Help with the matrix creation pls ? if possible not a hardcoded solution but a function .

Hi i need some help, i need to create a matrix that will have n columns (n is the only input) and the output would be a matrix of n x m in a way that every row has a sum of 1, where all the numbers are positive and have an increment of 0.1. For example i n = 3 the first couple of rows would look like this

0   0     1
0   0.1  0.9
0   0.2  0.8
....
1   0     0

[Steven Lord]

Your example matrix does not satisfy your requirement "where all the numbers are positive" since it contains 0 values. I assume you meant "where all the numbers are nonnegative?"

[Matej Stambuk]

You are right, my bad. should be nonnegative

Answer 1

[Stephen23]

This is Roger Stafford's memory-efficient solution, proposed here http://de.mathworks.com/matlabcentral/newsreader/view_thread/143037. It runs about twice as fast a Jos' and my other solutions.

n = 3;
d = 10;
c = nchoosek(1:d+n-1,n-1);
m = size(c,1);
t = ones(m,d+n-1);
t(repmat((1:m).',1,n-1)+(c-1)*m) = 0;
u = [zeros(1,m);t.';zeros(1,m)];
v = cumsum(u,1);
x = diff(reshape(v(u==0),n+1,m),1).'/d;

Where the output array is:

>> x
x =
   0.00000   0.00000   1.00000
   0.00000   0.10000   0.90000
   0.00000   0.20000   0.80000
   0.00000   0.30000   0.70000
   0.00000   0.40000   0.60000
   0.00000   0.50000   0.50000
   0.00000   0.60000   0.40000
   0.00000   0.70000   0.30000
   0.00000   0.80000   0.20000
   0.00000   0.90000   0.10000
   0.00000   1.00000   0.00000
   0.10000   0.00000   0.90000
   0.10000   0.10000   0.80000
   0.10000   0.20000   0.70000
   0.10000   0.30000   0.60000
   0.10000   0.40000   0.50000
   0.10000   0.50000   0.40000
   0.10000   0.60000   0.30000
   0.10000   0.70000   0.20000
   0.10000   0.80000   0.10000
   0.10000   0.90000   0.00000
   0.20000   0.00000   0.80000
   0.20000   0.10000   0.70000
   0.20000   0.20000   0.60000
   0.20000   0.30000   0.50000
   0.20000   0.40000   0.40000
   0.20000   0.50000   0.30000
   0.20000   0.60000   0.20000
   0.20000   0.70000   0.10000
   0.20000   0.80000   0.00000
   0.30000   0.00000   0.70000
   0.30000   0.10000   0.60000
   0.30000   0.20000   0.50000
   0.30000   0.30000   0.40000
   0.30000   0.40000   0.30000
   0.30000   0.50000   0.20000
   0.30000   0.60000   0.10000
   0.30000   0.70000   0.00000
   0.40000   0.00000   0.60000
   0.40000   0.10000   0.50000
   0.40000   0.20000   0.40000
   0.40000   0.30000   0.30000
   0.40000   0.40000   0.20000
   0.40000   0.50000   0.10000
   0.40000   0.60000   0.00000
   0.50000   0.00000   0.50000
   0.50000   0.10000   0.40000
   0.50000   0.20000   0.30000
   0.50000   0.30000   0.20000
   0.50000   0.40000   0.10000
   0.50000   0.50000   0.00000
   0.60000   0.00000   0.40000
   0.60000   0.10000   0.30000
   0.60000   0.20000   0.20000
   0.60000   0.30000   0.10000
   0.60000   0.40000   0.00000
   0.70000   0.00000   0.30000
   0.70000   0.10000   0.20000
   0.70000   0.20000   0.10000
   0.70000   0.30000   0.00000
   0.80000   0.00000   0.20000
   0.80000   0.10000   0.10000
   0.80000   0.20000   0.00000
   0.90000   0.00000   0.10000
   0.90000   0.10000   0.00000
   1.00000   0.00000   0.00000

[Matej Stambuk]

this is great, for a moment i thought ill have to run a program on external server :D Thank you

Answer 2

[Jos (10584)]

% brute force
A = [] ; 
for k=0:10 
  for j=0:10-k 
    A(end+1,:) = [k, j 10-k-j] ; 
  end
end
A = A ./ 10

[Stephen23]

This works for n=3, but how does this generalize to other n?

