August 08, 2019

# Numpy vs PyTorch for Linear Algebra

Numpy is one of the most popular linear algebra libraries right now. There’s also PyTorch - an open source deep learning framework developed by Facebook Research. While the latter is best known for its machine learning capabilities, it can also be used for linear algebra, just like Numpy.

The most important difference between the two frameworks is naming. Numpy calls tensors (high dimensional matrices or vectors) arrays while in PyTorch there’s just called tensors. Everything else is quite similar.

## Why PyTorch?

Even if you already know Numpy, there are still a couple of reasons to switch to PyTorch for tensor computation. The main reason is the GPU acceleration. As you’ll see, using a GPU with PyTorch is super easy and super fast. If you do large computations, this is beneficial because it speeds things up a lot.

The other reason is the integration with other parts of the PyTorch framework. Most people use linear algebra for some kind of machine learning nowadays. In this case, using PyTorch is probably a better choice because the data can be used with the rest of the framework.

import torch


## Why Numpy?

Numpy is the most commonly used computing framework for linear algebra. A good use case of Numpy is quick experimentation and small projects because Numpy is a light weight framework compared to PyTorch.

Moreover, PyTorch lacks a few advanced features as you’ll read below so it’s strongly recommended to use numpy in those cases.

import numpy as np


## Using Both

Fortunately, using one framework doesn’t exclude the other. You can get the best of both worlds by converting between Numpy arrays and PyTorch tensors.

# Numpy -> PyTorch
tensor = torch.from_numpy(np_array)

# PyTorch -> Numpy
ndarray = tensor.numpy()


## New tensors

Numpy:

zeros  = np.zeros((4, 4))
ones   = np.ones((4, 4))
random = np.random.random((4, 4))


PyTorch:

zeros  = torch.zeros(4, 4)
ones   = torch.ones(4, 4)
random = torch.rand(4, 4)


## Basic Linear Algebra

### Indexing

Numpy:

# Index item
array[0, 0] # returns a float

# Index row
array[0, :] # returns an array


PyTorch:

# Index item
torch[0, 0] # returns a tensor

# Index row
torch[0, :] # returns a tensor


Numpy:

array + array2
array - array2


PyTorch:

tensor + tensor2
tensor - tensor2


### (Element wise) multiplication

Numpy:

# Element wise
array * array

# Matrix multiplication
array @ array


PyTorch:

# Element wise
tensor * tensor

# Matrix multiplication
tensor @ tensor


### Shape and dimensions

Numpy:

shap    = array.shape
num_dim = array.ndim


PyTorch:

shape   = tensor.shape
shape   = tensor.size() # equal to .shape
num_dim = tensor.dim()


### Reshaping

Numpy:

new_array = array.reshape((8, 2))


PyTorch:

new_tensor = tensor.view(8, 2)


### Determinant

Numpy:

np.linalg.det(array)


PyTorch:

# not natively supported


### Inverse and Moore-Pensore inverse

Numpy:

# Inverse
np.linalg.inv(array)

# Moore Pensore inverse
np.linalg.pinv(array)


PyTorch:

# Inverse
tensor.inverse()

# Moore Pensore inverse
tensor.pinverse()


### Sum/mean/std

These functions return floating point numbers in Numpy where PyTorch returns 1 by 1 tensors.

Numpy:

# Sum
array.sum()

# Mean
array.mean()

# Standard Deviation
array.std()


PyTorch:

# Sum
tensor.sum()

# Mean
tensor.mean()

# Standard Deviation
tensor.std()


### Transpose

Numpy:

array.T
array.transpose()


PyTorch:

tensor.t()


## Saving to disk

Saving results to disk is a huge time server. Here’s how you’d do it in Numpy or PyTorch.

Numpy:

np.save('file.npy', array)


PyTorch:

torch.save(tensor, 'file')


## Using the GPU

This is where PyTorch really shines. By copying an array to the GPU memory, there’s a huge potential for performance improvements due to heavy parallelization. Note that PyTorch uses CUDA under the hood so only NVIDIA GPUs are supported.

# put the tensor in GPU memory
gpu_tensor = tensor.gpu()


In Google Colab I got a 20.9 time speed up in multiplying a 10000 by 10000 matrix by a scaler when using the GPU.

If you do an operation on two arrays, both must be either on the CPU or GPU.