Numerical differentiation (GSL) More...
#include <deriv_gsl.h>
This class computes the numerical derivative of a function. The stepsize h should be specified before use. If similar functions are being differentiated in succession, the user may be able to increase the speed of later derivatives by setting the new stepsize equal to the optimized stepsize from the previous differentiation, by setting h to h_opt.
The results will be incorrect for sufficiently difficult functions or if the step size is not properly chosen.
Some successive derivative computations can be made more efficient by using the optimized stepsize in deriv_gsl::h_opt , which is set by the most recent last derivative computation.
If the function returns a non-finite value, or if func_max is greater than zero and the absolute value of the function is larger than func_max, then this class attempts to decrease the step size by a factor of 10 in order to compute the derivative. The class gives up after 20 reductions of the step size.
If h is negative or zero, the initial step size is chosen to be or if
, then the initial step size is chosen to be
.
Setting deriv_base::verbose to a number greater than zero results in output for each call to central_deriv() which looks like:
deriv_gsl: step: 1.000000e-04 abscissas: 4.999500e-01 4.999000e-01 5.000500e-01 5.001000e-01 ordinates: 4.793377e-01 4.793816e-01 4.794694e-01 4.795132e-01 res: 8.775825e-01 trc: 1.462163e-09 rnd: 7.361543e-12
where the last line contains the result (res
), the truncation error (trc
) and the rounding error (rnd
). If deriv_base::verbose is greater than 1, a keypress is required after each iteration.
If the function always returns a finite value, then computing first derivatives requires either 1 or 2 calls to central_deriv() and thus either 4 or 8 function calls.
An example demonstrating the usage of this class is given in examples/ex_deriv.cpp
and the Differentiation example .
Definition at line 124 of file deriv_gsl.h.
Public Member Functions | |
virtual int | deriv_err (fp_t x, func_t &func, fp_t &dfdx, fp_t &err) |
Calculate the first derivative of func w.r.t. x and uncertainty. | |
virtual const char * | type () |
Return string denoting type ("deriv_gsl") | |
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virtual double | deriv (double x, funct &func) |
Calculate the first derivative of func w.r.t. x. More... | |
virtual double | deriv2 (double x, funct &func) |
Calculate the second derivative of func w.r.t. x. | |
virtual double | deriv3 (double x, funct &func) |
Calculate the third derivative of func w.r.t. x. | |
virtual double | get_err () |
Get uncertainty of last calculation. | |
virtual int | deriv_err (double x, funct &func, double &dfdx, double &err)=0 |
Calculate the first derivative of func w.r.t. x and the uncertainty. | |
virtual int | deriv2_err (double x, funct &func, double &d2fdx2, double &err) |
Calculate the second derivative of func w.r.t. x and the uncertainty. | |
virtual int | deriv3_err (double x, funct &func, double &d3fdx3, double &err) |
Calculate the third derivative of func w.r.t. x and the uncertainty. | |
Public Attributes | |
fp_t | h |
Initial stepsize. More... | |
fp_t | func_max |
Maximum absolute value of function, or a negative value for no maximum (default -1) | |
fp_t | h_opt |
The last value of the optimized stepsize. More... | |
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bool | err_nonconv |
If true, call the error handler if the routine does not "converge". | |
int | verbose |
Output control. | |
Protected Member Functions | |
template<class func2_t > | |
int | deriv_tlate (fp_t x, func2_t &func, fp_t &dfdx, fp_t &err) |
Internal template version of the derivative function. | |
virtual int | deriv_err_int (fp_t x, typename deriv_base< func_t, fp_t >::internal_func_t &func, fp_t &dfdx, fp_t &err) |
Internal version of calc_err() for second and third derivatives. | |
template<class func2_t > | |
int | central_deriv (fp_t x, fp_t hh, fp_t &result, fp_t &abserr_round, fp_t &abserr_trunc, func2_t &func) |
Compute derivative using 5-point rule. More... | |
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virtual double | deriv_int (double x, internal_func_t &func) |
Calculate the first derivative of func w.r.t. x. More... | |
virtual int | deriv_err_int (double x, internal_func_t &func, double &dfdx, double &err)=0 |
Calculate the first derivative of func w.r.t. x and the uncertainty. More... | |
double | derivfun (double x, funct *fp) |
The function for the second derivative. | |
double | derivfun2 (double x, funct *fp) |
The function for the third derivative. | |
Additional Inherited Members | |
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typedef std::function< double(double)> | internal_func_t |
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bool | from_deriv |
Avoids infinite loops in case the user calls the base class version. | |
double | derr |
The uncertainity in the most recent derivative computation. | |
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inlineprotected |
Compute the derivative using the 5-point rule (x-h, x-h/2, x, x+h/2, x+h) and the error using the difference between the 5-point and the 3-point rule (x-h,x,x+h). Note that the central point is not used for either.
This must be a class template because it is used by both deriv_err() and deriv_err_int().
Definition at line 268 of file deriv_gsl.h.
fp_t o2scl::deriv_gsl< func_t, fp_t >::h |
This should be specified before a call to deriv() or deriv_err(). If it is less than or equal to zero, then will used, or if
x
is zero, then will be used.
Definition at line 144 of file deriv_gsl.h.
fp_t o2scl::deriv_gsl< func_t, fp_t >::h_opt |
This is initialized to zero in the constructor and set by deriv_err() to the most recent value of the optimized stepsize.
Definition at line 156 of file deriv_gsl.h.
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