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/*
* Hermite interpolation functions.
*
*/
/*
* Copyright (c) 2000-2002 Eric Gourgoulhon
*
* 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 interpol_herm_C[] = "$Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/interpol_herm.C,v 1.13 2015/06/15 15:08:22 j_novak Exp $" ;
/*
* $Id: interpol_herm.C,v 1.13 2015/06/15 15:08:22 j_novak Exp $
* $Log: interpol_herm.C,v $
* Revision 1.13 2015/06/15 15:08:22 j_novak
* New file interpol_bifluid for interpolation of 2-fluid EoSs
*
* Revision 1.12 2015/06/10 14:39:18 a_sourie
* New class Eos_bf_tabul for tabulated 2-fluid EoSs and associated functions for the computation of rotating stars with such EoSs.
*
* Revision 1.11 2015/01/27 14:22:38 j_novak
* New methods in Eos_tabul to correct for EoS themro consistency (optional).
*
* Revision 1.10 2014/10/13 08:53:32 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.9 2013/12/12 16:07:30 j_novak
* interpol_herm_2d outputs df/dx, used to get the magnetization.
*
* Revision 1.8 2012/09/04 14:53:28 j_novak
* Replacement of the FORTRAN version of huntm by a C one.
*
* Revision 1.7 2011/10/04 16:05:19 j_novak
* Update of Eos_mag class. Suppression of loge, re-definition of the derivatives
* and use of interpol_herm_2d.
*
* Revision 1.6 2011/10/03 13:44:45 j_novak
* Updated the y-derivative for the 2D version
*
* Revision 1.5 2011/09/27 15:38:11 j_novak
* New function for 2D interpolation added. The computation of 1st derivative is
* still missing.
*
* Revision 1.4 2003/11/21 16:14:51 m_bejger
* Added the linear interpolation
*
* Revision 1.3 2003/05/15 09:42:12 e_gourgoulhon
* Added the new function interpol_herm_der
*
* Revision 1.2 2002/09/09 13:00:40 e_gourgoulhon
* Modification of declaration of Fortran 77 prototypes for
* a better portability (in particular on IBM AIX systems):
* All Fortran subroutine names are now written F77_* and are
* defined in the new file C++/Include/proto_f77.h.
*
* Revision 1.1.1.1 2001/11/20 15:19:29 e_gourgoulhon
* LORENE
*
* Revision 2.0 2000/11/22 19:31:42 eric
* *** empty log message ***
*
*
* $Header: /cvsroot/Lorene/C++/Source/Non_class_members/Utilities/interpol_herm.C,v 1.13 2015/06/15 15:08:22 j_novak Exp $
*
*/
// Headers Lorene
#include "tbl.h"
namespace Lorene {
//---------------------------------------------------------------
// Value bracketting in an ordered table (from Numerical Recipes)
//---------------------------------------------------------------
void huntm(const Tbl& xx, double& x, int& i_low) {
assert (xx.get_etat() == ETATQCQ) ;
int nx = xx.get_taille() ;
bool ascend = ( xx(nx-1) > xx(0) ) ;
int i_hi ;
if ( (i_low < 0)||(i_low>=nx) ) {
i_low = -1 ;
i_hi = nx ;
}
else {
int inc = 1 ;
if ( (x >= xx(i_low)) == ascend ) {
if (i_low == nx -1) return ;
i_hi = i_low + 1 ;
while ( (x >= xx(i_hi)) == ascend ) {
i_low = i_hi ;
inc += inc ;
i_hi = i_low + inc ;
if (i_hi >= nx) {
i_hi = nx ;
break ;
}
}
} else {
if (i_low == 0) {
i_low = -1 ;
return ;
}
i_hi = i_low-- ;
while ( (x < xx(i_low)) == ascend ) {
i_hi = i_low ;
inc += inc ;
if ( inc >= i_hi ) {
i_low = 0 ;
break ;
}
else i_low = i_hi - inc ;
}
}
}
while ( (i_hi - i_low) > 1) {
int i_med = (i_hi + i_low) / 2 ;
if ( (x>=xx(i_med)) == ascend ) i_low = i_med ;
else i_hi = i_med ;
}
if (x == xx(nx-1)) i_low = nx-2 ;
if (x == xx(0)) i_low = 0 ;
return ;
}
//---------------------
// Linear interpolation
//---------------------
void interpol_linear(const Tbl& xtab, const Tbl& ytab,
double x, int& i, double& y) {
assert(ytab.dim == xtab.dim) ;
//assert(dytab.dim == xtab.dim) ;
huntm(xtab, x, i) ;
int i1 = i + 1 ;
// double dx = xtab(i1) - xtab(i) ;
double y1 = ytab(i) ;
double y2 = ytab(i1) ;
double x1 = xtab(i) ;
double x2 = xtab(i1) ;
double x12 = x1-x2 ;
double a = (y1-y2)/x12 ;
double b = (x1*y2-y1*x2)/x12 ;
y = x*a+b ;
}
//------------------------------------------------------------
// Cubic Hermite interpolation, returning the first derivative
//------------------------------------------------------------
void interpol_herm(const Tbl& xtab, const Tbl& ytab, const Tbl& dytab,
double x, int& i, double& y, double& dy) {
assert(ytab.dim == xtab.dim) ;
assert(dytab.dim == xtab.dim) ;
huntm(xtab, x, i) ;
int i1 = i + 1 ;
double dx = xtab(i1) - xtab(i) ;
double u = (x - xtab(i)) / dx ;
double u2 = u*u ;
double u3 = u2*u ;
y = ytab(i) * ( 2.*u3 - 3.*u2 + 1.)
