Having a sequence of numbers of length L, I need to count how many non-decreasing and non-increasing sub-sequences of exact length are there. For example, if I have a sequence of length 15
I see that non-increasing sub-sequences are
and non-decreasing sub-sequences are
So here I have
Since the maximum length of a non-decreasing (or non-increasing) sub-sequence can be 15 in this case, I thought about representing frequencies through vectors x for non-increasing and y for non-decreasing sub-sequences:
x = (0,2,0,1,0,0,0,0,0,0,0,0,0,0,0)
y = (0,1,1,2,0,0,0,0,0,0,0,0,0,0,0)
Expanding this to general case of sequence of length L, I wanted to go through the sequence and, using loops, count frequencies of subsequences of the exact lengths. How would I do that? I would create zero-vectors of length L and I would add 1 to the l-th element of zero matrix every time I meet a sub-sequence of length l.
Since my sequence will be of length of few thousands, I wouldn't ask Matlab to write them, but I would ask it to write me particular frequency.
Is this a good approach? Is there some function in Matlab that is doing this?
How about that lovely one-line solution?
%// vector
A = [2, 4, 11, 13, 3, 5, 5, 6, 3, 3, 2, 4, 2, 14, 15]
%// number of digits in output
nout = 15;
seqFreq = @(vec,x) histc(accumarray(cumsum(~(-x*sign([x*1; diff(vec(:))]) + 1 )), ...
vec(:),[],@(x) numel(x)*~all(x == x(1)) ),1:nout).' %'
%// non-increasing sequences -> input +1
x = seqFreq(A,+1)
%// non-decreasing sequences -> input -1
y = seqFreq(A,-1)
x = 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0
y = 0 1 1 2 0 0 0 0 0 0 0 0 0 0 0
%// example for non-increasing
q = +1;
%// detect sequences: value = -1
seq = sign([q*1; diff(A(:))]);
%// find subs for accumarray
subs = cumsum(~(-q*seq + 1));
%// count number of elements and check if elements are equal, if not, set count to zero
counts = accumarray(subs,A(:),[],@(p) numel(p)*~all(p == p(1)) );
%// count number of sequences
x = histc(counts,1:nout);