I am looking for a fast formulation to do a numerical binning of a 2D numpy array. By binning I mean calculate submatrix averages or cumulative values. For ex. x = numpy.arange(16).reshape(4, 4) would have been splitted in 4 submatrix of 2x2 each and gives numpy.array([[2.5,4.5],[10.5,12.5]]) where 2.5=numpy.average([0,1,4,5]) etc...
How to perform such an operation in an efficient way... I don't have really any ideay how to perform this ...
Many thanks...
You can use a higher dimensional view of your array and take the average along the extra dimensions:
In [12]: a = np.arange(36).reshape(6, 6)
In [13]: a
Out[13]:
array([[ 0, 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, 31, 32, 33, 34, 35]])
In [14]: a_view = a.reshape(3, 2, 3, 2)
In [15]: a_view.mean(axis=3).mean(axis=1)
Out[15]:
array([[ 3.5, 5.5, 7.5],
[ 15.5, 17.5, 19.5],
[ 27.5, 29.5, 31.5]])
In general, if you want bins of shape (a, b) for an array of (rows, cols), your reshaping of it should be .reshape(rows // a, a, cols // b, b). Note also that the order of the .mean is important, e.g. a_view.mean(axis=1).mean(axis=3) will raise an error, because a_view.mean(axis=1) only has three dimensions, although a_view.mean(axis=1).mean(axis=2) will work fine, but it makes it harder to understand what is going on.
As is, the above code only works if you can fit an integer number of bins inside your array, i.e. if a divides rows and b divides cols. There are ways to deal with other cases, but you will have to define the behavior you want then.
See the SciPy Cookbook on rebinning, which provides this snippet:
def rebin(a, *args):
'''rebin ndarray data into a smaller ndarray of the same rank whose dimensions
are factors of the original dimensions. eg. An array with 6 columns and 4 rows
can be reduced to have 6,3,2 or 1 columns and 4,2 or 1 rows.
example usages:
>>> a=rand(6,4); b=rebin(a,3,2)
>>> a=rand(6); b=rebin(a,2)
'''
shape = a.shape
lenShape = len(shape)
factor = asarray(shape)/asarray(args)
evList = ['a.reshape('] + \
['args[%d],factor[%d],'%(i,i) for i in range(lenShape)] + \
[')'] + ['.sum(%d)'%(i+1) for i in range(lenShape)] + \
['/factor[%d]'%i for i in range(lenShape)]
print ''.join(evList)
return eval(''.join(evList))
I assume that you only want to know how to generally build a function that performs well and does something with arrays, just like numpy.reshape in your example. So if performance really matters and you're already using numpy, you can write your own C code for that, like numpy does. For example, the implementation of arange is completely in C. Almost everything with numpy which matters in terms of performance is implemented in C.
However, before doing so you should try to implement the code in python and see if the performance is good enough. Try do make the python code as efficient as possible. If it still doesn't suit your performance needs, go the C way.
You may read about that in the docs.
Related
I have been searching if there is an standard mehtod to create a subarray using relative indexes. Take the following array into consideration:
>>> m = np.arange(25).reshape([5, 5])
array([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14],
[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24]])
I want to access the 3x3 matrix at a specific array position, for example [2,2]:
>>> x = 2, y = 2
>>> m[slice(x-1,x+2), slice(y-1,y+2)]
array([[ 6, 7, 8],
[11, 12, 13],
[16, 17, 18]])
For example for the above somethig like m.subarray(pos=[2,2], shape=[3,3])
I want to sample a ndarray of n dimensions on a specific position which might change.
I did not want to use a loop as it might be inneficient. Scipy functions correlate and convolve do this very efficiently, but for all positions. I am interested only in the sampling of one.
The best answer could solve the issues at edges, in my case I would like for example to have wrap mode:
(a b c d | a b c d | a b c d)
--------------------EDITED-----------------------------
Based on the answer from #Carlos Horn, I could create the following function.
def cell_neighbours(array, index, shape):
pads = [(floor(dim/2), ceil(dim / 2)) for dim in shape]
array = np.pad(self.configuration, pads, "wrap")
views = np.lib.stride_tricks.sliding_window_view
return views(array, shape)[tuple(index)]
Last concern might be about speed, from docs: For many applications using a sliding window view can be convenient, but potentially very slow. Often specialized solutions exist.
From here maybe is easier to get a faster solution.
You could build a view of 3x3 matrices into the array as follows:
import numpy as np
m = np.arange(25).reshape(5,5)
m3x3view = np.lib.stride_tricks.sliding_window_view(m, (3,3))
Note that it will change slightly your indexing on half the window size meaning
x_view = x - 3//2
y_view = y - 3//2
print(m3x3view[x_view,y_view]) # gives your result
In case a copy operation is fine, you could use:
mpad = np.pad(m, 1, mode="wrap")
mpad3x3view = np.lib.stride_tricks.sliding_window_view(mpad, (3,3))
print(mpad3x3view[x % 5,y % 5])
to use arbitrary x, y integer values.