+ ytab(i1) * ( 3.*u2 - 2.*u3)
+ dytab(i) * dx * ( u3 - 2.*u2 + u )
- dytab(i1) * dx * ( u2 - u3 ) ;
dy = 6. * ( ytab(i) / dx * ( u2 - u )
- ytab(i1) / dx * ( u2 - u ) )
+ dytab(i) * ( 3.*u2 - 4.*u + 1. )
+ dytab(i1) * ( 3.*u2 - 2.*u ) ;
}
//-------------------------------------------------------------
// Cubic Hermite interpolation, returning the second derivative
//-------------------------------------------------------------
void interpol_herm_der(const Tbl& xtab, const Tbl& ytab, const Tbl& dytab,
double x, int& i, double& y, double& dy, double& ddy) {
assert(ytab.dim == xtab.dim) ;
assert(dytab.dim == xtab.dim) ;
huntm(xtab, x, i) ;
// i-- ; // Fortran --> C
int i1 = i + 1 ;
double dx = xtab(i1) - xtab(i) ;
double u = (x - xtab(i)) / dx ;
double u2 = u*u ;
double u3 = u2*u ;
y = ytab(i) * ( 2.*u3 - 3.*u2 + 1.)
+ ytab(i1) * ( 3.*u2 - 2.*u3)
+ dytab(i) * dx * ( u3 - 2.*u2 + u )
- dytab(i1) * dx * ( u2 - u3 ) ;
dy = 6. * ( ytab(i) - ytab(i1) ) * ( u2 - u ) / dx
+ dytab(i) * ( 3.*u2 - 4.*u + 1. )
+ dytab(i1) * ( 3.*u2 - 2.*u ) ;
ddy = 6 * ( ( ytab(i) - ytab(i1) ) * ( 2.*u - 1. ) / dx
+ dytab(i) * (6.*u - 4.)
