Thread by @akshay_pachaar

Broadcasting in NumPy is widely used, yet poorly understood❗️

Today, I'll clearly explain how broadcasting works!

Same rules apply to PyTorch & TensorFlow!

Let's go! 🚀

Broadcasting describes how NumPy treats arrays with different shapes during arithmetic operations.

The smaller array is “broadcast” across the larger array, such that the 2 have compatible shapes.

Check this out👇

In the image below, scalar "b" is being stretched into an array with the same shape as "a".

But how do we generalise these things?

continue reading ... 📖

💫 General Rules:

1) Broadcasting starts with the trailing (i.e. rightmost) dimensions and works its way left .

2) Two dimensions are compatible, either when they are equal or one of them is 1.

Check out the examples 👇

When ever a one dimensional array is involved in broadcasting, consider it as a row vector!

Array → [1, 2, 3] ; shape → (3,)
Treated as → [[1, 2, 3]] ; shape → (1, 3)

Remember, broadcasting occurs from trailing dimension!

Check this out👇

Let's check a scenario when broadcasting doesn't occur!

- a(4x3)
- b(4) will be treated as b(1x4)

Now, broadcasting starts from trailing dimension but (4x3) & (1x4) are not compatible!

Check this out👇

Let's take one more example to make out understanding concrete!

Remember, 1D array treated as a row vector while broadcasting!

Check this out👇

Here's how an array of shape (4x1) & (3,) broadcasts together!

Check this out👇

Why use broadcasting❓

Broadcasting provides a means of vectorising array operations so that looping occurs in C instead of Python.

It does this without making needless copies of data and usually leads to efficient algorithm implementations.

That's a wrap!

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