Vectorizing loop containing multiplication of a scalar and a matrix

How to implement the following algorithm in a vectorized manner? (Preferably without using functions other than `mat`)

mat = @(i) [i-1, i, 0; i, i+1, 0; 0, 0, 1];
w = [0.2,0.5,1,0.5,0.2];
s = 0;
for j = 1:5
    s = s + w(j)*mat(j);
end

the result is

s =
    4.8  7.2  0.0
    7.2  9.6  0.0
    0.0  0.0  2.4

Answer 1

[Bruno Luong]

w = [0.2,0.5,1,0.5,0.2];
i=reshape(1:length(w),1,1,[]);
z = zeros(size(i));
s=sum([i-1, i, 0+z; i, i+1, 0+z; 0+z, 0+z, 1+z].*reshape(w,size(i)),3)

s = 3×3

4.8000 7.2000 0 7.2000 9.6000 0 0 0 2.4000

[Masa]

I need a solution using 'mat' function. Assume the matrix that 'mat' returns is unknown (the one that I've written in the code is just a sample to clarify the problem).

[Bruno Luong]

Then your request is impossible. Vectorize meaning compute the whole thing in vector way. If you only allow the mat function to support scalar input there is nothing left to vectorize. You can use arrayfun but that is NOT vectorize and it might be slower and more difficul to maintain than code with for-loop.

[Masa]

so in such situations using for loop is inevitable.

[Rik]

You have two requirements:

1. The function may only accept 1 number at a time
2. You must compute multiple values

How exactly did you think you could avoid a loop?

[Bruno Luong]

"so in such situations using for loop is inevitable."

No you can use ARRAYFUN but that is no better (worse) than the for-loop

mat = @(i) [i-1, i, 0; i, i+1, 0; 0, 0, 1];
w = [0.2,0.5,1,0.5,0.2];
i = 1:5;
M=arrayfun(mat, i, 'unif', 0);
wdM = arrayfun(@(w,mc) w*mc{1}, w, M, 'unif', 0);
s=sum(cat(3,wdM{:}),3)

s = 3×3

4.8000 7.2000 0 7.2000 9.6000 0 0 0 2.4000

If you prefer such cryptic code instead of for-loop just go ahead.

[Masa]

Thanks, of course I'd rather using loops. I thought there might be some workaround using built-in functions of MATLAB (except 'arrayfun') to do the summation mentioned in the code more efficiently.