Trigonometric inverse tangent, element-wise.
The inverse of tan, so that if y = tan(x) then x = arctan(y).
x : array_like
out : ndarray
arctan is a multivalued 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 analytical function that has branch cuts [1j, infj] and [-1j, -infj] 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.
|||M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/|
|||Wikipedia, “Inverse trigonometric function”, http://en.wikipedia.org/wiki/Arctan|
We expect the arctan of 0 to be 0, and of 1 to be :
>>> 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()