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This is the standard batch matrix multiplication:
import torch
a = torch.arange(12, dtype=torch.float).view(2,3,2)
b = torch.arange(12, dtype=torch.float).view(2,3,2) - 1
c = a.matmul(b.transpose(-1,-2))
a,b,c
>>
(tensor([[[ 0., 1.],
[ 2., 3.],
[ 4., 5.]],
[[ 6., 7.],
[ 8., 9.],
[10., 11.]]]),
tensor([[[-1., 0.],
[ 1., 2.],
[ 3., 4.]],
[[ 5., 6.],
[ 7., 8.],
[ 9., 10.]]]),
tensor([[[ 0., 2., 4.],
[ -2., 8., 18.],
[ -4., 14., 32.]],
[[ 72., 98., 124.],
[ 94., 128., 162.],
[116., 158., 200.]]]))
This is the one that I have:
e = a.view(6,2)
f = b.view(6,2)
g = e.matmul(f.transpose(-1,-2))
e,f,g
>>
(tensor([[ 0., 1.],
[ 2., 3.],
[ 4., 5.],
[ 6., 7.],
[ 8., 9.],
[10., 11.]]),
tensor([[-1., 0.],
[ 1., 2.],
[ 3., 4.],
[ 5., 6.],
[ 7., 8.],
[ 9., 10.]]),
tensor([[ 0., 2., 4., 6., 8., 10.],
[ -2., 8., 18., 28., 38., 48.],
[ -4., 14., 32., 50., 68., 86.],
[ -6., 20., 46., 72., 98., 124.],
[ -8., 26., 60., 94., 128., 162.],
[-10., 32., 74., 116., 158., 200.]]))
It's obvious that g covers c. I want to know if there is an efficient way to retrieve/slice c from g. Note that such retrieving/slicing method should generalize well to any shape of a and b.
Got it. We can just slice g with fancy indexing. We just extract the matrix multiplication result within the same batch:
g = g.view(2,3,2,3)
res = g[range(2),:,range(2),:]
res
I would like to replace values in a NumpyArray, in only one column, on several selected rows only, using putmask. I wish to use indexing on the array to be modified as well as the mask used. Therefor I create a nd.array, a mask and and array of desired replacements. as follows:
import numpy as np
a = np.linspace(1,30,30)
a.shape(10,3)
mask = np.random.randint(2, size=8)
replacements = a[[2,4,5,6,7,8],0]*a[[2,4,5,6,7,8],1]
a
array([[ 1., 2., 3.],
[ 4., 5., 6.],
[ 7., 8., 9.],
[10., 11., 12.],
[13., 14., 15.],
[16., 17., 18.],
[19., 20., 21.],
[22., 23., 24.],
[25., 26., 27.],
[28., 29., 30.]])
mask
array([0, 1, 0, 0, 1, 0, 1, 1])
replacements
array([ 56., 182., 272., 380., 506., 650.])
np.putmask(a[[2,4,5,6,7,8],2], mask[2::], replacements)
My expected result would look like this:
a
array([[ 1., 2., 3.],
[ 4., 5., 6.],
[ 7., 8., 9.],
[10., 11., 12.],
[13., 14., 15.],
[16., 17., 272.],
[19., 20., 21.],
[22., 23., 506.],
[25., 26., 650.],
[28., 29., 30.]])
But instead I get this:
a
array([[ 1., 2., 3.],
[ 4., 5., 6.],
[ 7., 8., 9.],
[10., 11., 12.],
[13., 14., 15.],
[16., 17., 18.],
[19., 20., 21.],
[22., 23., 24.],
[25., 26., 27.],
[28., 29., 30.]])
Anybody has an idea maybe?
Note that you are using fancy indexing, so when using np.putmask you are modifying a copy rather than a sliced view, and thus the original array remains unchanged. You can check this by trying to index using slice notation, np.putmask(a[2:8,2], mask[2::], replacements) for instance, which would in this case modify the values in a.
