numpy.arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <ufunc 'arctan2'>
Elementwise arc tangent of x1/x2
choosing the quadrant correctly.
The quadrant (i.e., branch) is chosen so that arctan2(x1, x2)
is the signed angle in radians between the ray ending at the origin and passing through the point (1,0), and the ray ending at the origin and passing through the point (x2
, x1
). (Note the role reversal: the “y
coordinate” is the first function parameter, the “x
coordinate” is the second.) By IEEE convention, this function is defined for x2
= +/0 and for either or both of x1
and x2
= +/inf (see Notes for specific values).
This function is not defined for complexvalued arguments; for the socalled argument of complex values, use angle
.
Parameters: 


Returns: 

arctan2 is identical to the atan2
function of the underlying C library. The following special values are defined in the C standard: [1]
x1  x2  arctan2(x1,x2) 

+/ 0  +0  +/ 0 
+/ 0  0  +/ pi 
> 0  +/inf  +0 / +pi 
< 0  +/inf  0 / pi 
+/inf  +inf  +/ (pi/4) 
+/inf  inf  +/ (3*pi/4) 
Note that +0 and 0 are distinct floating point numbers, as are +inf and inf.
[1]  ISO/IEC standard 9899:1999, “Programming language C.” 
Consider four points in different quadrants:
>>> x = np.array([1, +1, +1, 1]) >>> y = np.array([1, 1, +1, +1]) >>> np.arctan2(y, x) * 180 / np.pi array([135., 45., 45., 135.])
Note the order of the parameters. arctan2
is defined also when x2
= 0 and at several other special points, obtaining values in the range [pi, pi]
:
>>> np.arctan2([1., 1.], [0., 0.]) array([ 1.57079633, 1.57079633]) >>> np.arctan2([0., 0., np.inf], [+0., 0., np.inf]) array([ 0. , 3.14159265, 0.78539816])
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https://docs.scipy.org/doc/numpy1.17.0/reference/generated/numpy.arctan2.html