arccos function
(Shortest import: from brian2 import arccos)
- brian2.units.unitsafefunctions.arccos(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])
Trigonometric inverse cosine, element-wise.
The inverse of
cos()
so that, ify = cos(x)
, thenx = arccos(y)
.- Parameters:
x : array_like
x
-coordinate on the unit circle. For real arguments, the domain is [-1, 1].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:
angle : ndarray
The angle of the ray intersecting the unit circle at the given
x
-coordinate in radians [0, pi]. This is a scalar ifx
is a scalar.
Notes
arccos()
is a multivalued function: for eachx
there are infinitely many numbersz
such thatcos(z) = x
. The convention is to return the anglez
whose real part lies in[0, pi]
.For real-valued input data types,
arccos()
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,
arccos()
is a complex analytic function that has branch cuts[-inf, -1]
and[1, inf]
and is continuous from above on the former and from below on the latter.The inverse
cos()
is also known asacos
or cos^-1.References
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. https://personal.math.ubc.ca/~cbm/aands/page_79.htm
Examples
>>> import numpy as np
We expect the arccos of 1 to be 0, and of -1 to be pi:
>>> np.arccos([1, -1]) array([ 0. , 3.14159265])
Plot arccos:
>>> import matplotlib.pyplot as plt >>> x = np.linspace(-1, 1, num=100) >>> plt.plot(x, np.arccos(x)) >>> plt.axis('tight') >>> plt.show()