What you could do is use np.where and reassign the values to the corresponding indices in a:
a[[2,4,5,6,7,8],2] = np.where(mask[2::], replacements, a[[2,4,5,6,7,8],2])
Output
array([[ 1., 2., 3.],
[ 4., 5., 6.],
[ 7., 8., 56.],
[ 10., 11., 12.],
[ 13., 14., 182.],
[ 16., 17., 272.],
[ 19., 20., 380.],
[ 22., 23., 506.],
[ 25., 26., 650.],
[ 28., 29., 30.]])
I would like to get an array of size 11x11 with different subarrays, for example the array M composed by the following arrays (shape in parenthesis):
CC(3x3) CA(3x4) CB(3x4)
AC(4x3) AA(4x4) AB(4x4)
BC(4x3) BA(4x4) BB(4x4)
I could use concatenate but it is not optimal. I also tried the stack function, but arrays must have the same shape. Do you have any ideas to do it?
Thanks a lot!
You want np.block(). It creates an array out of 'blocks', like what you have. For e.g.
>>> CC = 1*np.ones((3, 3))
>>> CA = 2*np.ones((3, 4))
>>> CB = 3*np.ones((3, 4))
>>> AC = 4*np.ones((4, 3))
>>> AA = 5*np.ones((4, 4))
>>> AB = 6*np.ones((4, 4))
>>> BC = 7*np.ones((4, 3))
>>> BA = 8*np.ones((4, 4))
>>> BB = 9*np.ones((4, 4))
>>> M = np.block([[CC, CA, CB],
[AC, AA, AB],
[BC, BA, BB]])
>>> M
array([[ 1., 1., 1., 2., 2., 2., 2., 3., 3., 3., 3.],
[ 1., 1., 1., 2., 2., 2., 2., 3., 3., 3., 3.],
[ 1., 1., 1., 2., 2., 2., 2., 3., 3., 3., 3.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 4., 4., 4., 5., 5., 5., 5., 6., 6., 6., 6.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.],
[ 7., 7., 7., 8., 8., 8., 8., 9., 9., 9., 9.]])
For a numpy array of dimension n, I'd like to apply np.nanmax() to n-1 dimensions producing a 1 dimensional array of maxima, ignoring all values set to np.nan.
q = np.arange(5*4*3.).reshape(3,4,5) % (42+1)
q[q%5==0] = np.nan
producing:
array([[[ nan, 1., 2., 3., 4.],
[ nan, 6., 7., 8., 9.],
[ nan, 11., 12., 13., 14.],
[ nan, 16., 17., 18., 19.]],
[[ nan, 21., 22., 23., 24.],
[ nan, 26., 27., 28., 29.],
[ nan, 31., 32., 33., 34.],
[ nan, 36., 37., 38., 39.]],
[[ nan, 41., 42., nan, 1.],
[ 2., 3., 4., nan, 6.],
[ 7., 8., 9., nan, 11.],
[ 12., 13., 14., nan, 16.]]])
If I know ahead of time that I want to use the last axis as the remaining dimension, I can use the -1 feature in .reshape() and do this:
np.nanmax(q.reshape(-1, q.shape[-1]), axis=0)
which produces the result I want:
array([ 12., 41., 42., 38., 39.])
However, suppose I don't know ahead of time to which one of the axes that I don't want to apply the maximum? Suppose I started with n=4 dimensions, and wanted it to apply to all axes except the mth axis, which could be 0, 1, 2, or 3? Would have to actually use a conditional if-elif-else ?
Is there something that would work like a hypothetical exeptaxis=m?
The axis argument of nanmax can be a tuple of axes over which the maximum is computed. In your case, you want that tuple to contain all the axes except m. Here's one way you could do that:
In [62]: x
Out[62]:
array([[[[ 4., 3., nan, nan],
[ 0., 2., 2., nan],
[ 4., 5., nan, 3.],
[ 2., 0., 3., 1.]],
[[ 2., 0., 0., 1.],
[ nan, 3., 0., nan],
[ 0., 1., nan, 2.],
[ 5., 4., 0., 1.]],
[[ 4., 0., 2., 0.],
[ 4., 0., 4., 5.],
[ 3., 4., 1., 0.],
[ 5., 3., 4., 3.]]],
[[[ 2., nan, 6., 4.],
[ 3., 1., 2., nan],
[ 5., 4., 1., 0.],
[ 2., 6., 0., nan]],
[[ 4., 1., 4., 2.],
[ nan, 1., 5., 5.],
[ 2., 0., 1., 1.],
[ 6., 3., 6., 5.]],
[[ 1., 0., 0., 1.],
[ 1., nan, 2., nan],
[ 3., 4., 0., 5.],
[ 1., 6., 2., 3.]]]])
