MATLAB: Least square fitting – lsqcurvefit – multiple equations – not enough input arguments –

Question

Hello everyone,

I am trying to fit some experimental data to a cerain model,

my data:

x_exp = [0.109112654
0.174029442
0.2775686
0.442708583
0.706098923
1.126193863
1.796225113
2.864892769
4.569366345
7.28791982
];
y_exp = [5247.044317
8170.755912
12604.15367
19261.43738
29160.90041
42700.48525
63815.24278
95016.30828
140804.9657
207196.2571
];

i want to fit this data using lsqcurvefit, but the problem is my model is not a one line code, it is contructed as follows, it has 4 parameters, o is the variable and my final output is G, i want to fit my y_exp with G:

% parameters are k , tau , Gg , G0
A = (o*tau)^-k * cos (k*pi/2);
B = (o*tau)^-k * sin (k*pi/2);
G1 = G0 + (((Gg-G0)* (1+A))/ (((1+A)^2)+B^2));
G2 = ((Gg-G0)* (-B)/ (((1+A)^2)+B^2));
G = ((G1^2 + G2^2)^0.5);

when i used lsqcurvefit, i constructed the code as follows, but i keep getting a message (Not enough input arguments):

% define A & B
A = @(x,xdata)(xdata*x(2))^-x(1) * cos (x(1)*pi/2);
B = @(x,xdata)(xdata*x(2))^-x(1) * sin (x(1)*pi/2);
% Define G' & G''
G1 = @(x,xdata)x(4) + (((x(3)-x(4))* (1+A(x)))/ (((1+A(x))^2)+B(x)^2));
G2 = @(x,xdata)((x(3)-x(4))* (-B(x))/ (((1+A(x))^2)+B(x)^2));
% Define G
G = @(x,xdata)((G1(x)^2 + G2(x)^2).^0.5);
x0 = [0.5 1E-4 1E+7 1E-5];
[x,resnorm,~,exitflag,output] = lsqcurvefit(G,x0,x_exp,y_exp)

can any one please help me with this?

Answer 1

There are few errors in writing the equations. Following code correct those

A = @(x,xdata)(xdata*x(2)).^-x(1) * cos (x(1)*pi/2);
B = @(x,xdata)(xdata*x(2)).^-x(1) * sin (x(1)*pi/2);
% Define G' & G''
G1 = @(x,xdata)x(4) + (((x(3)-x(4))* (1+A(x,xdata)))./(((1+A(x,xdata)).^2)+B(x,xdata).^2));
G2 = @(x,xdata)((x(3)-x(4))* (-B(x,xdata))./(((1+A(x,xdata)).^2)+B(x,xdata).^2));
% Define G
G = @(x,xdata)((G1(x,xdata).^2 + G2(x,xdata).^2).^0.5);
x0 = [0.5 1E-4 1E+7 1E-5];
[x,resnorm,~,exitflag,output] = lsqcurvefit(G,x0,x_exp,y_exp)

However, now the issue is that lsqcurvefit converges to a wrong output, which is not optimal. Are you sure your model is correct?