#!/usr/bin/env python # -*- coding: utf-8 -*- # Copyright 1999-2020 Alibaba Group Holding Ltd. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. import numpy as np from ... import opcodes as OperandDef from ..utils import infer_dtype from .core import TensorUnaryOp from .utils import arithmetic_operand @arithmetic_operand(sparse_mode='unary') class TensorArccos(TensorUnaryOp): _op_type_ = OperandDef.ARCCOS _func_name = 'arccos' [docs]@infer_dtype(np.arccos) def 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 : 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. 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 mars.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() """ op = TensorArccos(**kwargs) return op(x, out=out, where=where)