set Anonymous function through a series of matrix for "lsqcurvefit" or "lsqnonlin"

Hello.

I want to obtain some fitting parameters using "lsqcurvefit" or "lsqnonlin" code.

(Actually, my goal is to obtain Mueller matrix parameters in optics thorugh curve fitting.)

To obtain fitting parameters, I use complex fitting equations.

In my case, to write and set the fitting equation, I have to use some matrix calculation such as bottom.

Although I use a series of matrix, the final equation is (1x1) matrix such as

(1 x n)(n x m)(m x k)....(s x 1) --> (1 x 1) matrix

The problem is that, when I use the matrix to set anonymous function with several variables such as x(1) x(2)... , it doesn't work.

For easy example and explanation, I adopted and slightly changed an example from "lsqcurvefit" and "lsqnonlin page https://kr.mathworks.com/help/optim/ug/lsqnonlin.html#buuhch7-4 and https://kr.mathworks.com/help/optim/ug/lsqcurvefit.html#d123e61633.

clc
clear

x0 = [0.3,0.4];
F = @(x,k) 2 + 2*k - exp(k*x(1)) - exp(k*x(2));    % equation for curve fitting
ydata = linspace(0,0,10);

k = 1:10;
aa = lsqcurvefit(F,x0,k,ydata)

Actually, it works well.

However, when I tried to obtain the equation from

[1x4] * [4x1] --> [1x1]matrix,

it doens't work such as bottom script.

clc
clear

x0 = [0.3,0.4];
F = @(x,k) [2, 2, exp(k*x(1)), exp(k*x(2))] * [1; k; -1; -1]  % same as above equation, but from matrix expression
ydata = linspace(0,0,10);

k = 1:10;
aa = lsqcurvefit(F,x0,k,ydata)

In my case,

(1) I have to use several x coefficients, such as x(1) x(2) x(3) and so on, which I want to obtain from the lsqcurvefit.

(2) k have to be vectors [1,2,3,4,5,6,7,8,9,10], that is a input variable.

(3) When I type and express the equation in one line, not using the matrix, the equation becomes too long. So I want to obtain the equation from the matrix.

FInally, my question is that, for curfitting, how do I type the script to set the equation through the matrix??

Please help me.

Thank you

Answer 1

[Torsten]

x0 = [0.3,0.4];
F = @(x,k) arrayfun(@(k)[2, 2, exp(k*x(1)), exp(k*x(2))] * [1; k; -1; -1],k)  % same as above equation, but from matrix expression

F = function_handle with value:
    @(x,k)arrayfun(@(k)[2,2,exp(k*x(1)),exp(k*x(2))]*[1;k;-1;-1],k)

ydata = linspace(0,0,10);
k = 1:10;
aa = lsqcurvefit(F,x0,k,ydata)

Local minimum possible.
lsqcurvefit stopped because the size of the current step is less than
the value of the step size tolerance.

aa = 1×2

0.2578 0.2578

Answer 2

[Walter Roberson]

k = 1:10;

row vector of length 10

F = @(x,k) [2, 2, exp(k*x(1)), exp(k*x(2))] * [1; k; -1; -1]  % same as above equation, but from matrix expression

k is a row vector of length 10 so the exp() expressions are each length 10. You have two of them and you prepend two elements, so you end up with a 1 x 22 vector on the left side of the * operation.

[1; k; -1; -1]

that asks to create a row of length 1, then a row of length 10, then two more of length 1. That will fail.

If you used k(:) then you would be constructing 13 x 1. Which you cannot * with a 1 x 22

[Walter Roberson]

You need 1 row of 1s. You need 1 row of k. You need 1 row of exp(k*x1). You need 1 row of exp(k*x2). Total size 4 x length(k).

You need one column for constant addition. One each for the multipliers for the k and exp rows. total 1 x 4.

The 1 x 4 goes on the left side of * operator. 1 x 4 * 4 x N giving 1 x N

[YEONSOO LIM]

Thank you for reply.

I under stand that final equatiion become [1x22]*[1;1:10;-1;-1], which is very strange.

Then how can I make the sentance to set the equation through a series of matrix??

In my case, it is not easy to write the equation after calculating all the matrix by myself.

I also try to matlabFunction .

However, it only work well with only one x variation.

I want to use several x coefficient x(1) x(2) x(3) ....

If there is other way, please let me know.

Thank you.