//================================================================
/**
 * @packageDocumentation
 * @module std
 */
//================================================================
import { InvalidArgument } from "../../exception/InvalidArgument";

/**
 * Laguerre polynomials.
 *
 * @reference https://en.wikipedia.org/wiki/Laguerre_polynomials
 */
export function laguerre(n: number, x: number): number {
    return assoc_laguerre(n, 0, x);
}

/**
 * Associated laguerre polynomials.
 *
 * @reference https://en.wikipedia.org/wiki/Laguerre_polynomials#Generalized_Laguerre_polynomials
 */
export function assoc_laguerre(n: number, m: number, x: number): number {
    // VALIDATE PARAMETERS
    if ((n = Math.floor(n)) < 0 || (m = Math.floor(m)) < 0)
        throw new InvalidArgument(
            `Error on std.assoc_laguerre(): both n and m must be unsigned integer -> (n = ${n}, m = ${m}).`,
        );

    // MEMORIZATION
    const solutions: number[] = [1, -x + m + 1];

    // COMPUTE RETURN VALUE
    return _Compute_assoc_laguerre(n, m, x, solutions);
}

function _Compute_assoc_laguerre(
    n: number,
    m: number,
    x: number,
    solutions: number[],
): number {
    if (solutions.length > n) return solutions[n];

    const ln_1: number = _Compute_assoc_laguerre(n - 1, m, x, solutions);
    const ln_2: number = _Compute_assoc_laguerre(n - 2, m, x, solutions);

    let ret: number = (2 * n - 1 + m - x) * ln_1 - (n + m - 1) * ln_2;
    ret = ret / n;

    solutions[n] = ret;
    return ret;
}