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P2-11.4 Supplemental: Shape and Shared Data in NumPy

Section ID: P2-11.4 Version: v2026.09.15

Slices and Shared Data

Basic slicing creates a view sharing the original array's data. Setting the first value of scores[1:4] to 999 also changes position 1 in the original to 999.

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import numpy as np

scores = np.array([82, 75, 45, 90, 61])
middle = scores[1:4]

middle[0] = 999

print(scores)
print(middle)

Output:

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[ 82 999  45  90  61]
[999  45  90]

Position and Condition Selection as Copies

Fancy indexing with a position list and boolean indexing with a mask copy data when retrieving values. Changing the first value of picked to 500 and high_scores to 700 leaves the original [82, 75, 45, 90, 61] unchanged.

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scores = np.array([82, 75, 45, 90, 61])

picked = scores[[1, 3, 4]]
high_scores = scores[scores >= 80]

picked[0] = 500
high_scores[0] = 700

print(scores)
print(picked)
print(high_scores)

Output:

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[82 75 45 90 61]
[500  90  61]
[700  90]

scores[[1, 3, 4]] gathers values at positions 1, 3, and 4. This is fancy indexing.

scores[scores >= 80] selects values where the condition is true, using a boolean mask.

Adding an Axis of Length One

np.newaxis adds a length-one axis at the specified position. A (3,) score array can be viewed as (3, 1) or (1, 3). These results also share data with the original.

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scores = np.array([82, 75, 45])

print(scores.shape)
print(scores[:, np.newaxis].shape)
print(scores[np.newaxis, :].shape)

Output:

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

The values remain the same, but dimensionality and shape differ.

Expression Shape Reading
scores (3,) One-dimensional array of length three
scores[:, np.newaxis] (3, 1) Three-row, one-column vector-like view
scores[np.newaxis, :] (1, 3) One-row, three-column vector-like view

np.newaxis does not create new numbers; it organizes how the array aligns in a calculation.

Differences for Every Pair

Subtracting both 1 and 2 from each of [10, 20, 30] requires a three-by-two result. Changing the input shapes to (3, 1) and (1, 2) allows broadcasting over all six pairs.

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a = np.array([10, 20, 30])
b = np.array([1, 2])

diff = a[:, np.newaxis] - b[np.newaxis, :]

print(a[:, np.newaxis].shape)
print(b[np.newaxis, :].shape)
print(diff)

Output:

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(3, 1)
(1, 2)
[[ 9  8]
 [19 18]
 [29 28]]

The first row [9, 8] subtracts 1 and 2 from 10; the last row [29, 28] subtracts them from 30. Changing b to [1, 5] changes only the second column to [5, 15, 25]. Without the added axes, a - b fails because (3,) and (2,) are incompatible.

Reshape and Transpose

reshape groups elements into a new shape; .T swaps the row and column axes of a two-dimensional array. Both can produce (3, 2) while arranging values differently.

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matrix = np.array([[10, 11, 12], [20, 21, 22]])
print(matrix.reshape(3, 2))
print(matrix.T)

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[[10 11]
 [12 20]
 [21 22]]
[[10 20]
 [11 21]
 [12 22]]

If original rows represent students, columns represent students after transposition. reshape(3, 2) does not preserve that meaning automatically. A one-dimensional (3,) array still has shape (3,) after .T. Use [:, np.newaxis] to create a column-vector shape.

reshape returns a view when possible, but memory layout can require a copy. This small example checks actual data sharing.

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matrix = np.array([[10, 11, 12], [20, 21, 22]])
reshaped = matrix.reshape(3, 2)
transposed_flat = matrix.T.reshape(-1)

print(np.shares_memory(matrix, reshaped))
print(np.shares_memory(matrix, transposed_flat))

Outputs are True and False. A -1 dimension asks NumPy to infer that length from the element count. Flattening this transposed array in the default order requires copying. Do not assume every reshape is a view or every reshape a copy. Use .copy() explicitly when editing must preserve the original.

Case: Adjusting Only Selected Scores

Select positions 1 through 3 from [82, 75, 45, 90, 61] and add 10. Editing a slice directly also changes the original. Copy the selection with .copy() to compare original and adjusted values independently.

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scores = np.array([82, 75, 45, 90, 61])
adjusted = scores[1:4].copy()
adjusted += 10

print(scores)
print(adjusted)

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[82 75 45 90 61]
[ 85  55 100]

Remove .copy() and rerun the whole example: the original becomes [82, 85, 55, 100, 61]. If the intended “before” data changes too, a before-and-after comparison no longer uses the original baseline.

Condition selection produces a copy when reading into a new variable. Direct assignment such as scores[scores < 60] = 60 changes those positions in the original. Reading low = scores[scores < 60] and then assigning low[:] = 60 leaves the original unchanged.

flowchart TD
    select["selection method<br/>slice / fancy / mask"]
    share["does it share the original?<br/>view or copy"]
    reshape["change shape with newaxis<br/>how do axes change?"]
    broadcast["broadcasting rule<br/>how do shapes align?"]
    result["result and side effects<br/>value change and source impact"]

    select --> share
    select --> reshape
    reshape --> broadcast
    share --> result
    broadcast --> result

Example Code File

Run the examples in order to compare changes to the original array and its shape.

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python docs/assets/part-02/chapter-11/p2_11_4_views_shapes.py

Checklist

  • Can you distinguish x[1:4] from x[[1, 3, 4]]?
  • Can you explain what a boolean mask selects?
  • Can you distinguish (3,), (3, 1), and (1, 3)?
  • Can you explain how np.newaxis supports broadcasting?
  • Do you check whether a copy is needed to preserve original data?
  • Can you inspect both shape and data sharing when reading NumPy code?
  • Can you distinguish reshape from transpose and check shared storage with np.shares_memory?

Sources and References

  • NumPy Developers, Copies and views, NumPy Manual, checked on 2026-07-20. Used as the basis for the difference between views and copies, basic-indexing views, advanced-indexing copies, and .base checks.
  • NumPy Developers, Indexing on ndarrays, NumPy Manual, checked on 2026-07-20. Used to confirm that selection method affects shape and whether original data is shared.
  • NumPy Developers, Broadcasting, NumPy Manual, checked on 2026-07-20. Used as the basis for connecting np.newaxis and shape adjustment to broadcasting.
  • NumPy Developers, numpy.shares_memory, NumPy Manual, accessed: 2026-09-15. shared-memory checks for the small array examples.