How can I vectorize this Nested for loop

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Tulio
Tulio 2017 年 5 月 29 日

I'm trying to vectorize the inner loop but I'm not being able to.

 for i = 1:NTS          
    U(1) = 0;
    V(1) = 0;
    U(end)=1;
    V(end)=1;
    for j = 2:NAS-1
        U(j) = (b(j) * U(j-1) + a(j) * UOld(j) + c(j) * UOld(j+1)) / gamma(j);
         V(NAS-j+1) = (b(NAS-j+1) * VOld(NAS-j+1-1) + a(NAS-j+1) * VOld(NAS-j+1) + c(NAS-j+1) * V(NAS-j+1+1)) / gamma(NAS-j+1);
    end
end

I've tried the following code but I get a wrong result, can someone please help me out if that?

 U(2:NAS-1) = ((b(2:NAS-1) .* U(1:NAS-2) + a(2:NAS-1) .* UOld(2:NAS-1) + c(2:NAS-1) .* UOld(3:NAS)) ./ gamma(2:NAS-1));
 V(NAS-1:-1:2) = ((b(NAS-1:-1:2) .* VOld(NAS-2:-1:1) + a(NAS-1:-1:2) .* VOld(NAS-1:-1:2) + c(NAS-1:-1:2) .* 
 V(NAS:-1:3)) ./ gamma(NAS-1:-1:2));
    clc
    clear
    NTS=1;
    NAS=10;
    U=rand(1,10)*100;
    V=U;
    UU=zeros(1,10);
    VV=zeros(1,10);
    Gamma=ones(1,100)*(1-10.05);
    a=ones(1,10)*(1-0.05);
    b=ones(1,10)*(1-0.15);
    c=ones(1,10)*(1-0.35);
    UOld=U;
    VOld=V;
    UU=U;
    VV=V;
    for i=1:NTS
      UU(2:NAS-1) = ((b(2:NAS-1) .* UU(1:NAS-2) + a(2:NAS-1) .* UOld(2:NAS-1) + c(2:NAS-1) .* UOld(3:NAS)) ./ gamma(2:NAS-1));
      VV(NAS-1:-1:2) = ((b(NAS-1:-1:2) .* VOld(NAS-2:-1:1) + a(NAS-1:-1:2) .* VOld(NAS-1:-1:2) + c(NAS-1:-1:2) .* VV(NAS:-1:3)) ./ gamma(NAS-1:-1:2));
        for j = 2:NAS-1
            U(j) = (b(j) * U(j-1) + a(j) * UOld(j) + c(j) * UOld(j+1)) / gamma(j);
            V(NAS-j+1) = (b(NAS-j+1) * VOld(NAS-j+1-1) + a(NAS-j+1) * VOld(NAS-j+1) + c(NAS-j+1) * V(NAS-j+1+1)) / gamma(NAS-j+1);
        end
        display(sum(U(2:NAS-1)'-UU(2:NAS-1)'));
        display(sum(V(2:NAS-1)'-VV(2:NAS-1)'));
    end
    display([U' UU']);
    display([V' VV']);

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