Matrix iteration

Intermediate examples built on repeated matrix/vector multiplication. They show how an iterative process — a probability distribution evolving over time, or a ranking settling to a fixed point — is just Tensor::matmul applied in a loop.

Like the rest of the applied band, these use only the default numeric Tensor API, small hard-coded inputs, and deterministic output. They are teaching examples, not a graph or probability library.

Examples

33_markov_chain_weather.rs

Difficulty: Intermediate. Models a two-state (Sunny / Rainy) weather process with a row-stochastic transition matrix P. Each day applies v_next = v · P via vector × matrix matmul, and the distribution converges to the stationary π = [5/6, 1/6].

cargo run --example 33_markov_chain_weather

Source: 33_markov_chain_weather.rs

34_tiny_pagerank.rs

Difficulty: Intermediate. Ranks the nodes of a tiny directed graph with PageRank. A column-stochastic link matrix M is power-iterated with damping (r_next[i] = (1 - d)/N + d·(M·r)[i]) using matrix × vector matmul; the best-connected node wins, and the link-less node keeps only its teleport share.

cargo run --example 34_tiny_pagerank

Source: 34_tiny_pagerank.rs

What this is not

These are single-file demonstrations of accepted APIs. They do not imply a graph framework, a probability toolkit, or a production PageRank implementation.