gsl_inte.h

00001 /*
00002   -------------------------------------------------------------------
00003   
00004   Copyright (C) 2006, 2007, Andrew W. Steiner
00005   
00006   This file is part of O2scl.
00007   
00008   O2scl is free software; you can redistribute it and/or modify
00009   it under the terms of the GNU General Public License as published by
00010   the Free Software Foundation; either version 3 of the License, or
00011   (at your option) any later version.
00012   
00013   O2scl is distributed in the hope that it will be useful,
00014   but WITHOUT ANY WARRANTY; without even the implied warranty of
00015   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00016   GNU General Public License for more details.
00017   
00018   You should have received a copy of the GNU General Public License
00019   along with O2scl. If not, see <http://www.gnu.org/licenses/>.
00020 
00021   -------------------------------------------------------------------
00022 */
00023 #ifndef O2SCL_GSL_INTE_H
00024 #define O2SCL_GSL_INTE_H
00025 
00026 #include <gsl/gsl_machine.h>
00027 
00028 #ifndef DOXYGENP
00029 namespace o2scl {
00030 #endif
00031   
00032   /** 
00033       \brief GSL integration base
00034 
00035       This base class does not perform any actual integration. 
00036 
00037       \todo Move the documentation below to a more sensible place
00038       
00039       If the function integ() uses \c tolx and \c tolf 
00040       to attempt to ensure that
00041       \f[ 
00042       |\mathrm{result}-I| \leq \mathrm{Max}(\mathrm{tolx},
00043       \mathrm{tolf}|I|)
00044       \f]
00045       and returns a value \c abserr to attempt to ensure that
00046       \f[
00047       |\mathrm{result}-I| \leq \mathrm{abserr} \leq
00048       \mathrm{Max}(\mathrm{tolx},\mathrm{tolf}|I|)
00049       \f]
00050       where \c I  is the integral to be evaluated. Even when 
00051       integ() returns success, these inequalities will fail for 
00052       some functions.
00053   */
00054   class gsl_inte {
00055     
00056   public:
00057 
00058     gsl_inte() {
00059     }
00060     
00061   protected:
00062 
00063     /// Desc
00064     double rescale_error(double err, const double result_abs, 
00065                          const double result_asc) {
00066       err = fabs(err);
00067       
00068       if (result_asc != 0 && err != 0) {
00069         
00070         double scale = pow((200 * err / result_asc), 1.5);
00071         
00072         if (scale < 1) {
00073           err = result_asc * scale;
00074         } else {
00075           err = result_asc;
00076         }
00077       }
00078 
00079       if (result_abs > GSL_DBL_MIN / (50 * GSL_DBL_EPSILON)) {
00080 
00081         double min_err = 50 * GSL_DBL_EPSILON * result_abs;
00082         
00083         if (min_err > err) {
00084           err = min_err;
00085         }
00086       }
00087       
00088       return err;
00089     }
00090     
00091   };
00092   
00093   
00094 #ifndef DOXYGENP
00095 }
00096 #endif
00097 
00098 #endif

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