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.
This question is related to
python
numpy
magic-methods
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)!
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]])
Source: Stackoverflow.com