Create a matrix with sequencial values padded with zeros (without loops) - matlab

Question

I have two matrices aand b of 1 column and n rows.
These matrices represent min and max values.
From these I need to create a n by m matrix.
m is the max value of [a ; b]
The result must contain each value between a(:) and b(:), padded with zeros.
note: it's easy to do with a for loop, but I want to avoid loops.
Exemple :
Starting with these two matrices :
>> a = [3 ; 5 ; 2 ; 7 ; 4]
a =
3
5
2
7
4
>> b = [7 ; 7 ; 5 ; 8 ; 4]
b =
5
7
4
8
4
I want to end with this matrix :
result =
3 4 5 6 7 0 0 0
5 6 7 0 0 0 0 0
2 3 4 5 0 0 0 0
7 8 0 0 0 0 0 0
4 0 0 0 0 0 0 0
So far I have this :
>> result = zeros(size(a,1), max([a ; b]));
>> rows = [1:size(a,1)]
rows =
1 2 3 4 5
>> index = sub2ind(size(result), rows, b - a + 1)
>> result(index) = b
result =
0 0 0 0 7 0 0 0
0 0 7 0 0 0 0 0
0 0 0 5 0 0 0 0
0 8 0 0 0 0 0 0
4 0 0 0 0 0 0 0
>> result(:,1) = a
result =
3 0 0 0 7 0 0 0
5 0 7 0 0 0 0 0
2 0 0 5 0 0 0 0
7 8 0 0 0 0 0 0
4 0 0 0 0 0 0 0

Answer 1

I'd solve this with a simple loop, which is also probably the fastest solution
a = [3 ; 5 ; 2 ; 7 ; 4]
b = [7 ; 7 ; 5 ; 8 ; 4]
nSteps = b-a+1;
nRows = size(a,1);
result = zeros(nRows, max([a ; b]));
for iRow = 1:nRows
result(iRow,1:nSteps(iRow)) = a(iRow):b(iRow);
end
result =
3 4 5 6 7 0 0 0
5 6 7 0 0 0 0 0
2 3 4 5 0 0 0 0
7 8 0 0 0 0 0 0
4 0 0 0 0 0 0 0
In case you don't need readability, here's a non-loop solution:
result = ones(nRows, max([a ; b]));
result(:,1) = a;
result = cumsum(result,2);
result(bsxfun(#gt,result,b))=0
result =
3 4 5 6 7 0 0 0
5 6 7 0 0 0 0 0
2 3 4 5 0 0 0 0
7 8 0 0 0 0 0 0
4 0 0 0 0 0 0 0

Answer 2

Some problems aren't worth the effort of vectorising:
a = [3 ; 5 ; 2 ; 7 ; 4];
b = [7 ; 7 ; 5 ; 8 ; 4];
cols = max(max(a),max(b))
result = zeros(length(a),cols)
for i = 1:length(a)
A = a(i):b(i)
result(i,:) = padarray(A, [0 cols-length(A)], 0, 'post');
end