problem with vpa and symsum
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Hi i make the fumtiom
function z= Escattheory(r,phi)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
syms kk
[f,N,Nc,a,ra,k0,Z0] = parameter();
E0=1;
Z1=k0.*r;
Z2=k0.*ra;
factor1=besselj(kk,Z2).*besselh(kk,2,Z1)./besselh(kk,2,Z2)
factor2=(-1j).^kk.*cos(kk.*phi)
factor=-E0.*factor1.*factor2.*en(kk);
%z=vpa(symsum(factor,k,0,inf),3)
f_all=symsum(factor,kk,0,300);
y=vpa(f_all,3)
end
when i call the function Escattheory(r,phi) with argument r=ra=1 and phi =0 the resultas is - 1.22 + 5.05e-5i
if i use the sum like this
function z= Escattheory_test(r,phi)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
Escattheory_test(r,phi)
function y=Escattheory_test(r,phi)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
[f,N,Nc,a,ra,k0,Z0] = parameter();
E0=1;
Z1=k0.*r;
Z2=k0.*ra;
kk=0:200
factor1=besselj(kk,Z2).*besselh(kk,2,Z1)./besselh(kk,2,Z2)
factor2=(-1j).^kk.*cos(kk.*phi)
factor=-E0.*factor1.*factor2.*e_n(kk);
%z=vpa(symsum(factor,k,0,inf),3)
y=sum(factor)
end
the reuslts is -1-j0 what happen ??
thank you
Accepted Answer
The numerical bessel functions are not able to compute your sum correctly (for higher values of k, they return NaN) (see below). That's the reason why you get different results.
r = 1;
phi = 0;
Escattheory(r,phi)
Escattheory_test(r,phi)
function z= Escattheory(r,phi)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
syms kk
[f,N,Nc,a,ra,k0,Z0] = parameter();
E0=1;
Z1=k0.*r;
Z2=k0.*ra;
factor1=besselj(kk,Z2).*besselh(kk,2,Z1)./besselh(kk,2,Z2);
factor2=(-1j).^kk.*cos(kk.*phi);
factor=-E0.*factor1.*factor2.*e_n(kk)
%z=vpa(symsum(factor,k,0,inf),3)
f_all=symsum(factor,kk,0,300);
z=vpa(f_all,3);
end
function y=Escattheory_test(r,phi)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
[f,N,Nc,a,ra,k0,Z0] = parameter();
E0=1;
Z1=k0.*r;
Z2=k0.*ra;
kk=0:300;
factor1=besselj(kk,Z2).*besselh(kk,2,Z1)./besselh(kk,2,Z2);
factor2=(-1j).^kk.*cos(kk.*phi);
factor=-E0.*factor1.*factor2.*en(kk)
%z=vpa(symsum(factor,k,0,inf),3)
y=sum(factor);
end
function [f,N,Nc,a,ra,k0,Z0] = parameter()
%UNTITLED Summary of this function goes here
c0=3e8;
Z0=120.*pi;
ra=1;
a=0.92;
N=30;
Nc=30;
f=300e6;
lambda=c0./f;
k0=2*pi./lambda;
end
function y=en(k)
if k==0
y=1;
else
y=2;
end
end
function y=e_n(k)
y = piecewise(k==0,1,k~=0,2);
end
13 Comments
george veropoulos
on 13 Nov 2024
Moved: Stephen23
on 19 Nov 2024
I don't know - I'd use the symbolic solution in this case:
f_all=symsum(factor,kk,0,Inf);
z=vpa(f_all);
george veropoulos
on 13 Nov 2024
Moved: Stephen23
on 19 Nov 2024
george veropoulos
on 13 Nov 2024
The reults -1 prodeuce from the for loop or sum not from the syssum
No.
r = 1;
phi = 0;
format long
Escattheory(r,phi)
function z= Escattheory(r,phi)
%UNTITLED Summary of this function goes here
% Detailed explanation goes here
syms kk
[f,N,Nc,a,ra,k0,Z0] = parameter();
E0=1;
Z1=k0.*r;
Z2=k0.*ra;
factor1=besselj(kk,Z2).*besselh(kk,2,Z1)./besselh(kk,2,Z2);
factor2=(-1j).^kk.*cos(kk.*phi);
factor=-E0.*factor1.*factor2.*e_n(kk);
%z=vpa(symsum(factor,k,0,inf),3)
f_all=symsum(factor,kk,0,Inf);
z=double(f_all);
end
function [f,N,Nc,a,ra,k0,Z0] = parameter()
%UNTITLED Summary of this function goes here
c0=3e8;
Z0=120.*pi;
ra=1;
a=0.92;
N=30;
Nc=30;
f=300e6;
lambda=c0./f;
k0=2*pi./lambda;
end
function y=e_n(k)
y = piecewise(k==0,1,k~=0,2);
end
george veropoulos
on 14 Nov 2024
Moved: Torsten
on 14 Nov 2024
george veropoulos
on 14 Nov 2024
Moved: Torsten
on 14 Nov 2024
With
function y=e_n(k)
if k==0
y=1;
else
y=2;
end
end
MATLAB evaluates the sum
-2*sum_{k=0}^{k=Inf}(-i)^k J_k(2*pi)
with
function y=e_n(k)
y = piecewise(k==0,1,k~=0,2);
end
MATLAB evaluates the sum
-J_0(2*pi) -2*sum_{k=1}^{k=Inf}(-i)^k J_k(2*pi)
I can't exactly explain why. Maybe if-statements for the coefficients of a symbolic sum can only be implemented using a symbolic function (piecewise in this case).
george veropoulos
on 14 Nov 2024
Moved: Torsten
on 14 Nov 2024
george veropoulos
on 14 Nov 2024
Moved: Torsten
on 14 Nov 2024
As said, I don't know precisely why "piecewise" works with the symbolic solution while your if-construct gives a wrong answer.
My guess is that your function "e_n" is called with a symbolic (unspecified) variable (kk) that is not identified as "0" (which would give 1 for y), but as "else" (which always gives 2 for y).
But you might want to contact MATLAB support for a definite answer:
george veropoulos
on 14 Nov 2024
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