python numpy.where()如何工作?

问题:python numpy.where()如何工作?

我正在玩耍numpy并浏览文档,并且遇到了一些魔术。即我正在谈论numpy.where()

>>> x = np.arange(9.).reshape(3, 3)
>>> np.where( x > 5 )
(array([2, 2, 2]), array([0, 1, 2]))

它们如何在内部实现您能够将类似的东西传递x > 5给方法的功能?我想这与它有关,__gt__但是我正在寻找详细的解释。

I am playing with numpy and digging through documentation and I have come across some magic. Namely I am talking about numpy.where():

>>> x = np.arange(9.).reshape(3, 3)
>>> np.where( x > 5 )
(array([2, 2, 2]), array([0, 1, 2]))

How do they achieve internally that you are able to pass something like x > 5 into a method? I guess it has something to do with __gt__ but I am looking for a detailed explanation.


回答 0

他们如何在内部实现将x> 5之类的内容传递给方法的能力?

简短的答案是他们没有。

对numpy数组进行的任何逻辑运算都会返回布尔数组。(即__gt__,,__lt__等等都返回给定条件为true的布尔数组)。

例如

x = np.arange(9).reshape(3,3)
print x > 5

Yield:

array([[False, False, False],
       [False, False, False],
       [ True,  True,  True]], dtype=bool)

这就是为什么类似的东西if x > 5:如果x是一个numpy数组会引发ValueError的原因。它是True / False值的数组,而不是单个值。

此外,numpy数组可以由布尔数组索引。例如,在这种情况下,x[x>5]yields [6 7 8]

老实说,您实际需要的很少,numpy.where但它只返回布尔数组为的索引True。通常,您可以使用简单的布尔索引来完成所需的操作。

How do they achieve internally that you are able to pass something like x > 5 into a method?

The short answer is that they don’t.

Any sort of logical operation on a numpy array returns a boolean array. (i.e. __gt__, __lt__, etc all return boolean arrays where the given condition is true).

E.g.

x = np.arange(9).reshape(3,3)
print x > 5

yields:

array([[False, False, False],
       [False, False, False],
       [ True,  True,  True]], dtype=bool)

This is the same reason why something like if x > 5: raises a ValueError if x is a numpy array. It’s an array of True/False values, not a single value.

Furthermore, numpy arrays can be indexed by boolean arrays. E.g. x[x>5] yields [6 7 8], in this case.

Honestly, it’s fairly rare that you actually need numpy.where but it just returns the indicies where a boolean array is True. Usually you can do what you need with simple boolean indexing.


回答 1

旧答案, 这有点令人困惑。它为您提供了陈述正确的位置(所有位置)。

所以:

>>> a = np.arange(100)
>>> np.where(a > 30)
(array([31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
       48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64,
       65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
       82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
       99]),)
>>> np.where(a == 90)
(array([90]),)

a = a*40
>>> np.where(a > 1000)
(array([26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
       43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
       60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,
       77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,
       94, 95, 96, 97, 98, 99]),)
>>> a[25]
1000
>>> a[26]
1040

我将它用作list.index()的替代方法,但它还有许多其他用途。我从未将其用于2D阵列。

http://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html

新答案 似乎这个人在问一些更基本的问题。

问题是您如何实现允许功能(例如在哪里)知道所请求内容的东西。

首先请注意,调用任何比较运算符都会做一件有趣的事情。

a > 1000
array([False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True`,  True,  True,  True,  True,  True,  True,  True,  True,  True], dtype=bool)`

这是通过重载“ __gt__”方法来完成的。例如:

>>> class demo(object):
    def __gt__(self, item):
        print item


>>> a = demo()
>>> a > 4
4

如您所见,“ a> 4”是有效代码。

您可以在此处获得所有重载函数的完整列表和文档:http : //docs.python.org/reference/datamodel.html

令人难以置信的是,这样做非常简单。python中的所有操作都是以这种方式完成的。说a> b等于a。gt(b)!

