2020_High_Performance_Python_-or_Humans_O'Reilly_Media,_Inc. 580.pdf

then simply say “all other values are zero.” In addition to these memory
savings, many algorithms have special ways of dealing with sparse matri‐
ces that give additional computational benefits:
>>> from scipy import sparse
>>> A_sparse = sparse . random ( 2048 , 2048 , 0.05 ) . tocsr ()
>>> A_sparse
< 2048 x2048 sparse matrix of type '<class ' numpy . float64 '>'
with 209715 stored elements in Compressed Sparse Row format >
>>> % timeit A_sparse * A_sparse
150 ms ± 1.71 ms per loop ( mean ± std . dev . of 7 runs , 10 loops
each )
>>> A_dense = A_sparse . todense ()
>>> type ( A_dense )
numpy . matrix
>>> % timeit A_dense * A_dense
571 ms ± 14.5 ms per loop ( mean ± std . dev . of 7 runs , 1 loop each )
The simplest implementation of this is for COO matrices in SciPy, where