Question

I am trying to build an elegant transpose function using functions mapn and zip in Lua.

The mapn and zip are as follows (From the lua book):

function map(func, array)
 local new_array = {}
 for i,v in ipairs(array) do
   new_array[i] = func(v)
 end
 return new_array
end


function mapn(func, ...)
 local new_array = {}
 local i=1
 local arg_length = table.getn(arg)
 while true do
   local arg_list = map(function(arr) return arr[i] end, arg)
   if table.getn(arg_list) < arg_length then return new_array end
   new_array[i] = func(unpack(arg_list))
   i = i+1
 end
end

These work as expected.

I then define zip and transpose as:

function zip(...)
  return mapn(function(...) return {...} end,...)
end

function transpose(...)
  return zip(unpack(...))
end

Now transpose({{1,2},{3,4},{5,6}}) produces {{1,3,5},{2,4,6}} as expected.

But transpose({{1,2},{3,4},{5}}) does not produce {{1,3,5},{2,4}}. It only produces one row.

How can I get it to produce the result I wish for?

---

I just decided to write an “inelegant” function instead. It seems there’s no smooth way to use mapn and friends.

function transp(L)
  local n=#L


  local m,M=1e42,0
  --Get the beginning and end of resultant transpose list.
  for i=1,n do
    for k,v in pairs(L[i]) do
      if M<k then M=k end
      if m>k then m=k end
    end
  end

  local nt={}
  for i=m,M do
    local rt={}
    for j=1,n do
      rt[j]=L[j][i]
    end
    table.insert(nt,rt)
  end
  return nt
end

Please critique and improve this candidate solution.

Answer 1

I fixed a few things in your code and I think it works now as intended, I’ve added comments inline.

function map(func, array)
  local new_array = {}
  for i, v in ipairs(array) do
    new_array[#new_array + 1] = func(v)
  end 
  return new_array
end

function mapn(func, ...)
  -- Variadic arguments bound to an array.
  local arrays = {...}
  local new_array = {}
  -- Simple for-loop.
  local i = 1 
  while true do
    local arg_list = map(function(arr) return arr[i] end, arrays)
    if #arg_list == 0 then
      break
    end 
    new_array[i] = func(unpack(arg_list))
    i = i + 1 
  end 
  return new_array
end


-- Using 'mapn' instead of 'map' (probably how you intended).
function zip(...)
  return mapn(function(...) return {...} end,...)
end

-- Same as before.
function transpose(...)
  return zip(unpack(...))
end

Usage example:

for _, row in pairs(transpose({{1,2},{3,4},{5}})) do
  for _, col in pairs(row) do io.write(col .. ' ') end
  io.write('\n')
end
-- Output: 1 3 5 
--         2 4