DAI developerLab· about 45 min· in the browser

Lab: matrix multiplication and one layer of a neural network

Implement matrix–vector and matrix–matrix multiplication with loops, verify against NumPy, and build a layer `W x + b` with ReLU.

Teaches: Matrices and matrix multiplication

Requires: Vectors

Theory

(AB)ᵢⱼ = Σₖ Aᵢₖ Bₖⱼ: row i of A times column j of B. The dimensions must match: m×n times n×p gives m×p. A layer in a network is exactly this plus a bend.

Sub-tasks

matvec — matvec(A, x) with lists of lists.
matmul — matmul(A, B) — raise ValueError if the dimensions do not match.
lager (layer) — lager(W, x, b) = ReLU(W x + b).

The starter code

runs in your browser

def matvec(A, x):
    # TODO: en skalärprodukt per rad
    ...


def matmul(A, B):
    # TODO: kontrollera dimensioner, tre loopar
    ...


def lager(W, x, b):
    # TODO: ReLU(W x + b)
    ...

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Expected results

matvec([[1,2],[3,4]],[5,6]) = [17, 39]; 5×3 · 3×7 → 5×7; 3×4 · 3×4 → ValueError; lager (layer) gives no negative numbers.

Common mistakes

Swaps row and column in the inner loop.
Forgets to check len(A[0]) == len(B).
ReLU in the wrong place (before the bias).