Scipy 稀疏矩阵循环永远存在 - 需要提高效率

Question

What is the most efficient way time & memory wise of writing this loop with sparse matrix (currently using csc_matrix)

for j in range(0, reducedsize):
    xs = sum(X[:, j])
    X[:, j] = X[:, j] / xs.data[0]

example:

reduced size (int) - 2500
X (csc_matrix) - 908x2500

The loop does iterate but it takes a very long time compared to just using numpy.

Answer 1

In [388]: from scipy import sparse                                                      

Make a sample matrix:

In [390]: M = sparse.random(10,8,.2, 'csc')                                             

Matrix sum:

In [393]: M.sum(axis=0)                                                                 
Out[393]: 
matrix([[1.95018736, 0.90924629, 1.93427113, 2.38816133, 1.08713479,
         0.        , 2.45435481, 0.        ]])

those 0's produce warning when dividing - and nan in the results:

In [394]: M/_                                                                           
/usr/local/lib/python3.6/dist-packages/scipy/sparse/base.py:599: RuntimeWarning: invalid value encountered in true_divide
  return np.true_divide(self.todense(), other)
Out[394]: 
matrix([[0.        , 0.        , 0.        , 0.        , 0.27079623,
                nan, 0.13752665,        nan],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
                nan, 0.32825122,        nan],
        [0.        , 0.        , 0.        , 0.        , 0.        ,
                nan, 0.        ,        nan],
 ...
                nan, 0.        ,        nan]])

the 0s also give a problem with your approach:

In [395]: for i in range(8): 
     ...:     xs = sum(M[:,i]) 
     ...:     M[:,i] = M[:,i]/xs.data[0] 
     ...:                                                                               
---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-395-0195298ead19> in <module>
      1 for i in range(8):
      2     xs = sum(M[:,i])
----> 3     M[:,i] = M[:,i]/xs.data[0]
      4 

IndexError: index 0 is out of bounds for axis 0 with size 0

But if we compare the columns without 0 sum the values match:

In [401]: Out[394][:,:5]                                                                
Out[401]: 
matrix([[0.        , 0.        , 0.        , 0.        , 0.27079623],
        [0.        , 0.        , 0.        , 0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.        , 0.        ],
        [0.49648886, 0.25626608, 0.        , 0.19162678, 0.72920377],
        [0.        , 0.        , 0.30200765, 0.        , 0.        ],
        [0.50351114, 0.        , 0.30445113, 0.41129367, 0.        ],
        [0.        , 0.74373392, 0.        , 0.        , 0.        ],
        [0.        , 0.        , 0.39354122, 0.        , 0.        ],
        [0.        , 0.        , 0.        , 0.39707955, 0.        ]])
In [402]: M.A[:,:5]                                                                     
Out[402]: 
array([[0.        , 0.        , 0.        , 0.        , 0.27079623],
       [0.        , 0.        , 0.        , 0.        , 0.        ],
       [0.        , 0.        , 0.        , 0.        , 0.        ],
       [0.        , 0.        , 0.        , 0.        , 0.        ],
       [0.49648886, 0.25626608, 0.        , 0.19162678, 0.72920377],
       [0.        , 0.        , 0.30200765, 0.        , 0.        ],
       [0.50351114, 0.        , 0.30445113, 0.41129367, 0.        ],
       [0.        , 0.74373392, 0.        , 0.        , 0.        ],
       [0.        , 0.        , 0.39354122, 0.        , 0.        ],
       [0.        , 0.        , 0.        , 0.39707955, 0.        ]])

Back in [394] I should have first converted the matrix sum to sparse, so the result will also be sparse. Sparse doesn't have elementwise divide, so I had to take the dense matrix inverse first. The 0s are still a nuisance.

In [409]: M.multiply(sparse.csr_matrix(1/Out[393]))                                     
...
Out[409]: 
<10x8 sparse matrix of type '<class 'numpy.float64'>'
    with 16 stored elements in Compressed Sparse Column format>

Answer 2

If you want to do it without any memory overhead (in-place)

Always think on how the data is actually stored. A small example on a csc matrix .

shape=(5,5)
X=sparse.random(shape[0], shape[1], density=0.5, format='csc')
print(X.todense())

[[0.12146814 0.         0.         0.04075121 0.28749552]
 [0.         0.92208639 0.         0.44279661 0.        ]
 [0.63509196 0.42334964 0.         0.         0.99160443]
 [0.         0.         0.25941113 0.44669367 0.00389409]
 [0.         0.         0.         0.         0.83226886]]

i=0 #first column
print(X.data[X.indptr[i]:X.indptr[i+1]])
[0.12146814 0.63509196]

A Numpy solution

So the only thing we want to do here is to modify the nonzero entries column by column in place. This can be easily done using a partly vectorized numpy solution. data is just the array which contains all non zero values, indptr stores the information where each column begins and ends.

def Numpy_csc_norm(data,indptr):
    for i in range(indptr.shape[0]-1):
        xs = np.sum(data[indptr[i]:indptr[i+1]])
        #Modify the view in place
        data[indptr[i]:indptr[i+1]]/=xs

Regarding performance this in-place solution is already not too bad. If you want to improve the performance further you could use Cython/Numba/ or some other compiled code which can be wrapped up in Python more or less easily.

A Numba solution

@nb.njit(fastmath=True,error_model="numpy",parallel=True)
def Numba_csc_norm(data,indptr):
    for i in nb.prange(indptr.shape[0]-1):
        acc=0
        for j in range(indptr[i],indptr[i+1]):
            acc+=data[j]
        for j in range(indptr[i],indptr[i+1]):
            data[j]/=acc

Performance

#Create a not to small example matrix
shape=(50_000,10_000)
X=sparse.random(shape[0], shape[1], density=0.001, format='csc')

#Not in-place from hpaulj
def hpaulj(X):
    acc=X.sum(axis=0)
    return X.multiply(sparse.csr_matrix(1./acc))

%timeit X2=hpaulj(X)
#6.54 ms ± 67.8 µs per loop (mean ± std. dev. of 7 runs, 100 loops each)

#All 2 variants are in-place, 
#but this shouldn't have a influence on the timings

%timeit Numpy_csc_norm(X.data,X.indptr)
#79.2 ms ± 914 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)

#parallel=False -> faster on tiny matrices
%timeit Numba_csc_norm(X.data,X.indptr)
#626 µs ± 30.6 µs per loop (mean ± std. dev. of 7 runs, 1 loop each)

#parallel=True -> faster on larger matrices
%timeit Numba_csc_norm(X.data,X.indptr)
#185 µs ± 5.39 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)