- Once you evaluate the below details you get the answer
- What is the values of x1,x2,x3 ?
- How do you relate the given vector with ranking information?
- What is the logic behind the final matrix?
Vector ranking and transformation matrix
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Hello. Suppose we have a vector [1 4 3], here -x1+x2>0, -x1+x3>0 and also x2-x3>0. How can we transform this ranking information into a matrix like [-1 1 0; -1 0 1; 0 1 -1]? Is there a function to realize it? Thank you in advance for your time and help.
2 个评论
Stalin Samuel
2016-9-21
采纳的回答
Matt J
2016-9-21
编辑:Matt J
2016-9-21
n=length(x);
A=nchoosek(1:n,2);
m=size(A,1);
B=sparse(1:m, A(:,1),1,m,n) - sparse(1:m, A(:,2),1,m,n);
result=full(bsxfun(@times, sign(B*x), B))
6 个评论
Matt J
2016-9-21
Hmmm. The discrepancy disappeared after I re-pasted the for-loop code. In any case, here is an improved version for which I see a few factors speed-up over the loops.
x=randperm(1000).';
tic
n=length(x);
[I,J]=ndgrid(1:n);
idx=J>I;
m=nnz(idx);
B=sparse(1:m,J(idx),1,m,n) - sparse(1:m, I(idx),1,m,n);
result=bsxfun(@times, sign(B*x), B);
toc
%Elapsed time is 0.685717 seconds.
tic
T=length(x);
X=[x [1:T]'];
k=sortrows(X);
V=k(:,2);
s=1;Q=zeros(T*(T-1)/2,T);
for i =1:T
for j =1:T-i
Q(s,V(i))=-1;Q(s,V(i+j))=1;s=s+1;
end
end
toc
%Elapsed time is 2.316114 seconds.
更多回答(1 个)
Steven Lord
2016-9-21
If you're asking how to convert the inequalities (like -x1 + x2 < 0) into matrix form, I don't know if there's a function to do exactly that but the equationsToMatrix function comes close. You may be able to slightly modify your inequalities so they are equations then use equationsToMatrix to generate the matrices to use as your A, b, Aeq, and beq inputs to the Optimization Toolbox solvers (which is how I'm assuming you're planning to use those matrices.)
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