# arctan function

(Shortest import: `from brian2 import arctan)`

brian2.units.unitsafefunctions.arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])

  Trigonometric inverse tangent, element-wise.

  The inverse of tan, so that if `y = tan(x)` then `x = arctan(y)`.

  Parameters:

    x : array_like

    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:

    out : ndarray or scalar

    > Out has the same shape as `x`. Its real part is in `[-pi/2, pi/2]` (`arctan(+/-inf)` returns `+/-pi/2`). This is a scalar if `x` is a scalar.

  See also

  `arctan2`

    The “four quadrant” arctan of the angle formed by (`x`, `y`) and the positive `x`-axis.

  `angle`

    Argument of complex values.

  Notes

  `arctan()` is a multi-valued function: for each `x` there are infinitely many numbers `z` such that tan(`z`) = `x`. The convention is to return the angle `z` whose real part lies in [-pi/2, pi/2].

  For real-valued input data types, `arctan()` always returns real output. For each value that cannot be expressed as a real number or infinity, it yields `nan` and sets the `invalid` floating point error flag.

  For complex-valued input, `arctan()` is a complex analytic function that has [`1j, infj`] and [`-1j, -infj`] as branch cuts, and is continuous from the left on the former and from the right on the latter.

  The inverse tangent is also known as `atan` or tan^{-1}.

  References

  Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. https://personal.math.ubc.ca/~cbm/aands/page_79.htm

  Examples

  We expect the arctan of 0 to be 0, and of 1 to be pi/4:

      >>> import numpy as np
      >>> np.arctan([0, 1])
      array([ 0.        ,  0.78539816])

      >>> np.pi/4
      0.78539816339744828

  Plot arctan:

      >>> import matplotlib.pyplot as plt
      >>> x = np.linspace(-10, 10)
      >>> plt.plot(x, np.arctan(x))
      >>> plt.axis('tight')
      >>> plt.show()