I have a 2-d numpy array as follows:
a = np.array([[1,5,9,13],
[2,6,10,14],
[3,7,11,15],
[4,8,12,16]]
I want to extract it into patches of 2 by 2 sizes with out repeating the elements.
The answer should exactly be the same. This can be 3-d array or list with the same order of elements as below:
[[[1,5],
[2,6]],
[[3,7],
[4,8]],
[[9,13],
[10,14]],
[[11,15],
[12,16]]]
How can do it easily?
In my real problem the size of a is (36, 72). I can not do it one by one. I want programmatic way of doing it.
Using scikit-image:
import numpy as np
from skimage.util import view_as_blocks
a = np.array([[1,5,9,13],
[2,6,10,14],
[3,7,11,15],
[4,8,12,16]])
print(view_as_blocks(a, (2, 2)))
You can achieve it with a combination of np.reshape and np.swapaxes like so -
def extract_blocks(a, blocksize, keep_as_view=False):
M,N = a.shape
b0, b1 = blocksize
if keep_as_view==0:
return a.reshape(M//b0,b0,N//b1,b1).swapaxes(1,2).reshape(-1,b0,b1)
else:
return a.reshape(M//b0,b0,N//b1,b1).swapaxes(1,2)
As can be seen there are two ways to use it - With keep_as_view flag turned off (default one) or on. With keep_as_view = False, we are reshaping the swapped-axes to a final output of 3D, while with keep_as_view = True, we will keep it 4D and that will be a view into the input array and hence, virtually free on runtime. We will verify it with a sample case run later on.
Sample cases
Let's use a sample input array, like so -
In [94]: a
Out[94]:
array([[2, 2, 6, 1, 3, 6],
[1, 0, 1, 0, 0, 3],
[4, 0, 0, 4, 1, 7],
[3, 2, 4, 7, 2, 4],
[8, 0, 7, 3, 4, 6],
[1, 5, 6, 2, 1, 8]])
Now, let's use some block-sizes for testing. Let's use a blocksize of (2,3) with the view-flag turned off and on -
In [95]: extract_blocks(a, (2,3)) # Blocksize : (2,3)
Out[95]:
array([[[2, 2, 6],
[1, 0, 1]],
[[1, 3, 6],
[0, 0, 3]],
[[4, 0, 0],
[3, 2, 4]],
[[4, 1, 7],
[7, 2, 4]],
[[8, 0, 7],
[1, 5, 6]],
[[3, 4, 6],
[2, 1, 8]]])
In [48]: extract_blocks(a, (2,3), keep_as_view=True)
Out[48]:
array([[[[2, 2, 6],
[1, 0, 1]],
[[1, 3, 6],
[0, 0, 3]]],
[[[4, 0, 0],
[3, 2, 4]],
[[4, 1, 7],
[7, 2, 4]]],
[[[8, 0, 7],
[1, 5, 6]],
[[3, 4, 6],
[2, 1, 8]]]])
Verify view with keep_as_view=True
In [20]: np.shares_memory(a, extract_blocks(a, (2,3), keep_as_view=True))
Out[20]: True
Let's check out performance on a large array and verify the virtually free runtime claim as discussed earlier -
In [42]: a = np.random.rand(2000,3000)
In [43]: %timeit extract_blocks(a, (2,3), keep_as_view=True)
1000000 loops, best of 3: 801 ns per loop
In [44]: %timeit extract_blocks(a, (2,3), keep_as_view=False)
10 loops, best of 3: 29.1 ms per loop
Here's a rather cryptic numpy one-liner to generate your 3-d array, called result1 here:
In [60]: x
Out[60]:
array([[2, 1, 2, 2, 0, 2, 2, 1, 3, 2],
[3, 1, 2, 1, 0, 1, 2, 3, 1, 0],
[2, 0, 3, 1, 3, 2, 1, 0, 0, 0],
[0, 1, 3, 3, 2, 0, 3, 2, 0, 3],
[0, 1, 0, 3, 1, 3, 0, 0, 0, 2],
[1, 1, 2, 2, 3, 2, 1, 0, 0, 3],
[2, 1, 0, 3, 2, 2, 2, 2, 1, 2],
[0, 3, 3, 3, 1, 0, 2, 0, 2, 1]])
In [61]: result1 = x.reshape(x.shape[0]//2, 2, x.shape[1]//2, 2).swapaxes(1, 2).reshape(-1, 2, 2)
result1 is like a 1-d array of 2-d arrays:
In [68]: result1.shape
Out[68]: (20, 2, 2)
In [69]: result1[0]
Out[69]:
array([[2, 1],
[3, 1]])
In [70]: result1[1]
Out[70]:
array([[2, 2],
[2, 1]])
In [71]: result1[5]
Out[71]:
array([[2, 0],
[0, 1]])
In [72]: result1[-1]
Out[72]:
array([[1, 2],
[2, 1]])
(Sorry, I don't have time at the moment to give a detailed breakdown of how it works. Maybe later...)
