How to fix the error (Index exceeds matrix dimensions)?

could you please check my code. I got the following error

Index exceeds matrix dimensionshow .

Error in NnNonSymmetricLanczos (line 17)
    r=A*V(:,j)-alpha*V(:,j)-gamma*V(:,j-1);

function [alpha,beta,gamma,T] = alg(A,v,n)
n=4;
 
c = ones(n,1);
t = ones(1,n)./(1:n);
A = toeplitz(c,t);
v = randn(n,1);

V=v; W=v/norm(v)^2;
beta=0; gamma=0;
alpha=W(:,1)'*A*V(:,1); T(1,1)=alpha;
for j=1:n
if j==1
    r=A*V(:,j)-alpha*V(:,j);
    p=A'*W(:,j)-alpha*W(:,j);
else
    r=A*V(:,j)-alpha*V(:,j)-gamma*V(:,j-1);
    p=A'*W(:,j)-alpha*W(:,j)-beta*W(:,j-1);
end

    beta=norm(r);
    gamma=r'*p/beta;

end
T(j+1,j)=beta;
T(j,j+1)=gamma;
V=[V,r/beta];
W=[W,p/gamma];
alpha=W(:,j+1)'*A*V(:,j+1);
T(j+1,j+1)=alpha;


end

Answer 1

[Matt J]

V and W only have a single column, but you are indexing them V(:,j) and W(:,j) at j>1.

[Omar B.]

How can I fix that? they should have n coulmns

[Matt J]

You currently have these two lines creating a one-column matrix, V.

v = randn(n,1); 
V=v;

If V should have n columns, then you must change something here.

[Omar B.]

Thank you so much.