How to sum elements at the same index in array of arrays into a single array?

You can use Array.prototype.reduce() in combination with Array.prototype.forEach().

var array = [
        [0, 1, 3],
        [2, 4, 6],
        [5, 5, 7],
        [10, 0, 3]
    ],
    result = array.reduce(function (r, a) {
        a.forEach(function (b, i) {
            r[i] = (r[i] || 0) + b;
        });
        return r;
    }, []);
document.write('<pre>' + JSON.stringify(result, 0, 4) + '</pre>');

Update, a shorter approach by taking a map for reducing the array.

var array = [[0, 1, 3], [2, 4, 6], [5, 5, 7], [10, 0, 3]],
    result = array.reduce((r, a) => a.map((b, i) => (r[i] || 0) + b), []);
    
console.log(result);

Using Lodash 4:

function sum_columns(data) {
  return _.map(_.unzip(data), _.sum);
}

var result = sum_columns([
  [1, 2],
  [4, 8, 16],
  [32]
]);

console.log(JSON.stringify(result));
<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.11/lodash.js"></script>

For older Lodash versions and some remarks

Lodash 4 has changed the way _.unzipWith works, now the iteratee gets all the values passed as spread arguments at once, so we cant use the reducer style _.add anymore. With Lodash 3 the following example works just fine:

function sum_columns(data) {
  return _.unzipWith(data, _.add);
}

var result = sum_columns([
  [1, 2],
  [4, 8, 16],
  [32],
]);

console.log(JSON.stringify(result));
<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/3.10.1/lodash.js"></script>

_.unzipWith will insert undefineds where the row is shorter than the others, and _.sum treats undefined values as 0. (as of Lodash 3)

If your input data can contain undefined and null items, and you want to treat those as 0, you can use this:

function sum_columns_safe(data) {
  return _.map(_.unzip(data), _.sum);
}

function sum_columns(data) {
  return _.unzipWith(data, _.add);
}

console.log(sum_columns_safe([[undefined]])); // [0]
console.log(sum_columns([[undefined]]));      // [undefined]
<script src="https://cdnjs.cloudflare.com/ajax/libs/lodash.js/3.10.1/lodash.js"></script>

This snipet works with Lodash 3, unfortunately I didn't find a nice way of treating undefined as 0 in Lodash 4, as now sum is changed so _.sum([undefined]) === undefined


One-liner in ES6, with map and reduce

var a = [ [0, 1, 3], [2, 4, 6], [5, 5, 7], [10, 0, 3] ];

var sum = a[0].map((_, i) => a.reduce((p, _, j) => p + a[j][i], 0));

document.write(sum);