Here's a less cryptic version that uses a nested list comprehension. In this case, result2 is a python list of 2-d numpy arrays:
In [73]: result2 = [x[2*j:2*j+2, 2*k:2*k+2] for j in range(x.shape[0]//2) for k in range(x.shape[1]//2)]
In [74]: result2[5]
Out[74]:
array([[2, 0],
[0, 1]])
In [75]: result2[-1]
Out[75]:
array([[1, 2],
[2, 1]])
Related
I'm trying to concatenate 2 arrays element wise. I have the concatenation working to produce the correct shape but it has not been applied element wise.
So i have this array
[0, 1]
[2, 3]
[4, 5]
I want to append each element in the array with each element. the target result would be
[0, 1, 0, 1]
[0, 1, 2, 3]
[0, 1, 4, 5]
[2, 3, 0, 1]
[2, 3, 2, 3]
[2, 3, 4, 5]
[4, 5, 0, 1]
[4, 5, 2, 3]
[4, 5, 4, 5]
i think i may need to change an axis but then i can't get the broadcasting to work.
any help would be greatly appreciated. lots to learn in numpy !
a = np.arange(6).reshape(3, 2))
b = np.concatenate((a, a), axis=1)
One way would be stacking replicated versions created with np.repeat and np.tile -
In [52]: n = len(a)
In [53]: np.hstack((np.repeat(a,n,axis=0),np.tile(a,(n,1))))
Out[53]:
array([[0, 1, 0, 1],
[0, 1, 2, 3],
[0, 1, 4, 5],
[2, 3, 0, 1],
[2, 3, 2, 3],
[2, 3, 4, 5],
[4, 5, 0, 1],
[4, 5, 2, 3],
[4, 5, 4, 5]])
Another would be with broadcasted-assignment, since you mentioned broadcasting -
def create_mesh(a):
m,n = a.shape
out = np.empty((m,m,2*n),dtype=a.dtype)
out[...,:n] = a[:,None]
out[...,n:] = a
return out.reshape(-1,2*n)
One solution is to build on senderle's cartesian_product to extend this to 2D arrays. Here's how I usually do this:
# Your input array.
arr
# array([[0, 1],
# [2, 3],
# [4, 5]])
idxs = cartesian_product(*[np.arange(len(arr))] * 2)
arr[idxs].reshape(idxs.shape[0], -1)
# array([[0, 1, 0, 1],
# [0, 1, 2, 3],
# [0, 1, 4, 5],
# [2, 3, 0, 1],
# [2, 3, 2, 3],
# [2, 3, 4, 5],
# [4, 5, 0, 1],
# [4, 5, 2, 3],
# [4, 5, 4, 5]])
Suppose I have a matrix A with some arbitrary values:
array([[ 2, 4, 5, 3],
[ 1, 6, 8, 9],
[ 8, 7, 0, 2]])
And a matrix B which contains indices of elements in A:
array([[0, 0, 1, 2],
[0, 3, 2, 1],
[3, 2, 1, 0]])
How do I select values from A pointed by B, i.e.:
A[B] = [[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]]
EDIT: np.take_along_axis is a builtin function for this use case implemented since numpy 1.15. See #hpaulj 's answer below for how to use it.
