Error using imag: too many input arguments

Hi, I get the given error when trying to plot the contour of the given function

syms r x y k z
[ph,r] = meshgrid((0:5:360)*pi/180,0:.5:10);
[X,Y] = pol2cart(ph,r);
Z = X+i*Y;
J = besselj(k,l.*r);
J2 = besselj(k,m.*r);
Y = bessely(k,l.*r);
Y2 = bessely(k,m.*r);
H = besselh(k,r);
F1 = symsum((J).*exp(1i*k*ph),k,-5,5);
F2 = symsum((J2+Y2).*exp(1i.*k.*ph),k,-5,5);
F3 = symsum(H.*exp(1i.*k.*ph),k,-5,5);
pwu = nan(size(F1), 'like', F1);
mask = 0 <= r & r < 0.5;
pwu(mask) = F1(mask);
mask = 0.5 <= r & r < 1;
pwu(mask) = F2(mask);
mask = r >= 1;
pwu(mask) = F3(mask);
U = subs(pwu, {l, m}, {1.5, 3});hold on
contour(X,Y,imag(double(U),30))
axis equal
xlabel('r','FontSize',14);
ylabel('phi','FontSize',14);

The error lies in the 4th last line, however it appears to me as OK. What is wrong here?

thanks!

Answer 1

[Walter Roberson]

Count the bracket level!

contour(X,Y,imag(double(U),30))
       1        2      3 2   10

Notice that the ,30 is at nesting level 2 -- inside the imag() call.

[Sergio Manzetti]

Ah got it!!

[Sergio Manzetti]

Hi Walter, I did the correction, and got the new code:

syms r x y k z
[ph,r] = meshgrid((0:5:360)*pi/180,0:.5:10);
[X,Y] = pol2cart(ph,r);
Z = X+i*Y;
J = besselj(k,l.*r);
J2 = besselj(k,m.*r);
Y = bessely(k,l.*r);
Y2 = bessely(k,m.*r);
H = besselh(k,r);
F1 = symsum((J).*exp(1i*k*ph),k,-5,5);
F2 = symsum((J2+Y2).*exp(1i.*k.*ph),k,-5,5);
F3 = symsum(H.*exp(1i.*k.*ph),k,-5,5);
pwu = nan(size(F1), 'like', F1);
mask = 0 <= r & r < 0.5;
pwu(mask) = F1(mask);
mask = 0.5 <= r & r < 1;
pwu(mask) = F2(mask);
mask = r >= 1;
pwu(mask) = F3(mask);
U = subs(pwu, {l, m}, {1.5, 3});hold on
contour(X,Y,imag(double(U)),30)
axis equal
xlabel('r','FontSize',14);
ylabel('phi','FontSize',14);

but then I get a new error. "Input argumnets of contour must be numeric"

[Walter Roberson]

[ph,r] = meshgrid((0:5:360)*pi/180,0:.5:10);
[X,Y] = pol2cart(ph,r);

X and Y are numeric.

Y = bessely(k,l.*r);

but now Y is overwritten with something symbolic.

You need to refer back to the code I posted for you within the last couple of days, as I was careful in the code to avoid this problem.

[Sergio Manzetti]

Hi Walter, thanks. The code is precisely as you wrote it, but your code was for surface not for level curves. I just copied and pasted your code, and used it with the last three lines of contour instead.

This is your original surface code:

syms k l m
% l=zeta1, m=zeta2
[ph, r] = meshgrid((0:5:360)*pi/180,[0:.05:0.5, 1:.5:10]);
[x, y] = pol2cart(ph,r);
Z = x + 1i*y;
J = besselj(k,l.*r);
J2 = besselj(k,m.*r);
Y = bessely(k,l.*r);
Y2 = bessely(k,m.*r);
H = besselh(k,r);
F1 = symsum((J).*exp(1i*k*ph),k,-5,5);
F2 = symsum((J2+Y2).*exp(1i.*k.*ph),k,-5,5);
F3 = symsum(H.*exp(1i.*k.*ph),k,-5,5);
pwu = nan(size(F1), 'like', F1);
mask = 0 <= r & r < 0.5;
pwu(mask) = F1(mask);
mask = 0.5 <= r & r < 1;
pwu(mask) = F2(mask);
mask = r >= 1;
pwu(mask) = F3(mask);
U = subs(pwu, {l, m}, {1.5, 3});
surf(x, y, real(double(U)))
hold on
surf(x, y, zeros(size(x)))
hold off

[Sergio Manzetti]

Here is your code:

syms k l m
% l=zeta1, m=zeta2
[ph, r] = meshgrid((0:5:360)*pi/180,[0:.05:0.5, 1:.5:10]);
[x, y] = pol2cart(ph,r);
Z = x + 1i*y;
J = besselj(k,l.*r);
J2 = besselj(k,m.*r);
Y = bessely(k,l.*r);
Y2 = bessely(k,m.*r);
H = besselh(k,r);
F1 = symsum((J).*exp(1i*k*ph),k,-5,5);
F2 = symsum((J2+Y2).*exp(1i.*k.*ph),k,-5,5);
F3 = symsum(H.*exp(1i.*k.*ph),k,-5,5);
pwu = nan(size(F1), 'like', F1);
mask = 0 <= r & r < 0.5;
pwu(mask) = F1(mask);
mask = 0.5 <= r & r < 1;
pwu(mask) = F2(mask);
mask = r >= 1;
pwu(mask) = F3(mask);
U = subs(pwu, {l, m}, {1.5, 3});
surf(x, y, real(double(U)))
hold on
surf(x, y, zeros(size(x)))
hold off

[Walter Roberson]

My code had

[x, y] = pol2cart(ph,r);
Z = x + 1i*y;

Your code has

[X,Y] = pol2cart(ph,r);
Z = X+i*Y;

Notice y compared to Y . This is important because you have

Y = bessely(k,l.*r);

which assigns a symbolic result to Y, and then later when you want to

contour(X,Y,imag(double(U)),30)

then you are using the symbolic Y, not the numeric Y.

You should have just taken my code and changed

surf(x, y, real(double(U)))
hold on
surf(x, y, zeros(size(x)))
hold off

to

contour(x, y, imag(double(U)), 30);

[Sergio Manzetti]

Thanks Water. I will do this immediately!