from brian2 import arctan)
arctan(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])¶
Trigonometric inverse tangent, element-wise.
The inverse of tan, so that if
y = tan(x)then
x = arctan(y).
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
outarray will be set to the ufunc result. Elsewhere, the
outarray will retain its original value. Note that if an uninitialized
outarray is created via the default
out=None, locations within it where the condition is False will remain uninitialized.
For other keyword-only arguments, see the ufunc docs.
out : ndarray or scalar
Out has the same shape as
x. Its real part is in
+/-pi/2). This is a scalar if
xis a scalar.
- The “four quadrant” arctan of the angle formed by (
y) and the positive
- Argument of complex values.
arctan()is a multi-valued function: for each
xthere are infinitely many numbers
zsuch that tan(
x. The convention is to return the angle
zwhose 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
nanand sets the
invalidfloating 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
Abramowitz, M. and Stegun, I. A., Handbook of Mathematical Functions, 10th printing, New York: Dover, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
We expect the arctan of 0 to be 0, and of 1 to be pi/4:
>>> np.arctan([0, 1]) array([ 0. , 0.78539816])
>>> np.pi/4 0.78539816339744828
>>> import matplotlib.pyplot as plt >>> x = np.linspace(-10, 10) >>> plt.plot(x, np.arctan(x)) >>> plt.axis('tight') >>> plt.show()