Raphael - 8 months ago 108

Python Question

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!

Answer

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.

=======================

There's an overlap in issues with Scipy sparse matrix alternative for getrow()