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Notes NumPyReshaping & Views

Reshaping & ViewsTopic 39 of 777 min read

Transpose, .T & swapaxes

Flip rows and columns with .T and np.transpose, reorder axes of 3D data, and swap two axes with swapaxes — plus why you would transpose data at all.

Watch the lesson

1 video on CodeWithMunnaX

Our squad table is players × matches: each row is a player. But a match-day analyst wants to read it match by match — "show me everyone's score in match 3". Instead of rebuilding the data, you just flip it so matches become rows. That flip is the transpose.

Definition

Transposing an array reverses (or reorders) its axes. For a 2D array this means rows become columns and columns become rows: an array of shape (r, c) becomes (c, r), and the element at [i, j] moves to [j, i]. The data itself does not change, and the result is a view.

Flip across the diagonal — the main diagonal ([0,0], [1,1], …) stays put; everything else mirrors across it.
[i, j] → [j, i] — Rohit's match-3 score is scores[1, 2]; in the transpose it is T[2, 1].
View — no data is copied; NumPy just reads the same memory in a different order.

text

Original (players × matches), shape (3, 4):     Transposed (matches × players), shape (4, 3):

          M1  M2  M3  M4                                Virat  Rohit  Hardik
Virat  [  72  45  88  31 ]                        M1  [   72     56     45  ]
Rohit  [  56   0  74  88 ]                        M2  [   45      0     32  ]
Hardik [  45  32   0  67 ]                        M3  [   88     74      0  ]
                                                  M4  [   31     88     67  ]

Syntax

python

a.T                               # attribute (no brackets) — reverses all axes
a.transpose()                     # method — same as a.T
np.transpose(a, axes=None)        # function; axes lets you choose the new order
a.transpose(2, 0, 1)              # e.g. 3D: new axis 0 = old axis 2, ...
np.swapaxes(a, axis1, axis2)      # swap exactly two axes
a.swapaxes(axis1, axis2)
np.moveaxis(a, source, destination)   # move one axis to a new position

Parameter	Meaning	Default
`a`	input array	— required
`axes`	a tuple giving the new order of the old axes, e.g. `(1, 0)` or `(2, 0, 1)`	`None` = reverse all axes
`axis1`, `axis2`	(swapaxes) the two axes to exchange	— required
`source`, `destination`	(moveaxis) where the axis is now, and where it should go	— required

Example — players × matches → matches × players

python

import numpy as np

scores = np.array([
    [72, 45, 88, 31],   # Virat
    [56,  0, 74, 88],   # Rohit
    [45, 32,  0, 67],   # Hardik
])
t = scores.T
print("original:", scores.shape, " transposed:", t.shape)
print(t)
print("Rohit, match 3:", scores[1, 2], "==", t[2, 1])
print("same as np.transpose:", np.array_equal(t, np.transpose(scores)))

text

original: (3, 4)  transposed: (4, 3)
[[72 56 45]
 [45  0 32]
 [88 74  0]
 [31 88 67]]
Rohit, match 3: 74 == 74
same as np.transpose: True

How it works: .T turns the 3×4 table into a 4×3 table. Each row of t is now one match, so t[2] reads "everyone's score in match 3". Value 74 moved from [1, 2] to [2, 1].

Why would you transpose data?

Reason	IPL example
1. Change your analysis perspective	data is players × matches but you want to ask match-centric questions: `t[6].argmax()` = best player of match 7
2. Match shapes for an operation	matrix multiplication needs inner dimensions to agree: `(3, 4) @ (3, 4)` fails but `(3, 4) @ (4, 3)` works, so you write `A @ B.T`
3. Fit what another library expects	Pandas and scikit-learn want rows = records/observations, columns = features; if your data is the other way round, transpose it
4. Image data	images are `(height, width, channels)` but some deep-learning libraries want `(channels, height, width)` → `img.transpose(2, 0, 1)`

Example — match-centric view and a matrix product

python

import numpy as np

players = ["Virat", "Rohit", "Hardik"]
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
by_match = scores.T
for m, row in enumerate(by_match, start=1):
    print(f"Match {m}: best = {players[row.argmax()]} ({row.max()})")

print("scores @ scores.T shape:", (scores @ scores.T).shape)
try:
    scores @ scores
except ValueError as e:
    print("scores @ scores fails:", str(e)[:60], "...")

text

Match 1: best = Virat (72)
Match 2: best = Virat (45)
Match 3: best = Virat (88)
Match 4: best = Rohit (88)
scores @ scores.T shape: (3, 3)
scores @ scores fails: matmul: Input operand 1 has a mismatch in its core dimension ...

