for a project, I need an efficient function in python that solves to following task:
Given a very large List X of long sparse Vectors (=> big sparse Matrix) and another Matrix Y that contains a single Vector y, I want a List of "distances", that y has to every Element of X. Hereby the "distance" is defined like this:
Compare each Element of the two Vectors, always take the lower one and sum them up.
Example:
X = [[0,0,2],
[1,0,0],
[3,1,0]]
Y = [[1,0,2]]
The function should return dist = [2,1,1]
In my project, both X and Y contain a lot of zeros and come in as an instance of:
<class 'scipy.sparse.csr.csr_matrix'>
So far so good and I managed to write a functions that solves this task, but is very slow and horrible inefficient. I need some tips on how to efficienty process/iterate the sparse Matrices. This is my function:
def get_distances(X, Y):
Ret=[]
rows, cols = X.shape
for i in range(0,rows):
dist = 0
sample = X.getrow(i).todense()
test = Y.getrow(0).todense()
rows_s, cols_s = sample.shape
rows_t, cols_t = test.shape
for s,t in zip(range(0, cols_s), range(0, cols_t)):
dist += min(sample[0,s], test[0,t])
X_ret.append([dist])
return ret
To do my Operations, I convert the sparse matrices to dense matrices which is of course horrible, but I did not know how to do it better. Do you know how to improve my code and make the function faster?
Thank you a lot!
I revised your function and ran it in
import numpy as np
from scipy import sparse
def get_distances(X, Y):
ret=[]
for row in X:
sample = row.A
test = Y.getrow(0).A
dist = np.minimum(sample[0,:], test[0,:]).sum()
ret.append(dist)
return ret
X = [[0,0,2],
[1,0,0],
[3,1,0]]
Y = [[1,0,2]]
XM = sparse.csr_matrix(X)
YM = sparse.csr_matrix(Y)
print( get_distances(XM,YM))
print (np.minimum(XM.A, YM.A).sum(axis=1))
producing
1255:~/mypy$ python3 stack37056258.py
[2, 1, 1]
[2 1 1]
np.minimum takes element wise minimum of two arrays (may be 2d), so I don't need to iterate on columns. I also don't need to use indexing.
minimum is also implemented for sparse matrices, but I get a segmenation error when I try to apply it to your X (with 3 rows) and Y (with 1). If they are the same size this works:
Ys = sparse.vstack((YM,YM,YM))
print(Ys.shape)
print (XM.minimum(Ys).sum(axis=1))
Converting the single row matrix to an array also gets around the error - because it ends up using the dense version, np.minimum(XM.todense(), YM.A).
print (XM.minimum(YM.A).sum(axis=1))
When I try other element by element operations on these 2 matrices I get ValueError: inconsistent shapes, e.g. XM+YM, or XM<YM. Looks like sparse does not implement broadcasting as numpy arrays does.
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Comparison of ways of replicating a 1 row sparse matrix many times
In [271]: A=sparse.csr_matrix([0,1,0,0,1])
In [272]: timeit sparse.vstack([A]*3000).A
10 loops, best of 3: 32.3 ms per loop
In [273]: timeit sparse.kron(A,np.ones((3000,1),int)).A
1000 loops, best of 3: 1.27 ms per loop
For many times, kron is better than vstack.
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There's an overlap in issues with Scipy sparse matrix alternative for getrow()