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R1448/src/gradient.cpp
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gradient.cpp
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#include <iostream>
#include <string.h>
#include <cuda_runtime.h>
#include <math.h>
#include <sys/time.h>
#include <fstream>
#include <immintrin.h>
#include <map>
/*
#ifdef __AVX__
#include "simd_math_avx.h"
#endif
#ifdef __AVX512F__
#include "simd_math_avx512f.h"
#endif
*/
#include "structure_hpc.h"
#include "gradient.hpp"
#include "utils.hpp"
//#include "iacaMarks.h"
//
//
//
/**@brief Return the gradient of the projected lens potential for one clump
* !!! 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
*/
//
/// Useful functions
//
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;
//
//std::cout << "piemd_lderivatives" << std::endl;
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);
}
//
//// changes the coordinates of point P into a new basis (rotation of angle theta)
//// y' y x'
//// * | /
//// * | / theta
//// * | /
//// *|--------->x
/*
inline
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);
}
*/
//
//
struct point
grad_halo(const struct point *pImage, const struct Potential *lens)
{
struct point true_coord, true_coord_rot, result;
double X, Y, R, angular_deviation, u;
complex zis;
//
result.x = result.y = 0.;
//
/*positionning at the potential center*/
// Change the origin of the coordinate system to the center of the clump
true_coord.x = pImage->x - lens->position.x;
true_coord.y = pImage->y - lens->position.y;
//printf("x, y = %f, %f\n", lens->position.x, lens->position.y);
//
true_coord_rot = rotateCoordinateSystem(true_coord, lens->ellipticity_angle);
//
switch (lens->type)
{
case(5): /*Elliptical Isothermal Sphere*/
/*rotation of the coordiante axes to match the potential axes*/
//true_coord_rotation = rotateCoordinateSystem(true_coord, lens->ellipticity_angle);
//
R=sqrt(true_coord_rot.x*true_coord_rot.x*(1 - lens->ellipticity/3.) + true_coord_rot.y*true_coord_rot.y*(1 + lens->ellipticity/3.)); //ellippot = ellipmass/3
result.x = (1 - lens->ellipticity/3.)*lens->b0*true_coord_rot.x/(R);
result.y = (1 + lens->ellipticity/3.)*lens->b0*true_coord_rot.y/(R);
break;
case(8): /* PIEMD */
/*rotation of the coordiante axes to match the potential axes*/
/*Doing something....*/
complex zis = piemd_1derivatives_ci05(true_coord_rot.x, true_coord_rot.y, lens->ellipticity_potential, lens->rcore);
//
result.x = lens->b0*zis.re;
result.y = lens->b0*zis.im;
break;
case(81): //PIEMD Kassiola & Kovner,1993 I0.5c-I0.5cut
double t05;
if ( lens->ellipticity_potential > 2E-4 )
{
//printf("1 ");
t05 = lens->b0*lens->rcut/(lens->rcut - lens->rcore);
complex zis = piemd_1derivatives_ci05(true_coord_rot.x, true_coord_rot.y, lens->ellipticity_potential, lens->rcore);
complex zis_cut = piemd_1derivatives_ci05(true_coord_rot.x, true_coord_rot.y, lens->ellipticity_potential, lens->rcut);
result.x = t05 * (zis.re - zis_cut.re);
result.y = t05 * (zis.im - zis_cut.im);
//printf(" g = %f %f\n", result.x, result.y);
}
else if (( u = true_coord_rot.x*true_coord_rot.x + true_coord_rot.y*true_coord_rot.y) > 0. )
{
//printf("2 ");
// Circular dPIE Elliasdottir 2007 Eq A23 slighly modified for t05
X = lens->rcore;
Y = lens->rcut;
t05 = sqrt(u + X * X) - X - sqrt(u + Y * Y) + Y; // Faster and equiv to Elliasdottir (see Golse PhD)
t05 *= lens->b0 * Y / (Y - X) / u; // 1/u because t05/sqrt(u) and normalised Q/sqrt(u)
result.x = t05*true_coord_rot.x;
result.y = t05*true_coord_rot.y;
}
else
{
//printf("3 ");
result.x = 0.;
result.y = 0.;
}
break;
default:
std::cout << "ERROR: Grad 1 profil type of clump "<< lens->name << " unknown : "<< lens->type << std::endl;
break;
};
result = rotateCoordinateSystem(result, -lens->ellipticity_angle);
//printf(" rot grad = %f %f\n", result.x, result.y);
