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)
thenx = 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, theout
array will retain its original value. Note that if an uninitializedout
array is created via the defaultout=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 ifx
is a scalar.
See also
Notes
arctan()
is a multi-valued function: for eachx
there are infinitely many numbersz
such that tan(z
) =x
. The convention is to return the anglez
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 yieldsnan
and sets theinvalid
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()