/**
 * Construct a uniform transition matrix over `nStates`.
 * `transition[i][j] = 1 / nStates`.
 *
 * @param {number} nStates - Number of states (positive integer).
 * @returns {number[][]} Row-stochastic transition matrix.
 */
export function transition_uniform(nStates: number): number[][];
/**
 * Construct a self-loop transition matrix.
 * `transition[i][i] = p`, `transition[i][j] = (1 - p) / (nStates - 1)` for
 * `j != i`.
 *
 * @param {number} nStates - Number of states (> 1).
 * @param {number|number[]|Float64Array} prob - Self-transition probability,
 *   scalar or per-state vector. Each value must lie in [0, 1].
 * @returns {number[][]} Row-stochastic transition matrix.
 */
export function transition_loop(nStates: number, prob: number | number[] | Float64Array): number[][];
/**
 * Construct a cyclic transition matrix.
 * `transition[i][i] = p`, `transition[i][(i + 1) mod nStates] = 1 - p`.
 *
 * NOTE: `prob` is the SELF-transition (stay) probability —
 * e.g. `transition_cycle(4, 0.9)` has 0.9 on the diagonal and 0.1 one step
 * forward. (The prior pleco implementation had this inverted.)
 *
 * @param {number} nStates - Number of states (> 1).
 * @param {number|number[]|Float64Array} prob - Self-transition probability,
 *   scalar or per-state vector. Each value must lie in [0, 1].
 * @returns {number[][]} Row-stochastic transition matrix.
 */
export function transition_cycle(nStates: number, prob: number | number[] | Float64Array): number[][];
/**
 * Construct a localized transition matrix.
 * State `i` transitions only to nearby states, weighted by `window` over a band
 * of `width`. Off-band entries are zero (unless `wrap` extends locality modulo
 * `nStates`), and each row is normalized to sum to 1.
 *
 * @param {number} nStates - Number of states (> 1).
 * @param {number|number[]|Int32Array} width - Local band width, scalar or
 *   per-state vector. Each value must be >= 1.
 * @param {string} [window='triangle'] - Window shape ('triangle' or 'ones').
 * @param {boolean} [wrap=false] - Compute locality modulo nStates when true.
 * @returns {number[][]} Row-stochastic transition matrix.
 */
export function transition_local(nStates: number, width: number | number[] | Int32Array, window?: string, wrap?: boolean): number[][];