Answer 3

[Stephen23]

This code generates permutations (with replacement) of the vector 0:0.1:1, and then selects only the rows that sum to one. I don't claim that this is an efficient use of memory, but it works. For the most efficient code see my other answer.

N = 3;
V = 0:0.1:1;
[Y{N:-1:1}] = ndgrid(1:numel(V));
X = reshape(cat(N+1,Y{:}),[],N);
B = V(X);
Z = sum(B,2);
B = B(0.99<Z&Z<1.01,:);

And the output matrix for N=3 (N=4 is below):

>> B
B =
   0.00000   0.00000   1.00000
   0.00000   0.10000   0.90000
   0.00000   0.20000   0.80000
   0.00000   0.30000   0.70000
   0.00000   0.40000   0.60000
   0.00000   0.50000   0.50000
   0.00000   0.60000   0.40000
   0.00000   0.70000   0.30000
   0.00000   0.80000   0.20000
   0.00000   0.90000   0.10000
   0.00000   1.00000   0.00000
   0.10000   0.00000   0.90000
   0.10000   0.10000   0.80000
   0.10000   0.20000   0.70000
   0.10000   0.30000   0.60000
   0.10000   0.40000   0.50000
   0.10000   0.50000   0.40000
   0.10000   0.60000   0.30000
   0.10000   0.70000   0.20000
   0.10000   0.80000   0.10000
   0.10000   0.90000   0.00000
   0.20000   0.00000   0.80000
   0.20000   0.10000   0.70000
   0.20000   0.20000   0.60000
   0.20000   0.30000   0.50000
   0.20000   0.40000   0.40000
   0.20000   0.50000   0.30000
   0.20000   0.60000   0.20000
   0.20000   0.70000   0.10000
   0.20000   0.80000   0.00000
   0.30000   0.00000   0.70000
   0.30000   0.10000   0.60000
   0.30000   0.20000   0.50000
   0.30000   0.30000   0.40000
   0.30000   0.40000   0.30000
   0.30000   0.50000   0.20000
   0.30000   0.60000   0.10000
   0.30000   0.70000   0.00000
   0.40000   0.00000   0.60000
   0.40000   0.10000   0.50000
   0.40000   0.20000   0.40000
   0.40000   0.30000   0.30000
   0.40000   0.40000   0.20000
   0.40000   0.50000   0.10000
   0.40000   0.60000   0.00000
   0.50000   0.00000   0.50000
   0.50000   0.10000   0.40000
   0.50000   0.20000   0.30000
   0.50000   0.30000   0.20000
   0.50000   0.40000   0.10000
   0.50000   0.50000   0.00000
   0.60000   0.00000   0.40000
   0.60000   0.10000   0.30000
   0.60000   0.20000   0.20000
   0.60000   0.30000   0.10000
   0.60000   0.40000   0.00000
   0.70000   0.00000   0.30000
   0.70000   0.10000   0.20000
   0.70000   0.20000   0.10000
   0.70000   0.30000   0.00000
   0.80000   0.00000   0.20000
   0.80000   0.10000   0.10000
   0.80000   0.20000   0.00000
   0.90000   0.00000   0.10000
   0.90000   0.10000   0.00000
   1.00000   0.00000   0.00000

And the output matrix for N=4:

>> B
B =
   0.00000   0.00000   0.00000   1.00000
   0.00000   0.00000   0.10000   0.90000
   0.00000   0.00000   0.20000   0.80000
   0.00000   0.00000   0.30000   0.70000
   0.00000   0.00000   0.40000   0.60000
   0.00000   0.00000   0.50000   0.50000
   0.00000   0.00000   0.60000   0.40000
   0.00000   0.00000   0.70000   0.30000
   0.00000   0.00000   0.80000   0.20000
   0.00000   0.00000   0.90000   0.10000
   0.00000   0.00000   1.00000   0.00000
   0.00000   0.10000   0.00000   0.90000
  ....
   0.80000   0.00000   0.20000   0.00000
   0.80000   0.10000   0.00000   0.10000
   0.80000   0.10000   0.10000   0.00000
   0.80000   0.20000   0.00000   0.00000
   0.90000   0.00000   0.00000   0.10000
   0.90000   0.00000   0.10000   0.00000
   0.90000   0.10000   0.00000   0.00000
   1.00000   0.00000   0.00000   0.00000