Google-sheets – Sum rows of a array function that outputs a matrix [Google Spreadsheet]

If you're using the "new" Google Spreadsheets, in the "Edit" tab menu, under "Paste special", the last menu voice is "Paste transposed": it does exactly what you need in a single task.

A custom function will always receive either a rectangular array or a scalar value (number, string, boolean, or datetime) as each of its arguments. So the conversion from rectangular to jagged array has to happen inside the function. For example, by calling jagged(arr) on the input, where jagged is the following function:

function jagged(arr) {
  var rowLength = arr.map(function(row) {
    return row.reduce(function (a, b, i) {
      return b === '' ? a : i+1;
    }, 0);
  });
  return arr.map(function(row, i) {
    return row.slice(0, rowLength[i]);
  });
}

This function first computes the actual length of each row and then truncates the rows accordingly.

I emphasize that the call to jagged needs to happen from within the custom function that will use it, like so:

function myFunction (arr) {
  jarr = jagged(arr); 
  // proceed to work with the jagged array
}  

Putting =myFunction(jagged(A1:F3)) in a spreadsheet cell won't do it: the Sheets will automatically inflate the return values of jagged to a rectangular array before passing them to myFunction.