minimize function one element of array input

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franco otaola 2021-1-21

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/723373-minimize-function-one-element-of-array-input

Hello,

I was not sure how to even title the question.

I have a function that have several inputs, to give an easy example a function that calculates a line (ax+b=y) that aproximates the best some data.

param0=[1,2];	
[param,resnorm,~,exitflag]=lsqnonlin(@(param) LineFun(param,valuesX,valuesY),param0,[],[],optionsLsq);
function  [res]= LineFun(param,valuesX,valuesY)
    a=param(1);
    b=param(2);
    Vector=a*valuesX+b;
    res=valuesY-Vector;
end 

in the example I write the code will minimize the function so the best pair of values.

obviously, my case is a little bit more complicated than the example i gave but what for the porpouse it should be enought. what I would like to know is how can I (using the same function), minimize the function by one of the elements of the param. for example minimize the function with an a (param(1)) or a b (param(2)) fixed without the need to re define 3 times "similar" functions. something like this:

 param0=[1,2];
%minimize for the two param a and b
[param,resnorm,~,exitflag]=lsqnonlin(@(param) LineFun(param,valuesX,valuesY),param0,[],[],optionsLsq);
%minimize for the two param a (so b is fixed to 2)
[param,resnorm,~,exitflag]=lsqnonlin(@(param(1)) LineFun(param,valuesX,valuesY),param0(1),[],[],optionsLsq);
%minimize for the two param b (so a is fixed to 1)
[param,resnorm,~,exitflag]=lsqnonlin(@(param(2)) LineFun(param,valuesX,valuesY),param0(2),[],[],optionsLsq);
function  [res]= LineFun(param,valuesX,valuesY)
    a=param(1);
    b=param(2);
    Vector=a*valuesX+b;
    res=valuesY-Vector;
end 

I know that I could define 3 different functions where the param means a and b or a alone or b alone and have the value of the other parameter inside the function. but I can imagine that there is a more organized way to do it as I have several functions with several parameters.

best regards,