Labs¶

Hands-on labs accompany every volume. Each lab targets a specific skill and is graded by observable, reproducible output.

Lab Structure¶

Every lab includes:

1. Objective — One sentence stating exactly what you will build
2. Prerequisites — Chapters that must be completed first
3. Dataset — Source, size, description
4. Expected Output — What a correct solution produces
5. Starter Code — Scaffold provided so you focus on the core concept
6. Solution — Full reference solution (attempt the lab first!)
7. Extension Challenges — 2-3 stretch goals for advanced students

Lab Index¶

Lab 01: NumPy from Scratch¶

Objective: Implement matrix multiplication, broadcasting, and a linear algebra solver using only NumPy — no SciPy, no sklearn.

Prerequisites: Vol 1 Ch 2 (Mathematics), Vol 1 Ch 3 (Python Tools)

Dataset: None (synthetic data)

Tasks:

1. Implement matmul(A: np.ndarray, B: np.ndarray) -> np.ndarray without using @ or np.dot
2. Implement cosine_similarity(a: np.ndarray, b: np.ndarray) -> float
3. Implement PCA from scratch: centre, compute covariance matrix, eigendecompose, project
4. Verify your PCA matches sklearn.decomposition.PCA on the Iris dataset

# Starter code
import numpy as np
from sklearn.datasets import load_iris

def matmul(A: np.ndarray, B: np.ndarray) -> np.ndarray:
    """Matrix multiply A @ B without using np.dot or @."""
    assert A.shape[1] == B.shape[0], "Incompatible shapes"
    # Your implementation here
    ...

def cosine_similarity(a: np.ndarray, b: np.ndarray) -> float:
    """Cosine similarity between two 1-D vectors."""
    ...

def pca(X: np.ndarray, n_components: int) -> np.ndarray:
    """Project X onto its top n_components principal components."""
    ...

Expected Output:

matmul matches np.dot: True
cosine_similarity([1,0,0], [1,0,0]) = 1.0
cosine_similarity([1,0,0], [0,1,0]) = 0.0
PCA variance explained: [0.926, 0.053, 0.017, 0.005]
Custom PCA matches sklearn: True

Lab 02: Linear Regression from Scratch¶

Objective: Implement linear regression using the normal equation and gradient descent; compare them on the California Housing dataset.

Prerequisites: Vol 1 Ch 2, Vol 3 Ch 1

# Starter code
import numpy as np
from sklearn.datasets import fetch_california_housing
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split

class LinearRegressionNormal:
    """Linear regression via the normal equation."""
    def fit(self, X: np.ndarray, y: np.ndarray) -> "LinearRegressionNormal":
        ...
    def predict(self, X: np.ndarray) -> np.ndarray:
        ...

class LinearRegressionGD:
    """Linear regression via gradient descent."""
    def __init__(self, lr: float = 0.01, epochs: int = 1000) -> None:
        ...
    def fit(self, X: np.ndarray, y: np.ndarray) -> "LinearRegressionGD":
        ...
    def predict(self, X: np.ndarray) -> np.ndarray:
        ...

Extension: Add Ridge regularisation (\(\lambda ||w||^2\)) to both implementations and plot the regularisation path.