Extract sequences from vector

Dear Forum members,

I have a question I could not find any solution for. I have a vector, let's say

U=[2,2,5,7,3,4,4,4,2,2,2,3].

I also have a sequence, which is

s=[2,2,3].

I now want to find all the indexes in U, where my sequence s could be built from. In my case, that would be

(1,2,5), (9,10,12), (10,11,12), (9,11,12). So the problem is the sequences have to be build first from U and do not exist as in s. I find this quite tough and would be happy if someone had a solution.

I have Matlab 7.13.

Thanks a lot! Peter

[Azzi Abdelmalek]

Are you looking for all the sequences?, for example (2,5,7,3)

[Peter]

Hello Azzi!

I do not really understand what you mean with (2,5,7,3). Maybe my example was a bit confusing! I search for all values in U that could be used to build s, but only in chronological order, so I realized I forgot some in my example. U(1,1,12) would also correspond to s, or U(2,9,12), U(1,2,5) etc.

At the end of the day, I want to find the values (2,2,3) in U that are closest together, so in my example I would search for U(10,11,12). But: it can happen in my real data that the values of s are only in U with interruptions, otherwise it would be a simple task. My plan was to to first find all possible triples in U that could be used to build s and then find out via their indexes which triple is closest together.

Is this clearer now?

Kind regards and many thanks, Peter

Answer 1

[Babak]

http://www.mathworks.com/matlabcentral/answers/44977-how-can-i-generate-all-possible-combinations-from-multiple-sets-of-nchoosek

 perms

 nchoosek

might be helpful in finding combinations of the elements of different size vectors.

Answer 2

[Peter]

I think I could come up with a solution myself

x=[2,2,5,7,3,4,4,4,2,2,2,3]'; y=[2,2,3]';

p=0; s=0; t=0;

for i=1:length(x);
  for t=1+s:length(x); % here the code goes down one line
    if p<length(y);
      if x(t,1)==y(p+1,1);
        codes(p+1,s+1)=t;
        p=p+1;
      end;
    end;
  end;
s=s+1;
p=0;
end;

codes=codes';
codes=unique(codes,'rows');
k=find(sum(codes==0,2)>0);
codes(k,:)=[]; % incomplete triples from end of the code are removed
codes=codes';

The code goes through all records in U (here called x) and looks up s (here called y). The final matrix in codes contains all indices in x from which y can be built from.

[Babak]

Nice solution. I rather let "codes" be a cell object with option of having empty cells. Then you can support finding zero elements in y and your

 k=find(sum(codes==0,2)>0);

line wouldn't fail for length(y)>3.

Answer 3

[Saeid Abrari]

for dig=1:16

ndata = length(Frame);

ndata_1=length(digit(dig,:));

n_diff=abs(ndata-ndata_1);

Sound_1=[digit(dig,:)';zeros(n_diff,1)];

sx = sum(Frame.^2);

sy = sum(Sound_1.^2);

maxlag = ndata-1;

cnt = 0;

for lag = -maxlag:maxlag

cnt = cnt + 1;

sxy = 0;

for i=1:ndata

j = i + lag;

if j>0 && j<=ndata

sxy = sxy + Frame(i) * SoundVec_1(j);

end

end

cc(cnt) = sxy / sqrt(sx*sy); % correlation coefficient

ck(cnt) = sxy; % cross-correlation value

lags(cnt) = lag;

end

simil(dig)=max(cc);

[~,i] = max(cc);

Ts=1/Fs;

t1=Ts:Ts:FrameLen*Ts;

norm_ck=cc/max(cc);

lx = (length(norm_ck));

half = ceil(lx/2);

norm_ck_p=norm_ck(1:half);

td = i - ndata;

tau1=lags/Fs;

Answer 4

[Saeid Abrari]

for dig=1:12

ndata = length(Frame);

ndata_1=length(digit(dig,:));

n_diff=abs(ndata-ndata_1);

Sound_1=[digit(dig,:)';zeros(n_diff,1)];

sx = sum(Frame.^2);

sy = sum(Sound_1.^2);

maxlag = ndata-1;

cnt = 0;

for lag = -maxlag:maxlag

cnt = cnt + 1;

sxy = 0;

for i=1:ndata

j = i + lag;

if j>0 && j<=ndata

sxy = sxy + Frame(i) * SoundVec_1(j);

end

end

cc(cnt) = sxy / sqrt(sx*sy); % correlation coefficient

ck(cnt) = sxy; % cross-correlation value

lags(cnt) = lag;

end

simil(dig)=max(cc);

[~,i] = max(cc);

Ts=1/Fs;

t1=Ts:Ts:FrameLen*Ts;

norm_ck=cc/max(cc);

lx = (length(norm_ck));

half = ceil(lx/2);

norm_ck_p=norm_ck(1:half);

td = i - ndata;

tau1=lags/Fs;

%Find the maximum corellation index(digit)

if(max(simil)>0.5)

[seqm sequ(s_loc)]=max(simil);

s_loc=s_loc+1;

end