How to use fminsearch with a function containing vectors of symbols

Question

Benjamin9119 2019-1-14

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/439637-how-to-use-fminsearch-with-a-function-containing-vectors-of-symbols

评论： Torsten 2019-9-13

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

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Benjamin9119 2019-1-14

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 2019-1-14

编辑：Stephen23 2019-1-14

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)];

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Answer 1

Torsten 2019-1-14

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/439637-how-to-use-fminsearch-with-a-function-containing-vectors-of-symbols#answer_356293

编辑：Torsten 2019-1-14

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

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Taicheng Tsao 2019-9-13

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.