Error with using fminsearch

I am working on finding the point that is the closest to 15 locations (minimum distance from all). The x- and y-coordinates are stored in 2 variables. I created the function and extracted the scalar variables from the vector but I am getting an error stating that there are not enough input arguments. The function definition and code are below:

function distance=mindistance(xv)
x=xv(1);
y=xv(2);
% extracting scaler variables from vector in fminsearch
sources = readtable('Data.xlsx','Sheet','PROJECT');
xcoordinates=table2array(sources(:,3));
ycoordinates=table2array(sources(:,4));
distance=sqrt(((x-xcoordinates).^2)+((y-ycoordinates).^2));
end

point to start with for fminsearch

xvg=[-2000 1500];
[xvmin,minD]=fminsearch(mindistance,xvg);

Answer 1

[Walter Roberson]

For one definition of "minimum distance from all":

function [xvmin, minD] = mindistance_driver
  sources = readtable('Data.xlsx','Sheet','PROJECT');
  xcoordinates = sources{:,3};
  ycoordinates = source{:,4};
  
  xvg=[mean(xcoordinates), mean(ycoordinates)];
  [xvmin, minD]=fminsearch( @(x) mindistance(x, xcoordinates, ycoordinates), xvg);
end

function distance = mindistance(xv, xcoordinates, ycoordinates)
    x=xv(1);
    y=xv(2);
    distance = sum( sqrt(((x-xcoordinates).^2)+((y-ycoordinates).^2)) );
end

There are other definitions that can be computed much more efficiently. In particular, if you use

    distance = sqrt( sum( ((x-xcoordinates).^2)+((y-ycoordinates).^2) ) );

then you can demonstrate that mean(x) and mean(y) are the optimal coordinates, without needing to do any searching.

[Berenice Oseguera]

Thank you! This worked!

Answer 2

[per isakson]

Replace

[xvmin,minD]=fminsearch(mindistance,xvg);

by

[xvmin,minD]=fminsearch('mindistance',xvg);

or

[xvmin,minD]=fminsearch(@mindistance,xvg);

and see fminsearch, Find minimum of unconstrained multivariable function using derivative-free method

[Berenice Oseguera]

Hi, I tried this and unfortunately I am getting the error below:

Unable to perform assignment because the size of the left side is 1-by-1 and the size of the right side is 15-by-1.

Error in fminsearch (line 200)

fv(:,1) = funfcn(x,varargin{:});

[per isakson]

In my answer https://se.mathworks.com/matlabcentral/answers/497619-how-to-loop-over-a-customized-function#answer_407307 I've described a debugging session that is similar to the one you need to do.

The documentation on fminsearch says: "[...] returns a real scalar f (the objective function evaluated at x)"

I guess that the function, mindistance, may return a vector of complex numbers and that's the cause of the error.

Add

if not( isreal(distance) && isscalar(distance) )
    keyboard
end

as the last statements of mindistance. If I'm right the execution will halt at keyboard and you can inspect the variables of mindistance.

[Walter Roberson]

If the coordinates in the Data.xlsx are real-valued, then sqrt(((x-xcoordinates).^2)+((y-ycoordinates).^2)) will be strictly real valued given those real-valued initial conditions. The problem is that it is a vector of distances, and you need to go from the vector to "minimum distance from all", which could mean several different things. For example it might correspond to max() of the distances, or it might be the sum of the distances, or it might be sum-of-squared distances.

[per isakson]

I try to help OP find his/her programming mistakes. To that end I believe that reading documentation and the debugging process are important.

[Berenice Oseguera]

Thank you!