Can someone explain what this Numpy array property is called? - python

The code that I have in place goes something as follows:
import numpy as np
z = np.array([
[1, 2],
[3]
])
x = np.array([
[4, 5]
])
print(np.multiply(x,z))
The output of this program creates a list of lists. This is different than the regular broadcasting rules that apply on arrays with equal dimensions. Is there a name for this property? Also why does it explicitly mention the word list in the output?
[[list([1, 2, 1, 2, 1, 2, 1, 2]) list([3, 3, 3, 3, 3])]]
[Finished in 0.244s]

This is just normal cell-by-cell multiplication. Because your z array is not a true matrix (it does not have a square shape), Numpy interprets it as a row of two objects:
>>> z
array([[1, 2], [3]], dtype=object)
>>> z.shape
(2,)
From here here you multiply normally - the first object is multiplied by 4, the second by 5:
>>> [1, 2]*4
[1, 2, 1, 2, 1, 2, 1, 2]
>>> [3]*5
[3, 3, 3, 3, 3]
just normal Python list multiplication - this is the result you get. Indeed, your result is not a "list of lists". It's an array of shape (1, 2) of dtype=object, so a row of two objects (which happen to be lists):
>>> np.multiply(x,z)
array([[[1, 2, 1, 2, 1, 2, 1, 2], [3, 3, 3, 3, 3]]], dtype=object)
>>> np.multiply(x,z).shape
(1, 2)

Related

applying a function to a numpy array not working as I expected

>>> ndarr = np.array([0, 1, 2])
>>> (lambda x: x + 1) (ndarr)
array([1, 2, 3])
I see that it replaces every element with the function applied to it.
but when I do this to a two dimensional array:
>>> ndarr = np.array([[0, 1, 2], [3, 4, 5]])
>>> (lambda x: x[0]) (ndarr)
array([0, 1, 2])
I thought this would take the two elements of the array which are [0, 1, 2] and [3, 4, 5], apply the lambda to them resulting in 0 and 3, and the result would be [0, 3]. but this applies the function to the whole array instead. why? and wat do I do to get [0, 3]?
Applying + 1 on a numpy array will cause all elements to be incremented by one, as you have noticed.
However, this does not imply that every operation you perform using a numpy array will be a "mapping". In the second example, there is simply a nested list, and you select the first element of the outer list. The exact same would happen if you just used regular Python:
>>> nlist = [[0, 1, 2], [3, 4, 5]]
>>> (lambda x: x[0]) (nlist)
[0, 1, 2]
You are looking for a mapping if you want to apply an operation on each of the nested arrays. However, this problem can be solved with a slice most easily:
>>> ndarr = np.array([[0, 1, 2], [3, 4, 5]])
>>> ndarr[:,0]
array([0, 3])

Special shuffling of the array

I want to shuffle my numpy array a = [2, 2, 2, 1, 1] in this way: a = [2, 1, 2, 1, 2]. So that the same elements do not stand side by side if possible. I know about numpy.array.shuffle but it generates all possible permutations uniformly. Therefore, with the same probability, can appear a = [2, 1, 2, 1, 2] or a = [2, 2, 2, 1, 1]. Is there vectorised solution for more difficult arrays? For example, for this b = np.hstack([np.ones(101), np.ones(50) * 2, np.ones(20) * 3]) array.

Python Numpy array creation from multiple lists

I am learning more about numpy and need help creating an numpy array from multiple lists. Say I have 3 lists,
a = [1, 1, 1]
b = [2, 2, 2]
c = [3, 3, 3]
How can I create a new numpy array with each list as a column? Meaning that the new array would be [[1, 2, 3], [1, 2, 3], [1, 2, 3]]. I know how to do this by looping through the lists but I am not sure if there is an easier way to accomplish this. The numpy concatenate function seems to be close but I couldn't figure out how to get it to do what I'm after.
Thanks
Try with np.column_stack:
d = np.column_stack([a, b, c])
No need to use numpy. Python zip does a nice job:
In [606]: a = [1, 1, 1]
...: b = [2, 2, 2]
...: c = [3, 3, 3]
In [607]: abc = list(zip(a,b,c))
In [608]: abc
Out[608]: [(1, 2, 3), (1, 2, 3), (1, 2, 3)]
But if your heart is set on using numpy, a good way is to make a 2d array, and transpose it:
In [609]: np.array((a,b,c))
Out[609]:
array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])
In [610]: np.array((a,b,c)).T
Out[610]:
array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]])
Others show how to do this with stack and column_stack, but underlying these is a concatenate. In one way or other they turn the lists into 2d arrays that can be joined on axis=1, e.g.
In [616]: np.concatenate([np.array(x)[:,None] for x in [a,b,c]], axis=1)
Out[616]:
array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]])