You can use NumPy's advanced indexing -
A[np.arange(A.shape[0])[:,None],B]
One can also use linear indexing -
m,n = A.shape
out = np.take(A,B + n*np.arange(m)[:,None])
Sample run -
In [40]: A
Out[40]:
array([[2, 4, 5, 3],
[1, 6, 8, 9],
[8, 7, 0, 2]])
In [41]: B
Out[41]:
array([[0, 0, 1, 2],
[0, 3, 2, 1],
[3, 2, 1, 0]])
In [42]: A[np.arange(A.shape[0])[:,None],B]
Out[42]:
array([[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]])
In [43]: m,n = A.shape
In [44]: np.take(A,B + n*np.arange(m)[:,None])
Out[44]:
array([[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]])
More recent versions have added a take_along_axis function that does the job:
A = np.array([[ 2, 4, 5, 3],
[ 1, 6, 8, 9],
[ 8, 7, 0, 2]])
B = np.array([[0, 0, 1, 2],
[0, 3, 2, 1],
[3, 2, 1, 0]])
np.take_along_axis(A, B, 1)
Out[]:
array([[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]])
There's also a put_along_axis.
I know this is an old question, but another way of doing it using indices is:
A[np.indices(B.shape)[0], B]
output:
[[2 2 4 5]
[1 9 8 6]
[2 0 7 8]]
Following is the solution using for loop:
outlist = []
for i in range(len(B)):
lst = []
for j in range(len(B[i])):
lst.append(A[i][B[i][j]])
outlist.append(lst)
outarray = np.asarray(outlist)
print(outarray)
Above can also be written in more succinct list comprehension form:
outlist = [ [A[i][B[i][j]] for j in range(len(B[i]))]
for i in range(len(B)) ]
outarray = np.asarray(outlist)
print(outarray)
Output:
[[2 2 4 5]
[1 9 8 6]
[2 0 7 8]]
Suppose I have a matrix A with some arbitrary values:
array([[ 2, 4, 5, 3],
[ 1, 6, 8, 9],
[ 8, 7, 0, 2]])
And a matrix B which contains indices of elements in A:
array([[0, 0, 1, 2],
[0, 3, 2, 1],
[3, 2, 1, 0]])
How do I select values from A pointed by B, i.e.:
A[B] = [[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]]
EDIT: np.take_along_axis is a builtin function for this use case implemented since numpy 1.15. See #hpaulj 's answer below for how to use it.
You can use NumPy's advanced indexing -
A[np.arange(A.shape[0])[:,None],B]
One can also use linear indexing -
m,n = A.shape
out = np.take(A,B + n*np.arange(m)[:,None])
Sample run -
In [40]: A
Out[40]:
array([[2, 4, 5, 3],
[1, 6, 8, 9],
[8, 7, 0, 2]])
In [41]: B
Out[41]:
array([[0, 0, 1, 2],
[0, 3, 2, 1],
[3, 2, 1, 0]])
In [42]: A[np.arange(A.shape[0])[:,None],B]
Out[42]:
array([[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]])
In [43]: m,n = A.shape
In [44]: np.take(A,B + n*np.arange(m)[:,None])
Out[44]:
array([[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]])
More recent versions have added a take_along_axis function that does the job:
A = np.array([[ 2, 4, 5, 3],
[ 1, 6, 8, 9],
[ 8, 7, 0, 2]])
B = np.array([[0, 0, 1, 2],
[0, 3, 2, 1],
[3, 2, 1, 0]])
np.take_along_axis(A, B, 1)
Out[]:
array([[2, 2, 4, 5],
[1, 9, 8, 6],
[2, 0, 7, 8]])
There's also a put_along_axis.
