mxnet.np.arctan2

arctan2(x1, x2, out=None, **kwargs)

Element-wise arc tangent of x1/x2 choosing the quadrant correctly.

The quadrant (i.e., branch) is chosen so that atan2(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.

>>>np.atan2 is np.arctan2 True

Parameters

  • x1 (ndarray or scalar) – y-coordinates.

  • x2 (ndarray or scalar) – x-coordinates. x2 must be broadcastable to match the shape of x1 or vice versa.

  • out (ndarray or None, optional) – A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned.

Returns

  • out (ndarray or scalar) – Array of angles in radians, in the range [-pi, pi]. This is a scalar if x1 and x2 are scalars.

  • .. notes:: – atan2 is a alias for arctan2. It is a standard API in https://data-apis.org/array-api/latest/API_specification/generated/signatures.elementwise_functions.atan2.html instead of an official NumPy operator.

    atan2 is identical to the atan2 function of the underlying C library. The following special values are defined in the C standard: 1

    +========+========+==================+ | x1 | x2 | atan2(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.

    This function differs from the original numpy.arange in the following aspects:

    • Only support float16, float32 and float64.

References

1

ISO/IEC standard 9899:1999, “Programming language C.”

Examples

Consider four points in different quadrants:

>>> x = np.array([-1, +1, +1, -1])
>>> y = np.array([-1, -1, +1, +1])
>>> np.atan2(y, x) * 180 / np.pi
array([-135.,  -45.,   45.,  135.])

Note the order of the parameters. atan2 is defined also when x2 = 0 and at several other special points, obtaining values in the range [-pi, pi]:

>>> x = np.array([1, -1])
>>> y = np.array([0, 0])
>>> np.atan2(x, y)
array([ 1.5707964, -1.5707964])