How it works: looping over scores.T gives one match per iteration. For @, (3, 4) @ (4, 3) works because the inner sizes (4 and 4) match; (3, 4) @ (3, 4) does not.

Example — 3D arrays: transpose with axes, and swapaxes

python

import numpy as np

# 2 seasons x 3 players x 4 matches
data = np.arange(24).reshape(2, 3, 4)
print("original      :", data.shape)
print(".T            :", data.T.shape)                     # reverses all axes
print("transpose(1,0,2):", data.transpose(1, 0, 2).shape)  # players first
print("swapaxes(0, 2):", np.swapaxes(data, 0, 2).shape)
print("moveaxis(0, -1):", np.moveaxis(data, 0, -1).shape)

img = np.zeros((4, 6, 3))          # height, width, RGB channels
print("image HWC -> CHW:", img.transpose(2, 0, 1).shape)

text

original      : (2, 3, 4)
.T            : (4, 3, 2)
transpose(1,0,2): (3, 2, 4)
swapaxes(0, 2): (4, 3, 2)
moveaxis(0, -1): (3, 4, 2)
image HWC -> CHW: (3, 4, 6)

How it works: axes=(1, 0, 2) means "new axis 0 is old axis 1 (players), new axis 1 is old axis 0 (seasons), axis 2 stays". swapaxes(0, 2) exchanges just those two. moveaxis(0, -1) moves the seasons axis to the end and keeps the others in order.

Example — .T does nothing to a 1D array

python

import numpy as np

v = np.array([72, 45, 88])
print(v.shape, "->", v.T.shape)              # unchanged!
print(v.reshape(-1, 1).shape)                # a real column
print(v[:, np.newaxis].shape)                # also a column
print(v.reshape(1, -1).T.shape)              # row (1, 3) -> column (3, 1)

text

(3,) -> (3,)
(3, 1)
(3, 1)
(3, 1)

How it works: a 1D array has only one axis, so reversing its axes changes nothing. To get a column, first give it a second axis with reshape(-1, 1) or np.newaxis.

Common mistakes

❌ scores.T() → TypeError: 'numpy.ndarray' object is not callable. ✅ .T is an attribute: scores.T (or call scores.transpose()).
❌ Using .T to turn a 1D array into a column. ✅ v.reshape(-1, 1) or v[:, np.newaxis].
❌ Using reshape(4, 3) when you meant transpose. ✅ reshape re-reads in order; only .T maps [i, j] to [j, i].
❌ Modifying a transposed array and expecting the original to stay the same. ✅ .T is a view; use .T.copy() for independence.

Comparison — reshape vs transpose on a (2, 3) array

python

import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6]])
print("a.reshape(3, 2):")
print(a.reshape(3, 2))
print("a.T:")
print(a.T)

text

a.reshape(3, 2):
[[1 2]
 [3 4]
 [5 6]]
a.T:
[[1 4]
 [2 5]
 [3 6]]

	`a.reshape(3, 2)`	`a.T`
Shape	`(3, 2)`	`(3, 2)`
Row 0	`[1, 2]` — next values in reading order	`[1, 4]` — the old column 0
Meaning of rows	none — just regrouped	old columns

Interview tip

Q: Does a.T copy the data? How would you check? A: No, it returns a view — only the strides (how memory is stepped through) change. Check with np.shares_memory(a, a.T) → True. (If a owns its data, a.T.base is a is also True.)