+ dytab(i1) * (6.*u - 2.) ) / dx ;
}
//----------------------------------------------
// Bi-cubic Hermite interpolation, for 2D arrays
//----------------------------------------------
void interpol_herm_2d(const Tbl& xtab, const Tbl& ytab, const Tbl& ftab,
const Tbl& dfdxtab, const Tbl& dfdytab, const Tbl&
d2fdxdytab, double x, double y, double& f, double&
dfdx, double& dfdy) {
assert(ytab.dim == xtab.dim) ;
assert(ftab.dim == xtab.dim) ;
assert(dfdxtab.dim == xtab.dim) ;
assert(dfdytab.dim == xtab.dim) ;
assert(d2fdxdytab.dim == xtab.dim) ;
int nbp1, nbp2;
nbp1 = xtab.get_dim(0);
nbp2 = xtab.get_dim(1);
int i_near = 0 ;
int j_near = 0 ;
while ((xtab(i_near,0) <= x) && (nbp2 > i_near)) {
i_near++;
}
if (i_near != 0) {
i_near-- ;
}
j_near = 0;
while ((ytab(i_near,j_near) < y) && (nbp1 > j_near)) {
j_near++ ;
}
if (j_near != 0) {
j_near-- ;
}
int i1 = i_near+1 ; int j1 = j_near+1 ;
double dx = xtab(i1, j_near) - xtab(i_near, j_near) ;
double dy = ytab(i_near, j1) - ytab(i_near, j_near) ;
double u = (x - xtab(i_near, j_near)) / dx ;
double v = (y - ytab(i_near, j_near)) / dy ;
double u2 = u*u ; double v2 = v*v ;
double u3 = u2*u ; double v3 = v2*v ;
double psi0_u = 2.*u3 - 3.*u2 + 1. ;
double psi0_1mu = -2.*u3 + 3.*u2 ;
double psi1_u = u3 - 2.*u2 + u ;
double psi1_1mu = -u3 + u2 ;
double psi0_v = 2.*v3 - 3.*v2 + 1. ;
double psi0_1mv = -2.*v3 + 3.*v2 ;
double psi1_v = v3 - 2.*v2 + v ;
double psi1_1mv = -v3 + v2 ;
f = ftab(i_near, j_near) * psi0_u * psi0_v
+ ftab(i1, j_near) * psi0_1mu * psi0_v
+ ftab(i_near, j1) * psi0_u * psi0_1mv
+ ftab(i1, j1) * psi0_1mu * psi0_1mv ;
f += (dfdxtab(i_near, j_near) * psi1_u * psi0_v
- dfdxtab(i1, j_near) * psi1_1mu * psi0_v
+ dfdxtab(i_near, j1) * psi1_u * psi0_1mv
- dfdxtab(i1, j1) * psi1_1mu * psi0_1mv) * dx ;
f += (dfdytab(i_near, j_near) * psi0_u * psi1_v
+ dfdytab(i1, j_near) * psi0_1mu * psi1_v
- dfdytab(i_near, j1) * psi0_u * psi1_1mv
- dfdytab(i1, j1) * psi0_1mu * psi1_1mv) * dy ;
f += (d2fdxdytab(i_near, j_near) * psi1_u * psi1_v
- d2fdxdytab(i1, j_near) * psi1_1mu * psi1_v
- d2fdxdytab(i_near, j1) * psi1_u * psi1_1mv
+ d2fdxdytab(i1, j1) * psi1_1mu * psi1_1mv) * dx * dy ;
double dpsi0_u = 6.*(u2 - u) ;
double dpsi0_1mu = 6.*(u2 - u) ;
double dpsi1_u = 3.*u2 - 4.*u + 1. ;
double dpsi1_1mu = 3.*u2 - 2.*u ;
dfdx = (ftab(i_near, j_near) * dpsi0_u * psi0_v
- ftab(i1, j_near) * dpsi0_1mu * psi0_v
+ ftab(i_near, j1) * dpsi0_u * psi0_1mv
- ftab(i1, j1) * dpsi0_1mu * psi0_1mv ) / dx;
dfdx += (dfdxtab(i_near, j_near) * dpsi1_u * psi0_v
+ dfdxtab(i1, j_near) * dpsi1_1mu * psi0_v
+ dfdxtab(i_near, j1) * dpsi1_u * psi0_1mv
+ dfdxtab(i1, j1) * dpsi1_1mu * psi0_1mv) ;
dfdx += (dfdytab(i_near, j_near) * dpsi0_u * psi1_v
- dfdytab(i1, j_near) * dpsi0_1mu * psi1_v
- dfdytab(i_near, j1) * dpsi0_u * psi1_1mv
+ dfdytab(i1, j1) * dpsi0_1mu * psi1_1mv) * dy /dx ;