Old Answer it is kind of confusing. It gives you the LOCATIONS (all of them) of where your statment is true.

so:

>>> a = np.arange(100)
>>> np.where(a > 30)
(array([31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47,
       48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64,
       65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81,
       82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98,
       99]),)
>>> np.where(a == 90)
(array([90]),)

a = a*40
>>> np.where(a > 1000)
(array([26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42,
       43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59,
       60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76,
       77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93,
       94, 95, 96, 97, 98, 99]),)
>>> a[25]
1000
>>> a[26]
1040

I use it as an alternative to list.index(), but it has many other uses as well. I have never used it with 2D arrays.

http://docs.scipy.org/doc/numpy/reference/generated/numpy.where.html

New Answer It seems that the person was asking something more fundamental.

The question was how could YOU implement something that allows a function (such as where) to know what was requested.

First note that calling any of the comparison operators do an interesting thing.

a > 1000
array([False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False, False,
       False, False, False, False, False, False, False, False,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True,  True,  True,  True,  True,  True,  True,  True,  True,
        True`,  True,  True,  True,  True,  True,  True,  True,  True,  True], dtype=bool)`

This is done by overloading the “__gt__” method. For instance:

>>> class demo(object):
    def __gt__(self, item):
        print item


>>> a = demo()
>>> a > 4
4

As you can see, “a > 4” was valid code.

You can get a full list and documentation of all overloaded functions here: http://docs.python.org/reference/datamodel.html

Something that is incredible is how simple it is to do this. ALL operations in python are done in such a way. Saying a > b is equivalent to a.gt(b)!


回答 2

np.where返回一个元组,其长度等于在其上被调用的numpy ndarray的维数(换句话说ndim),并且元组的每个项目都是一个初始ndarray中条件为True的所有值的索引的numpy ndarray。(请不要将尺寸与形状混淆)

例如:

x=np.arange(9).reshape(3,3)
print(x)
array([[0, 1, 2],
      [3, 4, 5],
      [6, 7, 8]])
y = np.where(x>4)
print(y)
array([1, 2, 2, 2], dtype=int64), array([2, 0, 1, 2], dtype=int64))


y是长度为2的元组,因为x.ndim为2。元组的第一项包含所有大于4的元素的行号,第二项包含所有大于4的元素的列号。如您所见,[1,2,2 ,2]对应于5,6,7,8的行号,[2,0,1,2]对应于5,6,7,8的列号注意,ndarray沿第一维(行方向)遍历)。

同样,

x=np.arange(27).reshape(3,3,3)
np.where(x>4)


将返回长度为3的元组,因为x具有3个维度。

但是,等等,np.where还有更多!

当两个附加参数被添加到np.where; 它将对上述元组获得的所有那些成对的行-列组合执行替换操作。

x=np.arange(9).reshape(3,3)
y = np.where(x>4, 1, 0)
print(y)
array([[0, 0, 0],
   [0, 0, 1],
   [1, 1, 1]])

np.where returns a tuple of length equal to the dimension of the numpy ndarray on which it is called (in other words ndim) and each item of tuple is a numpy ndarray of indices of all those values in the initial ndarray for which the condition is True. (Please don’t confuse dimension with shape)

For example:

x=np.arange(9).reshape(3,3)
print(x)
array([[0, 1, 2],
      [3, 4, 5],
      [6, 7, 8]])
y = np.where(x>4)
print(y)
array([1, 2, 2, 2], dtype=int64), array([2, 0, 1, 2], dtype=int64))


y is a tuple of length 2 because x.ndim is 2. The 1st item in tuple contains row numbers of all elements greater than 4 and the 2nd item contains column numbers of all items greater than 4. As you can see, [1,2,2,2] corresponds to row numbers of 5,6,7,8 and [2,0,1,2] corresponds to column numbers of 5,6,7,8 Note that the ndarray is traversed along first dimension(row-wise).

Similarly,

x=np.arange(27).reshape(3,3,3)
np.where(x>4)


will return a tuple of length 3 because x has 3 dimensions.

But wait, there’s more to np.where!

when two additional arguments are added to np.where; it will do a replace operation for all those pairwise row-column combinations which are obtained by the above tuple.

x=np.arange(9).reshape(3,3)
y = np.where(x>4, 1, 0)
print(y)
array([[0, 0, 0],
   [0, 0, 1],
   [1, 1, 1]])