Key points to remember

Transpose flips rows and columns: shape (r, c) becomes (c, r) and [i, j] moves to [j, i].
.T is an attribute (no brackets); a.transpose() and np.transpose(a) do the same.
The transpose is a view — no data is copied.
For 3D+ arrays, transpose(axes) reorders axes in any order; .T reverses them all.
swapaxes(i, j) exchanges two axes; moveaxis(src, dst) moves one axis.
.T does nothing to a 1D array — use reshape(-1, 1) or [:, np.newaxis] for a column.
Transpose to change perspective (matches × players), to make shapes fit (A @ B.T), or to match what a library expects.

Try it yourself

Players × matches → matches × players

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
print(scores.shape, "->", scores.T.shape)
print(scores.T)

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
print(scores.shape, "->", scores.T.shape)
print(scores.T)

Best performer of each match

import numpy as np

players = ["Virat", "Rohit", "Hardik"]
scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
for m, row in enumerate(scores.T, start=1):
    print("Match", m, "->", players[row.argmax()], row.max())

import numpy as np

players = ["Virat", "Rohit", "Hardik"]
scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
for m, row in enumerate(scores.T, start=1):
    print("Match", m, "->", players[row.argmax()], row.max())

Reordering axes in 3D

import numpy as np

data = np.arange(24).reshape(2, 3, 4)
print(data.T.shape)
print(data.transpose(1, 0, 2).shape)
print(data.swapaxes(1, 2).shape)
print(np.moveaxis(data, -1, 0).shape)

import numpy as np

data = np.arange(24).reshape(2, 3, 4)
print(data.T.shape)
print(data.transpose(1, 0, 2).shape)
print(data.swapaxes(1, 2).shape)
print(np.moveaxis(data, -1, 0).shape)

Practice: match totals via transpose

import numpy as np

# 🏏 Your turn: transpose the table so each row is a match, then print
# each match's team total. Check it equals scores.sum(axis=0).
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])

by_match = scores.T
print(by_match.sum(axis=1))
print(scores.sum(axis=0))

import numpy as np

# 🏏 Your turn: transpose the table so each row is a match, then print
# each match's team total. Check it equals scores.sum(axis=0).
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])

by_match = scores.T
print(by_match.sum(axis=1))
print(scores.sum(axis=0))

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Opening notes

Notes NumPyReshaping & Views

Reshaping & ViewsTopic 39 of 777 min read

Transpose, .T & swapaxes

Flip rows and columns with .T and np.transpose, reorder axes of 3D data, and swap two axes with swapaxes — plus why you would transpose data at all.

Watch the lesson

1 video on CodeWithMunnaX

Definition

Transposing an array reverses (or reorders) its axes. For a 2D array this means rows become columns and columns become rows: an array of shape (r, c) becomes (c, r), and the element at [i, j] moves to [j, i]. The data itself does not change, and the result is a view.

Flip across the diagonal — the main diagonal ([0,0], [1,1], …) stays put; everything else mirrors across it.
[i, j] → [j, i] — Rohit's match-3 score is scores[1, 2]; in the transpose it is T[2, 1].
View — no data is copied; NumPy just reads the same memory in a different order.

text

Original (players × matches), shape (3, 4):     Transposed (matches × players), shape (4, 3):

          M1  M2  M3  M4                                Virat  Rohit  Hardik
Virat  [  72  45  88  31 ]                        M1  [   72     56     45  ]
Rohit  [  56   0  74  88 ]                        M2  [   45      0     32  ]
Hardik [  45  32   0  67 ]                        M3  [   88     74      0  ]
                                                  M4  [   31     88     67  ]

Syntax

python

a.T                               # attribute (no brackets) — reverses all axes
a.transpose()                     # method — same as a.T
np.transpose(a, axes=None)        # function; axes lets you choose the new order
a.transpose(2, 0, 1)              # e.g. 3D: new axis 0 = old axis 2, ...
np.swapaxes(a, axis1, axis2)      # swap exactly two axes
a.swapaxes(axis1, axis2)
np.moveaxis(a, source, destination)   # move one axis to a new position

