Indexing a vector within a bigger one in MATLAB

Here is as solution using 1D convolution. It may find multiple matches so start holds beginning indices of sub-vectors:

f = flip(b);

idx = conv(a,f,'same')==sum(b) & conv(~a,~f,'same')==sum(~b);

start = find(idx)-ceil(length(b)/2)+1;

result = start(1):start(1)+length(b)-1;

Solution with for loops:

a=[1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1];
b=[1,1,1,0,0,0];
c = [];
b_len = length(b)
maxind0 = length(a) - b_len + 1 %no need to search higher indexes 

for i=1:maxind0
  found = 0;
  for j=1:b_len
    if a(i+j-1) == b(j)
      found = found + 1;
    else
      break;
    end
  end

  if found == b_len  % if sequence is found fill c with indexes
    for j=1:b_len
      c(j)= i+j-1;
    end

    break
  end
end

c %display c

Does it need to be computationally efficient?

A not very efficient but short solution would be this:

a=[1,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,1,1];;
b=[1,1,1,0,0,0];
where = find(arrayfun(@(n) all(a(n+1:n+length(b))==b),0:length(a)-length(b)));

... gives you 15. Your result would be the vector where:where+length(b)-1.

edit: I tried it and I stand corrected. Here is a version with loops:

function where = find_sequence(a,b)

na = 0;
where = [];
while na < length(a)-length(b)
    c = false;
    for nb = 1:length(b)
        if a(na+nb)~=b(nb)
            na = na + 1;  % + nb
            c = true;                        
            break
        end

    end
    if ~c
        where = [where,na+1];
        na = na + 1;
    end   
end

Despite its loops and their bad reputation in Matlab, it's a lot faster:

a = round(rand(1e6,1));
b = round(rand(10,1));

tic;where1 = find(arrayfun(@(n) all(a(n+1:n+length(b))==b),0:length(a)-length(b)));toc;
tic;where2 = find_sequence(a,b);toc;


>> test_find_sequence
Elapsed time is 4.419223 seconds.
Elapsed time is 0.042969 seconds.