Object-oriented Scientific Computing Library: Version 0.910
Protected Member Functions
gsl_inte Class Reference

GSL integration base. More...

#include <gsl_inte.h>

Inheritance diagram for gsl_inte:
gsl_inte_kronrod< func_t > gsl_inte_qng< func_t > gsl_inte_qag< func_t > gsl_inte_singular< func_t > gsl_inte_qags< func_t > gsl_inte_transform< func_t > gsl_inte_cheb< func_t > gsl_inte_qagi< func_t > gsl_inte_qagil< func_t > gsl_inte_qagiu< func_t > gsl_inte_qawc< func_t > gsl_inte_qawo_sin< func_t > gsl_inte_qaws< func_t > gsl_inte_qawf_sin< func_t > gsl_inte_qawo_cos< func_t > gsl_inte_qawf_cos< func_t >

Detailed Description

This base class does not perform any actual integration, but just provides functions to be used in the integration classes based on GSL.

Definition at line 56 of file gsl_inte.h.

Protected Member Functions

double rescale_error (double err, const double result_abs, const double result_asc)
 QUADPACK's nonlinear rescaling of the absolute-error estimate.

Member Function Documentation

double gsl_inte::rescale_error ( double  err,
const double  result_abs,
const double  result_asc 
) [inline, protected]

The values $ \rho_{\mathrm{abs}} $ (stored in result_abs) and $ \rho_{\mathrm{abs}} $ (stored in result_asc) are assumed to be

\begin{eqnarray*} \rho_{\mathrm{abs}} &=& \int_a^b |f|\,dx, \\ \rho_{\mathrm{asc}} &=& \int_a^b |f - \mu(f)|\, dx, \qquad \mu(f) = \frac{1}{b-a}\int_a^b f\, dx, \end{eqnarray*}

all of which are computed from the best (i.e., finest-grid) approximation of the integrals. The rescaled error, $ \sigma_\mathrm{err}, $ is computed from the raw error, err, by

\[ \sigma_\mathrm{err} = \rho_\mathrm{asc} \cdot \min \left\{1, \; \left(\frac{200 |\mathrm{err}|}{\rho_\mathrm{asc}} \right)^{3/2} \right\}, \]

or

\[ \sigma_\mathrm{err} = 50\cdot \epsilon_\mathrm{mach} \cdot \rho_\mathrm{abs}, \]

whichever of the two is greater. The value $ \epsilon_\mathrm{mach} $ denotes "machine epsilon." (In the case that the second value underflows, the first value is automatically accepted.)

This function is used in gsl_inte_qng and gsl_inte_kronrod::gauss_kronrod_base().

Definition at line 100 of file gsl_inte.h.


The documentation for this class was generated from the following file:
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Documentation generated with Doxygen. Provided under the GNU Free Documentation License (see License Information).

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