Error in double integration

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Athira T Das
Athira T Das 2023-4-18
编辑： Athira T Das 2023-4-25
Ran in:
I need to evaluate a double integration but showing some error
lam=532*10^-9;
z=100;
k=2*pi/lam;
omega=30;s=5;
r=linspace(0,100,100);
w0=0.002;m=1;rho=1;p=1;
E = 1./(w0^2) + (1i*k)./(2*z);
Con1=(1i./(2*lam*z))*exp((omega^2./2 + r.^2 + omega)./E).*exp((-1i.*k.*r.^2)./(2*z)).*(pi./E).*(1./(2*1i*sqrt(E)))^m;
Con2=(1i./(2*lam*z))*exp((omega^2./2 + r.^2 + omega)./conj(E)).*exp((-1i.*k.*r.^2)./(2*z)).*(pi./conj(E)).*(1./(2*1i*sqrt(conj(E)))).^m;
syms ph phi
for l=0:m
E0 = Con1.*((exp(-r.*(cos(ph)+sin(ph))).*hermiteH(l,1i*(omega./2 - r*cos(ph))./sqrt(E)).*hermiteH(m-l,1i*(omega./2 - r*sin(ph))./sqrt(E))) - (exp(r.*(cos(ph)+sin(ph))).*hermiteH(l,-1i*(omega./2 + r*cos(ph))./sqrt(E)).*hermiteH(m-l,-1i*(omega./2 + r*sin(ph))./sqrt(E))));
E0s = Con2.*((exp(-r.*(cos(phi)+sin(phi))).*hermiteH(l,1i*(omega./2 - r*cos(phi))./sqrt(conj(E))).*hermiteH(m-l,1i*(omega./2 - r*sin(phi))./sqrt(conj(E)))) - (exp(r.*(cos(phi)+sin(phi))).*hermiteH(l,-1i*(omega./2 + r.*cos(phi))./sqrt(conj(E))).*hermiteH(m-l,-1i*(omega./2 + r*sin(phi))./sqrt(conj(E)))));
I = ((1i*p).^(m-l)).*nchoosek(m,l).*E0.*E0s.*exp(-1i.*s.*(ph-phi)).*exp(((-2.*r.^2)-(2.*r.^2.*cos(phi-ph)))./(rho.^2));
end
IQ = I;
ph_min = 0;
ph_max = 2*pi;
phi_min = 0;
phi_max = 2*pi;
fun = matlabFunction(IQ,'Vars',[ph,phi]);
result = integral2(fun, ph_min, ph_max, phi_min, phi_max);
Error using integral2Calc>integral2t/tensor
Integrand output size does not match the input size.

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
[q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral2 (line 105)
Q = integral2Calc(fun,xmin,xmax,yminfun,ymaxfun,opstruct);

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采纳的回答

Torsten
Torsten 2023-4-22
编辑：Torsten 2023-4-22
Ran in:
syms r ph phi
lam=532*10^-9;
z=100;
k=2*pi/lam;
omega=30;
w0=0.002;m=1;rho=1;p=1;
E = 1./(w0^2) + (1i*k)./(2*z);
Con1=(1i./(2*lam*z))*exp((omega^2./2 + r.^2 + omega)./E).*exp((-1i.*k.*r.^2)./(2*z)).*(pi./E).*(1./(2*1i*sqrt(E)))^m;
Con2=(1i./(2*lam*z))*exp((omega^2./2 + r.^2 + omega)./conj(E)).*exp((-1i.*k.*r.^2)./(2*z)).*(pi./conj(E)).*(1./(2*1i*sqrt(conj(E)))).^m;
for l=0:m
E0 = Con1.*((exp(-r.*(cos(ph)+sin(ph))).*hermiteH(l,1i*(omega./2 - r*cos(ph))./sqrt(E)).*hermiteH(m-l,1i*(omega./2 - r*sin(ph))./sqrt(E))) - (exp(r.*(cos(ph)+sin(ph))).*hermiteH(l,-1i*(omega./2 + r*cos(ph))./sqrt(E)).*hermiteH(m-l,-1i*(omega./2 + r*sin(ph))./sqrt(E))));
E0s = Con2.*((exp(-r.*(cos(phi)+sin(phi))).*hermiteH(l,1i*(omega./2 - r*cos(phi))./sqrt(conj(E))).*hermiteH(m-l,1i*(omega./2 - r*sin(phi))./sqrt(conj(E)))) - (exp(r.*(cos(phi)+sin(phi))).*hermiteH(l,-1i*(omega./2 + r.*cos(phi))./sqrt(conj(E))).*hermiteH(m-l,-1i*(omega./2 + r*sin(phi))./sqrt(conj(E)))));
I = ((1i*p).^(m-l)).*nchoosek(m,l).*E0.*E0s.*exp(-1i.*l.*(ph-phi)).*exp(((-2.*r.^2)-(2.*r.^2.*cos(phi-ph)))./(rho.^2));
end
IQ = I;
ph_min = 0;
ph_max = 2*pi;
phi_min = 0;
phi_max = 2*pi;
fun = matlabFunction(IQ,'Vars',[ph,phi,r]);
r_array = linspace(0,10,100);
result = arrayfun(@(r)integral2(@(ph,phi)fun(ph,phi,r),ph_min, ph_max, phi_min, phi_max),r_array)
result =
Columns 1 through 10 -0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i Columns 11 through 20 -0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i Columns 21 through 30 -0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 - 0.0000i Columns 31 through 40 0.0000 + 0.0000i 0.0000 + 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i Columns 41 through 50 -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 - 0.0000i Columns 51 through 60 0.0000 - 0.0000i -0.0000 + 0.0000i -0.0001 + 0.0001i 0.0000 - 0.0001i -0.0001 - 0.0001i 0.0002 - 0.0001i -0.0002 - 0.0002i -0.0000 - 0.0003i -0.0001 + 0.0004i -0.0001 + 0.0005i Columns 61 through 70 -0.0003 - 0.0007i -0.0009 - 0.0001i 0.0003 - 0.0012i -0.0016 + 0.0002i -0.0017 - 0.0012i 0.0017 + 0.0021i 0.0027 + 0.0023i -0.0047 - 0.0003i -0.0032 + 0.0053i -0.0068 - 0.0043i Columns 71 through 80 -0.0013 + 0.0105i -0.0099 + 0.0098i 0.0154 - 0.0098i 0.0166 - 0.0174i -0.0018 + 0.0315i 0.0370 + 0.0187i -0.0221 + 0.0498i 0.0713 - 0.0064i 0.0819 + 0.0464i -0.0977 - 0.0761i Columns 81 through 90 -0.1530 - 0.0558i 0.1956 - 0.0875i -0.0220 - 0.2810i 0.3640 - 0.0717i -0.3396 - 0.3510i -0.1472 - 0.6259i 0.1278 + 0.8370i 0.5641 + 0.9619i -1.4387 - 0.2965i -0.8911 + 1.7179i Columns 91 through 100 -2.4397 - 0.7423i 1.1402 + 3.1615i -0.5514 + 4.3955i 0.7996 - 5.7850i -2.3376 - 7.3367i 9.5097 + 3.5597i 7.1866 -11.3004i 16.7884 + 5.4952i -8.9062 -21.5352i 0.3631 -30.7457i

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