Indexing and slicing — basic, boolean masking, fancy indexing

5.4.3 · Coding › Scientific Computing (Python)

1. Basic slicing — `start:stop:step`

YEH kya return karta hai: ek view — ek naya array object jo same data buffer share karta hai. Slice ko mutate karna original ko mutate karta hai.

KYUN view (HOW yeh kaam karta hai): Ek slice sirf recipe ke offset aur strides change karta hai; koi data copy nahi hoti. Isliye yeh huge arrays ke liye bhi instant hai.

Worked example 2-D slicing

A = np.arange(12).reshape(3, 4)   # rows 0..2, cols 0..3
A[1, 2]      # -> 6     (row 1, col 2; comma dims ko separate karta hai)
A[0:2, 1:3]  # -> [[1,2],[5,6]]   (rows 0-1, cols 1-2)
A[:, -1]     # -> [3,7,11]  har row ka last column
A[::2, ::2]  # -> [[0,2],[8,10]] har doosra row & col

KYUN A[0:2,1:3]? Pehla index rows {0,1} pick karta hai, doosra cols {1,2} pick karta hai; intersection ek 2×2 block hai. Dono indices ranges hain, isliye result 2-D hai.

2. Boolean masking — condition se select karo

KYUN copy: select kiye gaye elements memory mein irregularly scattered hote hain; unhe single stride se describe nahi kar sakte, isliye NumPy unhe fresh contiguous memory mein gather karta hai.

Worked example Filtering

a = np.array([3, -1, 4, -2, 5])
mask = a > 0          # array([ True, False,  True, False,  True])
a[mask]               # -> array([3, 4, 5])
a[a > 0] = 0          # mask mein ASSIGN: a -> [0,-1,0,-2,0]
a[(a < 0) & (a > -2)] # & | ~  se combine karo  (and/or NAHI!)

KYUN & aur and nahi? Python ka and single booleans pe kaam karta hai; yahan hume pure array ke upar elementwise AND chahiye, jo & hai. Har condition ko parentheses mein wrap karo kyunki & < se zyada tightly bind karta hai.

3. Fancy (integer-array) indexing — position list se select karo

Worked example Reorder & repeat

a = np.array([10, 20, 30, 40])
a[[3, 0, 0, 2]]        # -> array([40, 10, 10, 30])  (order + repeats!)
idx = np.array([[0,1],[2,3]])
a[idx]                 # -> [[10,20],[30,40]]  shape idx follow karta hai

2-D fancy: A[[0,2],[1,3]] unhe pair karta hai → A[0,1], A[2,3] return karta hai (ek diagonal-style pick), 2×2 block nahi. Block ke liye np.ix_ ya slicing use karo.

Figure — Indexing and slicing — basic, boolean masking, fancy indexing

Common mistake Classic traps ko steel-man karna

Trap 1 — "Ek slice ek fresh copy hai, isliye ise edit karna safe hai." KYUN sahi lagta hai: pure-Python lists mein, lst[1:3] copy hoti hai. Fix: NumPy slices views hain; b = A[0]; b[0]=99 A ko bhi change karta hai. Independence chahiye toh A[0].copy() use karo.

Trap 2 — "A[[0,2],[1,3]] rows {0,2} × cols {1,3} ka 2×2 block deta hai." KYUN sahi lagta hai: basic slicing A[0:2,1:3] deta hai ek block, toh hum generalize karte hain. Fix: fancy index arrays pointwise zip hote hain: index 0 → (0,1), index 1 → (2,3). True block ke liye, A[np.ix_([0,2],[1,3])] use karo.

Trap 3 — mask mein and/or use karna. KYUN sahi lagta hai: English jaisa padhta hai. Fix: woh "ambiguous truth value" raise karte hain; &, |, ~ use karo parentheses ke saath.

Trap 4 — "Boolean mask 2-D array ka original 2-D shape rakhta hai." Fix: yeh hamesha 1-D mein flatten karta hai, kyunki selected cells ek rectangle nahi hoti.

Recall Feynman: ek 12-saal ke bacche ko samjhao

Socho ek lambi row hai numbered lockers ki jo toys se bhari hain.

Slicing = "lockers 2 se 8 tak kholo, har doosre ko skip karte hue." Fast hai, aur tum asli lockers dekh rahe ho — koi toy hatao toh woh sach mein hata hai.
Boolean masking = tumhare paas ek checklist hai: jin lockers mein laal toy hai unhe tick karo, phir sirf woh toys ek basket mein copy karo.
Fancy indexing = tum list do "lockers 5, 1, 1, 3 please" aur woh toys usi order mein lo, repeats bhi. Masking aur list ek basket (copy) banate hain; range sirf asli lockers mein peeks karti hai (view).

Flashcards

NumPy array ko index karne ke teen tarike kaunse hain?

Basic slicing (start:stop:step), boolean masking, fancy (integer-array) indexing.

Kya basic slicing view return karta hai ya copy?

Ek view — yeh original data buffer share karta hai (sirf offset/strides change hote hain).

Kya boolean masking aur fancy indexing view return karte hain ya copy?

Ek copy (fresh memory mein gather kiya jaata hai).

Mask mein and, or, not ki jagah &, |, ~ KYUN use karna padta hai?

Yeh array ke upar elementwise operate karte hain; and/or ko single boolean chahiye aur woh ambiguity error raise karte hain.

a[start:stop:step] (step>0) ki length ka formula?

⌈(s t o p - s t a r t) / s t e p ⌉

, clamped to ≥0.

2-D A ke liye A[[0,2],[1,3]] kya return karta hai?

Pointwise pairs A[0,1] aur A[2,3] — 2×2 block NAHI.

Rows {0,2} × cols {1,3} ka actual block kaise select karein?

A[np.ix_([0,2],[1,3])].

Jab idx ek 2×2 integer array ho toh a[idx] ki shape kya hogi?

idx ki shape ke jaisi (2×2); fancy indexing index array ki shape follow karta hai.

Boolean mask ek 2-D array ki dimensionality ka kya karta hai?

Selection ko 1-D mein flatten karta hai.

A ko change kiye bina uski pehli row safely edit kaise karein?

b = A[0].copy().

Connections

NumPy arrays — shape, strides, dtype (KYUN views saste hain)
Broadcasting (masks/index arrays array shape ke saath broadcast karte hain)
Views vs Copies — memory model
np.where and conditional selection
Vectorization — replacing Python loops
Pandas .loc / .iloc indexing (same ideas DataFrame level pe)