How to add a sparse row to a sparse matrix in Python?

Question

This task is pretty trivial in NumPy like so

import numpy as np

a= np.array([[1,2,3,0,9],[3,2,6,2,7],[0,0,0,8,0],[1,0,0,0,3]])
a + a[1]

Output:

array([[ 4,  4,  9,  2, 16],
       [ 6,  4, 12,  4, 14],
       [ 3,  2,  6, 10,  7],
       [ 4,  2,  6,  2, 10]])

See how the vector dimensions are automatically broadcasted to each row of the matrix.

But when it comes to sparse matrices, there is a dimension mismatch error.

from scipy.sparse import *

a= csr_matrix([[1,2,3,0,9],[3,2,6,2,7],[0,0,0,8,0],[1,0,0,0,3]])
a + a[1]

Output:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
<ipython-input-32-74c48fe5106e> in <module>()
      2 
      3 a= csr_matrix([[1,2,3,0,9],[3,2,6,2,7],[0,0,0,8,0],[1,0,0,0,3]])
----> 4 a + a[1]

/opt/anaconda2/lib/python2.7/site-packages/scipy/sparse/compressed.pyc in __add__(self, other)
    337         elif isspmatrix(other):
    338             if (other.shape != self.shape):
--> 339                 raise ValueError("inconsistent shapes")
    340 
    341             return self._binopt(other,'_plus_')

ValueError: inconsistent shapes

There is a function for sparse multiplication, e.g., a.multiply(a[1]) for a * a[1] (which does its job perfectly), but I couldn't find one for addition.

I'm new to sparse matrices. Please help.

Answer 1

numpy style broadcasting has not been implemented for sparse matrices.

Multiplication, especially matrix multiplication, is well developed. In fact actions like row sum and selection of rows are implemented as matrix multiplications - e.g. M * <column vector of 1s>. Multiplication often results in a matrix that's as sparse if not more so.

Addition/subtraction is not well developed. It often results in a denser matrix. The extreme case is adding a scalar to all elements. Even in your example, the result is dense. Both a and a[1,:] have to be quite sparse to justify a pure sparse addition.

In [713]: a= np.array([[1,2,3,0,9],[3,2,6,2,7],[0,0,0,8,0],[1,0,0,0,3]])
In [714]: aM = sparse.csr_matrix(a)
In [715]: aM
Out[715]: 
<4x5 sparse matrix of type '<class 'numpy.int32'>'
    with 12 stored elements in Compressed Sparse Row format>

We can replicate the selected row by matrix multiplication - first the broadcasted dense approach:

In [719]: np.ones((4,1))*aM[1,:]
Out[719]: 
array([[ 3.,  2.,  6.,  2.,  7.],
       [ 3.,  2.,  6.,  2.,  7.],
       [ 3.,  2.,  6.,  2.,  7.],
       [ 3.,  2.,  6.,  2.,  7.]])
In [720]: np.ones((4,1))*aM[1,:]+aM    # dense matrix addition
Out[720]: 
matrix([[  4.,   4.,   9.,   2.,  16.],
        [  6.,   4.,  12.,   4.,  14.],
        [  3.,   2.,   6.,  10.,   7.],
        [  4.,   2.,   6.,   2.,  10.]])

sparse matrix multiplication:

In [721]: sparse.csr_matrix(np.ones((4,1)))*aM[1,:]
Out[721]: 
<4x5 sparse matrix of type '<class 'numpy.float64'>'
    with 20 stored elements in Compressed Sparse Row format>

sparse matrix addition:

In [722]: sparse.csr_matrix(np.ones((4,1)))*aM[1,:]+aM
Out[722]: 
<4x5 sparse matrix of type '<class 'numpy.float64'>'
    with 20 stored elements in Compressed Sparse Row format>
In [723]: _.A
Out[723]: 
array([[  4.,   4.,   9.,   2.,  16.],
       [  6.,   4.,  12.,   4.,  14.],
       [  3.,   2.,   6.,  10.,   7.],
       [  4.,   2.,   6.,   2.,  10.]])

This would be a better demonstration if aM and especially aM[1:] was sparse. I could also have specified the np.ones as int dtype to match aM. And making it a csc matrix would be more compact.