In [63]: m = 0
In [64]: np.nanmax(x, axis=tuple(i for i in range(x.ndim) if i != m))
Out[64]: array([ 5., 6.])
I have a numpy 2-d array which I divided in several numpy 2-d blocks. All blocks have the same shape. On these blocks I performed K-means segementation using the scikit-learn module. The edges of each block are overlapping (each block has one row/column overlap with the adjacent block). What I want is to give the overlapping segments in two adjacent blocks the same value. My current code can be downloaded here.
Image of the blocks and their position in the original image:
Blocks in python code
blockNW=np.array([[ 0., 0., 0., 0., 5.],
[ 0., 0., 4., 5., 5.],
[ 0., 4., 4., 5., 2.],
[ 0., 4., 5., 5., 2.],
[ 5., 5., 2., 2., 2.]])
blockNE=np.array([[ 1., 18., 18., 18., 6.],
[ 1., 18., 7., 6., 6.],
[ 3., 7., 7., 7., 6.],
[ 3., 3., 3., 7., 7.],
[ 3., 3., 7., 7., 7.]])
blockSW=np.array([[ 8., 8., 8., 10., 10.],
[ 8., 8., 9., 10., 10.],
[ 8., 8., 9., 9., 10.],
[ 8., 8., 8., 9., 10.],
[ 8., 8., 9., 9., 11.]])
blockSE=np.array([[ 12., 12., 12., 12., 12.],
[ 12., 12., 12., 12., 13.],
[ 12., 12., 12., 13., 13.],
[ 12., 12., 13., 13., 13.],
[ 12., 13., 13., 13., 13.]])
blocksStacked=np.array([blockNW,blockNE,blockSW,blockSE])
What I want is to connect the overlapping segments. For this I would like to use as few for-loops as possible, because they are slowing down the code. My current steps are:
import math
import numpy as np
from scipy import ndimage,stats
n_blocks,blocksize = np.shape(blocksStacked)[0],np.shape(blocksStacked)[1]
# shape of original image
out_shp = (8,8)
# horizontal and vertical blocks
horizontal_blocks=math.ceil(out_shp[1]/float(blocksize))
vertical_blocks=math.ceil(out_shp[0]/float(blocksize))
# numpy 2_d array in the shape of the image with an unique ID for each block
blockindex=np.arange(horizontal_blocks*vertical_blocks).reshape(-1,horizontal_blocks)
Block index
def find_neighbours(values,neighbourslist):
'''function to find the index of neighbouring blocks'''
mode=stats.mode(values)
if mode.count>1:
values=np.delete(values,np.where(values==mode[0]))
else:
values=np.delete(values,np.where(values==np.median(values)))
neighbourslist.append(values)
return 0
#Locate overlapping rows and columns per block
neighbourlist=[]
kernel=np.array([[0,1,0],[1,1,1],[0,1,0]],dtype='uint8')
_ =ndimage.generic_filter(blockindex, find_neighbours, footprint=kernel,extra_arguments=(neighbourlist,))
#output (block 0 has neighbours 1 and 2, etc.):
>>> neighbourlist
[array([ 1., 2.]), array([ 0., 3.]), array([ 0., 3.]), array([ 1., 2.])]
Now the next step could be is to loop through all blocks and neighbors and select the overlapping rows or columns (If possible I would also like to remove these loops).
