A simple way to get dimensions of a matrix "by eye"

Course Q&A Deep Learning Specialization Neural Networks and Deep Learning
1

I can’t seem to remember how the notation specifies rows or columns.

I found though, a heuristic for it that works well, and it is simple.

Say we have the matrices:

X = [[1,2],[3,4],[5,6]]
Y = [[1],[3],[5]]
Z = [ [[4,2], [3,1], [4,45]], [[4,2], [3,1], [4,45]] ]

According to this method the dimensions [ ] are:

[ X ] = 3 x 2
[ Y ] = 3 x 1
[ Z ] = 2 x 3 x 2

The steps are:

  • Count the number of elements (L_1) at the lowest level
    • Then the dimension is the number L_1

This step is repeated for each dimension, and you write it backwards, i.e
D = L_n, \dots, L_3, L_2, L_1

So for Z, the lowest level elements are arrays [a,b] (that is the last number you specify).

  • Also the number of commas + 1 will yield the right value.

The next level has 2 , so D is 3. We have 3 x 2 so far.

To my eyes it is easier to see the inner dimension first.

You can check it in python as:

>>> import numpy as np
>>> np.array(Z)
array([[[ 4,  2],
        [ 3,  1],
        [ 4, 45]],

       [[ 4,  2],
        [ 3,  1],
        [ 4, 45]]])
>>> Z = np.array(Z)
>>> Z.shape
(2, 3, 2)
2

Sounds reasonable.

I may count the number of elements, not “commas”, simply because “comma” is too small… :slight_smile:
And, also use this to double check the number of array dimension. (= numpy ndim)

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But, to be honest, as the number of dimensions is too high in Tensorflow, I almost give up to see in detail in my eyes, and totally rely on the computer with applying shape, slice, ndim, etc. :slight_smile:

3

Thanks for your reply. Yes, absolutely, it is actually better to trust the program after you get the idea…