Numpy: vectorize matrix creation

If I want to create a matrix, I simply call
m = np.matrix([[x00, x01],
[x10, x11]])
, where x00, x01, x10 and x11 are numbers. However, I would like to vectorize this process. For example, if the x's are one-dimensional arrays with length l, then I would like m to become an array of matrices, or a lx2x2-dimensional array. Unfortunately,
zeros = np.zeros(10)
ones = np.ones(10)
m = np.matrix([[zeros, ones],
[zeros, ones]])
raises an error ("matrix must be 2-dimensional") and
m = np.array([[zeros, ones],
[zeros, ones]])
gives an 2x2xl-dimensional array instead. In order to solve this, I could call np.moveaxis(m, 2, 0), but I am looking for a direct solution that doesn't need to change the order of axes of a (potentially huge) array. This also only sets the axis-order right if I'm passing one-dimensional arrays as values for my matrix, not if they're higher dimensional.
Is there a general and efficient way of vectorizing the creation of matrices?
Let's try a 2d (4d after joining) case:
In [374]: ones = np.ones((3,4),int)
In [375]: arr = np.array([[ones*0, ones],[ones*2, ones*3]])
In [376]: arr
Out[376]:
array([[[[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]],
[[1, 1, 1, 1],
[1, 1, 1, 1],
[1, 1, 1, 1]]],
[[[2, 2, 2, 2],
[2, 2, 2, 2],
[2, 2, 2, 2]],
[[3, 3, 3, 3],
[3, 3, 3, 3],
[3, 3, 3, 3]]]])
In [377]: arr.shape
Out[377]: (2, 2, 3, 4)
Notice that the original array elements are 'together'. arr has its own databuffer, with copies of the original arrays, but it was made with relatively efficient block copies.
We can easily transpose axes:
In [378]: arr.transpose(2,3,0,1)
Out[378]:
array([[[[0, 1],
[2, 3]],
[[0, 1],
[2, 3]],
...
[[0, 1],
[2, 3]]]])
Now it's 12 (2,2) arrays. It is a view, using arr's databuffer. It just has a different shape and strides. Doing this transpose is quite efficient, and isn't any slower when arr is very big. And a lot of math on the transposed array will be nearly as efficient as on the original arr (because of stridded iteration). If there are differences in speed it will be because of caching at a deep level.
But some actions will require a copy. For example the transposed array can't be raveled without a copy. The original 0s,1s etc are no longer together.
In [379]: arr.transpose(2,3,0,1).ravel()
Out[379]:
array([0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1,
2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,
0, 1, 2, 3])
I could construct the same 1d array with
In [380]: tarr = np.empty((3,4,2,2), int)
In [381]: tarr[...,0,0] = ones*0
In [382]: tarr[...,0,1] = ones*1
In [383]: tarr[...,1,0] = ones*2
In [384]: tarr[...,1,1] = ones*3
In [385]: tarr.ravel()
Out[385]:
array([0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1,
2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3,
0, 1, 2, 3])
This tarr is effectively what you are trying to produce 'directly'.
Another way to look at this construction, is to assign the values to the array's .flat with strides - insert 0s at every 4th slot, 1s at the adjacent ones, etc.:
In [386]: tarr.flat[0::4] = ones*0
In [387]: tarr.flat[1::4] = ones*1
In [388]: tarr.flat[2::4] = ones*2
In [389]: tarr.flat[3::4] = ones*3
Here's another 'direct' way - use np.stack (a version of concatenate) to create a (3,4,4) array, which can then be reshaped:
np.stack((ones*0,ones*1,ones*2,ones*3),2).reshape(3,4,2,2)
That stack is, in essence:
In [397]: ones1 = ones[...,None]
In [398]: np.concatenate((ones1*0, ones1*1, ones1*2, ones1*3),axis=2)
Notice that this target (3,4,2,2) could be reshaped to (12,4) (and v.v) at no cost. So the original problem becomes: is it easier to construct a (4,12) and transpose, or construct the (12,4) first? It's really a 2d problem, not a (m+n)d one.
np.matrix must be a 2D array. From numpy documentation of np.matrix
Returns a matrix from an array-like object, or from a string of data.
A matrix is a specialized 2-D array that retains its 2-D nature
through operations. It has certain special operators, such as *
(matrix multiplication) and ** (matrix power).
Note
It is no longer recommended to use this class, even for linear
algebra. Instead use regular arrays. The class may be removed in the
future.
Is there any reason you want np.matrix? Most numpy operations should be doable in the array object as the matrix class is quasi-deprecated.
From your example I tried using the transpose (.T) method:
zeros = np.zeros(10)
ones = np.ones(10)
twos = np.ones(10) * 2
threes = np.ones(10) * 3
m = np.array([[zeros, ones], [twos, threes]]).T
>> array([[0,2],[1,3]],...)
or
m = np.transpose(np.array([[zeros, ones], [twos, threes]]), (2,0,1))
>> array([[0,1],[2,3]],...)
This yields a (10, 2, 2) array

