How do you check row/Column wise iteration in Lua

Question

I have been writing codes to perform loop in Column wise iteration and it makes me confuse all the time and I can't distinguish between Column and Row Wise Iteration.

I've written these code below to perform Column Wise Iteration but I'm not sure that it is performing in the right way. Also help me to understand with more examples of Row/Column Iteration

r = {}

for x = 1, 5 do
    table.insert(r, {})
end

for x = 1, 5 do
    for y = 1, 5 do
        table.insert(r[y], y)
        -- table.insert(r[x], 'A')
    end
end

for x = 1, 5 do
    for y = 1, 5 do
        io.write(r[x][y], ' : ')        
        -- io.write(r[y][x], ' :: ')
    end
    print()
end

OUTPUT:

1 : 1 : 1 : 1 : 1 : 
2 : 2 : 2 : 2 : 2 :
3 : 3 : 3 : 3 : 3 :
4 : 4 : 4 : 4 : 4 :
5 : 5 : 5 : 5 : 5 :

This one below is for Row Wise Iteration. I think!

L = {}

for i = 1, 5 do
    table.insert(L, {})
    for j = 1, 5 do
        L[i][j] = " # "
    end
end

for i = 1, 5 do
    for j = 1, 5 do
        io.write(L[i][j])
    end
    print()
end

OUTPUT:

 #  #  #  #  # 
 #  #  #  #  #
 #  #  #  #  #
 #  #  #  #  #
 #  #  #  #  # 

Answer 1

When more visualized and followed @LMD then you see more.
I had some time so feel free to play around with...

Lua 5.4.4  Copyright (C) 1994-2022 Lua.org, PUC-Rio
> L = require('rowcol')
> L:ij()
    A   B   C   D   E
    F   G   H   I   J
    K   L   M   N   O
    P   Q   R   S   T
    U   V   W   X   Y
> L:ji()
    A   F   K   P   U
    B   G   L   Q   V
    C   H   M   R   W
    D   I   N   S   X
    E   J   O   T   Y
> io.open('rowcol.lua'):read('a')
-- rowcol.lua

local L = setmetatable({ -- Data Part
[0x1] = {[0x1] = '\65', [0x2] = '\66', [0x3] = '\67', [0x4] = '\68', [0x5] = '\69'},
[0x2] = {[0x1] = '\70', [0x2] = '\71', [0x3] = '\72', [0x4] = '\73', [0x5] = '\74'},
[0x3] = {[0x1] = '\75', [0x2] = '\76', [0x3] = '\77', [0x4] = '\78', [0x5] = '\79'},
[0x4] = {[0x1] = '\80', [0x2] = '\81', [0x3] = '\82', [0x4] = '\83', [0x5] = '\84'},
[0x5] = {[0x1] = '\85', [0x2] = '\86', [0x3] = '\87', [0x4] = '\88', [0x5] = '\89'}
},{__index = { -- Methods Part
ij = function(self, i, ie, j, je)
for i = i or 0x1, ie or 0x5 do
    for j = j or 0x1, je or 0x5 do
        io.write('\t', self[i][j])
    end
    print()
end
end,
ji = function(self, i, ie, j, je)
for i = i or 0x1, ie or 0x5 do
    for j = j or 0x1, je or 0x5 do
        io.write('\t', self[j][i])
    end
    print()
end
end
}
})

return L

Both methods can handle both for range parameter...

> L:ji(5,5)
    E   J   O   T   Y
> L:ij(5,5)
    U   V   W   X   Y
> L:ij(5,5,5,5)
    Y
> L:ij(3,5,3,5)
    M   N   O
    R   S   T
    W   X   Y
> L:ji(3,5,3,5)
    M   R   W
    N   S   X
    O   T   Y
> L:ji(1,5,1,5)
    A   F   K   P   U
    B   G   L   Q   V
    C   H   M   R   W
    D   I   N   S   X
    E   J   O   T   Y
> L:ji(1,5,1,4)
    A   F   K   P
    B   G   L   Q
    C   H   M   R
    D   I   N   S
    E   J   O   T
> L:ji(1,5,1,3)
    A   F   K
    B   G   L
    C   H   M
    D   I   N
    E   J   O