How to Rotate the Ellipses at calculated angle?

I am using the code as given below to calculate the ellipses and rotate by an angle. But it is not rotated at given angle. Can anyone please help me to resolve this issue?

%cov is 2x2 covariance matrix that is generated through a long process
t = 0:0:2*pi; %time axis
%Xest is center of ellipse and contain values of x and Y

%cov = 2x2 matrix
lambda = eig(cov);
	 [S, D] = eig(cov);
	 scale = 2.447;  %for 95% confidense ellipse from sigma1
	 [a, a_i] = max(lambda); %find maximum eigenvalue
	 [b, b_i] = min(lambda); %find minimum eigenvalue
	 a = scale*sqrt(a); %scale according to confidence interval
	 b = scale*sqrt(b);
	 
	 if cov(1,1) > cov(2,2) %resolve tilt of the ellipse
        theta = atan2(S(2,a_i),S(1,a_i))
         x_axis = a
        y_axis= b
     else
        theta = atan2(S(2,b_i),S(1,b_i))
        x_axis = b
        y_axis = a
     end
     
     x = Xest(1) + x_axis*cos(t)*cos(theta) - y_axis*sin(t)*sin(theta);
     y = Xest(2) + x_axis*cos(t)*sin(theta) + y_axis*sin(t)*cos(theta);
     r = patch(x,y,'b');

[the cyclist]

What do you suggest we use for these values that are not specified in your code?

• cov
• t
• Xest

Tried

• cov = rand(2)
• t = pi/4
• Xest = [0; 0]

but all I got was a single value for x and y, so I am not sure where your ellipse comes from.

[Muhammad khan]

%cov is 2x2 covariance matrix that is generated through a long process
t = 0:0:2*pi; %time axis
%Xest is center of ellipse and contain values of x and Y
when we use the above mention paramters in a loop then we get different values of ellipses
with angle. Angle is calculated correctly but can't able to move exactly. can you help in this
regards?

[the cyclist]

That is helpful info.

But can you please give an example value of cov (maybe upload it in a MAT file), so that we can see the output that you see? (For me, some values of cov result in values of x and y that are imaginary, so only a straight line is plotted. For others, I see a tilted ellipse. I can tell if that is a problem with your code, or with what I am choosing as an input.)

Then, tell us what the problem is with your output, and what you expected instead. It's hard to help if we don't understand what the problem is better.

[Muhammad khan]

The result got from the above file is given below and same question why it is not rotated with the given angle?

[the cyclist]

The code you have posted does not produce that figure. The code you posted creates a single ellipse. What that ellipse looks like depends on the value of cov, which have not reported to us.

Also, in the code provide, it seems that the ellipse is always at least approximately along the line x==y, where in the figure above the ellipse is always along the vertical.

Therefore we cannot guess why your code is not doing what expect. You simply have not given us all the information.

[Muhammad khan]

cov = 14.7813169401575 18.14084502625

18.140845026252 33.2623639805209

the above covariance matrix is used in first iteration and the same code is used to produce the ellipses in the loop. Tthe result is same as shown in figure attached above.

[Image Analyst]

Your code gives this:

Error using cov (line 46)
Not enough input arguments.
Error in test (line 6)
lambda = eig(cov); 

[Muhammad khan]

if you use the covariance matrix i posted earlier you definetly get some results.

Answer 1

[Rafael Hernandez-Walls]

%cov is 2x2 covariance matrix that is generated through a long process
t = 0:0.1:2*pi; %time axis
%Xest is center of ellipse and contain values of x and Y
cov=[14.7813169401575                 18.14084502625
           18.140845026252            33.2623639805209];
       Xest=[0 0];
%cov = 2x2 matrix
lambda = eig(cov);
	 [S, D] = eig(cov);
	 scale = 2.447;  %for 95% confidense ellipse from sigma1
	 [a, a_i] = max(lambda); %find maximum eigenvalue
	 [b, b_i] = min(lambda); %find minimum eigenvalue
	 a = scale*sqrt(a); %scale according to confidence interval
	 b = scale*sqrt(b);
	 
	 if cov(1,1) > cov(2,2) %resolve tilt of the ellipse
        theta = atan2(S(2,a_i),S(1,a_i))
         x_axis = a
        y_axis= b
     else
        theta = atan2(S(2,b_i),S(1,b_i))
        x_axis = b
        y_axis = a
     end
     
     x = Xest(1) + x_axis*cos(t)*cos(theta) - y_axis*sin(t)*sin(theta);
     y = Xest(2) + x_axis*cos(t)*sin(theta) + y_axis*sin(t)*cos(theta);
     r = patch(x,y,'b');

[the cyclist]

OK, so this "answer" is just a recopying of OP's code, with the value of cov plugged in. Progress?

The following is the figure it produces. We continue to need more information from OP, about what the problem is. This ellipse looks nothing like the figure OP posted, so I find it impossible to give advice.

[Muhammad khan]

Ok i resolved it by myself. Thanks for all the comments and effort everyone did.