如何创建一个与NumPy ufuncs兼容的类数组类？

Question

我正在尝试使用行为类似于NumPy数组的类来实现自动微分.它不是子类numpy.ndarray,但包含两个数组属性.一个用于值,一个用于雅可比矩阵.每个操作都被重载以对值和雅可比行为进行操作.但是,我无法使NumPy ufuncs(例如np.log)在我的自定义"数组"上工作.

我创建了以下最小示例,说明了该问题.Two应该是NumPy数组的辐射加固版本,它可以计算两次,并确保结果相同.

它必须是支持索引,元素对数和长度.就像平常一样ndarray.当使用调用时,元素对数工作正常x.cos(),但在调用时会执行意外操作np.cos(x).

from __future__ import print_function
import numpy as np

class Two(object):
    def __init__(self, val1, val2):
        print("init with", val1, val2)
        assert np.array_equal(val1, val2)
        self.val1 = val1
        self.val2 = val2

    def __getitem__(self, s):
        print("getitem", s, "got", Two(self.val1[s], self.val2[s]))
        return Two(self.val1[s], self.val2[s])

    def __repr__(self):
        return "<<{}, {}>>".format(self.val1, self.val2)

    def log(self):
        print("log", self)
        return Two(np.log(self.val1), np.log(self.val2))

    def __len__(self):
        print("len", self, "=", self.val1.shape[0])
        return self.val1.shape[0]

x = Two(np.array([1,2]).T, np.array([1,2]).T)

索引按预期返回两个属性中的相关元素:

>>> print("First element in x:", x[0], "\n")
init with [1 2] [1 2]
init with 1 1
getitem 0 got <<1, 1>>
init with 1 1
First element in x: <<1, 1>> 

使用时调用元素对数可以正常工作x.cos():

>>> print("--- x.log() ---", x.log(), "\n")
log <<[1 2], [1 2]>>
init with [ 0.  0.69314] [ 0.  0.69314]
--- x.log() --- <<[ 0.  0.69314], [ 0.   0.69314]>> 

但是,np.log(x)不能按预期工作.它意识到对象有一个长度,所以它提取每个项目并在每个项目上取对数,然后返回一个两个对象的数组(dtype = object).

>>> print("--- np.log(x) with len ---", np.log(x), "\n") # WTF
len <<[1 2], [1 2]>> = 2
len <<[1 2], [1 2]>> = 2
init with 1 1
getitem 0 got <<1, 1>>
init with 1 1
init with 2 2
getitem 1 got <<2, 2>>
init with 2 2
len <<[1 2], [1 2]>> = 2
len <<[1 2], [1 2]>> = 2
init with 1 1
getitem 0 got <<1, 1>>
init with 1 1
init with 2 2
getitem 1 got <<2, 2>>
init with 2 2
len <<[1 2], [1 2]>> = 2
len <<[1 2], [1 2]>> = 2
init with 1 1
getitem 0 got <<1, 1>>
init with 1 1
init with 2 2
getitem 1 got <<2, 2>>
init with 2 2
log <<1, 1>>
init with 0.0 0.0
log <<2, 2>>
init with 0.693147 0.693147
--- np.log(x) with len --- [<<0.0, 0.0>> <<0.693147, 0.693147>>]

如果Two没有长度方法,它可以正常工作:

>>> del Two.__len__
>>> print("--- np.log(x) without len ---", np.log(x), "\n")
log <<[1 2], [1 2]>>
init with [ 0.          0.69314718] [ 0.   0.693147]
--- np.log(x) without len --- <<[ 0.   0.693147], [ 0.          0.693147]>>

如何创建满足要求的类(getitem,log,len)？我研究了子类化ndarray,但这似乎比它的价值更复杂.

另外,我找不到NumPy源代码中 x.__len__访问的位置,所以我也对此感兴趣.

编辑:我正在使用miniconda2与Python 2.7.11和NumPy 1.11.0.