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Changing the atan function so that it ranges from 0 to 2*pi

Asked by KA
on 12 Jun 2011
Latest activity Edited by Stephen Cobeldick on 27 Oct 2018
I know that the matlab atan function returns values in the range of -pi/2 to pi/2. How do i change it so that it goes over the full range 0 to 2*pi?
My first attempt was using a while loop, but it was incorrect.
I need to write a function mfile to set the built-in matlab function atan in the range of 0 to 2*pi without using atan2. im new to matlab so im unsure of what to do.
Thank you

  2 Comments

Although you don't want to use atan2, I thought I might just put this out there since atan2 returns a range between -pi to pi:
a = atan2(y, x);
a = a .* (a >= 0) + (a + 2 * pi) .* (a < 0);

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6 Answers

Answer by Paulo Silva
on 12 Jun 2011
 Accepted Answer

The Wikipedia got all explained, you just need to do the code, it's very simple.
function v=myatan(y,x)
if nargin==1 %just in case the user only gives the value of y myatan(y)
x=1;
end
v=nan;
if x>0
v=atan(y/x);
end
if y>=0 & x<0
v=pi+atan(y/x);
end
if y<0 & x<0
v=-pi+atan(y/x);
end
if y>0 & x==0
v=pi/2;
end
if y<0 & x==0
v=-pi/2;
end
if v<0
v=v+2*pi;
end
end

  1 Comment

thanks, very helpful

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Answer by Daniel Svedbrand on 14 Sep 2018

Adding mod 2*pi to atan2 should work just fine
shit = mod(atan2(y,x),2*pi);

  1 Comment

+1 simple and efficient. Someone sees the wood regardless of the trees!

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Answer by Walter Roberson
on 12 Jun 2011

Use atan2() instead.

  5 Comments

yes it is one of those "homework problems," and no Paulo did not do my homework, instead it helped me better understand how matlab works, and going through his code i noticed he was missing another if statement which is:
if y==0 && x==0
error('Invalid computation')
end
I also tried doing it a different way by using the derivation of atan2 on the wikipedia link he sent. So his answer actually helped me understand matlab, since it is my first time having to write a program in Matlab.
I didn't include that statement on purpose, when none of the others if statements are true the value of v is NaN, you could also do this:
if isnan(v)
error('Arguments must be different from zero')
end
ok, did not know that, thanks again

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Answer by Ali
on 9 Jan 2015

Hi all, I actually want to regenerate the results presented in figure 10 (part b) and figure 11 (part b) of this paper: http://wwwrel.ph.utexas.edu/Public/Students/liwj/papers/paper1.pdf Can you please help me for the case of 0 to 3*pi (or generally n*pi), namely for the n-fold complex plane? this figure might be also helpful to elucidate my question: http://upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Atan2Diagram.png/400px-Atan2Diagram.png Many thanks

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Answer by Kent Leung on 21 Mar 2018
Edited by Kent Leung on 21 Mar 2018

Better late than never. (Also posting as a future reference to myself.) The function below accepts y & x as vectors in Matlab. Rather than using 'if' statements, the below might be faster if there is some parallelization implemented in the built-in index searching.
Note: I have a slight disagreement with the above for the x>0 & y<0 case, as well as the for x=0 & y<0 case. The code below gives 0 to 2pi.
function v=myatan(y,x)
%---returns an angle in radians between 0 and 2*pi for atan
v=zeros(size(x));
v(x>0 & y>=0) = atan( y(x>0 & y>=0) ./ x(x>0 & y>=0) );
v(x>0 & y<0) = 2*pi+atan( y(x>0 & y<0) ./ x(x>0 & y<0) );
v(x<0 & y>=0) = pi+atan( y(x<0 & y>=0) ./ x(x<0 & y>=0) );
v(x<0 & y<0) = pi+atan( y(x<0 & y<0) ./ x(x<0 & y<0) );
v(x==0 & y>=0) = pi/2;
v(x==0 & y<0) = 3/2*pi;
end

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Answer by theodore panagos on 27 Oct 2018

You can use the formula:
atan(x,y)=pi-pi/2*(1+sgn(x))*(1-sgn(y^2))-pi/4*(2+sgn(x))*sgn(y) -sgn(x*y)*atan((abs(x)-abs(y))/(abs(x)+abs(y)))
x=x2-x1 and y=y2-y1

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