Patrick - 10 months ago 265

Python Question

I have a large

`csr_matrix`

Here is my current solution and the main idea is to process them row by row:

`row = csr_matrix.getrow(row_number).toarray()[0].ravel()`

top_ten_indicies = row.argsort()[-10:]

top_ten_values = row[row.argsort()[-10:]]

By doing this, the advantages of

`csr_matrix`

Answer

I don't see what the advantages of `csr`

format are in this case. Sure, all the nonzero values are collected in one `.data`

array, with the corresponding column indexes in `.indices`

. But they are in blocks of varying length. And that means they can't be processed in parallel or with `numpy`

array strides.

One solution is the pad those blocks into common length blocks. That's what `.toarray()`

does. Then you can find the maximum values with `argsort(axis=1) or with`

argpartition`.

Another is to break them into row sized blocks, and process each of those. That's what you are doing with the `.getrow`

. Another way of breaking them up is convert to `lil`

format, and process the sublists of the `.data`

and `.rows`

arrays.

A possible third option is to use the `ufunc`

`reduceat`

method. This lets you apply `ufunc`

`reduction`

methods to sequential blocks of an array. There are established `ufunc`

like `np.add`

that take advantage of this. `argsort`

is not such a function. But there is a way of constructing a `ufunc`

from a Python function, and gain some modest speed over regular Python iteration. [I need to look up a recent SO question that illustrates this.]

I'll illustrate some of this with a simpler function, sum over rows.

If `A2`

is a csr matrix.

```
A2.sum(axis=1) # the fastest compile csr method
A2.A.sum(axis=1) # same, but with a dense intermediary
[np.sum(l.data) for l in A2] # iterate over the rows of A2
[np.sum(A2.getrow(i).data) for i in range(A2.shape[0])] # iterate with index
[np.sum(l) for l in A2.tolil().data] # sum the sublists of lil format
np.add.reduceat(A2.data, A2.indptr[:-1]) # with reduceat
```

`A2.sum(axis=1)`

is implemented as a matrix multiplication. That's not relevant to the sort problem, but still an interesting way of looking at the summation problem. Remember `csr`

format was developed for efficient multiplication.

For a my current sample matrix (created for another SO sparse question)

```
<8x47752 sparse matrix of type '<class 'numpy.float32'>'
with 32 stored elements in Compressed Sparse Row format>
```

some comparative times are

```
In [694]: timeit np.add.reduceat(A2.data, A2.indptr[:-1])
100000 loops, best of 3: 7.41 µs per loop
In [695]: timeit A2.sum(axis=1)
10000 loops, best of 3: 71.6 µs per loop
In [696]: timeit [np.sum(l) for l in A2.tolil().data]
1000 loops, best of 3: 280 µs per loop
```

Everything else is 1ms or more.

I suggest focusing on developing your one-row function, something like:

```
def max_n(row_data, row_indices, n):
i = row_data.argsort()[-n:]
# i = row_data.argpartition(-n)[-n:]
top_values = row_data[i]
top_indices = row_indices[i] # do the sparse indices matter?
return top_values, top_indices, i
```

Then see how if fits in one of these iteration methods. `tolil()`

looks most promising.

I haven't addressed the question of how to collect these results. Should they be lists of lists, array with 10 columns, another sparse matrix with 10 values per row, etc.?

sorting each row of a large sparse & saving top K values & column index - Similar question from several years back, but unanswered.

Argmax of each row or column in scipy sparse matrix - Recent question seeking `argmax`

for rows of `csr`

. I discuss some of the same issues.

how to speed up loop in numpy? - example of how to use `np.frompyfunc`

to create a `ufunc`

. I don't know if the resulting function has the `.reduceat`

method.

Increasing value of top k elements in sparse matrix - get the top k elements of csr (not by row). Case for `argpartition`

.

The row summation implemented with `np.frompyfunc`

:

```
In [741]: def foo(a,b):
return a+b
In [742]: vfoo=np.frompyfunc(foo,2,1)
In [743]: timeit vfoo.reduceat(A2.data,A2.indptr[:-1],dtype=object).astype(float)
10000 loops, best of 3: 26.2 µs per loop
```

That's respectable speed. But I can't think of a way of writing a binary function (takes to 2 arguments) that would implement `argsort`

via reduction. So this is probably a deadend for this problem.