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Grad.cpp
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Mon, Oct 7, 19:21

Grad.cpp
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#include <Grad.h>
struct point module_potentialDerivatives_totalGradient(const int *Nlens, const struct point *pImage, PotentialSet *lens )
{
struct point grad, clumpgrad;
grad.x=0;
grad.y=0;
//This here could be done with function pointer to better acomodate future ass distributions functions
// However I'm unsure of the time of function pointers -> ask gilles
//for the moment lens and Nlens is organised the following way : 1. SIS, 2. PIEMD
//SIS is the first
for(int i=0; i<Nlens[0]; i++){
clumpgrad=grad_halo_sis(pImage,i,&lens[0]); //compute gradient for each clump separately
if(clumpgrad.x == clumpgrad.x or clumpgrad.y == clumpgrad.y){ //nan check
grad.x+=clumpgrad.x;
grad.y+=clumpgrad.y;
} // add the gradients
}
//PIEMD is the second
for(int i=0; i<Nlens[1]; i++){
clumpgrad=grad_halo_piemd(pImage,i,&lens[1]); //compute gradient for each clump separately
if(clumpgrad.x == clumpgrad.x or clumpgrad.y == clumpgrad.y){ //nan check
grad.x+=clumpgrad.x;
grad.y+=clumpgrad.y;
} // add the gradients
}
return(grad);
}
/**@brief Return the gradient of the projected lens potential for one PIEMD clump. Uses SoA insteand of AoS lenses for speed
*!!! You have to multiply by dlsds to obtain the true gradient for the expressions, see the papers :
*JP Kneib & P Natarajan, Cluster Lenses, The Astronomy and Astrophysics Review (2011) for 1 and 2 and JP Kneib PhD (1993) for 3
*
* @param pImage point where the result is computed in the lens plane
* @param lens mass distribution
*/
struct point grad_halo_piemd(const struct point *pImage, int iterator,PotentialSet *lens)
{
struct point true_coord, true_coord_rotation, result;
double R, angular_deviation;
complex zis;
result.x = result.y = 0.;
/*positionning at the potential center*/
true_coord.x = pImage->x - lens->x[iterator]; // Change the origin of the coordinate system to the center of the clump
true_coord.y = pImage->y - lens->y[iterator];
/* PIEMD */
/*rotation of the coordiante axes to match the potential axes*/
true_coord_rotation = rotateCoordinateSystem(true_coord, lens->ellipticity_angle[iterator]);
/*Doing something....*/
zis = piemd_1derivatives_ci05(true_coord_rotation.x, true_coord_rotation.y, lens->ellipticity_potential[iterator], lens->rcore[iterator]);
result.x=lens->b0[iterator] * zis.re;
result.y=lens->b0[iterator] * zis.im;
return result;
}
/**@brief Return the gradient of the projected lens potential for one SIS clump. Uses SoA insteand of AoS lenses for speed
*!!! You have to multiply by dlsds to obtain the true gradient for the expressions, see the papers :
*JP Kneib & P Natarajan, Cluster Lenses, The Astronomy and Astrophysics Review (2011) for 1 and 2 and JP Kneib PhD (1993) for 3
*
* @param pImage point where the result is computed in the lens plane
* @param lens mass distribution
*/
struct point grad_halo_sis(const struct point *pImage, int iterator,PotentialSet *lens)
{
struct point true_coord, true_coord_rotation, result;
double R, angular_deviation;
complex zis;
result.x = result.y = 0.;
/*positionning at the potential center*/
true_coord.x = pImage->x - lens->x[iterator]; // Change the origin of the coordinate system to the center of the clump
true_coord.y = pImage->y - lens->y[iterator];
/*Elliptical Isothermal Sphere*/
/*rotation of the coordiante axes to match the potential axes*/
true_coord_rotation = rotateCoordinateSystem(true_coord, lens->ellipticity_angle[iterator]);
