Minimizing a multivariable anonymous function that contains vectors using fminsearch

I am trying to minimize I0 and a in the function handle below. rBes and rCutFit are vectors with the same dimensions. The variables, wave, a, C, u, and r are constants that have already been defined in the script.

R2=@(I0,a) (rBes(u)-I0*((2*rCutFit((((2*pi)/wave)*a*sin(atan((u*C)/r))))/(((2*pi)/wave)*a*sin(atan((u*C)/r))))^.2)).^2; MIN=fminsearch(R2,[1,10^-6]);

I keep getting the error below everytime I run the code. Please let me know if you have any advice for fixing this.

"Not enough input arguments.

Error in @(I0,a)(rBes(u)-I0*((2*rCutFit((((2*pi)/wave)*a*sin(atan((u*C)/r))))/(((2*pi)/wave)*a*sin(atan((u*C)/r))))^.2)).^2

Error in fminsearch (line 189) fv(:,1) = funfcn(x,varargin{:});"

Answer 1

[James Tursa]

Make R2 accept a vector input. E.g., use x as the argument and replace I0 with x(1) and a with x(2)

R2=@(x) (rBes(u)-x(1)*((2*rCutFit((((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))/(((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))^.2)).^2;

MIN=fminsearch(R2,[1,10^-6]);

[Tana Si]

I have tried your suggestion. This is my code:

wave=473*10^-9; r=0.143; C=4.022*10^-5; u=30;

R2=@(x) (rBes(u)-x(2)*((2*rCutFit((((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))/(((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))^.2)).^2; MIN=fminsearch(R2,[1,10^-6]);

This is the error I received:

"Subscript indices must either be real positive integers or logicals.

Error in @(x)(rBes(u)-x(2)*((2*rCutFit((((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))/(((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))^.2)).^2

Error in fminsearch (line 189) fv(:,1) = funfcn(x,varargin{:});"

Please let me know if you have any further suggestions. Thanks.

[Walter Roberson]

What is rCutFit ?

[James Tursa]

You didn't replace that 2nd "a" with x(2)

Also, the error you are getting typically indicates you are shadowing a function with a variable. E.g., maybe you have a variable named "sin" or "atan" or "rCutFit" or "rBes" in your workspace that is shadowing those functions.

[Tana Si]

So sorry. I replaced the 2nd a and got the same error. rCutFit is a column vector with the same dimensions as rBes.

[Tana Si]

I do not have a variable named sin and atan, but I do have rCutFit and rBes as defined column vectors before. rBes is from experimental data and rCutFit is generated through MATLAB's besselj.

[Walter Roberson]

rCutFit((((2*pi)/wave)*x(2)*sin(atan((u*C)/r))))

mean that you want to calculate (((2*pi)/wave)*x(2)*sin(atan((u*C)/r))) and use that as an index into rCurFit . That is going to fail except under unlikely circumstances that the computation produces a positive integer.

Did you need a multiplication between rCurFit and the following expression?

[Tana Si]

I need to express the vector rCutFit, which was produced by the besselj function in MATLAB and reshaped by removing a section of its first values, as a function of ((2*pi)/wave)*sin(atan((u*C)/r)). rCutFit is J1 in the mathematical function attached with its input, kasin(theta)), expressed in a different form.

rBes is an experimentally derived vector and was not generated by MATLAB.

[Tana Si]

Please note that in the numerator, kasin(theta) is not a multiplicative factor, but an input into the J1 function (the bessel function of the first kind, first order).

[Walter Roberson]

Arrays (and vectors) have particular sizes at any one time, and are indexed with () notation and what follows in the () must be a list of positive integers, possibly together with colons.

Functions also use () notation to invoke them, and can have non-integral arguments that are function parameters.

You cannot use non-integral values (other than colon) in the () after a vector name (except in intermediate calculations provided the overall result of the calculation is positive integer).

If you need to perform a calculation on a non-integral argument and get a vector or array output, then you should make rCutFit into a function that does the appropriate bessel calculation and removes whatever and reshapes as is suitable.