Fancy (Integer-Array) Indexing

Slices only give regular patterns (a range, every k-th). What if you want Virat's scores in matches 1, 4 and 7 — or the top 3 scores in sorted order — or the players in a custom order? You pass a list of positions. NumPy calls this fancy indexing.

Definition

Fancy indexing (also called integer-array indexing) is selecting elements by passing a list or array of integer indexes inside the brackets, e.g. arr[[0, 3, 6]]. NumPy returns a new array (a copy) whose shape follows the shape of the index array, with the elements in exactly the order you listed — repeats allowed.

• List of indexes — note the double brackets: the outer [] is indexing, the inner [0, 3, 6] is the list of positions.
• Any order, repeats allowed — arr[[6, 0, 0]] is fine.
• Shape follows the index array — a 2×2 index array gives a 2×2 result.
• Copy — like boolean indexing (and unlike slicing), the result does not share memory with arr.

Syntax

arr[[i1, i2, i3]]               # 1D: pick these positions
arr2d[[r1, r2]]                 # 2D: pick whole rows
arr2d[:, [c1, c2]]              # 2D: pick whole columns
arr2d[[r1, r2], [c1, c2]]       # 2D: pick PAIRS (r1,c1) and (r2,c2)
arr2d[np.ix_([r1, r2], [c1, c2])]   # 2D: rows x columns grid (sub-table)

Example — 1D: chosen matches, custom order

import numpy as np

virat_runs = np.array([72, 45, 88, 31, 64, 0, 103, 52, 19, 77, 41, 93, 28, 66])

print("Matches 1, 4, 7      :", virat_runs[[0, 3, 6]])
print("Last, first, middle  :", virat_runs[[-1, 0, 7]])
print("Repeats allowed      :", virat_runs[[6, 6, 0]])
idx = np.array([[0, 1], [12, 13]])
print("Shape follows index array:")
print(virat_runs[idx])

Matches 1, 4, 7      : [ 72  31 103]
Last, first, middle  : [66 72 52]
Repeats allowed      : [103 103  72]
Shape follows index array:
[[72 45]
 [28 66]]

How it works: each number in the index list is looked up one by one, and the results are placed in the same order (and the same shape) as the index list.

Example — top 3 scores with argsort

virat_runs = np.array([72, 45, 88, 31, 64, 0, 103, 52, 19, 77, 41, 93, 28, 66])

order = np.argsort(virat_runs)        # indexes that would sort the array
top3_idx = order[::-1][:3]            # largest first, take 3
print("Top-3 indexes :", top3_idx)
print("Top-3 scores  :", virat_runs[top3_idx])
print("Match numbers :", top3_idx + 1)

Top-3 indexes : [ 6 11  2]
Top-3 scores  : [103  93  88]
Match numbers : [ 7 12  3]

How it works: np.argsort returns positions, not values. Feeding those positions back in with fancy indexing reorders the data. This "argsort + fancy index" pattern is how you rank players, sort rows by a column, etc.

Example — 2D: rows, columns, pairs and grids

scores = np.array([
    [72, 45, 88, 31, 64,  0, 103, 52],   # row 0: Virat
    [56,  0, 74, 88, 32, 45,  61, 17],   # row 1: Rohit
    [45, 32,  0, 67, 18, 54,  78, 22],   # row 2: Hardik
])

print("Rows 2 and 0 (Hardik, Virat):")
print(scores[[2, 0]])
print("Matches 1 and 8 for everyone:")
print(scores[:, [0, 7]])
print("Pairs (0,6) and (1,3):", scores[[0, 1], [6, 3]])
print("Grid rows {0,1} x cols {0,7}:")
print(scores[np.ix_([0, 1], [0, 7])])

Rows 2 and 0 (Hardik, Virat):
[[ 45  32   0  67  18  54  78  22]
 [ 72  45  88  31  64   0 103  52]]
Matches 1 and 8 for everyone:
[[72 52]
 [56 17]
 [45 22]]
Pairs (0,6) and (1,3): [103  88]
Grid rows {0,1} x cols {0,7}:
[[72 52]
 [56 17]]

How it works: with two index lists, NumPy pairs them up position by position: [0, 1] with [6, 3] means cells (0, 6) and (1, 3) → Virat's 103 and Rohit's 88. If you want every combination (a sub-table), use np.ix_ — or do it in two steps: scores[[0, 1]][:, [0, 7]].

Comparison — the three ways to select

Common mistakes

• ❌ virat_runs[0, 3, 6] (single brackets) — that means "axis 0 = 0, axis 1 = 3, axis 2 = 6" → IndexError: too many indices. ✅ virat_runs[[0, 3, 6]].
• ❌ scores[[0, 1], [0, 7]] expecting a 2×2 block. ✅ That returns 2 paired cells. Use scores[np.ix_([0, 1], [0, 7])].
• ❌ Two index lists of different lengths, e.g. scores[[0, 1, 2], [0, 1]] → IndexError: shape mismatch.
• ❌ Editing a fancy-indexed result and expecting the original to change. ✅ It's a copy; assign directly instead: scores[[0, 2], 0] = 0.

Interview tip

Q: What does arr[[1, 2], [3, 4]] return for a 2D array? A: Two elements: arr[1, 3] and arr[2, 4]. The two index arrays are broadcast together and paired element-wise; to get the 2×2 grid of rows {1, 2} and columns {3, 4}, use arr[np.ix_([1, 2], [3, 4])].