# First I create masks to select overlapping rows or columns:
upmask=np.ones((blocksize,blocksize),dtype=bool)
upmask[1:,:]=0
downmask=np.ones((blocksize,blocksize),dtype=bool)
downmask[:-1,:]=0
rightmask=np.ones((blocksize,blocksize),dtype=bool)
rightmask[:,:-1]=0
leftmask=np.ones((blocksize,blocksize),dtype=bool)
leftmask[:,1:]=0
# Now loop through all blocks and neighbours and select the overlapping rows/columsn
for i in range(n_blocks):
n_neighbours = len(neighbourlist[i])
block=blocksStacked[i,:,:]
for j in range(n_neighbours):
neighborindex=neighbourlist[i][j]
block_neighbour=blocksStacked[neighborindex,:,:]
if i+1==neighborindex:
blockvals=block[rightmask]
neighbourvals=block_neighbour[leftmask]
elif i-1==neighborindex:
blockvals=block[leftmask]
neighbourvals=block_neighbour[rightmask]
elif i+horizontal_blocks==neighborindex:
blockvals=block[downmask]
neighbourvals=block_neighbour[upmask]
elif i-horizontal_blocks==neighborindex:
blockvals=block[upmask]
neighbourvals=block_neighbour[downmask]
In each loop I end up with two numpy 1d arrays representing the overlapping columns or rows. For the first loop I will end up with:
>>> blockvals
array([5., 5., 2., 2., 2.])
>>> neighbourvals
array([1., 1., 3., 3., 3.])
I want to relabel the values of the overlapping segments to the values of the segments in the block which is not a neighbour:
blockNW=np.array([[ 0., 0., 0., 0., 5.],
[ 0., 0., 4., 5., 5.],
[ 0., 4., 4., 5., 2.],
[ 0., 4., 5., 5., 2.],
[ 5., 5., 2., 2., 2.]])
blockNE=np.array([[ 5., 18., 18., 18., 6.],
[ 5., 18., 7., 6., 6.],
[ 2., 7., 7., 7., 6.],
[ 2., 2., 2., 7., 7.],
[ 2., 2., 7., 7., 7.]])
Any idea on how to detect and relabel these overlapping segments?
Also my code looks a bit too cumbersome, any ideas on how to improve my code?
A few remarks:
Some segments will not overlap for 100%, so it should be possible to set a threshold. For example is segments are overlapping for more than 70% they should be relabeled
The output shape of the function should be similar to the shape of the stacked blocks
The desired output will look like this:
EDIT
With for-loops the code to solve the question would look something like this:
from scipy.stats import itemfreq
# Locate and re-label overlapping segments
for k in range(len(np.unique(blockvals))):
#Iterate over each value in the overlapping row/column of the block
blockval=np.unique(blockvals)[k]
#count of blockval
block_val_count=len(blockvals[np.where(blockvals==blockval)])
#Select values in neighbour on the same location
overlap=neighbourvals[np.where(blockvals==blockval)]
overlapfreq=itemfreq(overlap)
#select neighboring value which overlaps the most
neighval_overlap_count= np.max(overlapfreq[:,1])
neighval=overlapfreq[np.where(overlapfreq[:,1]==neighval_overlap_count),0][0]
# count occurence of selected neighboring value
neigh_val_count=len(neighbourvals[np.where(neighbourvals==neighval)])
#If overlap is more than 70% relabel the neigboring value to the value in the block
thresh=0.7
if (neighval_overlap_count/float(neigh_val_count)>=thresh) and (neighval_overlap_count/float(block_val_count)>=thresh):
blocksStacked[neighborindex,:,:,][np.where(blocksStacked[neighborindex,:,:]==neighval)]=blockval
#output
>>> blocksStacked
array([[[ 0., 0., 0., 0., 5.],
[ 0., 0., 4., 5., 5.],
[ 0., 4., 4., 5., 2.],
[ 0., 4., 5., 5., 2.],
[ 5., 5., 2., 2., 2.]],
[[ 5., 18., 18., 18., 6.],
[ 5., 18., 7., 6., 6.],
[ 2., 7., 7., 7., 6.],
[ 2., 2., 2., 7., 7.],
[ 2., 2., 7., 7., 7.]],
[[ 8., 8., 8., 10., 10.],
[ 8., 8., 9., 10., 10.],
[ 8., 8., 9., 9., 10.],
[ 8., 8., 8., 9., 10.],
[ 8., 8., 9., 9., 11.]],
[[ 10., 10., 10., 10., 10.],
[ 10., 10., 10., 10., 13.],
[ 10., 10., 10., 13., 13.],
[ 10., 10., 13., 13., 13.],
[ 10., 13., 13., 13., 13.]]])