AJO_1415_Ejemplo_propagación_nolineal

989 days ago by sevillad1415

valr = 10 vala = 80*pi/200 sigmar = 0.1 sigmaa = 1*pi/200 var('r,a') F(r,a) = ( r*sin(a), r*cos(a) ) (point(F(valr,vala),size=40,figsize=4,aspect_ratio=1)+point([0,0])).show() F(valr,vala) 
       

J = jacobian(F,(r,a))(valr,vala) Sigma_ra = diagonal_matrix([sigmar^2, sigmaa^2]) Sigma_xy = J * Sigma_ra * transpose(J) sigmax = (Sigma_xy[0,0]^0.5).n() sigmay = (Sigma_xy[1,1]^0.5).n() corrxy = (Sigma_xy[1,0]/sigmax/sigmay).n() sigmax; sigmay; corrxy 
       




e = [sqrt(w).n() for w in Sigma_xy.eigenvalues()] smax = max(e) smin = min(e) alfa = arctan(Sigma_xy[0,1]/(smax^2-Sigma_xy[0,0])) smax; smin; (alfa*200/pi).n() 
       




c = 2.447 punto = F(valr,vala) plot(ellipse(punto, smax, smin, pi/2-alfa,color="yellow"),figsize=6,aspect_ratio=1) + plot(ellipse(punto, c*smax, c*smin, pi/2-alfa),figsize=6,aspect_ratio=1) + point(punto) + point([0,0])