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/*
* Integration of f(x) in the interval [xx(0), xx(n-1)], with non-equally spaced
* n-size xx grid.
*
* The function f is approximated by piecewise parabolae, The integral of f
* is set to 0 at xx(0).
*/
/*
* Copyright (c) 2015 Jerome Novak
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
char integrate_1D_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/integrate_1D.C,v 1.1 2015/01/09 15:28:52 j_novak Exp $" ;
/*
* $Id: integrate_1D.C,v 1.1 2015/01/09 15:28:52 j_novak Exp $
* $Log: integrate_1D.C,v $
* Revision 1.1 2015/01/09 15:28:52 j_novak
* New integration function for general non-equally-spaced grids.
*
*
*/
// Headers Lorene
#include "tbl.h"
namespace Lorene {
Tbl integ1D(const Tbl& xx, const Tbl& ff) {
Tbl resu(ff) ;
if (ff.get_etat() != ETATZERO) {
assert (xx.get_etat() == ETATQCQ) ;
assert (ff.get_etat() == ETATQCQ) ;
int nx = xx.get_taille() ;
assert(nx > 2) ;
assert (ff.get_taille() == nx) ;
resu.set(0) = 0. ;
double x0 = xx(0) ;
double x1(0), x2(0), x3(0);
double a1(0), a2(0), a3(0);
double b1(0), b2(0), b3(0);
double c1(0), c2(0), c3(0) ;
for (int i=1; i<nx-1; i++) {
x1 = xx(i-1) ;
x2 = xx(i) ;
x3 = xx(i+1) ;
a1 = ff(i-1) / ( (x1 - x2)*(x1 - x3) ) ;
a2 = ff(i) / ( (x2 - x1)*(x2 - x3) ) ;
a3 = ff(i+1) / ( (x3 - x1)*(x3 - x2) ) ;
b1 = a1 + a2 + a3 ;
b2 = -(x2 + x3)*a1 - (x1 + x3)*a2 - (x1 + x2)*a3 ;
b3 = x2*x3*a1 + x1*x3*a2 + x1*x2*a3 ;
if (i==1) {
c1 = b1 ;
c2 = b2 ;
c3 = b3 ;
}
else {
c1 = 0.5*(b1 + c1) ;
c2 = 0.5*(b2 + c2) ;
c3 = 0.5*(b3 + c3) ;
}
resu.set(i) = resu(i-1) + c1*(x2*x2*x2 - x0*x0*x0)/3.
+ 0.5*c2*(x2*x2 - x0*x0) + c3*(x2 - x0) ;
c1 = b1 ;
c2 = b2 ;
c3 = b3 ;
x0 = x2 ;
}
x2 = xx(nx-1) ;
resu.set(nx-1) = resu(nx-2) + c1*(x2*x2*x2 - x0*x0*x0)/3.
+ 0.5*c2*(x2*x2 - x0*x0) + c3*(x2 - x0) ;
}
return resu ;
}
} // End of namespace Lorene
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