I got stuck with a loop after the value gets to NaN

% Newton-Raphson

clear; clc

% Symbolic math to compute the derivative

syms x y

u = x^2+x*y-10;

v = y+ 3*x*y^2-57;

dudx=diff(u,x);

dudy=diff(u,y);

dvdx=diff(v,x);

dvdy=diff(v,y);

% Covert symbolic functions into regular functions with inputs of (x,y)

u = matlabFunction(u);

v = matlabFunction(v);

dudx = matlabFunction(dudx,'Vars',[x y]);

dudy = matlabFunction(dudy,'Vars',[x y]);

dvdx = matlabFunction(dvdx,'Vars',[x y]);

dvdy = matlabFunction(dvdy,'Vars',[x y]);

% Initial guess for the root

xr=1;

yr=1;

% Maximum number of steps

N=1000;

tol=1e-5;

% Plot function

x=linspace(-5,5,100);

y=linspace(-5,5,100);

U=zeros(100,100);

V=zeros(100,100);

for i=1:100

for j=1:100

U(i,j)=u(x(i),y(j));

V(i,j)=v(x(i),y(j));

end

end

figure(1); clf(1);

% Plot u(x,y)

surf(x,y,U')

hold on

% Plot v(x,y)

surf(x,y,V')

% Iterate

for i=1:1000

% Store the old value

xro=xr;

yro=yr;

% Update xr & yr

xr=xro-(u(xro,yro)*dvdy(xro,yro)-v(xro,yro)*dudy(xro,yro)) ...

/ (dudx(xro,yro)*dvdy(xro,yro)-dudy(xro,yro)*dvdx(xro,yro));

yr=yro-(v(xro,yro)*dudx(xro,yro)-u(xro,yro)*dvdy(xro,yro) ...

/ (dudx(xro,yro)*dvdy(xro,yro)-dudy(xro,yro)*dvdx(xro,yro)));

% Plot current guess for root

hold on

plot3(xr,yr,u(xr,yr),'o','Markersize',10)

plot3(xr,yr,u(xr,yr),'o','Markersize',10)

pause(1);

% Output to command window

fprintf('Iter=%5i, xr=%5.5f, yr=%5.5f, Error=%5.5e \n', ...

i,xr,yr,max(abs(xr-xro),max(abs(yr-yro))))

% Stop loop if converged

if max(abs(xr-xro),abs(yr-yro))<tol

fprintf('The root is (x,y)=(%5.10f,%5.10f) \n',xr,yr)

break %stop the loop

end

end

[Image Analyst]

What does "stuck" mean to you? It's not a while loop so can't hang in an infinite loop. You have only 1000 iterations. So what's "stuck"? Did you step through it with the debugger? Are there any error messages? (I can't run it because I don't have the Symbolic Toolbox.)

[alexander fastiggi]

if you run the code, after the 5th iteration the value of xr,yr will go to NaN and the loop is suppose to 'break' when the value is NaN

[Paul Hoffrichter]

If xr is NaN, then max(abs(xr-xro),abs(yr-yro)) is also NaN and max(abs(xr-xro),abs(yr-yro))<tol is false. To test for NaN, use isnan. But then you drop into the if-body, and since xr is NaN, you will get NaN for the result.

Answer 1

[per isakson]

The values of xr and yr do not converge to a solution that you expect. xr goes to zero and yr goes to "infinity".

>> Newton_Raphson_multidim
Iter=  100, xr= 1.17, yr=1.57e+02, Error=1.56e+02 
Iter=  100, xr= 0.14, yr=-1.37e+07, Error=1.37e+07 
Iter=  100, xr=-0.00, yr=1.10e+21, Error=1.10e+21 
Iter=  100, xr= 0.00, yr=5.96e+57, Error=5.96e+57 
Iter=  100, xr= 0.00, yr=-1.19e+154, Error=1.19e+154 
Iter=  100, xr=  NaN, yr=  NaN, Error=  NaN 
Iter=  100, xr=  NaN, yr=  NaN, Error=  NaN 
Iter=  100, xr=  NaN, yr=  NaN, Error=  NaN 

"the loop is suppose to 'break' when the value is NaN" I modified the "ouput" statements

        % Output to command window
        fprintf('Iter=%5i, xr=%5.2f, yr=%5.2e, Error=%5.2e \n', ...
            i,xr,yr,max(abs(xr-xro),max(abs(yr-yro))))
        
        % Stop loop if converged
        if max(abs(xr-xro), abs(yr-yro))<tol || isnan(xr) || isnan(yr)
            fprintf('The root is (x,y)=(%5.2e,%5.2e) \n',xr,yr)
            break %stop the loop
        end

Now I get

>> Newton_Raphson_multidim
Iter=  100, xr= 1.17, yr=1.57e+02, Error=1.56e+02 
Iter=  100, xr= 0.14, yr=-1.37e+07, Error=1.37e+07 
Iter=  100, xr=-0.00, yr=1.10e+21, Error=1.10e+21 
Iter=  100, xr= 0.00, yr=5.96e+57, Error=5.96e+57 
Iter=  100, xr= 0.00, yr=-1.19e+154, Error=1.19e+154 
Iter=  100, xr=  NaN, yr=  NaN, Error=  NaN 
The root is (x,y)=(  NaN,  NaN) 
>> 

[alexander fastiggi]

thank you!