I'm making an array of sums of random choices from a negative binomial distribution (nbd), with each sum being of non-regular length. Right now I implement it as follows:
import numpy
from numpy.random import default_rng
rng = default_rng()
nbd = rng.negative_binomial(1, 0.5, int(1e6))
gmc = [12, 35, 4, 67, 2]
n_pp = np.empty(len(gmc))
for i in range(len(gmc)):
n_pp[i] = np.sum(rng.choice(nbd, gmc[i]))
This works, but when I perform it over my actual data it's very slow (gmc is of dimension 1e6), and I would like to vary this for multiple values of n and p in the nbd (in this example they're set to 1 and 0.5, respectively).
I'd like to work out a pythonic way to do this which eliminates the loop, but I'm not sure it's possible. I want to keep default_rng for the better random generation than the older way of doing it (np.random.choice), if possible.
The distribution of the sum of m samples from the negative binomial distribution with parameters (n, p) is the negative binomial distribution with parameters (m*n, p). So instead of summing random selections from a large, precomputed sample of negative_binomial(1, 0.5), you can generate your result directly with negative_binomial(gmc, 0.5):
In [68]: gmc = [12, 35, 4, 67, 2]
In [69]: npp = rng.negative_binomial(gmc, 0.5)
In [70]: npp
Out[70]: array([ 9, 34, 1, 72, 7])
(The negative_binomial method will broadcast its inputs, so we can pass gmc as an argument to generate all the samples with one call.)
More generally, if you want to vary the n that is used to generate nbd, you would multiply that n by the corresponding element in gmc and pass the product to rng.negative_binomial.
I've got a 3D tensor x (e.g 4x4x100). I want to obtain a subset of this by explicitly choosing elements across the last dimension. This would have been easy if I was choosing the same elements across last dimension (e.g. x[:,:,30:50] but I want to target different elements across that dimension using the 2D tensor indices which specifies the idx across third dimension. Is there an easy way to do this in numpy?
A simpler 2D example:
x = [[1,2,3,4,5,6],[10,20,30,40,50,60]]
indices = [1,3]
Let's say I want to grab two elements across third dimension of x starting from points specified by indices. So my desired output is:
[[2,3],[40,50]]
Update: I think I could use a combination of take() and ravel_multi_index() but some of the platforms that are inspired by numpy (like PyTorch) don't seem to have ravel_multi_index so I'm looking for alternative solutions
Iterating over the idx, and collecting the slices is not a bad option if the number of 'rows' isn't too large (and the size of the sizes is relatively big).
In [55]: x = np.array([[1,2,3,4,5,6],[10,20,30,40,50,60]])
In [56]: idx = [1,3]
In [57]: np.array([x[j,i:i+2] for j,i in enumerate(idx)])
Out[57]:
array([[ 2, 3],
[40, 50]])
Joining the slices like this only works if they all are the same size.
An alternative is to collect the indices into an array, and do one indexing.
For example with a similar iteration:
idxs = np.array([np.arange(i,i+2) for i in idx])
But broadcasted addition may be better:
In [58]: idxs = np.array(idx)[:,None]+np.arange(2)
In [59]: idxs
Out[59]:
array([[1, 2],
[3, 4]])
In [60]: x[np.arange(2)[:,None], idxs]
Out[60]:
array([[ 2, 3],
[40, 50]])
ravel_multi_index is not hard to replicate (if you don't need clipping etc):
In [65]: np.ravel_multi_index((np.arange(2)[:,None],idxs),x.shape)
Out[65]:
array([[ 1, 2],
[ 9, 10]])
In [66]: x.flat[_]
Out[66]:
array([[ 2, 3],
[40, 50]])
In [67]: np.arange(2)[:,None]*x.shape[1]+idxs
Out[67]:
array([[ 1, 2],
[ 9, 10]])
along the 3D axis:
x = [x[:,i].narrow(2,index,2) for i,index in enumerate(indices)]
x = torch.stack(x,dim=1)
by enumerating you get the index of the axis and index from where you want to start slicing in one.
narrow gives you a zero-copy length long slice from a starting index start along a certain axis
you said you wanted:
dim = 2
start = index
length = 2
then you simply have to stack these tensors back to a single 3D.
This is the least work intensive thing i can think of for pytorch.
EDIT
if you just want different indices along different axis and indices is a 2D tensor you can do:
x = [x[:,i,index] for i,index in enumerate(indices)]
x = torch.stack(x,dim=1)
You really should have given a proper working example, making it unnecessarily confusing.
Here is how to do it in numpy, now clue about torch, though.
