How to do summation and integration?
6 views (last 30 days)
Show older comments
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1369529/image.png)
clc;close all;clear all
syms r ph phi z
m=1
lam=532 *10^-9;
k=2*pi/lam;
omega=30;
w0=0.002;rho=1;p=1;R=0.06;
N=3
for h=-N:1:N
E1 = 1./(w0^2) + (1i*k)./(2*z);
Con11=(1i./(2.*lam.*z)).*exp((omega.^2./2 + r.^2 + omega)./E1).*exp((-1i.*k.*r.^2)./(2.*z)).*(pi./E1).*(1./(2.*1i.*sqrt(E1))).^m;
Con21=(1i./(2.*lam.*z)).*exp((omega.^2./2 + r.^2 + omega)./conj(E1)).*exp((-1i.*k.*r.^2)./(2.*z)).*(pi./conj(E1)).*(1./(2.*1i.*sqrt(conj(E1)))).^m;
for s=0:m
E01 = Con11.*((exp(-r.*(cos(ph)+sin(ph))).*hermiteH(s,1i*(omega./2 - r*cos(ph))./sqrt(E1)).*hermiteH(m-s,1i*(omega./2 - r*sin(ph))./sqrt(E1))) - (exp(r.*(cos(ph)+sin(ph))).*hermiteH(s,-1i*(omega./2 + r*cos(ph))./sqrt(E1)).*hermiteH(m-s,-1i*(omega./2 + r*sin(ph))./sqrt(E1))));
E0s1 = Con21.*((exp(-r.*(cos(phi)+sin(phi))).*hermiteH(s,1i*(omega./2 - r*cos(phi))./sqrt(conj(E1))).*hermiteH(m-s,1i*(omega./2 - r*sin(phi))./sqrt(conj(E1)))) - (exp(r.*(cos(phi)+sin(phi))).*hermiteH(s,-1i*(omega./2 + r.*cos(phi))./sqrt(conj(E1))).*hermiteH(m-s,-1i*(omega./2 + r*sin(phi))./sqrt(conj(E1)))));
Q = ((1i*p).^(m-s)).*nchoosek(m,s).*E01.*E0s1.*exp(-1i.*(h-m).*(ph-phi)).*exp((-2.^(5/6)).*(r.^(5/3)).*((1-cos(phi-ph)).^(5/6)).*(rho.^(-5/3)));
end
q = Q.*r;
fun = matlabFunction(q,'Vars',[ph,phi,r,z]);
z=linspace(0.01,10);
R = abs(arrayfun(@(z)integral3(@(ph,phi,r)fun(ph,phi,r,z),0,2*pi,0,2*pi,0,R),z));
end
R
0 Comments
Answers (1)
Walter Roberson
on 29 Apr 2023
Edited: Walter Roberson
on 29 Apr 2023
fun = matlabFunction(q,'Vars',[ph,phi,r,z]);
z=linspace(0.01,10);
That is within a loop. The first time sym z is in effect but immediately after you replace z with numeric z. The second time through z is no longer symbolic and so cannot be used in 'Vars'
0 Comments
See Also
Categories
Find more on Symbolic Math Toolbox in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!