Code covered by the BSD License

# Dynamic Time Warping

### Timothy Felty (view profile)

08 Dec 2004 (Updated )

Dynamic time warping program. Calculates the similarity between 2 vectors.

[Dist,D,k,w]=dtw(t,r)
```function [Dist,D,k,w]=dtw(t,r)
%Dynamic Time Warping Algorithm
%Dist is unnormalized distance between t and r
%D is the accumulated distance matrix
%k is the normalizing factor
%w is the optimal path
%t is the vector you are testing against
%r is the vector you are testing
[rows,N]=size(t);
[rows,M]=size(r);
%for n=1:N
%    for m=1:M
%        d(n,m)=(t(n)-r(m))^2;
%    end
%end
d=(repmat(t(:),1,M)-repmat(r(:)',N,1)).^2; %this replaces the nested for loops from above Thanks Georg Schmitz

D=zeros(size(d));
D(1,1)=d(1,1);

for n=2:N
D(n,1)=d(n,1)+D(n-1,1);
end
for m=2:M
D(1,m)=d(1,m)+D(1,m-1);
end
for n=2:N
for m=2:M
D(n,m)=d(n,m)+min([D(n-1,m),D(n-1,m-1),D(n,m-1)]);
end
end

Dist=D(N,M);
n=N;
m=M;
k=1;
w=[];
w(1,:)=[N,M];
while ((n+m)~=2)
if (n-1)==0
m=m-1;
elseif (m-1)==0
n=n-1;
else
[values,number]=min([D(n-1,m),D(n,m-1),D(n-1,m-1)]);
switch number
case 1
n=n-1;
case 2
m=m-1;
case 3
n=n-1;
m=m-1;
end
end
k=k+1;
w=cat(1,w,[n,m]);
end
```

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