dfdx += (d2fdxdytab(i_near, j_near) * dpsi1_u * psi1_v
+ d2fdxdytab(i1, j_near) * dpsi1_1mu * psi1_v
- d2fdxdytab(i_near, j1) * dpsi1_u * psi1_1mv
- d2fdxdytab(i1, j1) * dpsi1_1mu * psi1_1mv) * dy ;
double dpsi0_v = 6.*(v2 - v) ;
double dpsi0_1mv = 6.*(v2 - v) ;
double dpsi1_v = 3.*v2 - 4.*v + 1. ;
double dpsi1_1mv = 3.*v2 - 2.*v ;
dfdy = (ftab(i_near, j_near) * psi0_u * dpsi0_v
+ ftab(i1, j_near) * psi0_1mu * dpsi0_v
- ftab(i_near, j1) * psi0_u * dpsi0_1mv
- ftab(i1, j1) * psi0_1mu * dpsi0_1mv) / dy ;
dfdy += (dfdxtab(i_near, j_near) * psi1_u * dpsi0_v
- dfdxtab(i1, j_near) * psi1_1mu * dpsi0_v
- dfdxtab(i_near, j1) * psi1_u * dpsi0_1mv
+ dfdxtab(i1, j1) * psi1_1mu * dpsi0_1mv) * dx / dy ;
dfdy += (dfdytab(i_near, j_near) * psi0_u * dpsi1_v
+ dfdytab(i1, j_near) * psi0_1mu * dpsi1_v
+ dfdytab(i_near, j1) * psi0_u * dpsi1_1mv
+ dfdytab(i1, j1) * psi0_1mu * dpsi1_1mv) ;
dfdy += (d2fdxdytab(i_near, j_near) * psi1_u * dpsi1_v
- d2fdxdytab(i1, j_near) * psi1_1mu * dpsi1_v
+ d2fdxdytab(i_near, j1) * psi1_u * dpsi1_1mv
- d2fdxdytab(i1, j1) * psi1_1mu * dpsi1_1mv) * dx ;
return ;
}
void interpol_herm_2d_sans(const Tbl& xtab, const Tbl& ytab, const Tbl& ftab,
const Tbl& dfdxtab, const Tbl& dfdytab, double x,
double y, double& f, double& dfdx, double& dfdy) {
assert(ytab.dim == xtab.dim) ;
assert(ftab.dim == xtab.dim) ;
assert(dfdxtab.dim == xtab.dim) ;
assert(dfdytab.dim == xtab.dim) ;
int nbp1, nbp2;
nbp1 = xtab.get_dim(0);
nbp2 = xtab.get_dim(1);
int i_near = 0 ;
int j_near = 0 ;
while ((xtab(i_near,0) <= x) && (nbp2 > i_near)) {
i_near++;
}
if (i_near != 0) {
i_near-- ;
}
j_near = 0;
while ((ytab(i_near,j_near) < y) && (nbp1 > j_near)) {
j_near++ ;
}
if (j_near != 0) {
j_near-- ;
}
int i1 = i_near+1 ; int j1 = j_near+1 ;
double dx = xtab(i1, j_near) - xtab(i_near, j_near) ;
double dy = ytab(i_near, j1) - ytab(i_near, j_near) ;
double u = (x - xtab(i_near, j_near)) / dx ;
double v = (y - ytab(i_near, j_near)) / dy ;
double u2 = u*u ; double v2 = v*v ;
double u3 = u2*u ; double v3 = v2*v ;
double psi0_u = 2.*u3 - 3.*u2 + 1. ;
double psi0_1mu = -2.*u3 + 3.*u2 ;
double psi1_u = u3 - 2.*u2 + u ;
double psi1_1mu = -u3 + u2 ;
double psi0_v = 2.*v3 - 3.*v2 + 1. ;
double psi0_1mv = -2.*v3 + 3.*v2 ;
double psi1_v = v3 - 2.*v2 + v ;
double psi1_1mv = -v3 + v2 ;
f = ftab(i_near, j_near) * psi0_u * psi0_v
+ ftab(i1, j_near) * psi0_1mu * psi0_v
+ ftab(i_near, j1) * psi0_u * psi0_1mv
+ ftab(i1, j1) * psi0_1mu * psi0_1mv ;
f += (dfdxtab(i_near, j_near) * psi1_u * psi0_v
- dfdxtab(i1, j_near) * psi1_1mu * psi0_v
+ dfdxtab(i_near, j1) * psi1_u * psi0_1mv
- dfdxtab(i1, j1) * psi1_1mu * psi0_1mv) * dx ;
f += (dfdytab(i_near, j_near) * psi0_u * psi1_v
+ dfdytab(i1, j_near) * psi0_1mu * psi1_v
- dfdytab(i_near, j1) * psi0_u * psi1_1mv
- dfdytab(i1, j1) * psi0_1mu * psi1_1mv) * dy ;
