NumPy Fundamentals (Data Science)

ndarray Fundamentals

A NumPy array is a homogeneous, fixed-type, contiguous block with a shape:

import numpy as np

a = np.array([[1, 2, 3], [4, 5, 6]], dtype=np.float64)  # 2×3, default float64
np.zeros((2, 4)); np.ones(5, dtype=np.int32)
np.arange(0, 10, 2)        # [0 2 4 6 8]
np.linspace(0, 1, 5)       # 5 evenly spaced floats
a.shape, a.dtype, a.ndim, a.size
a[0, 1], a[:, 0], a[1, :]          # row/col slicing

Basic slicing returns a view — v = a[0]; v[0] = 99 changes a too — because views share the same memory with new strides. Type is uniform: mixing Python objects forces dtype=object, which forfeits nearly all speed. Build matrices with np.eye/np.diag, random with np.random.default_rng(seed) for reproducibility.

Vectorization and Broadcasting

Broadcasting compares shapes right-to-left: dimensions are compatible when equal or one of them is 1.

m = np.ones((3, 4))
m * 2                      # scalar stretches over the whole array
row = np.array([10, 20, 30, 40])
m + row                    # (3,4) + (4,) → row broadcasts across rows
col = np.array([[1.], [2.], [3.]])
m * col + row              # outer-ish combos without nested loops

Common reductions and transforms:

m.mean(), m.sum(axis=0)    # column totals; axis=1 → per row
np.sqrt(m); np.exp(m); np.where(m > 0.5, 1.0, 0.0)
mask = m[m > 0.5]          # boolean masking selects elements

One expression replaces an entire nested loop — the operation runs in compiled C over contiguous memory with no per-element Python dispatch, which is where the 10–100× speedups come from.

Views, Copies, and Numerical Pitfalls

• View vs copy: slicing and reshape return views; boolean/fancy indexing returns copies. Call .copy() when independence matters.
• dtype defaults: floats default to float64, integers to platform int_ — pass dtype=np.float64 to reductions explicitly when width matters.
• NaN propagates: one np.nan poisons mean() — use np.nanmean/np.nansum, and remember comparisons with NaN are always False.
• Shape errors are loud: mismatched non-1 dimensions raise ValueError; transpose with .T or [:, None] to force alignment.
• Never grow arrays in a loop — preallocate or collect in a list and convert once.

Interview angle: give the broadcasting rule in one sentence, show an outer-product example, and name the view/copy distinction as a common mutation bug.