Parameter	Meaning	Default
`a`	input array	— required
`axes`	a tuple giving the new order of the old axes, e.g. `(1, 0)` or `(2, 0, 1)`	`None` = reverse all axes
`axis1`, `axis2`	(swapaxes) the two axes to exchange	— required
`source`, `destination`	(moveaxis) where the axis is now, and where it should go	— required

Example — players × matches → matches × players

python

import numpy as np

scores = np.array([
    [72, 45, 88, 31],   # Virat
    [56,  0, 74, 88],   # Rohit
    [45, 32,  0, 67],   # Hardik
])
t = scores.T
print("original:", scores.shape, " transposed:", t.shape)
print(t)
print("Rohit, match 3:", scores[1, 2], "==", t[2, 1])
print("same as np.transpose:", np.array_equal(t, np.transpose(scores)))

text

original: (3, 4)  transposed: (4, 3)
[[72 56 45]
 [45  0 32]
 [88 74  0]
 [31 88 67]]
Rohit, match 3: 74 == 74
same as np.transpose: True

How it works: .T turns the 3×4 table into a 4×3 table. Each row of t is now one match, so t[2] reads "everyone's score in match 3". Value 74 moved from [1, 2] to [2, 1].

Why would you transpose data?

Reason	IPL example
1. Change your analysis perspective	data is players × matches but you want to ask match-centric questions: `t[6].argmax()` = best player of match 7
2. Match shapes for an operation	matrix multiplication needs inner dimensions to agree: `(3, 4) @ (3, 4)` fails but `(3, 4) @ (4, 3)` works, so you write `A @ B.T`
3. Fit what another library expects	Pandas and scikit-learn want rows = records/observations, columns = features; if your data is the other way round, transpose it
4. Image data	images are `(height, width, channels)` but some deep-learning libraries want `(channels, height, width)` → `img.transpose(2, 0, 1)`

Example — match-centric view and a matrix product

python

import numpy as np

players = ["Virat", "Rohit", "Hardik"]
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])
by_match = scores.T
for m, row in enumerate(by_match, start=1):
    print(f"Match {m}: best = {players[row.argmax()]} ({row.max()})")

print("scores @ scores.T shape:", (scores @ scores.T).shape)
try:
    scores @ scores
except ValueError as e:
    print("scores @ scores fails:", str(e)[:60], "...")

text

Match 1: best = Virat (72)
Match 2: best = Virat (45)
Match 3: best = Virat (88)
Match 4: best = Rohit (88)
scores @ scores.T shape: (3, 3)
scores @ scores fails: matmul: Input operand 1 has a mismatch in its core dimension ...

How it works: looping over scores.T gives one match per iteration. For @, (3, 4) @ (4, 3) works because the inner sizes (4 and 4) match; (3, 4) @ (3, 4) does not.

Example — 3D arrays: transpose with axes, and swapaxes

python

import numpy as np

# 2 seasons x 3 players x 4 matches
data = np.arange(24).reshape(2, 3, 4)
print("original      :", data.shape)
print(".T            :", data.T.shape)                     # reverses all axes
print("transpose(1,0,2):", data.transpose(1, 0, 2).shape)  # players first
print("swapaxes(0, 2):", np.swapaxes(data, 0, 2).shape)
print("moveaxis(0, -1):", np.moveaxis(data, 0, -1).shape)

img = np.zeros((4, 6, 3))          # height, width, RGB channels
print("image HWC -> CHW:", img.transpose(2, 0, 1).shape)

text

original      : (2, 3, 4)
.T            : (4, 3, 2)
transpose(1,0,2): (3, 2, 4)
swapaxes(0, 2): (4, 3, 2)
moveaxis(0, -1): (3, 4, 2)
image HWC -> CHW: (3, 4, 6)

Example — .T does nothing to a 1D array

python

import numpy as np

v = np.array([72, 45, 88])
print(v.shape, "->", v.T.shape)              # unchanged!
print(v.reshape(-1, 1).shape)                # a real column
print(v[:, np.newaxis].shape)                # also a column
print(v.reshape(1, -1).T.shape)              # row (1, 3) -> column (3, 1)

text

(3,) -> (3,)
(3, 1)
(3, 1)
(3, 1)

How it works: a 1D array has only one axis, so reversing its axes changes nothing. To get a column, first give it a second axis with reshape(-1, 1) or np.newaxis.