return result;
}
//
//
//
struct point module_potentialDerivatives_totalGradient(const int nhalos, const struct point* pImage, const struct Potential* lens)
{
struct point grad, clumpgrad;
//
grad.x = 0;
grad.y = 0;
//
for(int i = 0; i < nhalos; i++)
{
clumpgrad = grad_halo(pImage, &lens[i]); //compute gradient for each clump separately
//std::cout << clumpgrad.x << " " << clumpgrad.y << std::endl;
//nan check
//if(clumpgrad.x == clumpgrad.x or clumpgrad.y == clumpgrad.y)
{
// add the gradients
grad.x += clumpgrad.x;
grad.y += clumpgrad.y;
}
}
//
return(grad);
}
//
// SOA versions, vectorizable
//
struct point module_potentialDerivatives_totalGradient_5_SOA(const struct point *pImage, const struct Potential_SOA *lens, int shalos, int nhalos)
{
asm volatile("# module_potentialDerivatives_totalGradient_SIS_SOA begins");
//
struct point grad, clumpgrad;
grad.x = 0;
grad.y = 0;
for(int i = shalos; i < shalos + nhalos; i++)
{
//
struct point true_coord, true_coord_rotation;
//
true_coord.x = pImage->x - lens->position_x[i];
true_coord.y = pImage->y - lens->position_y[i];
//
true_coord_rotation = rotateCoordinateSystem(true_coord, lens->ellipticity_angle[i]);
double R = sqrt(true_coord_rotation.x*true_coord_rotation.x*(1 - lens->ellipticity_potential[i])+true_coord_rotation.y*true_coord_rotation.y*(1 + lens->ellipticity_potential[i]));
//
grad.x += (1 - lens->ellipticity[i]/3.)*lens->b0[i]*true_coord_rotation.x/R;
grad.y += (1 + lens->ellipticity[i]/3.)*lens->b0[i]*true_coord_rotation.y/R;
}
return grad;
}
//
//
//
struct point module_potentialDerivatives_totalGradient_8_SOA(const struct point *pImage, const struct Potential_SOA *lens, int shalos, int nhalos)
{
asm volatile("# module_potentialDerivatives_totalGradient_SOA begins");
// 6 DP loads, i.e. 48 Bytes: position_x, position_y, ellipticity_angle, ellipticity_potential, rcore, b0
//
struct point grad, clumpgrad;
grad.x = 0;
grad.y = 0;
//
for(int i = shalos; i < shalos + nhalos; i++)
{
//IACA_START;
//
struct point true_coord, true_coord_rot; //, result;
//double R, angular_deviation;
complex zis;
//
//result.x = result.y = 0.;
//
true_coord.x = pImage->x - lens->position_x[i];
true_coord.y = pImage->y - lens->position_y[i];
/*positionning at the potential center*/
// Change the origin of the coordinate system to the center of the clump
true_coord_rot = rotateCoordinateSystem(true_coord, lens->ellipticity_angle[i]);
//
double x = true_coord_rot.x;
double y = true_coord_rot.y;
double eps = lens->ellipticity_potential[i];
double rc = lens->rcore[i];
//
//std::cout << "piemd_lderivatives" << std::endl;
//
double sqe = sqrt(eps);
//
double cx1 = (1. - eps)/(1. + eps);
double cxro = (1. + eps)*(1. + eps);
double cyro = (1. - eps)*(1. - eps);
//
double rem2 = x*x/cxro + y*y/cyro;
//
complex zci, znum, zden, zres;
double norm;
//
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) )
//
zis.re = zres.re;
zis.im = zres.im;
//
//zres.re = zis.re*b0;
//zres.im = zis.im*b0;
// rotation
clumpgrad.x = zis.re;
clumpgrad.y = zis.im;
clumpgrad = rotateCoordinateSystem(clumpgrad, -lens->ellipticity_angle[i]);
//
clumpgrad.x = lens->b0[i]*clumpgrad.x;
clumpgrad.y = lens->b0[i]*clumpgrad.y;
//
//clumpgrad.x = lens->b0[i]*zis.re;
//clumpgrad.y = lens->b0[i]*zis.im;
//nan check
//if(clumpgrad.x == clumpgrad.x or clumpgrad.y == clumpgrad.y)
//{
// add the gradients
grad.x += clumpgrad.x;
grad.y += clumpgrad.y;
//}
}
//IACA_END;
//
return(grad);
}
struct point module_potentialDerivatives_totalGradient_81_SOA(const struct point *pImage, const struct Potential_SOA *lens, int shalos, int nhalos)
{
asm volatile("# module_potentialDerivatives_totalGradient_SOA begins");
//std::cout << "# module_potentialDerivatives_totalGradient_SOA begins" << std::endl;
