I am having trouble visualizing scalars, vectors and matrices as how they are written in a math/physics class to how they would be represented in plain Python and numpy and their corresponding notions of dimensions, axes and shapes.

1. If I have a scalar, say 5

>>> b = np.array(5)
>>> np.ndim(b)
0

I have 0 dimensions for 5 but what are the axes here? There are functions for ndim and shape but not axes.

2. For a vector like this:

we say that we have 2 dimensions in physics/math class because it represents a 2D vector but it looks like numpy uses a different notion of this.

Why is it that ndim gives 1 and shape gives what the dimension is?

>>> c = np.array([1,-3])
>>> c
array([ 1, -3])
>>> c.ndim
1
>>> c.shape
(2,)

np.ndim gives 1 then?

I have looked at

4. When it comes to multidimensional arrays, how would I represent/visualize multiple values for all the points in a 3D cube? Say we have a Rubik's cube and each of the sub cubes has a temperature and a color represented with red, green and blue so 4 values for each cube?

CodePudding user response：

A scalar is not an array, so it has 0 dimensions.

np.array([1,-3]) is a 1D array, so c.shape returns a tuple with only one element (2,), just the first dimension and it's telling you there is only 1 dimension and 2 elements in that dimension.

You are correct np.array([[1], [-3]]) is the vector you have in 2. c.shape gives (2,1) meaning there are 2 rows and 1 column. c.ndim gives 2 since there are 2 dimensions x and y. It's a 2D/planar array

For 3., you would create it as np.array([[1,2,3], [4,5,6], [7,8,9]]). shape returns (3,3) meaning 3 rows and 3 columns. ndim returns 2 because it's still a 2D/planar array.

CodePudding user response：

A ndarray has a shape, a tuple. ndim is the length of that tuple, and may be 0. The array has ndim axes (sometimes called dimensions).

 np.array(5)

has shape (), 0 ndim and no axes.

np.array([1,2,3,4])

has (4,) shape, and 1 axis. It can be reshaped to (4,1), or (1,4) or (2,2) or even (2,1,2) or (1,4,1).

Your A can be created with

A = np.arange(1,10).reshape(3,3)

That's a 9 element 1d array reshaped to (3,3)

numpy arrays have a print display, with [] marking dimensional nesting. A.tolist() produces a list with 3 elements, each a 3 element list.

Rows, columns, planes are useful ways of talking about arrays, but are not a formal part of their definition.