arccos(x, out=None, where=None, **kwargs)¶
Trigonometric inverse cosine, element-wise.
The inverse of cos so that, if
y = cos(x), then
x = arccos(y).
- x : array_like
- x-coordinate on the unit circle. For real arguments, the domain is [-1, 1].
- out : Tensor, None, or tuple of Tensor 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 tensor is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs.
- where : array_like, optional
- Values of True indicate to calculate the ufunc at that position, values of False indicate to leave the value in the output alone.
- angle : Tensor
- The angle of the ray intersecting the unit circle at the given x-coordinate in radians [0, pi]. If x is a scalar then a scalar is returned, otherwise an array of the same shape as x is returned.
cos, arctan, arcsin
arccos is a multivalued function: for each x there are infinitely many numbers z such that cos(z) = x. The convention is to return the angle z 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 yields
nanand sets the invalid 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 as acos or cos^-1.
M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/
We expect the arccos of 1 to be 0, and of -1 to be pi: >>> import mars.tensor as mt
>>> mt.arccos([1, -1]).execute() array([ 0. , 3.14159265])
>>> import matplotlib.pyplot as plt >>> x = mt.linspace(-1, 1, num=100) >>> plt.plot(x.execute(), mt.arccos(x).execute()) >>> plt.axis('tight') >>> plt.show()