Constrained Non linear least squares returns equation parameters much different from true set

Hello all,

I'm pacticing 3-4 parametrs fitting for kinetic rate equations, started with a simple example and looked at lsqnonlin option.

I'm getting results that are fare from my initial set even for different initial guess.

Also checked the levenberg-marquardt option (It is unconstrained).

Please advise of more definitions for a better convergance.

Thank you,

YA

zzx % For cleaning = clc +clear all

n=50;

x = linspace(0.5,4.1,n);

y=linspace(0.5,4.1,n);

p0=[1.75 1.4 2.5 1.8];

z=zeros(n);

k=0;

w=[x,y];

for i = 1:n

for j=1:n

k=k+1;

z(i,j)=p0(1)*x(i)^p0(2)+(y(j)^p0(3))+p0(4);

t(k)=z(i,j);

end

end

nexttile

surf(x,y,z)

title('True plot')

t0=t;

t=t0+randn(size(t0))*0.1;

fun=@(p)p(1)*w(1)^p(2)+(w(2)^p(3))+p(4)-t;

p00=[1.8 1.1 2.1 1.3];

lb=[1 1 2 0];

ub=[4 5 5 2];

options = optimoptions('lsqnonlin','Display','iter');

p=lsqnonlin(fun,p00,lb,ub,options)

for i = 1:n

for j=1:n

k=k+1;

z1(i,j)=p(1)*x(i)^p(2)+(y(j)^p(3))+p(4);

t(k)=z(i,j);

end

end

nexttile

surf(x,y,z1)

title('Regression plot')

Answer 1

[Alan Weiss]

I don't know exactly where your error is, but I reworked your code, and in my reworked version lsqnonlin returns the correct answer.

N = 50;
v = linspace(0.5,4.1,N);
[X,Y] = meshgrid(v);
p0=[1.75    1.4    2.5    1.8];
Z = p0(1)*X.^p0(2) + (Y.^p0(3)) + p0(4);
nexttile
surf(X,Y,Z)
title('True plot')

t = Z + randn(size(Z))*0.1;
fun = @(p)p(1)*X.^p(2)+(Y.^p(3)) + p(4) - t;

p00 = [1.8 1.1 2.1 1.3];
lb = [1 1 2 0];
ub = [4 5 5 2];
options = optimoptions('lsqnonlin','Display','iter');
p = lsqnonlin(fun,p00,lb,ub,options)

Z2 = p(1)*X.^p(2) + (Y.^p(3)) + p(4);

nexttile
surf(X,Y,Z2)
title('Regression plot')

Alan Weiss

MATLAB mathematical toolbox documentation

[Yaron Aviezer]

The difference is the full matrix form.

Looks that it works well also in unconstrained version.

Thank you sir