An error occurred when implementing gradient descent

Given equation:

What can I modify in my code to plot the desired contour and plot the graph in this way:

Answer 1

[Torsten]

What can I modify in my code to plot the desired contour and plot the graph in this way

Change the line

f = -200*(y-x^2)^2+ (1-x^2)^2; 

to

f = 200*(y-x^2)^2+ (1-x^2)^2; 

I suggest using

f = @(x)200*(x(2)-x(1)^2)^2+ (1-x(1)^2)^2; 
g = @(x)[200*2*(x(2)-x(1)^2)*(-2*x(1))+2*(1-x(1)^2)*(-2*x(1)),200*2*(x(2)-x(1)^2)];
%f = 200*(y-x^2)^2+ (1-x^2)^2;
%g = gradient(f, [x, y]);
lr = 0.001; 
eps = 1e-8; 
iteration_limit = 1e4; 
p = [0.3 0.5]; 
for i=1:iteration_limit 
    pGrad = g(p(end,:));  
    %pGrad = [subs(g(1),[x y],p(end,:)) subs(g(2),[x y],p(end,:))]; 
    pTMP = p(end,:) - lr*pGrad; 
    %p = [p;double(pTMP)]; 
    p = [p;pTMP];
    %if sum( (p(end,:)-p(end-1,:)).^2 ) < eps 
    if sqrt(sum( (p(end,:)-p(end-1,:)).^2 ) )< eps
        break
    end
end

instead of the symbolic variant.

[Nikky schulz]

I changed the code to:

syms x y

f = @(x)100*(x(2)-x(1)^2)^2+ (1-x(1)^2)^2;

g = @(x)[400*x(1)^3-400*(x(1))*(x(2))+2*(x(1))-2,200*(x(2)-x(1)^2)];

lr = 0.001;

eps = 1e-8;

iteration_limit = 1e4;

p = [0.3 0.5];

for i=1:iteration_limit

pGrad = g(p(end,:));

%pGrad = [subs(g(1),[x y],p(end,:)) subs(g(2),[x y],p(end,:))];

pTMP = p(end,:) - lr*pGrad;

%p = [p;double(pTMP)];

p = [p;pTMP];

%if sum( (p(end,:)-p(end-1,:)).^2 ) < eps

if sqrt(sum( (p(end,:)-p(end-1,:)).^2 ) )< eps

break

end

end

v = -10:.1:10;

[X, Y] = meshgrid(v,v);

contour(v,v,subs(f,[x y],{X,Y}))

hold on

quiver(v,v,subs(g(1), [x y], {X,Y}),subs(g(2), [x y], {X,Y}))

plot(p(:,1),p(:,2))

hold off

subtitle(['Path Trajectory started from ',mat2str(round(p(1,:),3)),' with \eta=',num2str(lr)])

if i<iteration_limit

title(['converged to ',mat2str(round(p(end,:),3)),' after ',mat2str(i),' steps'])

else

title(['stopped at ',mat2str(round(p(end,:),3)),' without converging'])

end

There was an error:

[Torsten]

Copy my ode as is (I don't have a line syms x y in it)

Of course, you will have to modify the output section (subs does not exist for numerical computations).

[Nikky schulz]

Can you show me how it's done? I edited this chunk of code and it showed an error again. Once again, thanks so much for helping me.

Edited code:

v = -10:.1:10; 
[X, Y] = meshgrid(v,v);
contour(v,v,subs(f,[x(1) x(2)],{X,Y})) 
hold on
quiver(v,v,, [x(1) x(2)], {X,Y}),g(2), [x(1) x(2)], {X,Y}))
plot(p(:,1),p(:,2)) 
hold off
subtitle(['Path Trajectory started from ',mat2str(round(p(1,:),3)),' with \eta=',num2str(lr)])
if i<iteration_limit
    title(['converged to ',mat2str(round(p(end,:),3)),' after ',mat2str(i),' steps'])
else
    title(['stopped at ',mat2str(round(p(end,:),3)),' without converging'])
end

Error Message:

[Torsten]

f = @(x,y)200*(y-x.^2).^2+ (1-x.^2).^2; 
g1 = @(x,y) 200*2*(y-x.^2).*(-2*x)+2*(1-x.^2).*(-2*x);
g2 = @(x,y) 200*2*(y-x.^2);
g = @(x,y)[g1(x,y),g2(x,y)];
lr = 0.001; 
eps = 1e-8; 
iteration_limit = 1e4; 
p = [0.3 0.5]; 
for i=1:iteration_limit 
    pGrad = g(p(end,1),p(end,2));  
    pTMP = p(end,:) - lr*pGrad; 
    p = [p;pTMP];
    if sqrt(sum( (p(end,:)-p(end-1,:)).^2 ) )< eps
        break
    end
end
v = -2:.01:2; 
[X, Y] = meshgrid(v,v);
contour(v,v,f(X,Y)) 
hold on
quiver(v,v,g1(X,Y),g2(X,Y))
plot(p(:,1),p(:,2)) 
hold off
subtitle(['Path Trajectory started from ',mat2str(round(p(1,:),3)),' with \eta=',num2str(lr)])
if i<iteration_limit
    title(['converged to ',mat2str(round(p(end,:),3)),' after ',mat2str(i),' steps'])
else
    title(['stopped at ',mat2str(round(p(end,:),3)),' without converging'])
end