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Notes NumPyReshaping & Views

Reshaping & ViewsTopic 40 of 776 min read

newaxis, expand_dims & squeeze

Add a length-1 dimension with np.newaxis / None or np.expand_dims, and remove length-1 dimensions with np.squeeze — the key to making shapes broadcast.

Five players each have a form rating: [1.15, 1.0, 0.95, 1.05, 1.1] — shape (5,). You want to multiply each player's row of a (5, 14) scores table by his rating. NumPy refuses, because broadcasting lines up shapes from the right (14 vs 5). The fix is not to change the data, but to add an extra dimension so the ratings become a column (5, 1). Adding and removing such size-1 dimensions is a small but everyday NumPy skill.

Definition

A length-1 dimension (also called a singleton axis) is an axis of size 1. It adds no new data but changes the array's shape and number of dimensions (ndim). np.newaxis (an alias for None) and np.expand_dims insert a length-1 axis; np.squeeze removes length-1 axes.

No new data — (5,) and (5, 1) and (1, 5) all hold the same 5 numbers.
Changes shape — but shape decides how broadcasting, matrix multiplication and many functions behave.
Views — all three return views; nothing is copied.

text

v = [1.15, 1.0, 0.95, 1.05, 1.1]          shape (5,)      ndim 1

v[np.newaxis, :]  -> [[1.15, 1.0, 0.95, 1.05, 1.1]]        shape (1, 5)  a row
v[:, np.newaxis]  -> [[1.15]
                      [1.0 ]
                      [0.95]                                shape (5, 1)  a column
                      [1.05]
                      [1.1 ]]

Syntax

python

a[np.newaxis, :]            # new axis at the front   (5,) -> (1, 5)
a[:, np.newaxis]            # new axis at the end     (5,) -> (5, 1)
a[:, None]                  # None works exactly like np.newaxis
np.expand_dims(a, axis)     # insert a length-1 axis at position 'axis'
np.squeeze(a, axis=None)    # remove length-1 axes (all, or only 'axis')
a.squeeze(axis=None)

Parameter	Meaning	Default
`np.newaxis` / `None`	used inside square brackets to mark where a new axis goes	—
`axis` (expand_dims)	position of the new axis in the result; an int or a tuple; negative counts from the end	— required
`axis` (squeeze)	which length-1 axis/axes to remove; `None` = remove all of them	`None`

Example — adding a dimension

python

import numpy as np

form = np.array([1.15, 1.0, 0.95, 1.05, 1.1])
print("original     :", form.shape, "ndim", form.ndim)
print("[np.newaxis] :", form[np.newaxis, :].shape)
print("[:, newaxis] :", form[:, np.newaxis].shape)
print("[:, None]    :", form[:, None].shape)
print("expand_dims 0:", np.expand_dims(form, axis=0).shape)
print("expand_dims 1:", np.expand_dims(form, axis=1).shape)
print("np.newaxis is None:", np.newaxis is None)

text

original     : (5,) ndim 1
[np.newaxis] : (1, 5)
[:, newaxis] : (5, 1)
[:, None]    : (5, 1)
expand_dims 0: (1, 5)
expand_dims 1: (5, 1)
np.newaxis is None: True

How it works: wherever you put np.newaxis in the index, a size-1 axis appears in that position. np.expand_dims(form, axis=1) does the same as form[:, np.newaxis] but reads more clearly in some code.

Example — why it matters: per-player broadcasting

python

import numpy as np

scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
form = np.array([1.1, 1.0, 0.9])        # one rating per player, shape (3,)

try:
    scores * form
except ValueError as e:
    print("ValueError:", e)

adjusted = scores * form[:, np.newaxis] # (3, 4) * (3, 1) -> works
print(adjusted.round(1))

text

ValueError: operands could not be broadcast together with shapes (3,4) (3,) 
[[79.2 49.5 96.8 34.1]
 [56.   0.  74.  88. ]
 [40.5 28.8  0.  60.3]]

How it works: comparing shapes from the right, (3, 4) vs (3,) compares 4 with 3 → fail. After form[:, np.newaxis] the shape is (3, 1): 4 vs 1 (1 stretches) and 3 vs 3 → OK. Every score in row i is multiplied by form[i].

