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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

更多回答（1 个）

Surya
Surya 2023-4-20
Hi,
The error message suggests that the size of the output of the integrand function does not match the input size. This usually happens when there is a mismatch between the dimensions of the output and the dimensions expected by the integration function.
In your code, the integrand function fun has two input arguments ph and phi, and its output IQ is a complex-valued array. However, the dimensions of IQ are not consistent with the expected dimensions by integral2 function.
To fix the error, you may need to reshape the output of the integrand function IQ to match the expected dimensions. For example, if you expect a scalar output, you can modify your code as follows:
fun = matlabFunction(IQ,'Vars',[ph,phi]);
result = integral2(@(x,y) reshape(fun(x,y),[],1), ph_min, ph_max, phi_min, phi_max);
Here, the integral2 function expects a scalar output, so we use the reshape function to convert the output of the fun function to a column vector. The [] argument in reshape infers the size of the second dimension based on the size of the input, while the 1 specifies the size of the first dimension as 1.
Hope it helps.

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