[SOLVED] CS matlab function NS = newtonsolver(A,x,s)

function NS = newtonsolver(A,x,s)
%NEWTONSOLVERPrepare linear solver for Newton system.
%
%NS = newtonsolver(A,x,s) returns a MATLAB struct that holds the
%factorization of the Newton matrix for solving the step equations in
%the IPM.

[m n] = size(A);
NS = struct();

% Factorization Method
%
% 1: augmented system, LU factorization
% 2: augmented system, LDL factorization (MATLAB only)
% 3: normal equations, Cholesky factorization (not implemented)

NS.method = 1;

% ********************************************************************
% LU factorization of KKT matrix
% ==============================
%
% Reduce Newton system
%
% [ A 00 ] (dx) (r)
% [ 0 A I ] (dy) = (p)
% [ S 0X ] (ds) (q)
%
% to the KKT system
%
% [ -D^(-2) A ] (dx) = (p-Xq)
% [A0] (dy) (r),
%
% where D is diagonal with D(i,i) = sqrt(x(i)/s(i)). Denote the matrix
% by K and calculate its LU factorization
%
% K(pp,qq) = L*U.
%
% This factorization is available in both MATLAB and OCTAVE and uses
% UMFPACK when K is sparse.
% ********************************************************************

if (NS.method == 1)
NS.x = x;
NS.s = s;
K = [-diag(s./x), A; A, sparse(m,m)];
[NS.L,NS.U,NS.pp,NS.qq] = lu(K,vector);
end

% ********************************************************************
% LDL factorization of KKT matrix
% ================================
%
% Perform the same reduction as above but calculate its symmetric
% indefinite factorization
%
% K(pp,pp) = L*D*L.
%
% MATLAB uses MA57 when K is sparse, which is not available in OCTAVE.
% ********************************************************************

if (NS.method == 2)
NS.x = x;
NS.s = s;
K = [-diag(s./x), A; A, sparse(m,m)];
[NS.L,NS.D,NS.pp] = ldl(K,vector);
end

end