Example — removing dimensions with squeeze

Many operations leave behind useless size-1 axes — e.g. picking one player with a slice, or an image with a single colour channel.

python

import numpy as np

one_player = np.array([[72, 45, 88, 31]])           # shape (1, 4)
print(one_player.shape, "->", one_player.squeeze().shape)

column = np.array([[72], [45], [88]])                # shape (3, 1)
print(column.shape, "->", np.squeeze(column).shape)

gray = np.zeros((1, 4, 4, 1))                        # batch of 1 image, 1 channel
print(gray.shape, "-> all:", gray.squeeze().shape, " axis=0 only:", gray.squeeze(axis=0).shape)

try:
    np.zeros((3, 4)).squeeze(axis=0)
except ValueError as e:
    print("ValueError:", e)

text

(1, 4) -> (4,)
(3, 1) -> (3,)
(1, 4, 4, 1) -> all: (4, 4)  axis=0 only: (4, 4, 1)
ValueError: cannot select an axis to squeeze out which has size not equal to one

How it works: squeeze() with no axis removes every size-1 axis. squeeze(axis=0) removes only that one. Asking to squeeze an axis whose size isn't 1 is an error.

Example — several axes at once and newaxis vs reshape

python

import numpy as np

v = np.array([72, 45, 88])
print(np.expand_dims(v, axis=(0, 2)).shape)  # tuple of positions
print(v[np.newaxis, :, np.newaxis].shape)     # same thing with newaxis
print(v.reshape(1, 3, 1).shape)               # same thing with reshape
print(np.array_equal(v[:, np.newaxis], v.reshape(-1, 1)))

text

(1, 3, 1)
(1, 3, 1)
(1, 3, 1)
True

Common mistakes

❌ np.newaxis(form) or form.newaxis. ✅ It goes inside the brackets: form[:, np.newaxis].
❌ Trying form.T to make a column. ✅ .T does nothing to 1D — use form[:, np.newaxis].
❌ a.squeeze(axis=0) when axis 0 has size 3 → ValueError: cannot select an axis to squeeze out which has size not equal to one. ✅ Check a.shape first.
❌ Calling squeeze() with no axis on data where a size-1 axis is meaningful (e.g. a batch that happens to contain one image) — it disappears too. ✅ Pass the exact axis.

Comparison — four ways to make a (5,) array a column (5, 1)

Way	Code	Notes
newaxis	`v[:, np.newaxis]`	most common in NumPy code
None	`v[:, None]`	identical, shorter
expand_dims	`np.expand_dims(v, axis=1)`	explicit, works with tuples of axes
reshape	`v.reshape(-1, 1)`	also works; from the broadcasting notebook

Interview tip

Q: What is the difference between shapes (5,), (5, 1) and (1, 5)? A: All hold 5 values. (5,) is a 1D array with no row/column orientation. (5, 1) is a 2D column (5 rows, 1 column) and broadcasts down the rows of a (5, n) array. (1, 5) is a 2D row and broadcasts across the columns of an (m, 5) array.

Key points to remember

A length-1 (singleton) axis adds no data but changes shape and ndim — which controls broadcasting.
np.newaxis is just None; use it inside brackets: v[:, np.newaxis] makes a column, v[np.newaxis, :] a row.
np.expand_dims(a, axis) inserts a size-1 axis at a position (int or tuple).
np.squeeze(a) removes all size-1 axes; squeeze(axis=k) removes only axis k and errors if its size isn't 1.
To broadcast one value per row against a (n, m) array, turn the (n,) array into (n, 1).
newaxis, expand_dims, squeeze and reshape(-1, 1) all return views — no data is copied.

Try it yourself

Row and column versions of a 1D array

import numpy as np

v = np.array([1.15, 1.0, 0.95])
print(v[np.newaxis, :], v[np.newaxis, :].shape)
print(v[:, np.newaxis], v[:, np.newaxis].shape)
print(np.expand_dims(v, 1).shape)

import numpy as np

v = np.array([1.15, 1.0, 0.95])
print(v[np.newaxis, :], v[np.newaxis, :].shape)
print(v[:, np.newaxis], v[:, np.newaxis].shape)
print(np.expand_dims(v, 1).shape)

Per-player form adjustment

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
form = np.array([1.1, 1.0, 0.9])
print((scores * form[:, None]).round(1))

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
form = np.array([1.1, 1.0, 0.9])
print((scores * form[:, None]).round(1))

Squeezing size-1 axes

import numpy as np

a = np.zeros((1, 3, 1, 2))
print(a.squeeze().shape)
print(a.squeeze(axis=0).shape)
print(a.squeeze(axis=2).shape)

import numpy as np

a = np.zeros((1, 3, 1, 2))
print(a.squeeze().shape)
print(a.squeeze(axis=0).shape)
print(a.squeeze(axis=2).shape)

