List with sparse data consumes less memory then the same data as numpy array

Question

I am working with very high dimensional vectors for machine learning and was thinking about using numpy to reduce the amount of memory used. I run a quick test to see how much memory I could save using numpy (1)(3):

Standard list

import random
random.seed(0)
vector = [random.random() for i in xrange(2**27)]

Numpy array

import numpy
import random
random.seed(0)
vector = numpy.fromiter((random.random() for i in xrange(2**27)), dtype=float)

Memory usage (2)

Numpy array: 1054 MB
Standard list: 2594 MB

Just like I expected.

By allocing a continues block of memory with native floats numpy only consumes about half of the memory the standard list is using.

Because I know my data is pretty spare, I did the same test with sparse data.

Standard list

import random
random.seed(0)
vector = [random.random() if random.random() < 0.00001 else 0.0 for i in xrange(2 ** 27)]

Numpy array

from numpy import fromiter
from random import random
random.seed(0)
vector = numpy.fromiter((random.random() if random.random() < 0.00001 else 0.0 for i in xrange(2 ** 27)), dtype=float)

Memory usage (2)

Numpy array: 1054 MB
Standard list: 529 MB

Now all of the sudden, the python list uses half the amount of memory the numpy array uses! Why?

One thing I could think of is that python dynamically switches to a dict representation when it detects that it contains very sparse data. Checking this could potentially add a lot of extra run-time overhead so I don't really think that this is going on.

Notes

1. I started a fresh new python shell for every test.
2. Memory measured with htop.
3. Run on 32bit Debian.

Answer 1

A Python list is just an array of references (pointers) to Python objects. In CPython (the usual Python implementation) a list gets slightly over-allocated to make expansion more efficient, but it never gets converted to a dict. See the source code for further details: List object implementation

In the sparse version of the list, you have a lot of pointers to a single int 0 object. Those pointers take up 32 bits = 4 bytes, but your numpy floats are certainly larger, probably 64 bits.

FWIW, to make the sparse list / array tests more accurate you should call random.seed(some_const) with the same seed in both versions so that you get the same number of zeroes in both the Python list and the numpy array.