hankel.hhs

/**
 * @Author Jianan Lin (林家南)
 * @param input: an array or some numbers, must be odd length
 * @returns - a hankel matrix
 * definition: https://en.wikipedia.org/wiki/Hankel_matrix
 * 
 */



function hankel(input) {

    *import math: ndim
    *import math: deep_copy
    *import math: flatten

    // argument check
    if (arguments.length === 0) {
        throw new Error('Exception occurred in hankel - no argument given');
    }

    // hankel(1, 2, 3)
    if (typeof input === 'number') {
        if (arguments.length % 2 === 0) {
            throw new Error('Exception occurred in hankel - length of input must be odd');
        }
        let raw_in = [];
        for (let i = 0; i < arguments.length; i++) {
            raw_in.push(arguments[i]);
        }
        let mid = parseInt(raw_in.length / 2);
        let result = new Array();
        for (let i = 0; i <= mid; i++) {
            result[i] = new Array();
            for (let j = 0; j <= mid; j++) {
                result[i][j] = 0;
            }
        }
        for (let i = 0; i <= mid; i++) {
            for (j = 0; j <= i; j++) {
                result[i - j][j] = raw_in[i];
                result[mid - i + j][mid - j] = raw_in[raw_in.length - i - 1];
            }
        }
        return mat(result);
    }

    // hankel([1, 2, 3])
    else {
        let raw_in = flatten(input);
        if (raw_in.length % 2 === 0) {
            throw new Error('Exception occurred in hankel - length of input must be odd');
        }
        let mid = parseInt(raw_in.length / 2);
        let result = new Array();
        for (let i = 0; i <= mid; i++) {
            result[i] = new Array();
            for (let j = 0; j <= mid; j++) {
                result[i][j] = 0;
            }
        }
        for (let i = 0; i <= mid; i++) {
            for (j = 0; j <= i; j++) {
                result[i - j][j] = raw_in[i];
                result[mid - i + j][mid - j] = raw_in[raw_in.length - i - 1];
            }
        }
        return mat(result);
    }
}