Accessing elements in coo_matrix

Question

This is a very simple question. For SciPy sparse matrices like coo_matrix, how does one access individual elements?

To give an analogy to Eigen linear algebra library. One can access element (i,j) using coeffRef as follows:

myMatrix.coeffRef(i,j)

Answer 1

From the docs for coo_matrix:

 |  Intended Usage
 |      - COO is a fast format for constructing sparse matrices
 |      - Once a matrix has been constructed, convert to CSR or
 |        CSC format for fast arithmetic and matrix vector operations
 |      - By default when converting to CSR or CSC format, duplicate (i,j)
 |        entries will be summed together.  This facilitates efficient
 |        construction of finite element matrices and the like. (see example)

And indeed, csr_matrix supports the indexing in an expected way:

>>> from scipy.sparse import coo_matrix
>>> m = coo_matrix([[1, 2, 3], [4, 5, 6]])
>>> m1 = m.tocsr()
>>> m1[1, 2]
6
>>> m1
<2x3 sparse matrix of type '<type 'numpy.int64'>'
    with 6 stored elements in Compressed Sparse Row format>

(The way I found the above quote from the docs was >>> help(m) which is equivalent to the online docs).

Answer 2

To expand on converting a coo matrix to csr to index, here are some timings for a small sparse matrix

Make the matrix

In [158]: M=sparse.coo_matrix([[0,1,2,0,0],[0,0,0,1,0],[0,1,0,0,0]])

In [159]: timeit M[1,2]
TypeError: 'coo_matrix' object is not subscriptable

In [160]: timeit M.tocsc()[1,2]
1000 loops, best of 3: 375 µs per loop

In [161]: timeit M.tocsr()[1,2]
1000 loops, best of 3: 241 µs per loop

In [162]: timeit M.todok()[1,2]
10000 loops, best of 3: 65.8 µs per loop

In [163]: timeit M.tolil()[1,2]
1000 loops, best of 3: 270 µs per loop

Apparently for selecting a single element, dok, is fastests (counting the conversion time). This format is actually a dictionary, which of course has fast element access.

But if you are frequently accessing whole rows, or whole columns, or iterating over rows or columns, you need to read the docs more carefully, and may be do your own time tests of typical arrays.

If you are setting values, not just reading them, timings and even implementation can be different. You will get an efficiency warning if you try to change a 0 element of a csr or csc format.