CODEWITHSUNDEEP
algorithmmatlabmath
John
John

Reputation: 3080

How to compute sum of sum with changing upper range

I am implement the function to get the value of W with input is k, epsilon, and Omega. The function W is defined as enter image description here

Please don't worry about the complex of equation. It is very easy with three known parameter k, epsilon and Omega. Now, I want to implement it in matlab. However, my problem is how to set the range of first loop with upper range min(g-1,k). Let see my implementation for more detail. Is it correct

 function W=getW(k,epsilon,Omega)
 n=ceil((1+epsilon)*k);
 sumIn=0;
 sumOut=0;
 g=2;
 for h=1 :min(n-1,k)    
     for g=2:n
        sumIn=sumIn+(g-h)*getA(k,epsilon,g,Omega)*getT(k,g,h);    
     end
     sumOut=sumOut+sumIn;
 end
 sumOut
end
function A=getA(k,epsilon,g,Omega)
    n=ceil((1+epsilon)*k);
    A=nchoosek(n,g)*(Omega)^g*(1-Omega)^(n-g)
end
function T=getT(k,g,h)
    T=nchoosek(k,h)*getS(g,h)/(k^g);
end
function S=getS(g,h)
    sumSX=0;
    for x=1:h-1
    sumSX=sumSX+(-1)^(x-h+1)*nchoosek(h,x)*x^g;
    end
    S=h^g-sumSX;
end

To run it set W=getW(500,0.1,0.02)

Upvotes: 0

Views: 241

Answers (2)

solid
solid

Reputation: 387

It does not work because Matlab don’t check the line with FOR again, at least it does not in the debugger. I guess when Matlab interprets the line for h=1 :min(g-1,k) it calculates ones how many times it needs to repeat the loop. In this case it is once because g is 2. Even when g changes it never checks that line again. To avoid this just use while for the outer loop. With

function W=getW(k,epsilon,Omega)
n=ceil((1+epsilon)*k);    
sumOut=0;
g=2;
h=1;
while(h <= min(g-1,k))
    sumIn=0;
    for g=2:n
        sumIn=sumIn+(g-h)*getA(k,epsilon,g,Omega)*getT(k,g,h);    
    end
    sumOut=sumOut+sumIn;
    h=h+1;
end

function A=getA(k,epsilon,g,Omega)
    n=ceil((1+epsilon)*k);
    A=nchoosek(n,g)*(Omega)^g*(1-Omega)^(n-g)
end
function T=getT(k,g,h)
    T=nchoosek(k,h)*getS(g,h)/(k^g);
end
function S=getS(g,h)
    sumSX=0;
    for x=1:h-1
        sumSX=sumSX+(-1)^(x-h+1)*nchoosek(h,x)*x^g;
    end
    S=h^g-sumSX;
end

Upvotes: 1

Erti-Chris Eelmaa
Erti-Chris Eelmaa

Reputation: 26318

I think the condition you're looking for is:

min((1+epsilon)*k - 1, k);

The g-1 is supposed to be evaluated after the right hand side loop is done, and take the last value of g.

Upvotes: 1

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