MATLAB: Put elements into corresponding locations of upper triangular matrix

Question

Hi all,

Imagine I have a vector:

inpt = (1:6)';

Now I'd like to put elements of inpt in the upper triangular part of a 3 by 3 matrix otpt, so I have:

otpt =
     1     2     4
     0     3     5
     0     0     6

What's the best way to do it? Thanks!

Answer 1

Start with nested loops:

v = 1:6;
n = round((sqrt(8 * numel(v) + 1) - 1) / 2);
M = zeros(n, n);
c = 0;
for i2 = 1:n
  for i1 = 1:i2
    c         = c + 1;
    M(i1, i2) = v(c);
  end
end

In the next step you can vectorize the inner loop: Move the loop index inside the assignment:

n = round((sqrt(8 * numel(v) + 1) - 1) / 2);
M = zeros(n, n);
a = 1;
for k = 1:n
  b         = a + k - 1;
  M(1:k, k) = v(a:b);
  a         = b + 1;
end

Is this nicer? Questionable, but maybe faster.

Now use a built-in function:

n = round((sqrt(8 * numel(v) + 1) - 1) / 2);
M(triu(ones(n)) == 1) = v;

or better:

M(triu(true(n))) = v;

[EDITED] Some timings - what did you expect?

v = 1:5050;
tic; for k = 1:10000; y = SerialTriU(v); end, toc
Elapsed time is 0.772492 seconds.   % Two loops
Elapsed time is 2.448738 seconds.   % Inner loop vectorized
Elapsed time is 1.029641 seconds.   % TRIU(ONES)
Elapsed time is 0.659360 seconds.   % TRIU(TRUE)