A table with 2 columns where one column increases sequentially while the other column displaying the same number till a limit is reached - matlab

Question

I have been trying to write a code where the users enters two numbers in order to get 2 columns. It is very hard to explain by words what I am trying to achieve so here is an example:
If the user inputs a = 1 and b = 1, the following table should be created:
ans =
1 1
If the user inputs a = 2 and b = 2:
ans =
1 1
1 2
2 1
2 2
If the user inputs a = 2 and b = 5:
ans =
1 1
1 2
1 3
1 4
1 5
2 1
2 2
2 3
2 4
2 5
For other values of a and b, the matrix should be constructed according to the above shown sequence.

Answer 1

This can be achieved straight-forward by the use of repelem and repmat:
[repelem((1:a).',b),repmat((1:b).',a,1)]
A more elegant way is using meshgrid and reshape it after:
[A,B] = meshgrid(1:a,1:b);
[A(:),B(:)]
Let's create an anonymous function and test the first approach:
>> fun = #(a,b) [repelem((1:a).',b),repmat((1:b).',a,1)];
>> fun(1,1)
ans =
1 1
>> fun(2,2)
ans =
1 1
1 2
2 1
2 2
>> fun(2,5)
ans =
1 1
1 2
1 3
1 4
1 5
2 1
2 2
2 3
2 4
2 5

Answer 2

Here is an alternative way
for example a = 2 and b = 5
A(1:b*a,1) = reshape(mtimes((1:a).',ones(1,b)).',1,b*a)
A(1:b*a,2) = reshape(mtimes((1:b).',ones(1,a)),1,b*a)
A =
1 1
1 2
1 3
1 4
1 5
2 1
2 2
2 3
2 4
2 5
There is just one logic, in the code below you define a matrix of row size and a and column size b
>> mtimes((1:a).',ones(1,b))
ans =
1 1 1 1 1
2 2 2 2 2
and the next step simply reshapes the matrix column wise for a and row wise for b by taking a transpose
A(1:b*a,1) = reshape(mtimes((1:a).',ones(1,b)).',1,b*a)
A(1:b*a,2) = reshape(mtimes((1:b).',ones(1,a)),1,b*a)