You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: update_gbound.m
    path of file: ./repos/lrslibrary/algorithms/mc/IALM-MC/utils
    
    the code of the file until where you have to start completion: function anorm = update_gbound(anorm,alpha,beta,j)
%UPDATE_GBOUND   Update Gerscgorin estimate of 2-norm 
%  ANORM = UPDATE_GBOUND(ANORM,ALPHA,BETA,J) updates the Gersgorin bound
%  for the tridiagonal in the Lanczos process after the J'th step.
%  Applies Gerscgorins circles to T_K'*T_k instead of T_k itself
%  since this gives a tighter bound.

if j==1 % Apply Gerscgorin circles to T_k'*T_k to estimate || A ||_2
  i=j; 
  % scale to avoid overflow
  scale = max(abs(alpha(i)),abs(beta(i+1)));
  alpha(i) = alpha(i)/scale;
  beta(i) = beta(i)/scale;
  anorm = 1.01*scale*sqrt(alpha(i)^2+beta(i+1)^2 + abs(alpha(i)*beta(i+1)));
elseif j==2
  i=1;
  % scale to avoid overflow
  scale = max(max(abs(alpha(1:2)),max(abs(beta(2:3)))));
  alpha(1:2) = alpha(1:2)/scale;
  beta(2:3) = beta(2:3)/scale;
  
  anorm = max(anorm, scale*sqrt(alpha(i)^2+beta(i+1)^2 + ...
      abs(alpha(i)*beta(i+1) + alpha(i+1)*beta(i+1)) + ...
      abs(beta(i+1)*beta(i+2))));
  i=2;
  anorm = max(anorm,scale*sqrt(abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1))) );
elseif j==3
  % scale to avoid overflow
  scale = max(max(abs(alpha(1:3)),max(abs(beta(2:4)))));
  alpha(1:3) = alpha(1:3)/scale;
  beta(2:4) = beta(2:4)/scale;
  i=2;
  anorm = max(anorm,scale*sqrt(abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1) + alpha(i+1)*beta(i+1)) + ...
      abs(beta(i+1)*beta(i+2))) );
  i=3;
  anorm = max(anorm,scale*sqrt(abs(beta(i)*beta(i-1)) + ...
      abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1))) );
else
  % scale to avoid overflow
  %  scale = max(max(abs(alpha(j-2:j)),max(abs(beta(j-2:j+1)))));
  %  alpha(j-2:j) = alpha(j-2:j)/scale;
  %  beta(j-2:j+1) = beta(j-2:j+1)/scale;
  
  % Avoid scaling, which is slow. At j>3 the estimate is usually quite good
  % so just make sure that anorm is not made infinite by overflow.
  i = j-1;
  anorm1 = sqrt(abs(beta(i)*beta(i-1)) + ...
      abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...

    
function anorm = update_gbound(anorm,alpha,beta,j)
%UPDATE_GBOUND   Update Gerscgorin estimate of 2-norm 
%  ANORM = UPDATE_GBOUND(ANORM,ALPHA,BETA,J) updates the Gersgorin bound
%  for the tridiagonal in the Lanczos process after the J'th step.
%  Applies Gerscgorins circles to T_K'*T_k instead of T_k itself
%  since this gives a tighter bound.

if j==1 % Apply Gerscgorin circles to T_k'*T_k to estimate || A ||_2
  i=j; 
  % scale to avoid overflow
  scale = max(abs(alpha(i)),abs(beta(i+1)));
  alpha(i) = alpha(i)/scale;
  beta(i) = beta(i)/scale;
  anorm = 1.01*scale*sqrt(alpha(i)^2+beta(i+1)^2 + abs(alpha(i)*beta(i+1)));
elseif j==2
  i=1;
  % scale to avoid overflow
  scale = max(max(abs(alpha(1:2)),max(abs(beta(2:3)))));
  alpha(1:2) = alpha(1:2)/scale;
  beta(2:3) = beta(2:3)/scale;
  
  anorm = max(anorm, scale*sqrt(alpha(i)^2+beta(i+1)^2 + ...
      abs(alpha(i)*beta(i+1) + alpha(i+1)*beta(i+1)) + ...
      abs(beta(i+1)*beta(i+2))));
  i=2;
  anorm = max(anorm,scale*sqrt(abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1))) );
elseif j==3
  % scale to avoid overflow
  scale = max(max(abs(alpha(1:3)),max(abs(beta(2:4)))));
  alpha(1:3) = alpha(1:3)/scale;
  beta(2:4) = beta(2:4)/scale;
  i=2;
  anorm = max(anorm,scale*sqrt(abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1) + alpha(i+1)*beta(i+1)) + ...
      abs(beta(i+1)*beta(i+2))) );
  i=3;
  anorm = max(anorm,scale*sqrt(abs(beta(i)*beta(i-1)) + ...
      abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1))) );
else
  % scale to avoid overflow
  %  scale = max(max(abs(alpha(j-2:j)),max(abs(beta(j-2:j+1)))));
  %  alpha(j-2:j) = alpha(j-2:j)/scale;
  %  beta(j-2:j+1) = beta(j-2:j+1)/scale;
  
  % Avoid scaling, which is slow. At j>3 the estimate is usually quite good
  % so just make sure that anorm is not made infinite by overflow.
  i = j-1;
  anorm1 = sqrt(abs(beta(i)*beta(i-1)) + ...
      abs(beta(i)*alpha(i-1) + alpha(i)*beta(i)) + ...
      beta(i)^2+alpha(i)^2+beta(i+1)^2 +  ...
      abs(alpha(i)*beta(i+1) + alpha(i+1)*beta(i+1)) + ...
      abs(beta(i+1)*beta(i+2)));
  if isfinite(anorm1)
    anorm = max(anorm,anorm1);
  end