How to add items into a numpy array

I need to accomplish the following task:
from:
a = array([[1,3,4],[1,2,3]...[1,2,1]])
(add one element to each row) to:
a = array([[1,3,4,x],[1,2,3,x]...[1,2,1,x]])
I have tried doing stuff like a[n] = array([1,3,4,x])
but numpy complained of shape mismatch. I tried iterating through a and appending element x to each item, but the changes are not reflected.
Any ideas on how I can accomplish this?
Appending data to an existing array is a natural thing to want to do for anyone with python experience. However, if you find yourself regularly appending to large arrays, you'll quickly discover that NumPy doesn't easily or efficiently do this the way a python list will. You'll find that every "append" action requires re-allocation of the array memory and short-term doubling of memory requirements. So, the more general solution to the problem is to try to allocate arrays to be as large as the final output of your algorithm. Then perform all your operations on sub-sets (slices) of that array. Array creation and destruction should ideally be minimized.
That said, It's often unavoidable and the functions that do this are:
for 2-D arrays:
np.hstack
np.vstack
np.column_stack
np.row_stack
for 3-D arrays (the above plus):
np.dstack
for N-D arrays:
np.concatenate
import numpy as np
a = np.array([[1,3,4],[1,2,3],[1,2,1]])
b = np.array([10,20,30])
c = np.hstack((a, np.atleast_2d(b).T))
returns c:
array([[ 1, 3, 4, 10],
[ 1, 2, 3, 20],
[ 1, 2, 1, 30]])
One way to do it (may not be the best) is to create another array with the new elements and do column_stack. i.e.
>>>a = array([[1,3,4],[1,2,3]...[1,2,1]])
[[1 3 4]
[1 2 3]
[1 2 1]]
>>>b = array([1,2,3])
>>>column_stack((a,b))
array([[1, 3, 4, 1],
[1, 2, 3, 2],
[1, 2, 1, 3]])
Appending a single scalar could be done a bit easier as already shown (and also without converting to float) by expanding the scalar to a python-list-type:
import numpy as np
a = np.array([[1,3,4],[1,2,3],[1,2,1]])
x = 10
b = np.hstack ((a, [[x]] * len (a) ))
returns b as:
array([[ 1, 3, 4, 10],
[ 1, 2, 3, 10],
[ 1, 2, 1, 10]])
Appending a row could be done by:
c = np.vstack ((a, [x] * len (a[0]) ))
returns c as:
array([[ 1, 3, 4],
[ 1, 2, 3],
[ 1, 2, 1],
[10, 10, 10]])
np.insert can also be used for the purpose
import numpy as np
a = np.array([[1, 3, 4],
[1, 2, 3],
[1, 2, 1]])
x = 5
index = 3 # the position for x to be inserted before
np.insert(a, index, x, axis=1)
array([[1, 3, 4, 5],
[1, 2, 3, 5],
[1, 2, 1, 5]])
index can also be a list/tuple
>>> index = [1, 1, 3] # equivalently (1, 1, 3)
>>> np.insert(a, index, x, axis=1)
array([[1, 5, 5, 3, 4, 5],
[1, 5, 5, 2, 3, 5],
[1, 5, 5, 2, 1, 5]])
or a slice
>>> index = slice(0, 3)
>>> np.insert(a, index, x, axis=1)
array([[5, 1, 5, 3, 5, 4],
[5, 1, 5, 2, 5, 3],
[5, 1, 5, 2, 5, 1]])
If x is just a single scalar value, you could try something like this to ensure the correct shape of the array that is being appended/concatenated to the rightmost column of a:
import numpy as np
a = np.array([[1,3,4],[1,2,3],[1,2,1]])
x = 10
b = np.hstack((a,x*np.ones((a.shape[0],1))))
returns b as:
array([[ 1., 3., 4., 10.],
[ 1., 2., 3., 10.],
[ 1., 2., 1., 10.]])
target = []
for line in a.tolist():
new_line = line.append(X)
target.append(new_line)
return array(target)

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