In numpy, what does selection by [:,None] do?
Question:
I’m taking the Udacity course on deep learning and I came across the following code:
def reformat(dataset, labels):
dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
# Map 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]
labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
return dataset, labels
What does labels[:,None]
actually do here?
Answers:
http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html
numpy.newaxis
The newaxis object can be used in all slicing operations to create an axis of length one. :const: newaxis is an alias for ‘None’, and ‘None’ can be used in place of this with the same result.
http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.expand_dims.html
Demonstrating with part of your code
In [154]: labels=np.array([1,3,5])
In [155]: labels[:,None]
Out[155]:
array([[1],
[3],
[5]])
In [157]: np.arange(8)==labels[:,None]
Out[157]:
array([[False, True, False, False, False, False, False, False],
[False, False, False, True, False, False, False, False],
[False, False, False, False, False, True, False, False]], dtype=bool)
In [158]: (np.arange(8)==labels[:,None]).astype(int)
Out[158]:
array([[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0]])
None
is an alias for NP.newaxis. It creates an axis with length 1. This can be useful for matrix multiplcation etc.
>>>> import numpy as NP
>>>> a = NP.arange(1,5)
>>>> print a
[1 2 3 4]
>>>> print a.shape
(4,)
>>>> print a[:,None].shape
(4, 1)
>>>> print a[:,None]
[[1]
[2]
[3]
[4]]
I came here after having the exact same problem doing the same Udacity course. What I wanted to do is transpose the one dimensional numpy series/array which does not work with numpy.transpose([1, 2, 3]).
So I wanted to add you can transpose like this (source):
numpy.matrix([1, 2, 3]).T
It results in:
matrix([[1],
[2],
[3]])
which is pretty much identical (type is different) to:
x=np.array([1, 2, 3])
x[:,None]
But I think it’s easier to remember…
to explain it in plain english, it allows operations between two arrays of different number of dimensions.
It does this by adding a new, empty dimension which will automagically fit the size of the other array.
So basically if:
Array1 = shape[100]
and
Array2 = shape[10,100]
Array1 * Array2
will normally give an error.
Array1[:,None] * Array2
will work.
If you see code from experienced NumPy users, you will often see them use a special slicing syntax instead of calling reshape.
x = v[None, :]
or
x = v[:, None]
Those lines create a slice that looks at all of the items of v but asks NumPy to add a new dimension of size 1 for the associated axis.
(To clarify the answer by @GWW and the comment by @BlueRine S) While working with numpy arrays it is a good idea to clearly treat one dimensional arrays as row or column vectors. This has been pointed out by Andrew Ng also, to avoid bugs in the code.
>>> import numpy as NP
>>> a = NP.arange(1,5)
>>> a
array([1, 2, 3, 4])
>>> a.shape
(4,)
>>> a[:,None].shape
(4, 1)
>>> a[:,None]
array([[1],
[2],
[3],
[4]])
>>> a[None,:].shape
(1, 4)
>>> a[None,:]
array([[1, 2, 3, 4]])
>>> np.reshape(a, (1, -1))
array([[1, 2, 3, 4]])
>>> np.reshape(a, (-1, 1))
array([[1],
[2],
[3],
[4]])
I’m taking the Udacity course on deep learning and I came across the following code:
def reformat(dataset, labels):
dataset = dataset.reshape((-1, image_size * image_size)).astype(np.float32)
# Map 0 to [1.0, 0.0, 0.0 ...], 1 to [0.0, 1.0, 0.0 ...]
labels = (np.arange(num_labels) == labels[:,None]).astype(np.float32)
return dataset, labels
What does labels[:,None]
actually do here?
http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html
numpy.newaxis
The newaxis object can be used in all slicing operations to create an axis of length one. :const: newaxis is an alias for ‘None’, and ‘None’ can be used in place of this with the same result.
http://docs.scipy.org/doc/numpy-1.10.1/reference/generated/numpy.expand_dims.html
Demonstrating with part of your code
In [154]: labels=np.array([1,3,5])
In [155]: labels[:,None]
Out[155]:
array([[1],
[3],
[5]])
In [157]: np.arange(8)==labels[:,None]
Out[157]:
array([[False, True, False, False, False, False, False, False],
[False, False, False, True, False, False, False, False],
[False, False, False, False, False, True, False, False]], dtype=bool)
In [158]: (np.arange(8)==labels[:,None]).astype(int)
Out[158]:
array([[0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0]])
None
is an alias for NP.newaxis. It creates an axis with length 1. This can be useful for matrix multiplcation etc.
>>>> import numpy as NP
>>>> a = NP.arange(1,5)
>>>> print a
[1 2 3 4]
>>>> print a.shape
(4,)
>>>> print a[:,None].shape
(4, 1)
>>>> print a[:,None]
[[1]
[2]
[3]
[4]]
I came here after having the exact same problem doing the same Udacity course. What I wanted to do is transpose the one dimensional numpy series/array which does not work with numpy.transpose([1, 2, 3]).
So I wanted to add you can transpose like this (source):
numpy.matrix([1, 2, 3]).T
It results in:
matrix([[1],
[2],
[3]])
which is pretty much identical (type is different) to:
x=np.array([1, 2, 3])
x[:,None]
But I think it’s easier to remember…
to explain it in plain english, it allows operations between two arrays of different number of dimensions.
It does this by adding a new, empty dimension which will automagically fit the size of the other array.
So basically if:
Array1 = shape[100]
and
Array2 = shape[10,100]
Array1 * Array2
will normally give an error.
Array1[:,None] * Array2
will work.
If you see code from experienced NumPy users, you will often see them use a special slicing syntax instead of calling reshape.
x = v[None, :]
or
x = v[:, None]
Those lines create a slice that looks at all of the items of v but asks NumPy to add a new dimension of size 1 for the associated axis.
(To clarify the answer by @GWW and the comment by @BlueRine S) While working with numpy arrays it is a good idea to clearly treat one dimensional arrays as row or column vectors. This has been pointed out by Andrew Ng also, to avoid bugs in the code.
>>> import numpy as NP
>>> a = NP.arange(1,5)
>>> a
array([1, 2, 3, 4])
>>> a.shape
(4,)
>>> a[:,None].shape
(4, 1)
>>> a[:,None]
array([[1],
[2],
[3],
[4]])
>>> a[None,:].shape
(1, 4)
>>> a[None,:]
array([[1, 2, 3, 4]])
>>> np.reshape(a, (1, -1))
array([[1, 2, 3, 4]])
>>> np.reshape(a, (-1, 1))
array([[1],
[2],
[3],
[4]])