e_mag.c
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	#include<stdio.h>
	#include<math.h>
	#include<fonction.h>
	#include<constant.h>
	#include<dimension.h>
	#include<structure.h>

	/****************************************************************/
	/* nom: e_mag */
	/* auteur: Jean-Paul Kneib */
	/* date: 10/02/92 */
	/* place: Toulouse */
	/****************************************************************
	* Return an ellipse that contains the inverse of the eigenvalues of the
	* amplification matrix [ a=1/(1-k+gamma), b=1/(1-k-gamma) ] and the
	* orientation of the proper magnification axis.
	*
	* Used to convert source to image plane. (inverse of the lens equation)
	* Used in e_test.c
	*/

	struct ellipse e_mag(struct point *position, double dl0s, double dos, double zs)
	{
	struct ellipse ampli;
	double A, B, C;
	struct matrix M;

	M = e_grad2(position, dl0s, zs);
	M.a /= dos;
	M.b /= dos;
	M.c /= dos;
	A = 1. - M.a;
	B = -M.b;
	C = 1. - M.c;
	ampli = diag(A, B, C);

	return(ampli);
	}

	struct ellipse e_mag_gal(struct galaxie *image)
	{
	struct ellipse ampli;
	double A, B, C;
	struct matrix M;

	M = e_grad2_gal(image, NULL);
	M.a /= image->dos;
	M.b /= image->dos;
	M.c /= image->dos;
	A = 1. - M.a;
	B = -M.b;
	C = 1. - M.c;
	ampli = diag(A, B, C);

	return(ampli);
	}