Matrix with Bell Triangle

I need to reshape a portion of a matrix computed with the values of a bell triangle where n is the number of rows of a matrix. How can I generate a matrix contain the bell values? I mean, as an example, for n= 4 but could be any value:

                    1
                 1     2
              2     3     5
           5     7    10    15

empty space with 0.

[Guillaume]

How do you represent that triangle as a matrix (which by definition is a rectangle) ?

[Millone]

Sorry, you are right, it is a rectangle. I would just put 0 in the empty cells.

[Millone]

I would non even mind to have it on one side of the matrix:

1 0 0 0

1 2 0 0

2 3 5 0

5 7 10 15

[Titus Edelhofer]

Hi Millone,

a loop over the rows and using cumsum will do the job ... have you tried this?

Titus

[Millone]

No, I have no tried it but I give it a test. Thanks

[Millone]

I do not get it! I am just approaching Matlab!

Answer 1

[John D'Errico]

Simple. Just use loops.

n = 5;
BellTri = zeros(n);
BellTri(1,1) = 1;
for i = 2:n
  BellTri(i,1) = BellTri(i-1,i-1);
  for j = 2:i
    BellTri(i,j) = BellTri(i - 1,j-1) + BellTri(i,j-1);
  end
end

BellTri
BellTri =
     1     0     0     0     0
     1     2     0     0     0
     2     3     5     0     0
     5     7    10    15     0
    15    20    27    37    52

Answer 2

[Titus Edelhofer]

O.k., when there is a full solution, I'm happy to share mine as well ;-)

function B = bell(n)
B = zeros(n);
B(1,1) = 1;
for row=2:n
  B(row, 1:row) = B(row-1,row-1) + cumsum([0 B(row-1, 1:row-1)]);
end

Titus

Answer 3

[Andrei Bobrov]

n = 5;

a = zeros(n);
a(1) = 1;
for jj = 1:n-1
   a(jj+1,1:jj+1) = cumsum(a(jj,[jj,1:jj]),2);
end

Answer 4

[Guillaume]

Assuming you're talking about this, I've tried to come up with a clever way to generate it, but didn't find any (didn't spend too much time on it either). When all else fail, loops always work:

bell = zeros(n);
bell(1) = 1;
for row = 2 : n
    bell(row, 1) = bell(row-1, row-1);
    for col = 2 : row
       bell(row, col) = bell(row, col-1) + bell(row-1, col-1);
    end
end