maxframe.tensor.arccos

maxframe.tensor.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).

Parameters:

• 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.

• **kwargs

Returns:

angle – 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.

Return type:

Tensor

See also

cos, arctan, arcsin

Notes

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 nan and 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.

References

M. Abramowitz and I.A. Stegun, “Handbook of Mathematical Functions”, 10th printing, 1964, pp. 79. http://www.math.sfu.ca/~cbm/aands/

Examples

We expect the arccos of 1 to be 0, and of -1 to be pi: >>> import maxframe.tensor as mt

>>> mt.arccos([1, -1]).execute()
array([ 0.        ,  3.14159265])

Plot arccos:

>>> 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()