Complex implicit function 2D plot

I am trying to plot a implicit function of the form

H2 = 100;
n2 = 2.0;
n1 = 1.47;
rho = 0;
m = 1;
fun = @(x,y) sqrt((2.*pi/x)^2.*n2^2-y^2).*H2-2.*atan( ((n2/n1)^(2.*rho)).*sqrt((y^2-n1^2.*(2.*pi/x)^2)/(n2^2.*(2.*pi/x)^2-y^2)) )-m.*pi;

I already tried

ezplot(fun, [300, 700, 0, 1]);

But it shows no plot and there is a warning

Warning: Function failed to evaluate on array inputs; vectorizing the function may speed up its 
evaluation and avoid the need to loop over array elements. 

Any help?

Thanks

[dpb]

Need the dot operators on the power and division terms in the function as well as the multiplication.

Try vectorize

[Jiacong Sun]

I have used dot operator .* in the function but it doesn't work :(

[Torsten]

x=300:40:700;
y=0:0.1:1;
fun(x,y)

Does it work and produce reasonable results ?

[Jiacong Sun]

I tried this:

x=300:40:700;
y=0:0.1:1;
fun(x,y) = sqrt((2.*pi/x)^2.*n2^2-y^2).*H2-2.*atan( ((n2/n1)^(2.*rho)).*sqrt((y^2-n1^2.*(2.*pi/x)^2)/(n2^2.*(2.*pi/x)^2-y^2)) )-m.*pi;
ezplot(fun,[300,700,0,1]);

It shows error:

Error using  / 
Matrix dimensions must agree.

:(

[Walter Roberson]

Earlier, dbp said,

Need the dot operators on the power and division terms in the function as well as the multiplication.

fun(x,y) = sqrt((2.*pi/x)^2.*n2^2-y^2).*H2-2.*atan( ((n2/n1)^(2.*rho)).*sqrt((y^2-n1^2.*(2.*pi/x)^2)/(n2^2.*(2.*pi/x)^2-y^2)) )-m.*pi;

is not using the dot operators for the power and division terms.

Also, you need to change to something that would look more like

fun = @(x,y) sqrt((2.*pi/x)^2.*n2^2-y^2).*H2-2.*atan( ((n2/n1)^(2.*rho)).*sqrt((y^2-n1^2.*(2.*pi/x)^2)/(n2^2.*(2.*pi/x)^2-y^2)) )-m.*pi;

if you want to use ezplot. ezplot must be passed a function handle.

[Jiacong Sun]

Hi, I changed the code to:

x=300:40:700;
y=0:0.1:1;
fun = @(x,y) sqrt((2.*pi/x)^2.*n2^2-y^2).*H2-2.*atan( ((n2/n1)^(2.*rho)).*sqrt((y^2-n1^2.*(2.*pi/x)^2)/(n2^2.*(2.*pi/x)^2-y^2)) )-m.*pi;
ezplot(fun,[300,700,0,1]);

It shows:

Warning: Function failed to evaluate on array inputs; vectorizing the function may speed up its
evaluation and avoid the need to loop over array elements. 

And there is no output.

I think the 'y' is too small and the software cannot solve it. Do you have any possible solution?

[Walter Roberson]

fun = @(x,y) sqrt((2.*pi./x).^2.*n2.^2-y.^2).*H2-2.*atan( ((n2./n1).^(2.*rho)).*sqrt((y.^2-n1.^2.*(2.*pi./x).^2)./(n2.^2.*(2.*pi./x).^2-y.^2)) )-m.*pi;
fsurf(fun,[300,700,0,0.045]);

The surface is mostly complex-valued. The imaginary portion is 0 for some Y values between about 0.0132 and 0.045. If you do not constrain the plot, you will see almost nothing.

[Jiacong Sun]

It seems 'fsurf' is a good way to check the function. I will set some constrain to it. Thank you a lot.