Weird behavior from Octave's atan2

Question

I'm trying to port some Octave code to Java. I'm trying out atan2 so I have the following tries

octave3.2:53> m1 = [1,2;3,4]
m1 =

   1   2
   3   4

octave3.2:54> m2=[5,6;7,8]
m2 =

   5   6
   7   8

octave3.2:55> atan2(m1,m2)
ans =

   0.19740   0.32175
   0.40489   0.46365

octave3.2:56> atan(1/5)
ans =  0.19740
octave3.2:57> atan(2/6)
ans =  0.32175
octave3.2:58> atan(3/7)
ans =  0.40489
octave3.2:59> atan(4/8)
ans =  0.46365

So it seems to me that atan2 applies atan cell-wise, to the quotient of the first argument divided by the second argument. I got this well in Java. However, the following piece of code gives off something weird...

y
x
theta = atan2(y,x) 

For which I get a trace something like,

y =

  -0.50000  -0.50000  -0.50000  -0.50000  -0.50000  -0.50000  -0.50000  -0.50000  -0.50000  -0.50000
  -0.40000  -0.40000  -0.40000  -0.40000  -0.40000  -0.40000  -0.40000  -0.40000  -0.40000  -0.40000
  -0.30000  -0.30000  -0.30000  -0.30000  -0.30000  -0.30000  -0.30000  -0.30000  -0.30000  -0.30000
  -0.20000  -0.20000  -0.20000  -0.20000  -0.20000  -0.20000  -0.20000  -0.20000  -0.20000  -0.20000
  -0.10000  -0.10000  -0.10000  -0.10000  -0.10000  -0.10000  -0.10000  -0.10000  -0.10000  -0.10000
   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000   0.00000
   0.10000   0.10000   0.10000   0.10000   0.10000   0.10000   0.10000   0.10000   0.10000   0.10000
   0.20000   0.20000   0.20000   0.20000   0.20000   0.20000   0.20000   0.20000   0.20000   0.20000
   0.30000   0.30000   0.30000   0.30000   0.30000   0.30000   0.30000   0.30000   0.30000   0.30000
   0.40000   0.40000   0.40000   0.40000   0.40000   0.40000   0.40000   0.40000   0.40000   0.40000

x =

  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000
  -0.50000  -0.40000  -0.30000  -0.20000  -0.10000   0.00000   0.10000   0.20000   0.30000   0.40000

theta =

  -2.35619  -2.24554  -2.11122  -1.95130  -1.76819  -1.57080  -1.37340  -1.19029  -1.03038  -0.89606
  -2.46685  -2.35619  -2.21430  -2.03444  -1.81577  -1.57080  -1.32582  -1.10715  -0.92730  -0.78540
  -2.60117  -2.49809  -2.35619  -2.15880  -1.89255  -1.57080  -1.24905  -0.98279  -0.78540  -0.64350
  -2.76109  -2.67795  -2.55359  -2.35619  -2.03444  -1.57080  -1.10715  -0.78540  -0.58800  -0.46365
  -2.94420  -2.89661  -2.81984  -2.67795  -2.35619  -1.57080  -0.78540  -0.46365  -0.32175  -0.24498
   3.14159   3.14159   3.14159   3.14159   3.14159   0.00000   0.00000   0.00000   0.00000   0.00000
   2.94420   2.89661   2.81984   2.67795   2.35619   1.57080   0.78540   0.46365   0.32175   0.24498
   2.76109   2.67795   2.55359   2.35619   2.03444   1.57080   1.10715   0.78540   0.58800   0.46365
   2.60117   2.49809   2.35619   2.15880   1.89255   1.57080   1.24905   0.98279   0.78540   0.64350
   2.46685   2.35619   2.21430   2.03444   1.81577   1.57080   1.32582   1.10715   0.92730   0.78540

What's with that? I think the first cell of theta should ~0.785398. The other cells seem wrong too. Is there anything I missed?

Answer 1

Found the answer on my own. atan2 isn't simply atan applied cell-wise. The sign of the operands matter as well.

For more info see: http://sunsite.univie.ac.at/textbooks/octave/octave_17.html

And then for how to implement atan2 by yourself (as I'm doing) see: http://en.wikipedia.org/wiki/Atan2

Answer 2

Atan2 is not quiet atan as it takes into account the quadrant.

see: http://en.wikipedia.org/wiki/Atan2

your first case is atan(x/y) - Pi