[python] What are the advantages of NumPy over regular Python lists?

What are the advantages of NumPy over regular Python lists?

I have approximately 100 financial markets series, and I am going to create a cube array of 100x100x100 = 1 million cells. I will be regressing (3-variable) each x with each y and z, to fill the array with standard errors.

I have heard that for "large matrices" I should use NumPy as opposed to Python lists, for performance and scalability reasons. Thing is, I know Python lists and they seem to work for me.

What will the benefits be if I move to NumPy?

What if I had 1000 series (that is, 1 billion floating point cells in the cube)?

Here's a nice answer from the FAQ on the scipy.org website:

What advantages do NumPy arrays offer over (nested) Python lists?

Python’s lists are efficient general-purpose containers. They support (fairly) efficient insertion, deletion, appending, and concatenation, and Python’s list comprehensions make them easy to construct and manipulate. However, they have certain limitations: they don’t support “vectorized” operations like elementwise addition and multiplication, and the fact that they can contain objects of differing types mean that Python must store type information for every element, and must execute type dispatching code when operating on each element. This also means that very few list operations can be carried out by efficient C loops – each iteration would require type checks and other Python API bookkeeping.

NumPy is not just more efficient; it is also more convenient. You get a lot of vector and matrix operations for free, which sometimes allow one to avoid unnecessary work. And they are also efficiently implemented.

For example, you could read your cube directly from a file into an array:

x = numpy.fromfile(file=open("data"), dtype=float).reshape((100, 100, 100))

Sum along the second dimension:

s = x.sum(axis=1)

Find which cells are above a threshold:

(x > 0.5).nonzero()

Remove every even-indexed slice along the third dimension:

x[:, :, ::2]

Also, many useful libraries work with NumPy arrays. For example, statistical analysis and visualization libraries.

Even if you don't have performance problems, learning NumPy is worth the effort.

All have highlighted almost all major differences between numpy array and python list, I will just brief them out here:

1. Numpy arrays have a fixed size at creation, unlike python lists (which can grow dynamically). Changing the size of ndarray will create a new array and delete the original.

2. The elements in a Numpy array are all required to be of the same data type (we can have the heterogeneous type as well but that will not gonna permit you mathematical operations) and thus will be the same size in memory

3. Numpy arrays are facilitated advances mathematical and other types of operations on large numbers of data. Typically such operations are executed more efficiently and with less code than is possible using pythons build in sequences

Alex mentioned memory efficiency, and Roberto mentions convenience, and these are both good points. For a few more ideas, I'll mention speed and functionality.

Functionality: You get a lot built in with NumPy, FFTs, convolutions, fast searching, basic statistics, linear algebra, histograms, etc. And really, who can live without FFTs?

Speed: Here's a test on doing a sum over a list and a NumPy array, showing that the sum on the NumPy array is 10x faster (in this test -- mileage may vary).

from numpy import arange
from timeit import Timer

Nelements = 10000
Ntimeits = 10000

x = arange(Nelements)
y = range(Nelements)

t_numpy = Timer("x.sum()", "from __main__ import x")
t_list = Timer("sum(y)", "from __main__ import y")
print("numpy: %.3e" % (t_numpy.timeit(Ntimeits)/Ntimeits,))
print("list:  %.3e" % (t_list.timeit(Ntimeits)/Ntimeits,))

which on my systems (while I'm running a backup) gives:

numpy: 3.004e-05
list:  5.363e-04