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formeli.c
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Fri, Jan 3, 23:11

formeli.c
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#include<stdio.h>
#include<math.h>
#include<fonction.h>
#include<constant.h>
#include<dimension.h>
#include<structure.h>
/****************************************************************/
/* nom: formeli */
/* auteur: Jean-Paul Kneib */
/* date: 10/02/92 */
/* place: Toulouse */
/*****************************************************************
* Diagonalisation d'une matrice de forme ou de deformation
* Matrice de forme : M= | a b |
* | b c |
* lambda et mu : racines de det(M - XI)=0
*
* Return the diagonalized form of the input matrice M. Theta is the
* shear orientation, a and b are the proper magnification axis.
*
* If :
* 1) a = 1 - [g2].a = 1 - DLS/DS * d2phixx
* 2) c = 1 - [g2].c = 1 - DLS/DS * d2phiyy
* 3) b = - [g2].b = - DLS/DS * d2phixy
* then :
* with gamma = DLS/DS * SQRT ( 0.25 * (d2Phiyy - d2Phixx)^2 + (d2Phixy)^2 )
* with k = 0.5 * DLS/DS * ( d2Phixx + d2Phiyy ) (cf phd_JPK eq 2.55)
*
* delta = (a-c)^2+4b^2
* = [ DLS/DS * (d2Phiyy - d2Phixx) ]^2 + 4*[ DLS/DS * d2Phixy ]^2
* = 4*gamma^2 (cf phd_JPK eq 2.56)
*
* lambda = 0.5*(a + c + SQRT(delta) )
* = .5*( 2 - DLS/DS * (d2Phixx + d2Phiyy) + 2*gamma)
* = ( 1 - k + gamma )
*
* mu = ( 1 - k - gamma )
*
* Global variables used :
* - none
*/
struct ellipse formeli(double a, double b, double c)
{
struct ellipse eli;
double e, delta, lambda, mu;
// eq carateristique : det(M-xI) = 0
delta = (a - c)*(a - c) + 4*b*b; // 4*gamma^2 (cf phd_JPK eq 2.56)
e = sqrt(delta); /*e is 2 * shear, ie 2*gamma*/
lambda = .5*(a + c + e); // 1 - k + gamma
mu = .5*(a + c - e); // 1 - k - gamma
eli.a = lambda;
eli.b = mu;
if (lambda != mu && fabs(b) > 1e-5)
eli.theta = atan2(lambda - a, b); // cf phd_JPK eq 2.58, and
// tan(theta)= ( -cos(2theta) +- 1 ) / sin(2theta)
// ADDED by EJ 29/11/2007
else if ( a >= c ) // ellipse aligned along the major axis of magnification
eli.theta = 0.;
else
eli.theta = PI / 2.; // ellipse aligned along the minor axis of magnification
return(eli);
}

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