Translate an equation into a code - matlab

Question

Can you help me please translate this equation into a code?
I tried this code but its only the first part
theSum = sum(M(:, y) .* S(:, y) ./ (1 + K(:, y)))

Answer 1

EDIT: sorry, I was having a brainfart. The answer below makes no assumptions on the nature of M, K, etc, which is why I recommended functions like that. But they're clearly matrices. I'll make another answer, I'll leave this here for reference though in case it's useful
I would start by making the M, K, X, L, and O expressions into simple functions, so that you can easily call them as M(z,y), X(z,y) (or X(z,j) depending on the input you need ) etc.
Then you will convert each summation into a for loop and collect the result (you can think about vectorisation later, right now focus on translating the problem). The double summation is essentially a nested for loop, where the result of the inner loop is used in the outer one at each outer iteration.
So your end result should look something like:
Summation1 = 0;
for z = 1 : Z
tmp = M(z,y) / K(z,y) * (X(z,y) / (1 + L(z,y));
Summation1 = Summation1 + tmp;
end
Summation2 = 0;
for j = 1 : Y
if j ~= y
for z = 1 : Z
tmp = (M(z,j) * X(z,j) * O(j)) / (K(z,j)^2 * (1 + L(z,j)) * X(z,y);
Summation2 = Summation2 + tmp;
end
end
end
Result = Summation1 - Summation2;
(Btw, this assumes that all operations are on scalars. If M(z,y) outputs a vector, adjust for elementwise operations appropriately)

Answer 2

IF M, K, etc are all matrices, and all operations are expected to be element-wise, then this is a vectorised approach for this equation.
Left summation is
S1 = M(1:Z,y) ./ K(1:Z,y) .* X(1:Z,y) ./ (1 + L(1:Z,y));
S1 = sum(S1);
Right summation is (assuming (O is a horizontal vector)
S2 = M(1:Z, 1:Y) .* X(1:X, 1:Y) .* repmat(O(1:Y), [Z,1]) ./ ...
(K(1:Z, 1:Y) .^ 2 .* (1 + L(1:Z, 1:Y))) .* X(1:Z, 1:Y);
S2(:,y) = []; % remove the 'y' column from the matrix
S2 = sum(S2(:)); % add all elements
End result: S1 - S2

Answer 3

this is lambda version vectorized:
equation = #(y,M,K,X,L,O) ...
sum(M(:,y)./K(:,y).*X(:,y)./(1+L(:,y))) ...
-sum(sum( ...
bsxfun( ...
#times ...
,M(:,[1:y-1,y+1:end]) ...
.* X(:,[1:y-1,y+1:end]) ...
.* O(:,[1:y-1,y+1:end]) ...
./ (K(:,[1:y-1,y+1:end]) .^ 2 ...
.*(1+ L(:,[1:y-1,y+1:end]))) ...
,X(:,y) ...
) ...
));
%%% example:
y = 3;
Y = 5;
Z = 10;
M = rand(Y, Z);K = rand(Y, Z);X = rand(Y, Z);L = rand(Y, Z);O = rand(Y, Z);
equation(y,M,K,X,L,O)