Marquardt.m

%Marquardt's Method for Multiple Variable Functions


clc;
close all;
%Insert starting points
x01=0;
x02=0;
%Function F in Symbolic Format
a='(x1^2+x2-11)^2+(x1+x2^2-7)^2';

%Insert the desired magnitude of final direction vector (0.0001 is fine)
eserror=0.0001;

Max_Iterations=20000;
convergance_criterion=0.0001;

k=0
gamma=100

%Leave the rest unchanged
%=================================

syms x1 x2
syms alpha real %difining alpha as real prevents matlab to solve function with conj(alpha)

% Hessian Of F

A=[diff(diff(a,x1),x1),diff(diff(a,x1),x2);...
    diff(diff(a,x2),x1),diff(diff(a,x2),x2)]
%First Order Derivative of F

B=[diff(a,x1);diff(a,x2)];
% pretty(simplify(A))


subs(subs(A,x1,x01),x2,x02)

mag_of_B=sqrt(subs(subs(diff(a,x1),x1,x01),x2,x02)^2+subs(subs(diff(a,x2),x1,x01),x2,x02)^2)
records=[];
while (mag_of_B>convergance_criterion)&(k<Max_Iterations)
    k=k+1;
    temp=([x01;x02]-inv(subs(subs(A,x1,x01),x2,x02)+gamma*eye(size(subs(subs(A,x1,x01),x2,x02))))*(subs(subs(B,x1,x01),x2,x02)))'
    disp('x1 x2');
    [x01;x02]
    disp('Hk')
    subs(subs(A,x1,x01),x2,x02)
    disp('gamm es');
    gamma*eye(size(subs(subs(A,x1,x01),x2,x02)))
    disp('diff');
    (subs(subs(B,x1,x01),x2,x02))

    disp('------------');
    F_eval_old=subs(subs(a,x1,x01),x2,x02);
    x01=temp(1,1);
    x02=temp(1,2);
    F_eval_new=subs(subs(a,x1,x01),x2,x02);
    if F_eval_new<F_eval_old
        gamma=.5*gamma;
    else
        gamma=2*gamma;
    end
    mag_of_B=sqrt(subs(subs(diff(a,x1),x1,x01),x2,x02)^2+subs(subs(diff(a,x2),x1,x01),x2,x02)^2)
    records=[records;[k,x01,x02,subs(subs(a,x1,x01),x2,x02)]];

end
records