"Transpose/Zip" function not working as expected - lua

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

Answer 2

The {5} in your example is being ignored because of this line:
if table.getn(arg_list) < arg_length then return new_array end
What you may want to do instead is break out of the loop only when arg_list is empty.
This will then give the result you want provided that the rows are monotonically increasing in length.
For the more general case, when later rows may be shorter than earlier ones
(e.g. {{1,2},{3,4,5},{6}}), you will need to keep track of the row lengths to allow for holes. This can be done by adding an optional argument (and extra return value) to map to indicate the maximum index i for which func(array[i]) was evaluated:
function map(func, array, len)
local new_array = {}
len = len or #array
for i=1,len do
new_array[i] = func(array[i])
end
return new_array, len
end
function mapn(func, ...)
local new_array = {}
local i=1
local arg_length = select('#', ...)
local args = {...}
while true do
local arg_list, num_results = map(function(arr) return arr[i] end, args, arg_length)
if not next(arg_list) then return new_array end
new_array[i] = func(unpack(arg_list, 1, num_results))
i = i+1
end
end
function zip(...)
return mapn(function(...) return {...} end,...)
end
function transpose(...)
return zip(unpack(...))
end