// 6 DP loads, i.e. 48 Bytes: position_x, position_y, ellipticity_angle, ellipticity_potential, rcore, b0
//
struct point grad, clumpgrad;
grad.x = 0;
grad.y = 0;
//
for(int i = shalos; i < shalos + nhalos; i++)
{
//IACA_START;
//
struct point true_coord, true_coord_rot; //, result;
//double R, angular_deviation;
complex zis;
//
//result.x = result.y = 0.;
//
true_coord.x = pImage->x - lens->position_x[i];
true_coord.y = pImage->y - lens->position_y[i];
/*positionning at the potential center*/
// Change the origin of the coordinate system to the center of the clump
true_coord_rot = rotateCoordinateSystem(true_coord, lens->ellipticity_angle[i]);
//
double x = true_coord_rot.x;
double y = true_coord_rot.y;
double eps = lens->ellipticity_potential[i];
double rc = lens->rcore[i];
double rcut = lens->rcut[i];
double b0 = lens->b0[i];
double t05 = b0*rcut/(rcut - rc);
//printf("b0 = %f, rcut = %f, rc = %f, t05 = %f\n", b0, rcut, rc, t05);
//
//std::cout << "piemd_lderivatives" << std::endl;
//
double sqe = sqrt(eps);
//
double cx1 = (1. - eps)/(1. + eps);
double cxro = (1. + eps)*(1. + eps);
double cyro = (1. - eps)*(1. - eps);
//
double rem2 = x*x/cxro + y*y/cyro;
//
complex zci, znum, zden, zres_rc, zres_rcut;
double norm;
//
zci.re = 0;
zci.im = -0.5*(1. - eps*eps)/sqe;
//
// step 1
//
{
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_rc.re = zci.re*zis.re - zci.im*zis.im; // Re( zci*ln(zis) )
zres_rc.im = zci.im*zis.re + zis.im*zci.re; // Im( zci*ln(zis) )
}
//
// step 2
//
{
znum.re = cx1*x;
znum.im = 2.*sqe*sqrt(rcut*rcut + rem2) - y/cx1;
//
zden.re = x;
zden.im = 2.*rcut*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_rcut.re = zci.re*zis.re - zci.im*zis.im; // Re( zci*ln(zis) )
zres_rcut.im = zci.im*zis.re + zis.im*zci.re; // Im( zci*ln(zis) )
}
zis.re = t05*(zres_rc.re - zres_rcut.re);
zis.im = t05*(zres_rc.im - zres_rcut.im);
//printf("%f %f\n", zis.re, zis.im);
//
//zres.re = zis.re*b0;
//zres.im = zis.im*b0;
// rotation
clumpgrad.x = zis.re;
clumpgrad.y = zis.im;
clumpgrad = rotateCoordinateSystem(clumpgrad, -lens->ellipticity_angle[i]);
//
//clumpgrad.x = lens->b0[i]*clumpgrad.x;
//clumpgrad.y = lens->b0[i]*clumpgrad.y;
//
//clumpgrad.x = lens->b0[i]*zis.re;
//clumpgrad.y = lens->b0[i]*zis.im;
//nan check
//if(clumpgrad.x == clumpgrad.x or clumpgrad.y == clumpgrad.y)
//{
// add the gradients
grad.x += clumpgrad.x;
grad.y += clumpgrad.y;
//printf("grad = %f %f\n", clumpgrad.x, clumpgrad.y);
//}
}
//IACA_END;
//
return(grad);
}
//
//
//
typedef struct point (*halo_func_t) (const struct point *pImage, const struct Potential_SOA *lens, int shalos, int nhalos);
halo_func_t halo_func[100] =
{
0, 0, 0, 0, 0, module_potentialDerivatives_totalGradient_5_SOA, 0, 0, module_potentialDerivatives_totalGradient_8_SOA, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, module_potentialDerivatives_totalGradient_81_SOA, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
//
//
//
struct point module_potentialDerivatives_totalGradient_SOA(const struct point *pImage, const struct Potential_SOA *lens, int nhalos)
{
struct point grad, clumpgrad;
//
grad.x = clumpgrad.x = 0;
grad.y = clumpgrad.y = 0;
//
int shalos = 0;
//
//module_potentialDerivatives_totalGradient_81_SOA(pImage, lens, 0, nhalos);
//return;
/*
int* p_type = &(lens->type)[0];
int* lens_type = (int*) malloc(nhalos*sizeof(int));
memcpy(lens_type, &(lens->type)[0], nhalos*sizeof(int));
*/
//quicksort(lens_type, nhalos);
//
while (shalos < nhalos)
{
int lens_type = lens->type[shalos];
int count = 1;
while (lens->type[shalos + count] == lens_type) count++;
//std::cerr << "type = " << lens_type << " " << count << " " << shalos << std::endl;
//
clumpgrad = (*halo_func[lens_type])(pImage, lens, shalos, count);
//
grad.x += clumpgrad.x;
grad.y += clumpgrad.y;
shalos += count;
}
return(grad);
}
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