Conditional cumsum - how to create?

This is probably easy, but my brain isn't working today...

How can you do the following operation in a vectorized way? I'd think it should be possible with some combination of cumsum, diff & logical indexing:

input = rand(10,1);
output = zeros(size(input);
output(1) = input(1);
for ind = 2:numel(input)
  dif = input(ind) - input(ind-1);
   if dif < 0
      output(ind) = output(ind-1) + dif;
   else
      output(ind) = output(ind-1);
   end
end

[the cyclist]

It would be useful if you also described conceptually what you are trying to do.

[Eric Sampson]

Basically it's a copy of the input, but anytime that the original increases from one val to the next, the output should be hold constant. Sort of like a copy that can only go down :)

Answer 1

[Roger Stafford]

Try this.

 outp = cumsum([inp(1);min(diff(inp),0)]);

[Eric Sampson]

Ding ding ding! Roger wins, to Matt's detriment :) Thanks!

Answer 2

[Matt Tearle]

There may be better ways, but this works:

d = [true;diff(input)<0];
idx = find(d);
output = input(idx(cumsum(d)));

When the array is large enough, there's a pretty decent speedup (~50x)

[Eric Sampson]

Matt that looks promising, but I don't think it generates the same results as the algorithm?

[Matt Tearle]

I copy/pasted your code and checked mine against it:

input = rand(100000,1);

tic
output = zeros(size(input));
output(1) = input(1);
for ind = 2:numel(input)
   if (input(ind) - input(ind-1)) < 0
      output(ind) = input(ind);
   else
      output(ind) = output(ind-1);
   end
end
t1=toc;

tic
d = [true;diff(input)<0];
idx = find(d);
output2 = input(idx(cumsum(d)));
t2=toc;

max(abs(output-output2))
t1/t2

I always seem to get a difference of 0.

[Eric Sampson]

Argh, I'm sorry Matt. See my revised problem statement. This was clearly a case of 'do what I mean, not what I say' :)

[Sean de Wolski]

As you know, the DWIM Toolbox still hasn't been released to the public.

[Eric Sampson]

Sean, wasn't Loren or Steve supposed to be on that? Slackers.