NumPy: Arrays, Dtypes, Broadcasting, Indexing and Linear Algebra Reference Guide

# Install — pick the wheel that matches your accelerator
pip install "numpy>=2"                       # 2.x, modern default
pip install "numpy>=1.26,<2"                 # if a dependency pins to 1.x

# Conda — ships with MKL by default
conda install -c conda-forge numpy

# Confirm BLAS backend (huge perf difference)
python -c "import numpy; numpy.show_config()"

# Reproducible random numbers — the modern Generator API
python -c "
import numpy as np
rng = np.random.default_rng(seed=42)
print(rng.standard_normal(3))
"

import numpy as np

a = np.arange(20).reshape(4, 5)
# array([[ 0,  1,  2,  3,  4],
#        [ 5,  6,  7,  8,  9],
#        [10, 11, 12, 13, 14],
#        [15, 16, 17, 18, 19]])

# Slicing (returns a VIEW — writes propagate to the source)
a[1:3, 2:]                                    # rows 1-2, cols 2-end
a[::2]                                        # every other row
a[..., -1]                                    # ellipsis: last col along any rank

# Boolean mask — broadcasts, returns a copy
mask = a > 10
a[mask]                                       # 1-D array of matching values
a[mask] = 0                                   # in-place edit

# Fancy indexing with integer arrays — returns a copy
rows = np.array([0, 2])
cols = np.array([1, 4])
a[rows, cols]                                 # picks (0,1) and (2,4)

# np.ix_ for cross-product of indices
a[np.ix_(rows, cols)]                         # 2x2 submatrix

# View vs copy — check with .base
b = a[1:3]
b.base is a                                   # True → b is a view

# Force a copy when needed
c = a[1:3].copy()

import numpy as np

# Broadcasting rule: align trailing dims, expand dims of size 1.
a = np.arange(12).reshape(3, 4)              # (3, 4)
b = np.array([10, 20, 30, 40])               # (4,)    → broadcasts along rows
c = np.array([[1], [2], [3]])                # (3, 1)  → broadcasts along cols

a + b                                         # (3, 4) — row-wise add
a + c                                         # (3, 4) — column-wise add

# Add a new axis explicitly — clearer than reshape
x = np.array([1, 2, 3])                       # (3,)
x[:, None]                                    # (3, 1)  same as x.reshape(-1, 1)
x[None, :]                                    # (1, 3)

# Outer product via broadcasting — no Python loop
x[:, None] * np.array([10, 20])[None, :]      # (3, 2)

# Pairwise distance — vectorized
pts = np.random.default_rng(0).standard_normal((100, 2))
d   = np.linalg.norm(pts[:, None, :] - pts[None, :, :], axis=-1)   # (100,100)

# Linear regression — closed form (normal equation), pure NumPy.
import numpy as np

rng = np.random.default_rng(0)

# Synthetic data: y = 3x1 - 2x2 + 1 + noise
N = 500
X = rng.standard_normal((N, 2))
y = X @ np.array([3.0, -2.0]) + 1.0 + rng.standard_normal(N) * 0.1

# Add the bias column → design matrix
X_b = np.c_[np.ones(N), X]                    # (N, 3)

# Normal equation: theta = (X.T X)^-1 X.T y  — solve, don't invert
theta, *_ = np.linalg.lstsq(X_b, y, rcond=None)
print("theta =", theta)                       # ≈ [1.0, 3.0, -2.0]

# Predictions + R^2
y_hat = X_b @ theta
ss_res = ((y - y_hat) ** 2).sum()
ss_tot = ((y - y.mean()) ** 2).sum()
r2 = 1 - ss_res / ss_tot
print(f"R^2 = {r2:.4f}")