thi-ng/umbrella

import { EPS } from "@thi.ng/math/api";
import { eqDelta } from "@thi.ng/math/eqdelta";
import type { ReadonlyMat } from "./api.js";

/**
 * Returns true, if given square matrix of size `n` is orthagonal, i.e. check if
 * `A * AT = I`.
 *
 * https://en.wikipedia.org/wiki/Orthogonal_matrix
 *
 * @param m -
 * @param n -
 * @param eps -
 */
export const isOrthagonal = (m: ReadonlyMat, n: number, eps = EPS) => {
    for (let i = 0; i < n; i++) {
        const ii = i * n;
        for (let j = 0; j < n; j++) {
            const jj = j * n;
            let acc = 0;
            for (let k = 0; k < n; k++) {
                acc += m[ii + k] * m[jj + k];
            }
            if (
                (i == j && !eqDelta(acc, 1, eps)) ||
                (i != j && !eqDelta(acc, 0, eps))
            ) {
                return false;
            }
        }
    }
    return true;
};