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

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KA
KA 2011-6-12
评论： DGM 2024-10-17
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 个评论
wenjun kou
wenjun kou 2017-3-8
编辑：wenjun kou 2017-3-8
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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Daniel Svedbrand
Daniel Svedbrand 2018-9-14
编辑：John D'Errico 2023-8-3
Adding mod 2*pi to atan2 should work just fine
z = mod(atan2(y,x),2*pi);
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Feruza Amirkulova
Feruza Amirkulova 2023-8-3
Yes, mod(atan2(y,x),2*pi) worked and its gradients are the same as for (atan2(y,x)).

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更多回答（5 个）

Walter Roberson
Walter Roberson 2011-6-12
Use atan2() instead.
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Paulo Silva
Paulo Silva 2011-6-12
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

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Paulo Silva
Paulo Silva 2011-6-12
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
  2 个评论
Mehmet Can Türk
Mehmet Can Türk 2022-4-9
编辑：Mehmet Can Türk 2022-4-9
I checked the Wikipedia link and tested the code. First of all, thank you so much for the contribution.
I wanted to convert atan2 function from Matlab into another environment which supports only atan function. So I deleted the if block and everything worked perfectly.

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theodore panagos
theodore panagos 2018-10-27
编辑：DGM 2024-10-17
You can use the formula:
x = x2-x1;
y = y2-y1;
th = pi/2*(1-sign(x))*(1-sign(y^2)) + pi/4*(2-sign(x))*sign(y) - sign(x*y)*atan((abs(x)-abs(y))/(abs(x)+abs(y)));
  1 个评论
DGM
DGM 2024-10-17
Ran in:
To demonstrate for nonscalar inputs:
% fake xy data
x = randn(10,1);
y = randn(10,1);
% the reference
th0 = atan2(y,x);
% the given implementation
th = pi/2*(1 - sign(x)).*(1 - sign(y.^2)) ...
+ pi/4*(2 - sign(x)).*sign(y) ...
- sign(x.*y).*atan((abs(x)-abs(y))./(abs(x)+abs(y)));
% compare
immse(th0,th)
ans = 1.5484e-32

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Kent Leung
Kent Leung 2018-3-21
编辑：Kent Leung 2018-3-21
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
Ali Ali
Ali Ali 2024-6-7
编辑：Ali Ali 2024-6-7
If you want to use atan2(y,x) (atan2(Y,X), returns values in the closed interval [-pi,pi]), considering that atan(b)=atan(b+pi), you can use this equation (use atan2(Y,X) instead of atan(y/x) in this equation) for your work.
  2 个评论
DGM
DGM 2024-6-7
Ran in:
what?
atan(b) ~= atan(b+pi)
atan(b) ~= atan(b)+pi
atan2(y,x) ~= atan2(y,x)+pi
The angle between the x-axis and a unit vector along x is 0 degrees, not 90 degrees.
atan2d(0,1) + 90 % NO
ans = 90
mod(atan2d(0,1),360) % YES
ans = 0
Stephen23
Stephen23 2024-6-8
Ran in:
" atan(b)=atan(b+pi) "
Lets check that right now:
b = linspace(-5,5,100);
X = atan(b);
Y = atan(b+pi);
plot(b(:),[X(:),Y(:)])
Nope, not the same. Not even close.

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