Common mistakes

❌ scores.T() → TypeError: 'numpy.ndarray' object is not callable. ✅ .T is an attribute: scores.T (or call scores.transpose()).
❌ Using .T to turn a 1D array into a column. ✅ v.reshape(-1, 1) or v[:, np.newaxis].
❌ Using reshape(4, 3) when you meant transpose. ✅ reshape re-reads in order; only .T maps [i, j] to [j, i].
❌ Modifying a transposed array and expecting the original to stay the same. ✅ .T is a view; use .T.copy() for independence.

Comparison — reshape vs transpose on a (2, 3) array

python

import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6]])
print("a.reshape(3, 2):")
print(a.reshape(3, 2))
print("a.T:")
print(a.T)

text

a.reshape(3, 2):
[[1 2]
 [3 4]
 [5 6]]
a.T:
[[1 4]
 [2 5]
 [3 6]]

	`a.reshape(3, 2)`	`a.T`
Shape	`(3, 2)`	`(3, 2)`
Row 0	`[1, 2]` — next values in reading order	`[1, 4]` — the old column 0
Meaning of rows	none — just regrouped	old columns

Interview tip

Key points to remember

Transpose flips rows and columns: shape (r, c) becomes (c, r) and [i, j] moves to [j, i].
.T is an attribute (no brackets); a.transpose() and np.transpose(a) do the same.
The transpose is a view — no data is copied.
For 3D+ arrays, transpose(axes) reorders axes in any order; .T reverses them all.
swapaxes(i, j) exchanges two axes; moveaxis(src, dst) moves one axis.
.T does nothing to a 1D array — use reshape(-1, 1) or [:, np.newaxis] for a column.
Transpose to change perspective (matches × players), to make shapes fit (A @ B.T), or to match what a library expects.

Try it yourself

Players × matches → matches × players

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
print(scores.shape, "->", scores.T.shape)
print(scores.T)

import numpy as np

scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
print(scores.shape, "->", scores.T.shape)
print(scores.T)

Best performer of each match

import numpy as np

players = ["Virat", "Rohit", "Hardik"]
scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
for m, row in enumerate(scores.T, start=1):
    print("Match", m, "->", players[row.argmax()], row.max())

import numpy as np

players = ["Virat", "Rohit", "Hardik"]
scores = np.array([[72, 45, 88, 31], [56, 0, 74, 88], [45, 32, 0, 67]])
for m, row in enumerate(scores.T, start=1):
    print("Match", m, "->", players[row.argmax()], row.max())

Reordering axes in 3D

import numpy as np

data = np.arange(24).reshape(2, 3, 4)
print(data.T.shape)
print(data.transpose(1, 0, 2).shape)
print(data.swapaxes(1, 2).shape)
print(np.moveaxis(data, -1, 0).shape)

import numpy as np

data = np.arange(24).reshape(2, 3, 4)
print(data.T.shape)
print(data.transpose(1, 0, 2).shape)
print(data.swapaxes(1, 2).shape)
print(np.moveaxis(data, -1, 0).shape)

Practice: match totals via transpose

import numpy as np

# 🏏 Your turn: transpose the table so each row is a match, then print
# each match's team total. Check it equals scores.sum(axis=0).
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])

by_match = scores.T
print(by_match.sum(axis=1))
print(scores.sum(axis=0))

import numpy as np

# 🏏 Your turn: transpose the table so each row is a match, then print
# each match's team total. Check it equals scores.sum(axis=0).
scores = np.array([
    [72, 45, 88, 31],
    [56,  0, 74, 88],
    [45, 32,  0, 67],
])

by_match = scores.T
print(by_match.sum(axis=1))
print(scores.sum(axis=0))

Revision Flashcards

1 / 6

Tap a card to flip it and see the answer.