Simple Recursive relation

Question

Suppose I have vectors z1 z2 z3 z4 and b and matrices D1 D2 D3 D4.

I want to construct:

b1 = D2*z2 + D3*z3 +D4*z4 -b

b2 = D1*z1 + D3*z3 +D4*z4 -b

b3 = D1*z1 + D2*z2 +D4*z4 -b

b4 = D1*z1 + D2*z2 +D3*z3 -b

I planned to store my z vectors and D matrices in cells and extract them to create b by a for loop. e.g.

for i = 1:3

  b(i) = D{i+1}*z{i+1} + D{i}*z{i};

end

Of course it certainly fails because it involves D{i}*z{i} at each i step. Can you please help me to accomplish my task?

Shai · Accepted Answer · 2017-10-26 18:58:17Z

2

You can do it like this (no recursion, but still any pair-wise product is only computed once).

pairs = zeros(size(D{1},1), 4);
for ii=4:-1:1,
    pairs(:,ii) = D{ii}*z{ii};
end

Once you have the product of all pairs, you can take the sum

all_sum = sum(pairs, 2) - b_vec; % D1*z1 + D2*z2 + D3*z3 +D4*z4 -b

To get the proper b_i you only need to subtract pairs(:,ii) from the sum:

for ii=4:-1:1
    b{ii} = all_sum - pairs{ii};
end

answered Oct 26, 2017 at 13:37

Shai

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