Consider an one dimensional convolution, and change the multiplication part (a*b) to power (a^b) and summation part (Sigma) to multiplication (Phi). How can I write a program for this using vectorization.

Mathematically I want to implement a function. A and B are two integer arrays.

I have implemented the program using for loops (submitted below). How can I write a program for this using vectorization.

m=length(a);
n=length(b);
A=[a,zeros(1,n)];
B=[b,zeros(1,m)];
out=zeros(1,m+n-1);
for i=1:m+n-1
    out(i)=1;
    for j=1:m
        if i-j+1>0
            out(i)=out(i)*(A(j)^B(i-j+1));
        end
    end
end

Thank you.

Answer 1

[Matt J]

out= exp( conv(log(A),B) );

   out=round(real(out));

[John D'Errico]

Matt beat me to it.

[Matt J]

Hmmm. Unfortunately, though, this will break down if A or B contain zeros, because then the convolution will generate NaNs.

The approach should handle negative integers, however.

[Shaik Ahmad]

Thank you for fast response Matt. As you mentioned, how can we avoid that zero's problem.

[Matt J]

Come to think of it, it should be fine if B (but not A) contains zeros.

[Shaik Ahmad]

If both A and B contains zeros then it is showing NaN. For remaining two situations where any one variable contains zeros, is working fine.

[Matt J]

Are these all non-negative integers? If A contains some zeros and B contains both negative and positive values, then some of your original A^B expressions will have 0^B, which will be inf when B<0 and 0 when B>0. The product of these expressions will then be NaN.

[Shaik Ahmad]

Yes, you are correct. How can I overcome that problem. Any other solutions.

[Matt J]

Are they all non-negative integers?