MATLAB: Global fit of two set data points with common parameters (lsqcurvefit) but different models

lsqcurvefitnonlinear regression

Hi. I have two set of data points (with common xdata set e.g. (x,y1,y2)). That means two yexp are there for each (x1,x2,x3..). Now for lsqcurvefit, I have designed my set of two functions (which are partially different but use same set of parameters) and the output for two functions are collected in a Y(calc) vector. e.g

Y(calc)= [(y1calc(x1),y1calc(x2),y1calc(x3)….y2calc(x1),y2calc(x2)y2calc(x3)…], where y1calc's are calculated values from model1 and y2calc's are from model2. Also the Ydata (exp) that I am giving is in same order so that lsqcurvefit can work correctly. Xdata for which Y's are calculated at each points are repeated according to Y(calc) e.g. Xdata=(x1,x2,x3….x1,x2,x3) Is this the right approach to the situation? I hope I was able to explain it correctly. Thanks

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Xdata for which Y's are calculated at each points are repeated according to Y(calc) e.g. Xdata=(x1,x2,x3....x1,x2,x3) Is this the right approach to the situation?

No, duplicating the Xdata is unnecessary and likely to cause errors. You should write your model function Ycalc=F(x,Xdata) so that it takes as input an Xdata matrix containing a single copy of all the x-values

    Xdata=[x1,x2,x3,...xN]

and returns as output a matrix of all the y-values

   Ycalc=[(y1calc(x1),y1calc(x2),y1calc(x3)
           y2calc(x1),y2calc(x2)y2calc(x3)...]

The output Ycalc should be a matrix of the same size and shape as your Ydata input and the elements Ycalc(i) should be ordered such that you want Ycalc(i) to fit Ydata(i) as closely as possible. That is all that lsqcurvefit cares about.

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MATLAB: Lsqcurvefit question (Function value and YDATA sizes are not equal.)

Hi,

Use elementwise operations to declare your function:

xdata=[1,5,10,20,50];
ydata=[0.3, 1.6, 2.8, 4.6, 7.6];
fun=@(x,xdata)x(1).*1-x(1).*(1-exp(((-1).*x(2)).*xdata))./(x(2).*xdata);
x0=[10,5];
x=lsqcurvefit(fun,x0,xdata,ydata);

This version works.

Best regards

Stephan

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables and a complex function expression

You didn’t show your code, so I’m not certain what you’re doing.

You have to combine your independent variables in a matrix (I prefer column vectors for the independent and dependent variables), present them as one variable, then address the individual columns as the individual variables in your objective function.

For example:

x1x2x3 = [x1(:) x2(:) x3(:)];
y = y(:);
y = (k,x) k(1).*(1-exp(k(2).*x1x2x3(:,1))).*x1x2x3(:,3).^2 + ...

I’m not certain I parsed the parentheses correctly, so I’ll let you sort that.

Here, you would call nlinfit as:

k_est = nlinfit(x1x2x3, y, modelfun, k0);

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MATLAB: Lsqcurvefit question (Function value and YDATA sizes are not equal.)

MATLAB: How to do parameter fitting for a system of equations with 3 independent variables and a complex function expression

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