numpy.arctan2(x1, x2[, out]) = <ufunc 'arctan2'>

Element-wise 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 complex-valued arguments; for the so-called argument of complex values, use angle.

Parameters :

x1 : array_like, real-valued


x2 : array_like, real-valued

x-coordinates. x2 must be broadcastable to match the shape of x1 or vice versa.

Returns :

angle : ndarray

Array of angles in radians, in the range [-pi, pi].

See also

arctan, tan, angle


arctan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: [R6]

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.


[R6](1, 2) 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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