Initialize high dimensional sparse matrix

I want to initialize 300,000 x 300,0000 sparse matrix using sklearn, but it requires memory as if it was not sparse:

>>> from scipy import sparse
>>> sparse.rand(300000,300000,.1)   

it gives the error:

MemoryError: Unable to allocate 671. GiB for an array with shape (300000, 300000) and data type float64

which is the same error as if I initialize using numpy:

np.random.normal(size=[300000, 300000])

Even when I go to a very low density, it reproduces the error:

>>> from scipy import sparse
>>> from scipy import sparse
>>> sparse.rand(300000,300000,.000000000001)
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File ".../python3.8/site-packages/scipy/sparse/construct.py", line 842, in rand
    return random(m, n, density, format, dtype, random_state)
  File ".../lib/python3.8/site-packages/scipy/sparse/construct.py", line 788, in random
    ind = random_state.choice(mn, size=k, replace=False)
  File "mtrand.pyx", line 980, in numpy.random.mtrand.RandomState.choice
  File "mtrand.pyx", line 4528, in numpy.random.mtrand.RandomState.permutation
MemoryError: Unable to allocate 671. GiB for an array with shape (90000000000,) and data type int64

Is there a more memory-efficient way to create such a sparse matrix?

Answer

Just generate only what you need.

from scipy import sparse
import numpy as np

n, m = 300000, 300000
density = 0.00000001
size = int(n * m * density)

rows = np.random.randint(0, n, size=size)
cols = np.random.randint(0, m, size=size)
data = np.random.rand(size)

arr = sparse.csr_matrix((data, (rows, cols)), shape=(n, m))

This lets you build monster sparse arrays provided they’re sparse enough to fit into memory.

>>> arr
<300000x300000 sparse matrix of type '<class 'numpy.float64'>'
    with 900 stored elements in Compressed Sparse Row format>

This is probably how the sparse.rand constructor should be working anyway. If any row, col pairs collide it’ll add the data values together, which is probably fine for all applications I can think of.