Output of streamline in Matlab is empty - matlab

Question

I want to use streamline to show a vector field. The vector field is singular in a point. I want to remove regions near the singularity (fo example regions which their distance to singularity is less than 1). I wrote below code but it doesn't show anything. Could anyone help me?
clear all;
close all;
r1 = 1; r2 = 5; % Radii of your circles
x_0 = 0; y_0 = 0; % Centre of circles
[x,y] = meshgrid(x_0-r2:0.2:x_0+r2,y_0-r2:0.2:y_0+r2); % meshgrid of points
idx = ((x-x_0).^2 + (y-y_0).^2 > r1^2 & (x-x_0).^2 + (y-y_0).^2 < r2^2);
x = sort(x(idx));
[x, index] = unique(x);
y = sort(y(idx));
[y, index] = unique(y);
U=cos(x)/sqrt(x.^2+y.^2);
V=sin(x)/sqrt(x.^2+y.^2);
streamslice(x,y,U,V);

Answer 1

The problem with your code is that U and V are all zeros, so you get white space. The reason for that is that you don't use elementwise division with ./. So as a first step you should write:
U = cos(x)./sqrt(x.^2+y.^2);
V = sin(x)./sqrt(x.^2+y.^2);
Now U and V are not zeros but are also not matrices anymore, so they are not a valid input for streamslice. The reason for that is that x and y are converted to vectors when calling:
x = sort(x(idx));
y = sort(y(idx));
My guess is that you can remove all this indexing, and simply write:
r1 = 1; r2 = 5; % Radii of your circles
x_0 = 0; y_0 = 0; % Centre of circles
[x,y] = meshgrid(x_0-r2:0.2:x_0+r2,y_0-r2:0.2:y_0+r2); % meshgrid of points
U = cos(x)./sqrt(x.^2+y.^2);
V = sin(x)./sqrt(x.^2+y.^2);
streamslice(x,y,U,V);
so you get:

Answer 2

I think you misunderstood the concept of streamslice. Is this you expecting?
close all;
r1 = 1; r2 = 5; % Radii of your circles
x_0 = 0; y_0 = 0; % Centre of circles
[xx,yy] = meshgrid(x_0-r2:0.2:x_0+r2,y_0-r2:0.2:y_0+r2); % meshgrid of points
% idx = ((xx-x_0).^2 + (yy-y_0).^2 > r1^2 & (xx-x_0).^2 + (yy-y_0).^2 < r2^2);
% x = sort(xx(idx));
% [x, index] = unique(x);
% y = sort(yy(idx));
% [y, index] = unique(y);
U=cos(xx)./sqrt(xx.^2+yy.^2);
V=sin(xx)./sqrt(xx.^2+yy.^2);
streamslice(xx,yy,U,V);