How to use fminsearch with a function containing vectors of symbols

Hello Matlab community,

Firstly, I apologise for my lack of knowledge when asking this question – I am a new Matlab user taking on a task that is quite likely out of my depth.

I have a cost function (f) that I wish to minimise using fminsearch (I believe this is what I should use for a sum of squared errors minimisation).

My function is

f = norm(h1 .x k1) – norm(h2 .x k2)

Where:

h1 and h2 are nx3 matrices of known values; and

k1 = [cos(x1)*cos(y1), cos(x1)*sin(y1), sin(x1)].’ ;
k2 = [cos(x2)*cos(y2), cos(x2)*sin(y2), sin(x2)].’

This is where I am a bit stuck, I am wanting to find the values of x1, x2, y1, y2 for which the cost function is minimised, however I am unsure of how to do this (i.e. get it in a form which I can use fminsearch) for a function (f) containing symbolic values.

I have tried a number of different approaches based on Googling (what I think may be) relevant search terms but due to my basic knowledge in Matlab I seem to have got myself pretty confused.

Does anyone have any hints or suggestions for which I can use to do this or any more search terms you suggest for me to Google? Once again, apologies for the broad question but any help would fantastic!

Many thanks in advance!

Kind Regards,

Ben

[Stephen23]

"however I am unsure of how to do this (i.e. get it in a form which I can use fminsearch) for a function (f) containing symbolic values."

Why does f contain symbolic variables? If h1 and h2 are numeric matrices, then surely you are trying to find four unknown numeric values.

[Benjamin9119]

Hi Stephen,

Thank you for your response.

f will contain symbolic variables (x1, x2, y1, y2) as the function consists of vectors k1 and k2 which contain these unknowns (for which I am wanting to solve for).

Sorry if I have not explained this very well, I hope this makes sense.

Thanks,

Ben

[Torsten]

If y1, x2, y1 and y2 are the variables to be optimized, they are not symbolic because "fminsearch" passes them to your objective function as numerical values.

[Benjamin9119]

Thanks Torsten,

This is probably where my understanding lets me down. If I have:

f = @(h1, h2, k1, k2) norm(h1.*k1)-norm(h2.*k2)

How do i pass the variables x1, x2, y1, y2 into this function which contains the vectors k1 and k2?

[Stephen23]

Note simpler syntax:

k1 = [cos(x1)*cos(y1); cos(x1)*sin(y1); sin(x1)];
k2 = [cos(x2)*cos(y2); cos(x2)*sin(y2); sin(x2)];

Answer 1

[Torsten]

Write a function for f:

function main
  h1 = ...:
  h2 = ...;
  x0 = [x10,x20,y10,y20]; % initial guess for solution
  x = fminsearch(@(x)f(x,h1,h2),x0)
end

function obj = f(x,h1,h2)
  x1 = x(1);
  x2 = x(2);
  y1 = x(3);
  y2 = x(4);
  k1 = [cos(x1)*cos(y1), cos(x1)*sin(y1), sin(x1)].' ;
  k2 = [cos(x2)*cos(y2), cos(x2)*sin(y2), sin(x2)].';
  obj = norm(h1*k1)-norm(h2*k2);
end

[Benjamin9119]

Thank you very much for your answer Torsten, it is now working perfectly!

Thank you all for your patience with me, I could not have asked for a more pleasant first experience with posting a question to this community - it really is a credit to you all!

With thanks,

Ben

[Taicheng Tsao]

I have a question. The result just display in the Command Window without being assigned in the 'x', so I want to know how I can use the result in the subsequent process. Thanks very much.

[Torsten]

After the line

x = fminsearch(@(x)f(x,h1,h2),x0)

x is available for further use.