double dpsi0_u = 6.*(u2 - u) ;
double dpsi0_1mu = 6.*(u2 - u) ;
double dpsi1_u = 3.*u2 - 4.*u + 1. ;
double dpsi1_1mu = 3.*u2 - 2.*u ;
dfdx = (ftab(i_near, j_near) * dpsi0_u * psi0_v
- ftab(i1, j_near) * dpsi0_1mu * psi0_v
+ ftab(i_near, j1) * dpsi0_u * psi0_1mv
- ftab(i1, j1) * dpsi0_1mu * psi0_1mv ) / dx;
dfdx += (dfdxtab(i_near, j_near) * dpsi1_u * psi0_v
+ dfdxtab(i1, j_near) * dpsi1_1mu * psi0_v
+ dfdxtab(i_near, j1) * dpsi1_u * psi0_1mv
+ dfdxtab(i1, j1) * dpsi1_1mu * psi0_1mv) ;
dfdx += (dfdytab(i_near, j_near) * dpsi0_u * psi1_v
- dfdytab(i1, j_near) * dpsi0_1mu * psi1_v
- dfdytab(i_near, j1) * dpsi0_u * psi1_1mv
+ dfdytab(i1, j1) * dpsi0_1mu * psi1_1mv) * dy /dx ;
double dpsi0_v = 6.*(v2 - v) ;
double dpsi0_1mv = 6.*(v2 - v) ;
double dpsi1_v = 3.*v2 - 4.*v + 1. ;
double dpsi1_1mv = 3.*v2 - 2.*v ;
dfdy = (ftab(i_near, j_near) * psi0_u * dpsi0_v
+ ftab(i1, j_near) * psi0_1mu * dpsi0_v
- ftab(i_near, j1) * psi0_u * dpsi0_1mv
- ftab(i1, j1) * psi0_1mu * dpsi0_1mv) / dy ;
dfdy += (dfdxtab(i_near, j_near) * psi1_u * dpsi0_v
- dfdxtab(i1, j_near) * psi1_1mu * dpsi0_v
- dfdxtab(i_near, j1) * psi1_u * dpsi0_1mv
+ dfdxtab(i1, j1) * psi1_1mu * dpsi0_1mv) * dx / dy ;
dfdy += (dfdytab(i_near, j_near) * psi0_u * dpsi1_v
+ dfdytab(i1, j_near) * psi0_1mu * dpsi1_v
+ dfdytab(i_near, j1) * psi0_u * dpsi1_1mv
+ dfdytab(i1, j1) * psi0_1mu * dpsi1_1mv) ;
return ;
}
//--------------------------------------------------------------------
// Quintic Hermite interpolation using data from the second derivative
//--------------------------------------------------------------------
void interpol_herm_2nd_der(const Tbl& xtab, const Tbl& ytab, const Tbl& dytab,
const Tbl& d2ytab, double x, int& i, double& y,
double& dy) {
assert(ytab.dim == xtab.dim) ;
assert(dytab.dim == xtab.dim) ;
assert(d2ytab.dim == xtab.dim) ;
huntm(xtab, x, i) ;
int i1 = i + 1 ;
double dx = xtab(i1) - xtab(i) ;
double u = (x - xtab(i)) / dx ;
double u2 = u*u ;
double u3 = u2*u ;
double u4 = u2*u2 ;
double u5 = u3*u2 ;
double v = 1. - u ;
double v2 = v*v ;
double v3 = v2*v ;
double v4 = v2*v2 ;
double v5 = v3*v2 ;
y = ytab(i) * ( -6.*u5 + 15.*u4 - 10.*u3 + 1. )
+ ytab(i1) * ( -6.*v5 + 15.*v4 - 10.*v3 + 1. )
+ dytab(i) * dx * ( -3.*u5 + 8.*u4 -6.*u3 + u )
- dytab(i1) * dx * ( -3.*v5 + 8.*v4 -6.*v3 + v )
+ d2ytab(i) * dx*dx * ( -0.5*u5 + 1.5*u4 - 1.5*u3 + 0.5*u2 )
+ d2ytab(i1) * dx*dx * ( -0.5*v5 + 1.5*v4 - 1.5*v3 + 0.5*v2 ) ;
dy = 30.*( ytab(i) / dx * ( -u4 + 2.*u3 - u2 )
- ytab(i1) / dx * ( -v4 + 2.*v3 - v2 ) )
+ dytab(i) * ( -15.*u4 + 32.*u3 - 18.*u2 + 1. )
+ dytab(i1) * ( -15.*v4 + 32.*v3 - 18.*v2 + 1. )
+ d2ytab(i) * dx * ( -2.5*u4 + 6.*u3 -4.5*u2 + u )
- d2ytab(i1) * dx * ( -2.5*v4 + 6.*v3 -4.5*v2 + v ) ;
}
} // End of namespace Lorene
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