The following picks a slice of length n along the third dimension starting from points idx depending on the other two dimensions:
# example
a = np.arange(60).reshape(2, 3, 10)
idx = [(1,2,3),(4,3,2)]
n = 4
# build auxiliary 4D array where the last two dimensions represent
# a sliding n-window of the original last dimension
j,k,l = a.shape
s,t,u = a.strides
aux = np.lib.stride_tricks.as_strided(a, (j,k,l-n+1,n), (s,t,u,u))
# pick desired offsets from sliding windows
aux[(*np.ogrid[:j, :k], idx)]
# array([[[ 1, 2, 3, 4],
# [12, 13, 14, 15],
# [23, 24, 25, 26]],
# [[34, 35, 36, 37],
# [43, 44, 45, 46],
# [52, 53, 54, 55]]])
I came up with below using broadcasting:
x = np.array([[1,2,3,4,5,6,7,8,9,10],[10,20,30,40,50,60,70,80,90,100]])
i = np.array([1,5])
N = 2 # number of elements I want to extract along each dimension. Starting points specified in i
r = np.arange(x.shape[-1])
r = np.broadcast_to(r, x.shape)
ii = i[:, np.newaxis]
ii = np.broadcast_to(ii, x.shape)
mask = np.logical_and(r-ii>=0, r-ii<=N)
output = x[mask].reshape(2,3)
Does this look alright?
I'm trying to perform an operation of multiplying a slice of a 2D matrix by a constant.
For example, if i wanted to multiply everything but the first 2 columns
To perform this in numpy, one could do:
a = np.array([[0,7,4],
[1,6,4],
[0,2,4],
[4,2,7]])
a[:, 2:] = 2.0*a[:, 2:]
>> a
>> array([[ 0, 7, 8],
[ 1, 6, 8],
[ 0, 2, 8],
[ 4, 2, 14]])
However, at least from what i've searched, tensorflow currently doesn't have a straightforward way to do this.
My current solution is to create a originally as two separate Tensors a1 and a2, multiply the second one by 2.0 and then concatenate them across axis=1. The operation is simple enough that this is possible. However I have two questions
Is that the most efficient way to do this
Is there a better (general/efficient) way to perform this to bring the functionality closer to numpy's slicing magic (perhaps https://www.tensorflow.org/api_docs/python/tf/scatter_
One option is to perform entrywise multiplication, as follows:
import tensorflow as tf
a = tf.Variable(initial_value=[[0,7,4],[1,6,4],[0,2,4],[4,2,7]])
b = tf.mul(a,[1,1,2])
s=tf.InteractiveSession()
s.run(tf.global_variables_initializer())
b.eval()
This prints
array([[ 0, 7, 8],
[ 1, 6, 8],
[ 0, 2, 8],
[ 4, 2, 14]])
More generally, if a has more columns, you can do something like that:
import tensorflow as tf
a = tf.Variable(initial_value=[[0,7,4],[1,6,4],[0,2,4],[4,2,7]])
b = tf.mul(a,[1,1]+[2 for i in range(a.get_shape()[1]-2)])
s=tf.InteractiveSession()
s.run(tf.global_variables_initializer())
b.eval()
Or if your matrix has many columns you could replace
b = tf.mul(a,[1,1]+[2 for i in range(a.get_shape()[1]-2)])
with
import numpy as np
b = tf.mul(a,np.concatenate((np.array([1,1]),2*np.ones(a.get_shape()[1]-2))))
i have a 4 dimensional array -- say a=numpy.array(40,40,4,1000)
I also have an index array -- say b = np.arrange(35)
I am looking to make an array doing something like c = a[b,b,3,999] where the resulting array would look something like d = numpy.array(35,35). Would appreciate any thoughts on what the right way to do this is. Thank you. Neela.
Since b=np.arange(35) is just the first 35 indices, use slices instead:
c = a[:35,:35,3,999]
If the values in b are not contiguous, then you will need to adjust its shape
c = a[b[:,None], b[None,:], 3, 999]
e.g.
In [754]: a=np.arange(3*4*5).reshape(3,4,5)
In [755]: b=np.array([2,0,1])
In [756]: a[b[:,None],b[None,:],3]
Out[756]:
array([[53, 43, 48],
[13, 3, 8],
[33, 23, 28]])
b[:,None] is a (3,1) array, b[None,:] a (1,3), together they broadcast to (3,3) arrays.
You may need to read up on broadcasting and advanced indexing.
More explicitly this indexing is:
a[[[2],[0],[1]], [[2,0,1]], 3]
np.ix_ is a handy tool for generating indexes like this:
In [795]: I,J = np.ix_(b,b)
In [796]: I
Out[796]:
array([[2],
[0],
[1]])
In [797]: J
Out[797]: array([[2, 0, 1]])
In [798]: a[I,J,3]
Out[798]:
array([[53, 43, 48],
[13, 3, 8],
[33, 23, 28]])