51 lines
1.4 KiB
Matlab
51 lines
1.4 KiB
Matlab
% proc gmchol(A);
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% /* calculates the Gill-Murray generalized choleski decomposition */
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% /* input matrix A must be non-singular and symmetric */
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% /* Author: Jeff Gill. Part of the Hessian Project. */
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% local i,j,k,n,sum,R,theta_j,norm_A,phi_j,delta,xi_j,gamm,E,beta_j;
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function AA = generalized_cholesky(A);
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n = rows(A);
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R = eye(n);
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E = zeros(n,n);
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norm_A = max(transpose(sum(abs(A))));
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gamm = max(abs(diag(A)));
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delta = max([eps*norm_A;eps]);
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for j = 1:n;
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theta_j = 0;
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for i=1:n;
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somme = 0;
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for k=1:i-1;
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somme = somme + R(k,i)*R(k,j);
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end;
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R(i,j) = (A(i,j) - somme)/R(i,i);
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if (A(i,j) -somme) > theta_j;
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theta_j = A(i,j) - somme;
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end;
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if i > j;
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R(i,j) = 0;
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end;
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end;
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somme = 0;
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for k=1:j-1;
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somme = somme + R(k,j)^2;
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end;
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phi_j = A(j,j) - somme;
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if j+1 <= n;
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xi_j = max(abs(A((j+1):n,j)));
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else;
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xi_j = abs(A(n,j));
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end;
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beta_j = sqrt(max([gamm ; (xi_j/n) ; eps]));
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if all(delta >= [abs(phi_j);((theta_j^2)/(beta_j^2))]);
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E(j,j) = delta - phi_j;
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elseif all(abs(phi_j) >= [((delta^2)/(beta_j^2));delta]);
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E(j,j) = abs(phi_j) - phi_j;
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elseif all(((theta_j^2)/(beta_j^2)) >= [delta;abs(phi_j)]);
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E(j,j) = ((theta_j^2)/(beta_j^2)) - phi_j;
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end;
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R(j,j) = sqrt(A(j,j) - somme + E(j,j));
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end;
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AA = transpose(R)*R; |