# numpy.arctan2

numpy.arctan2(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj]) = <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

      y-coordinates.

    x2 array_like, real-valued

      x-coordinates. If `x1.shape != x2.shape`, they must be broadcastable to a common shape (which becomes the shape of the output).

    out ndarray, None, or tuple of ndarray and 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. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.

    where array_like, optional

      This condition is broadcast over the input. At locations where the condition is True, the out array will be set to the ufunc result. Elsewhere, the out array will retain its original value. Note that if an uninitialized out array is created via the default `out=None`, locations within it where the condition is False will remain uninitialized.

    **kwargs

      For other keyword-only arguments, see the ufunc docs.

  Returns
    angle ndarray

      Array of angles in radians, in the range `[-pi, pi]`. This is a scalar if both x1 and x2 are scalars.

  See also

  `arctan`, `tan`, `angle`

  Notes

  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.

  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.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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