I know this is an old question, but another way of doing it using indices is:
A[np.indices(B.shape)[0], B]
output:
[[2 2 4 5]
[1 9 8 6]
[2 0 7 8]]
Following is the solution using for loop:
outlist = []
for i in range(len(B)):
lst = []
for j in range(len(B[i])):
lst.append(A[i][B[i][j]])
outlist.append(lst)
outarray = np.asarray(outlist)
print(outarray)
Above can also be written in more succinct list comprehension form:
outlist = [ [A[i][B[i][j]] for j in range(len(B[i]))]
for i in range(len(B)) ]
outarray = np.asarray(outlist)
print(outarray)
Output:
[[2 2 4 5]
[1 9 8 6]
[2 0 7 8]]
Can someone explain to me what the second line of this code does?
objp = np.zeros((48,3), np.float32)
objp[:,:2] = np.mgrid[0:8,0:6].T.reshape(-1,2)
Can someone explain to me what exactly the np.mgrid[0:8,0:6] part of the code is doing and what exactly the T.reshape(-1,2) part of the code is doing?
Thanks and good job!
The easiest way to see these is to use smaller values for mgrid:
In [11]: np.mgrid[0:2,0:3]
Out[11]:
array([[[0, 0, 0],
[1, 1, 1]],
[[0, 1, 2],
[0, 1, 2]]])
In [12]: np.mgrid[0:2,0:3].T # (matrix) transpose
Out[12]:
array([[[0, 0],
[1, 0]],
[[0, 1],
[1, 1]],
[[0, 2],
[1, 2]]])
In [13]: np.mgrid[0:2,0:3].T.reshape(-1, 2) # reshape to an Nx2 matrix
Out[13]:
array([[0, 0],
[1, 0],
[0, 1],
[1, 1],
[0, 2],
[1, 2]])
Then objp[:,:2] = sets the 0th and 1th columns of objp to this result.
The second line creates a multi-dimensional mesh grid, transposes it, reshapes it so that it represents two columns and inserts it into the first two columns of the objp array.
Breakdown:
np.mgrid[0:8,0:6] creates the following mgrid:
>> np.mgrid[0:8,0:6]
array([[[0, 0, 0, 0, 0, 0],
[1, 1, 1, 1, 1, 1],
[2, 2, 2, 2, 2, 2],
[3, 3, 3, 3, 3, 3],
[4, 4, 4, 4, 4, 4],
[5, 5, 5, 5, 5, 5],
[6, 6, 6, 6, 6, 6],
[7, 7, 7, 7, 7, 7]],
[[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5],
[0, 1, 2, 3, 4, 5]]])
The .T transposes the matrix, and the .reshape(-1,2) then reshapes it into two a two-column array shape. These two columns are then the correct shape to replace two columns in the original array.
I think this should be easy, but I'm not sure of an efficient way to do it.
I'd like to build a matrix in numpy that has the cityblock / manhattan closeness to the center of the matrix, in numpy, for any odd size.
For a size of 5, the output would be:
array([[0, 1, 2, 1, 0],
[1, 2, 3, 2, 1],
[2, 3, 4, 3, 2],
[1, 2, 3, 2, 1],
[0, 1, 2, 1, 0]])
What's the best way of doing this? Thanks
Easy and efficient with broadcasting -
def closeness_manhattan(N):
r = np.arange(N)
a = np.minimum(r,r[::-1])
return a[:,None] + a
Sample runs -
In [14]: closeness_manhattan(4)
Out[14]:
array([[0, 1, 1, 0],
[1, 2, 2, 1],
[1, 2, 2, 1],
[0, 1, 1, 0]])
In [15]: closeness_manhattan(5)
Out[15]:
array([[0, 1, 2, 1, 0],
[1, 2, 3, 2, 1],
[2, 3, 4, 3, 2],
[1, 2, 3, 2, 1],
[0, 1, 2, 1, 0]])