Practice: bonus runs per match

import numpy as np

# 🏏 Your turn: add a different bonus to each PLAYER (row) using np.newaxis,
# then add a bonus per MATCH (column) using the 1D array directly.
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
player_bonus = np.array([5, 10, 15])
match_bonus = np.array([1, 2, 3, 4])

print(scores + player_bonus[:, np.newaxis])
print(scores + match_bonus)

import numpy as np

# 🏏 Your turn: add a different bonus to each PLAYER (row) using np.newaxis,
# then add a bonus per MATCH (column) using the 1D array directly.
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
player_bonus = np.array([5, 10, 15])
match_bonus = np.array([1, 2, 3, 4])

print(scores + player_bonus[:, np.newaxis])
print(scores + match_bonus)

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Opening notes

Notes NumPyReshaping & Views

Reshaping & ViewsTopic 40 of 776 min read

newaxis, expand_dims & squeeze

Add a length-1 dimension with np.newaxis / None or np.expand_dims, and remove length-1 dimensions with np.squeeze — the key to making shapes broadcast.

Definition

A length-1 dimension (also called a singleton axis) is an axis of size 1. It adds no new data but changes the array's shape and number of dimensions (ndim). np.newaxis (an alias for None) and np.expand_dims insert a length-1 axis; np.squeeze removes length-1 axes.

No new data — (5,) and (5, 1) and (1, 5) all hold the same 5 numbers.
Changes shape — but shape decides how broadcasting, matrix multiplication and many functions behave.
Views — all three return views; nothing is copied.

text

v = [1.15, 1.0, 0.95, 1.05, 1.1]          shape (5,)      ndim 1

v[np.newaxis, :]  -> [[1.15, 1.0, 0.95, 1.05, 1.1]]        shape (1, 5)  a row
v[:, np.newaxis]  -> [[1.15]
                      [1.0 ]
                      [0.95]                                shape (5, 1)  a column
                      [1.05]
                      [1.1 ]]

Syntax

python

a[np.newaxis, :]            # new axis at the front   (5,) -> (1, 5)
a[:, np.newaxis]            # new axis at the end     (5,) -> (5, 1)
a[:, None]                  # None works exactly like np.newaxis
np.expand_dims(a, axis)     # insert a length-1 axis at position 'axis'
np.squeeze(a, axis=None)    # remove length-1 axes (all, or only 'axis')
a.squeeze(axis=None)

Parameter	Meaning	Default
`np.newaxis` / `None`	used inside square brackets to mark where a new axis goes	—
`axis` (expand_dims)	position of the new axis in the result; an int or a tuple; negative counts from the end	— required
`axis` (squeeze)	which length-1 axis/axes to remove; `None` = remove all of them	`None`

Example — adding a dimension

python

import numpy as np

form = np.array([1.15, 1.0, 0.95, 1.05, 1.1])
print("original     :", form.shape, "ndim", form.ndim)
print("[np.newaxis] :", form[np.newaxis, :].shape)
print("[:, newaxis] :", form[:, np.newaxis].shape)
print("[:, None]    :", form[:, None].shape)
print("expand_dims 0:", np.expand_dims(form, axis=0).shape)
print("expand_dims 1:", np.expand_dims(form, axis=1).shape)
print("np.newaxis is None:", np.newaxis is None)

text

original     : (5,) ndim 1
[np.newaxis] : (1, 5)
[:, newaxis] : (5, 1)
[:, None]    : (5, 1)
expand_dims 0: (1, 5)
expand_dims 1: (5, 1)
np.newaxis is None: True

Example — why it matters: per-player broadcasting

python

import numpy as np

scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
form = np.array([1.1, 1.0, 0.9])        # one rating per player, shape (3,)

try:
    scores * form
except ValueError as e:
    print("ValueError:", e)

adjusted = scores * form[:, np.newaxis] # (3, 4) * (3, 1) -> works
print(adjusted.round(1))

text

ValueError: operands could not be broadcast together with shapes (3,4) (3,) 
[[79.2 49.5 96.8 34.1]
 [56.   0.  74.  88. ]
 [40.5 28.8  0.  60.3]]

Example — removing dimensions with squeeze

Many operations leave behind useless size-1 axes — e.g. picking one player with a slice, or an image with a single colour channel.

python

import numpy as np

one_player = np.array([[72, 45, 88, 31]])           # shape (1, 4)
print(one_player.shape, "->", one_player.squeeze().shape)

column = np.array([[72], [45], [88]])                # shape (3, 1)
print(column.shape, "->", np.squeeze(column).shape)

gray = np.zeros((1, 4, 4, 1))                        # batch of 1 image, 1 channel
print(gray.shape, "-> all:", gray.squeeze().shape, " axis=0 only:", gray.squeeze(axis=0).shape)

try:
    np.zeros((3, 4)).squeeze(axis=0)
except ValueError as e:
    print("ValueError:", e)

text

(1, 4) -> (4,)
(3, 1) -> (3,)
(1, 4, 4, 1) -> all: (4, 4)  axis=0 only: (4, 4, 1)
ValueError: cannot select an axis to squeeze out which has size not equal to one

How it works: squeeze() with no axis removes every size-1 axis. squeeze(axis=0) removes only that one. Asking to squeeze an axis whose size isn't 1 is an error.

