multinomial.hhs

/**
 * @author Jianan Lin (林家南)
 * @param input - a series of numbers a1, ... an, or an array / matrix / tensor
 * @returns - a number = (a1 + ... + an)! / (a1! * ... * an!)
 * 
 */


function multinomial(input) {

    *import math: is_number
    *import math: flatten
    *import math: deep_copy

    let length = arguments.length;

    // if there are no arguments, there is an error
    if (length === 0) {
        throw new Error('Exception occurred in multinomial - no argument given');
    }

    // if we input a series of numbers
    if (is_number(input)) {
        for (let i = 0; i < length; i++) {
            if (arguments[i] < 0 || parseInt(arguments[i]) !== arguments[i]) {
                throw new Error('Exception occurred in multinomial - arguments must be non-negative integers');
            }
        }

        let sum = 0;
        for (let i = 0; i < length; i++) {
            sum += arguments[i];
        }

        let result = private_factorial(sum);
        for (let i = 0; i < length; i++) {
            result /= private_factorial(arguments[i]);
        }

        return result;
    }

    else {
        if (length !== 1) {
            throw new Error('Exception occurred in multinomial - wrong argument number');
        }

        if ( !(Array.isArray(arguments[0])) && !(arguments[0] instanceof Mat) && !(arguments[0] instanceof Tensor)) {
            throw new Error('Exception occurred in multinomial - argument is of length 1, not a number, but is not a Mat, Tensor or JS Array');
        }

        let in_type = input instanceof Mat || input instanceof Tensor;
        let raw_in = in_type ? input.clone().val : deep_copy(input);
        raw_in = flatten(raw_in);

        let array_length = raw_in.length;
        for (let i = 0; i < array_length; i++) {
            if (raw_in[i] < 0 || parseInt(raw_in[i]) !== raw_in[i]) {
                throw new Error('Exception occurred in multinomial - elements must be non-negative integers');
            }
        }

        let sum = 0;
        for (let i = 0; i < array_length; i++) {
            sum += raw_in[i];
        }

        let result = private_factorial(sum);
        for (let i = 0; i < array_length; i++) {
            result /= private_factorial(raw_in[i]);
        }

        return result;
    }
    
    // when we use this function, we have ensured that input is valid
    function private_factorial(input) {
        let result = 1;
        for (let i = 2; i <= input; i++) {
            result *= i;
        }
        return result;
    }
}