I need to fit two x,y data sets to two different functions that share the same parameters. Is there a simple way to do this?

I have one data set that reprents the population of one species as a function if x, and the other that represents the population another species as a function of x. These populations depend on the same paramters. When one d creases the other increases. So I have two functions, but the same parameters. I want to fit these two data sets simultaneously for the 5 parameters. I figu ed out how to fit two datasets to the same function with different parameters, but I need to fit two dTa sets to different functions with the same parameters and I cannot figure it out. Thanks for any insight. Cathy

[Star Strider]

Continuation of: https://www.mathworks.com/matlabcentral/answers/312589-i-need-to-fit-several-data-sets-to-the-same-parameters-is-there-a-function-that-allows-simultaneous

Answer 1

[Star Strider]

If you write your functions correctly, this will work. (I tested it with arbitrary data and functions. It works.)

The Code —

x_mtx = [x1(:) x2(:)];                                                  % Concatenate Vectors To Create ‘x_mtx’
y_mtx = [y1(:) y2(:)];                                                  % Concatenate Vectors To Create ‘y_mtx’

fun1 = @(x,xdata) ...;                                                  % Objective Function #1
fun2 = @(x,xdata) ...;                                                  % Objective Function #2

fun = @(x,xdata) [fun1(x,xdata(:,1)),  fun2(x,xdata(:,2))];             % Composite Function

x0 = rand(5,1);                                                         % Initial Parameter Estimates
X = lsqcurvefit(fun, x0, x_mtx, y_mtx);                                 % Estimate Parameters

Obviously, your different ‘x’ and ‘y’ data vectors all have to have the same lengths, or you will not be able to create the ‘x_mtx’ and ‘y_mtx’ arrays, and so will not be able to estimate your parameters.

[Catherine Royer]

Thanks much It sort of works but the recovered parameter numbers are pretty wrong. The x-mtx and y_mtx matrices are created just fine. The parameter vector is read ok (I gave it appropriate values).

I am confused about how to refer to the x-axis data in the functions. As far as I can tell xdata never gets defined. Should the x-axis data in function 1 be x1 or xdata1? Ibid for function 2, which is similar (x2 or xdata2)?

fun1 = @(x,xdata) x(1).*(1./(1 + (x(2).*exp(x(3).*x1)) + (x(2).*exp(x(3).*x1).*(x(4).*exp(x(5).*x1)))))  
fun2 = @(x,xdata) x(1).*((x(2).*exp(x(3).*x2)./(1 + (x(2).*exp(x(3).*x2)) + (x(2).*exp(x(3).*x2).*(x(4).*exp(x(5).*x2))))))

[Star Strider]

My pleasure.

The ‘xdata’ value becomes defined as ‘x_mtx’ when lsqcurvefit calls ‘fun’ and passes ‘x_mtx’ to it.

Parameter estimation and other optimisation problems are sensitive to the initial parameter estimates. If you have the Global Optimization Toolbox, consider using the patternsearch or GlobalSearch functions to get better initial estimates. Your functions have products of exponential functions that may be difficult to estimate successfully.

You refer to ‘x-axis’. If you are trying to plot it, you need to plot:

figure(1)
plot(x_mtx(:,1), y_mtx(:,1), fun1(x,x_mtx(:,1))
hold on
plot(x_mtx(:,2), y_mtx(:,2), fun2(x,x_mtx(:,2))
hold off
grid

That is how I have referred to them and defined them in ‘fun’.

[Changjiang]

Hi Star,

Why I got the error:

"Error using lsqcurvefit

Function value and YDATA sizes are not equal."

I just copied the code you wrote.

Best

CJ

[Star Strider]

I have no idea in your specific instance.

This can occur if the objective function returns matrices that are transposes of the data, so check that.