Example — several axes at once and newaxis vs reshape

python

import numpy as np

v = np.array([72, 45, 88])
print(np.expand_dims(v, axis=(0, 2)).shape)  # tuple of positions
print(v[np.newaxis, :, np.newaxis].shape)     # same thing with newaxis
print(v.reshape(1, 3, 1).shape)               # same thing with reshape
print(np.array_equal(v[:, np.newaxis], v.reshape(-1, 1)))

text

(1, 3, 1)
(1, 3, 1)
(1, 3, 1)
True

Common mistakes

❌ np.newaxis(form) or form.newaxis. ✅ It goes inside the brackets: form[:, np.newaxis].
❌ Trying form.T to make a column. ✅ .T does nothing to 1D — use form[:, np.newaxis].
❌ a.squeeze(axis=0) when axis 0 has size 3 → ValueError: cannot select an axis to squeeze out which has size not equal to one. ✅ Check a.shape first.
❌ Calling squeeze() with no axis on data where a size-1 axis is meaningful (e.g. a batch that happens to contain one image) — it disappears too. ✅ Pass the exact axis.

Comparison — four ways to make a (5,) array a column (5, 1)

Way	Code	Notes
newaxis	`v[:, np.newaxis]`	most common in NumPy code
None	`v[:, None]`	identical, shorter
expand_dims	`np.expand_dims(v, axis=1)`	explicit, works with tuples of axes
reshape	`v.reshape(-1, 1)`	also works; from the broadcasting notebook

Interview tip

Key points to remember

A length-1 (singleton) axis adds no data but changes shape and ndim — which controls broadcasting.
np.newaxis is just None; use it inside brackets: v[:, np.newaxis] makes a column, v[np.newaxis, :] a row.
np.expand_dims(a, axis) inserts a size-1 axis at a position (int or tuple).
np.squeeze(a) removes all size-1 axes; squeeze(axis=k) removes only axis k and errors if its size isn't 1.
To broadcast one value per row against a (n, m) array, turn the (n,) array into (n, 1).
newaxis, expand_dims, squeeze and reshape(-1, 1) all return views — no data is copied.

Try it yourself

Row and column versions of a 1D array

import numpy as np

v = np.array([1.15, 1.0, 0.95])
print(v[np.newaxis, :], v[np.newaxis, :].shape)
print(v[:, np.newaxis], v[:, np.newaxis].shape)
print(np.expand_dims(v, 1).shape)

import numpy as np

v = np.array([1.15, 1.0, 0.95])
print(v[np.newaxis, :], v[np.newaxis, :].shape)
print(v[:, np.newaxis], v[:, np.newaxis].shape)
print(np.expand_dims(v, 1).shape)

Per-player form adjustment

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
form = np.array([1.1, 1.0, 0.9])
print((scores * form[:, None]).round(1))

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
form = np.array([1.1, 1.0, 0.9])
print((scores * form[:, None]).round(1))

Squeezing size-1 axes

import numpy as np

a = np.zeros((1, 3, 1, 2))
print(a.squeeze().shape)
print(a.squeeze(axis=0).shape)
print(a.squeeze(axis=2).shape)

import numpy as np

a = np.zeros((1, 3, 1, 2))
print(a.squeeze().shape)
print(a.squeeze(axis=0).shape)
print(a.squeeze(axis=2).shape)

Practice: bonus runs per match

import numpy as np

# 🏏 Your turn: add a different bonus to each PLAYER (row) using np.newaxis,
# then add a bonus per MATCH (column) using the 1D array directly.
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
player_bonus = np.array([5, 10, 15])
match_bonus = np.array([1, 2, 3, 4])

print(scores + player_bonus[:, np.newaxis])
print(scores + match_bonus)

import numpy as np

# 🏏 Your turn: add a different bonus to each PLAYER (row) using np.newaxis,
# then add a bonus per MATCH (column) using the 1D array directly.
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
player_bonus = np.array([5, 10, 15])
match_bonus = np.array([1, 2, 3, 4])

print(scores + player_bonus[:, np.newaxis])
print(scores + match_bonus)

Revision Flashcards

1 / 5

Tap a card to flip it and see the answer.