Vectorizing a recursive for loop avoiding numerical underflow

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Josh Parks 2020-3-23

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https://ww2.mathworks.cn/matlabcentral/answers/512532-vectorizing-a-recursive-for-loop-avoiding-numerical-underflow

评论： Josh Parks 2020-3-24

Hi all,

I'm currently trying to vectorize a couple nested for loops that have a scaling coefficient (c) in there to prevent numerical underflow (note a(i,j) always less than 1). Any help is much appreciate!

Thanks,

Josh

N = 4;
T = 120000000;
M = 170;
O = randi(M,1,T);
B = zeros(N,M);
alpha = zeros(N,T);
A = rand(N);
B = rand(N,M);
c = zeros(1,T);
%compute alpha_t(i)
for t = 2:T
    for j = 1:N
        for i = 1:N
            alpha(j,t) = alpha(j,t) + alpha(i,t-1)*A(i,j);
        end %i
        alpha(j,t) = alpha(j,t)*B(j,O(t));
        c(t) = c(t) + alpha(j,t);
    end %j
    %scale alpha_t
    c(t) = 1/c(t);
    for j = 1:N
        alpha(j,t) = c(t)*alpha(j,t);
    end
end %t

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Sriram Tadavarty 2020-3-24

The last loop can be removed directly with

alpha(:,t) = c(t)*alpha(:,t);

Josh Parks 2020-3-24

Thanks, I saw the last one, the recursion is the part that's confusing me

And yes, these are right, they're getting added to each inner loop iteration, just forgot to initialize :)

%alpha_1
for i = 1:N
    alpha(i,1) = pi(i)*B(1,O(1));
    c(1) = c(1) + alpha(i,1);
end
%scale alpha_1
c(1) = 1/c(1);
for i = 1:N
    alpha(i,1) = c(1)*alpha(i,1);
end