Question

I have a 2D matrix, say M=zeros(10,10);

I have another column matrix, V=[1;2;3;4;5;6;5;4;3;2];

I would like to be able to set M(i,j) = 1 for all j >= V(i)

I know I can do this in a loop

for i=1:10
   M(i,V(i):10) = 1;
end

but it seems that it would be possible to use some form of Matlab indexing to avoid using a loop. For example something like :

M(:,V:10)=1;

or

M(:,V(:):10)=1;

but neither of these produces the expected result.

Is there some syntactic sugar I can use to achieve this or should I revert to looping?

Answer 1

Since you’re looking for syntactic sugar, here’s a sort of esoteric way of doing it. 🙂

Assuming the length of V is the size of both dimensions in the desired matrix M, first create an identity matrix of the same size, then index appropriately and take cumsum:

V = [1;2;3;4;5;6;5;4;3;2]; #% 10x1 vector
E = eye(length(V), length(V)); #%10x10 identity matrix
M = cumsum(E(V,:),2)

M =

     1     1     1     1     1     1     1     1     1     1
     0     1     1     1     1     1     1     1     1     1
     0     0     1     1     1     1     1     1     1     1
     0     0     0     1     1     1     1     1     1     1
     0     0     0     0     1     1     1     1     1     1
     0     0     0     0     0     1     1     1     1     1
     0     0     0     0     1     1     1     1     1     1
     0     0     0     1     1     1     1     1     1     1
     0     0     1     1     1     1     1     1     1     1
     0     1     1     1     1     1     1     1     1     1

Ok, now: less fun, but (on my machine) faster than any of the other options that have been tested so far:

n=10000;
V = randi(n-1, 1, n); #% as in @KevinRatelle's answer (but not transposed)

tic;
Vlinear = reshape(V + (0:n-1)*n, 1, []); #% find linear indices of first "ones"
M = zeros(n);
M(Vlinear)=1;
M=cumsum(M);
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