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Object-oriented Scientific Computing Library: Version 0.910
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Chebyshev integration base class (GSL) More...
#include <gsl_inte_qawc.h>
This class provides the basic Chebyshev integration functions for use in the GSL-based integration classes which require them. See GSL-based integration routines in the User's guide for general information about the GSL integration classes.
Definition at line 42 of file gsl_inte_qawc.h.
Protected Member Functions | |
void | compute_moments (double cc, double *moment) |
Compute the Chebyshev moments. | |
template<class func2_t > | |
void | inte_cheb_series (func2_t &f, double a, double b, double *cheb12, double *cheb24) |
Compute Chebyshev series expansion using a FFT method. |
void gsl_inte_cheb< func_t >::inte_cheb_series | ( | func2_t & | f, |
double | a, | ||
double | b, | ||
double * | cheb12, | ||
double * | cheb24 | ||
) | [inline, protected] |
The Chebyshev coefficients for the truncated expansions,
are computed for and
using an FFT algorithm from Tolstov62 that is adapted so that the both sets of coefficients are computed simultaneously.
Given the function specified in f
, this function computes the 13 Chebyshev coefficients, of degree 12 and 25 Chebyshev coefficients of degree 24,
, for the interval
using a FFT method.
These coefficients are constructed to approximate the original function with
and
where is the Chebyshev polynomial of degree
evaluated at the point
.
It is assumed that memory for cheb12
and cheb24
has been allocated beforehand.
Originally written in QUADPACK by R. Piessens and E. de Doncker, translated into C for GSL by Brian Gough, and then rewritten for O2scl .
Definition at line 111 of file gsl_inte_qawc.h.
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