Multidimensional Slicing

For Numpy arrays with more than 1 dimension, we slice by passing one selector per axis.

General form:

2D array: arr[row_selector, col_selector]
3D array: arr[axis0_selector, axis1_selector, axis2_selector]
nD array: arr[selector0, selector1, ..., selectorN]

Each selector can be:

an integer (pick one index)
a slice (start:end:step)
a list/array of indices
a boolean mask
... (ellipsis, “fill the rest”)
None (add a new axis)

2D Basics

matrix = np.array([
    [1, 2, 3, 4],
    [5, 6, 7, 8],
    [9, 10, 11, 12],
])
 
matrix.shape
# (3, 4)

matrix[0, 0]      # 1 (single value)
matrix[1, :]      # [5, 6, 7, 8] (row)
matrix[:, 2]      # [3, 7, 11] (column)
matrix[0:2, 1:3]  # [[2, 3], [6, 7]]

Negative Indexing and Reverse Slicing

matrix[-1, -1]  # 12 (last row, last column)
matrix[::-1, :] # rows reversed
matrix[:, ::-1] # columns reversed
matrix[:, -2:]  # last 2 columns

3D Slicing

cube = np.arange(2 * 3 * 4).reshape(2, 3, 4)
cube.shape
# (2, 3, 4)
 
cube[0, :, :]    # first 2D block
cube[:, 1, :]    # all blocks, second row
cube[:, :, 2]    # all blocks, third column
cube[:, 1, 1:4]  # slice on last axis

Ellipsis and New Axis

cube[..., 0]        # same as cube[:, :, 0]
cube[:, None, :, :] # adds one dimension

None (or np.newaxis) is useful to reshape arrays before broadcasting.

Integer and Boolean Indexing

matrix[[0, 2], :]   # take rows 0 and 2
matrix[:, [1, 3]]   # take columns 1 and 3
 
mask = matrix % 2 == 0
matrix[mask]        # flattened array with all even values

Assignment with Slices

matrix[:, 0] = 0     # set first column to zero
matrix[0:2, 1:3] = 9 # set a submatrix

Shape Behavior (Important)

Using an integer index removes that axis. Using a slice preserves it.

matrix[1, :].shape   # (4,)
matrix[1:2, :].shape # (1, 4)

View vs Copy

Basic slicing (like arr[1:4, :]) usually returns a view.
Advanced indexing (lists/boolean masks) usually returns a copy.

This matters when you modify the result and expect the original array to change.

Equinox

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