How to do summation and integration?

Question

Athira T Das 2023-4-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1955004-how-to-do-summation-and-integration

编辑： Walter Roberson 2023-4-29

clc;close all;clear all
syms r ph phi z 
m=1 
m = 1
lam=532 *10^-9;
k=2*pi/lam;
omega=30;
w0=0.002;rho=1;p=1;R=0.06;
N=3
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
Error using sym/matlabFunction>checkVars
Variable names must be valid MATLAB variable names.

Error in sym/matlabFunction (line 158)
vars = checkVars(funvars,opts);
R

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Answer 1

Walter Roberson 2023-4-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1955004-how-to-do-summation-and-integration#answer_1225729

编辑：Walter Roberson 2023-4-29

在 MATLAB Online 中打开

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'