Question about systolic array algorithm

[sgmath12]

In line 12, I think A' should be like this:

A' = [(i,j) -> ((j = 0) ? w(i,j)*I'(i,j), A(i,j-1)) + (W(i,j)*I'(i,j)))]

But in lecture note,

A' = [(i,j) -> ((j = 0) ? 0, A(i,j-1)) + (W(i,j)*I'(i,j)))].

But if we set 0, then it is weird because the values of first column of A will be always 0, then

A(i,j-1)) = 0 when j = 1.

Am I right?

thanks.

[yongsubaek]

A' = [(i,j) -> ((j = 0) ? w(i,j)*I'(i,j), A(i,j-1)) + (W(i,j)*I'(i,j)))]
should be
A' = [(i,j) -> ((j = 0) ? w(i,j)*I'(i,j), ( A(i,j-1) + (W(i,j)*I'(i,j)))]

and

A' = [(i,j) -> ((j = 0) ? 0, A(i,j-1)) + (W(i,j)*I'(i,j)))]
should be
A' = [(i,j) -> ((j = 0) ? 0, A(i,j-1)) + (W(i,j)*I'(i,j))]

(Note that "(" and ")" are the only difference)

Then both mean
if j = 0
A'(i,j) = W(i,j)*I'(i,j)
else
A'(i,j) = A(i,j-1) + W(i,j)*I'(i,j)

I think there are some typo

[CauchyComplete]

Professor discussed it in the class. Just removing the rightmost ')' will do. Note that the parentheses do not match, i.e. there is one extra ')'.

[sgmath12]

Thank you.