Please help with For Loop

    u1 = v(:,1);

    a2 = v(:,1)\v(:,2);
    u2 = v(:,2) - v(:,1)*a2;

    a3 = v(:,[1 2])\v(:,3);
    u3 = v(:,3) - v(:,[1 2])*a3;

    a4 = v(:,[1 2 3])\v(:,4);
    u4 = v(:,4) - v(:,[1 2 3])*a4;

    % Structural residuals   and covariance 
    b02 = [ 1           0        0        0;
           -a2(1)       1        0        0;
           -a3(1)    -a3(2)      1        0;
           -a4(1)    -a4(2)    -a4(3)     1 ];
    u  = [u1 u2 u3 u4 ];

Please advise how can I estimate a , u and b with for loop...in case I have many more variables then just four.

Answer 1

[Walter Roberson]

Index your variables instead of using fixed variable name. Use cell arrays.

a{K} = v(:,K-1)\v(:,K);
u{K} = v(:,K) - v(:,K-1)*a{K};

[Raisul Islam]

Are you sure Walter? Each v is a 5000 by 1 vector. And how will I create the lower triangular matrix with loop?

[Raisul Islam]

OK walter. for a{k} its fine, because a returns scaler. for 32 column that's fine. But for u , its not fine. The loop returns scaler. Where the loop is supposed to return vectors of size m by n. Note, v is sized m by n.

[Walter Roberson]

u(:,1) = v(:,1);
for K = 2 : size(v,2)
  a(K) = v(:,K-1)\v(:,K);
  u(:,K) = v(:,K) - v(:,K-1)*a(K);
end

[Raisul Islam]

Thank you so much. That worked easily. Can you help me with the final part. How can I make the lower triangular matrix with a loop? Thnx

[Walter Roberson]

Correction:

ncol = size(v,2);

u(:,1) = v(:,1);
a = zeros(ncol, ncol);
for K = 2 : size(v,2)
  a(1:K-1,K) = v(:,1:K-1)\v(:,K);
  u(:,K) = v(:,K) - v(:,1:K-1)*a(1:K-1,K);
end

b = diag(ones(1,ncol)) - tril(a.');

[Raisul Islam]

thank you so much