R=sqrt(true_coord_rotation.x*true_coord_rotation.x*(1-lens->ellipticity[iterator]/3.)+true_coord_rotation.y*true_coord_rotation.y*(1+lens->ellipticity[iterator]/3.)); //ellippot = ellipmass/3
result.x=(1-lens->ellipticity[iterator]/3.)*lens->b0[iterator]*true_coord_rotation.x/(R);
result.y=(1+lens->ellipticity[iterator]/3.)*lens->b0[iterator]*true_coord_rotation.y/(R);
return result;
}
/**** usefull functions for PIEMD profile : see old lenstool ****/
/** I*w,v=0.5 Kassiola & Kovner, 1993 PIEMD, paragraph 4.1
*
* Global variables used :
* - none
*/
complex piemd_1derivatives_ci05(double x, double y, double eps, double rc)
{
double sqe, cx1, cxro, cyro, rem2;
complex zci, znum, zden, zis, zres;
double norm;
sqe = sqrt(eps);
cx1 = (1. - eps) / (1. + eps);
cxro = (1. + eps) * (1. + eps);
cyro = (1. - eps) * (1. - eps);
rem2 = x * x / cxro + y * y / cyro;
/*zci=cpx(0.,-0.5*(1.-eps*eps)/sqe);
znum=cpx(cx1*x,(2.*sqe*sqrt(rc*rc+rem2)-y/cx1));
zden=cpx(x,(2.*rc*sqe-y));
zis=pcpx(zci,lncpx(dcpx(znum,zden)));
zres=pcpxflt(zis,b0);*/
// --> optimized code
zci.re = 0;
zci.im = -0.5 * (1. - eps * eps) / sqe;
znum.re = cx1 * x;
znum.im = 2.*sqe * sqrt(rc * rc + rem2) - y / cx1;
zden.re = x;
zden.im = 2.*rc * sqe - y;
norm = zden.re * zden.re + zden.im * zden.im; // zis = znum/zden
zis.re = (znum.re * zden.re + znum.im * zden.im) / norm;
zis.im = (znum.im * zden.re - znum.re * zden.im) / norm;
norm = zis.re;
zis.re = log(sqrt(norm * norm + zis.im * zis.im)); // ln(zis) = ln(|zis|)+i.Arg(zis)
zis.im = atan2(zis.im, norm);
// norm = zis.re;
zres.re = zci.re * zis.re - zci.im * zis.im; // Re( zci*ln(zis) )
zres.im = zci.im * zis.re + zis.im * zci.re; // Im( zci*ln(zis) )
//zres.re = zis.re*b0;
//zres.im = zis.im*b0;
return(zres);
}
/// Useful functions
// changes the coordinates of point P into a new basis (rotation of angle theta)
// y' y x'
// * | /
// * | / theta
// * | /
// *|--------->x
struct point rotateCoordinateSystem(struct point P, double theta)
{
struct point Q;
Q.x = P.x*cos(theta) + P.y*sin(theta);
Q.y = P.y*cos(theta) - P.x*sin(theta);
return(Q);
}
/** @brief This module function calculates profile depended information like the impactparameter b0 and the potential ellipticity epot
*
* @param lens: mass distribution for which to calculate parameters
*/
void module_readParameters_calculatePotentialparameter(Potential *lens){
switch (lens->type)
{
case(5): /*Elliptical Isothermal Sphere*/
//impact parameter b0
lens->b0 = 4* pi_c2 * lens->vdisp * lens->vdisp ;
//ellipticity_potential
lens->ellipticity_potential = lens->ellipticity/3 ;
break;
case(8): /* PIEMD */
//impact parameter b0
lens->b0 = 6.*pi_c2 * lens->vdisp * lens->vdisp;
//ellipticity_parameter
if ( lens->ellipticity == 0. && lens->ellipticity_potential != 0. ){
// emass is (a2-b2)/(a2+b2)
lens->ellipticity = 2.*lens->ellipticity_potential / (1. + lens->ellipticity_potential * lens->ellipticity_potential);
//printf("1 : %f %f \n",lens->ellipticity,lens->ellipticity_potential);
}
else if ( lens->ellipticity == 0. && lens->ellipticity_potential == 0. ){
lens->ellipticity_potential = 0.00001;
//printf("2 : %f %f \n",lens->ellipticity,lens->ellipticity_potential);
}
else{
// epot is (a-b)/(a+b)
lens->ellipticity_potential = (1. - sqrt(1 - lens->ellipticity * lens->ellipticity)) / lens->ellipticity;
//printf("3 : %f %f \n",lens->ellipticity,lens->ellipticity_potential);
}
break;
default:
std::cout << "ERROR: LENSPARA profil type of clump "<< lens->name << " unknown : "<< lens->type << std::endl;
//printf( "ERROR: LENSPARA profil type of clump %s unknown : %d\n",lens->name, lens->type);
break;
};
}

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