements where n is the length of xgrid abs_tol the absolute error bound for each segment rel_tol the fractional error bound for each segment. If the error is smaller than either the relative or absolute tolerance, the integration step is finished. derivs number of derivatives to trust, which sets the order of the integrator. The order is 3*derivs + 4. derivs can be 0, 1, or 2. adapt if true, use recursive adaptation, otherwise do simple evaluation on the grid provided with no error checking. extrapolate if true, use simple Richardson extrapolation on the final 2 steps to reduce the error.
- Returns
- sum of partial integrals, which is the definite integral from the first value in xgrid to the last.
| 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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Definition at line 519 of file c2_function.hh.
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decrement our reference count. Do not destroy at zero.
- Returns
- final owner count, to check whether object should disappear.
Definition at line 509 of file c2_function.hh.
Referenced by c2_function< G4double >::release_ownership().
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reset the counter
Definition at line 397 of file c2_function.hh.
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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.
- Parameters
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rb a pointer to the recur struct.
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Definition at line 391 of file c2_function.hh.
Referenced by c2_binary_function< float_type >::c2_binary_function(), c2_composed_function_p< float_type >::c2_composed_function_p(), LJZBLScreening(), and c2_plugin_function_p< G4double >::set_function().
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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.
- Parameters
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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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Definition at line 538 of file c2_function.hh.
Referenced by interpolating_function_p< float_type >::clone_data().
Here is the caller graph for this function:| 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 | ||
| throw | ( | c2_exception | |
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| 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 | ||
| throw | ( | c2_exception | |
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create a new c2_function from this one which is square-normalized with the provided weight on the interval
- Parameters
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amin lower bound of the domain for integration amax upper bound of the domain for integration weight a c2_function providing the weight norm the desired integral for the function over the region
- Returns
- a new c2_function with the desired norm.
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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
- Parameters
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[in] x the point at which to evaluate the function [out] yprime the first derivative (if pointer is non-null) [out] yprime2 the second derivative (if pointer is non-null)
- Returns
- the value of the function
Implemented in c2_piecewise_function_p< float_type >, c2_connector_function_p< float_type >, c2_inverse_function_p< float_type >, c2_power_law_p< float_type >, c2_quadratic_p< float_type >, c2_linear_p< float_type >, c2_linear_p< G4double >, c2_identity_p< float_type >, c2_recip_p< float_type >, c2_sqrt_p< float_type >, c2_exp_p< float_type >, c2_log_p< float_type >, c2_tan_p< float_type >, c2_cos_p< float_type >, c2_sin_p< float_type >, interpolating_function_p< float_type >, c2_constant_p< float_type >, c2_cached_function_p< float_type >, c2_scaled_function_p< float_type >, c2_binary_function< float_type >, c2_plugin_function_p< float_type >, c2_plugin_function_p< G4double >, and c2_classic_function_p< float_type >.
Referenced by c2_function< G4double >::fill_fblock(), and c2_function< G4double >::operator()().
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Definition at line 390 of file c2_function.hh.
Referenced by 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(), and c2_plugin_function_p< G4double >::set_function().
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Definition at line 389 of file c2_function.hh.
Referenced by 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(), and c2_plugin_function_p< G4double >::set_function().
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this point may be used to record where a calculation ran into trouble
Definition at line 551 of file c2_function.hh.
Referenced by c2_function< G4double >::get_trouble_point().
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Definition at line 548 of file c2_function.hh.
Referenced by c2_function< G4double >::get_evaluations(), c2_function< G4double >::increment_evaluations(), and c2_function< G4double >::reset_evaluations().
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Definition at line 547 of file c2_function.hh.
Referenced by c2_function< G4double >::set_domain(), and c2_function< G4double >::xmax().
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protected |
Definition at line 547 of file c2_function.hh.
Referenced by c2_function< G4double >::set_domain(), and c2_function< G4double >::xmin().
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Definition at line 545 of file c2_function.hh.
Referenced by c2_function< G4double >::set_sampling_grid_pointer(), and c2_function< G4double >::~c2_function().
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mutableprivate |
Definition at line 630 of file c2_function.hh.
Referenced by c2_function< G4double >::claim_ownership(), c2_function< G4double >::count_owners(), c2_function< G4double >::release_ownership_for_return(), and c2_function< G4double >::~c2_function().
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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
Definition at line 628 of file c2_function.hh.
Referenced by c2_function< G4double >::~c2_function().
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protected |
Definition at line 544 of file c2_function.hh.
Referenced by c2_function< G4double >::get_sampling_grid_pointer(), c2_function< G4double >::set_sampling_grid_pointer(), and c2_function< G4double >::~c2_function().
The documentation for this class was generated from the following file:
- geant4.10.03/examples/extended/electromagnetic/TestEm7/include/c2_function.hh
