How to pass summation of function handles to fminsearch

Hi, everyone

I am trying to pass a sum of function handles to fminsearch, however it always give me the error: Not enough input arguments. Error in @(i,x)sum(fun(2:3,x)) Error in fminsearch (line 200) fv(:,1) = funfcn(x,varargin{:});

Here is the simplified version of my code:

fun = @(x,i)100*(x(2) - x(1)^2)^2 + (i - x(1))^2;

sum_A=@(i,x) sum(fun(2:3,x)); // I have to do this summation in my real code

x0 = [-1.2,1];

x = fminsearch(sum_A,x0);

Why does it aways throw me an error that Not enough input arguments? In fact, sum_A just has 2 variables, what is problem here?

Any help is greatly appreciated! Thank you very much

Answer 1

[John BG]

ok,

it's all about making fminsearch work with the 2 input function as defined, right?

define the 2nd vector in advance the same way that you have defined x

s=[1 2 3];x=[3 4 5]

x0=[-1,2 1]  % initial for fminsearch

this works

f = @(x,c) x(1).^2+c.*x(2).^2;  
c = [1.5 2];                        
fminsearch(@(x) f(x,c(1)),[0.3;1])

 =
   1.0e-04 *
  -0.244731948340174
   0.315866965061825
.

and this works too

f = @(x,c) x(1).^2+c(1).*x(2).^2;  % The parameterized function.
c = [1.5 2];                        % The parameter.
fminsearch(@(x) f(x,c(1)),[0.3;1])

= 1.0e-04 * -0.244731948340174 0.315866965061825

and this works too

          f = @(x,c) (x(1).^2+c(1)).*x(2).^2;  % The parameterized function.
          c = [1.5 2];                        % The parameter.
         fminsearch(@(x) f(x,c),[0.3;1])

.

If you manage in any of these ways, would you please consider marking my answer as accepted answer?

thanks for attention

John BG

<mailto:[e-mail] [e-mail]>

Answer 2

[Darshit Mehta]

fminsearch can only take functions with one input argument (it can be a vector though). So your sum_A needs to be rewritten. Also, you don't need 'i' as an argument for sum_A in the example you have provided.

[Albert]

Dear Mehta Thank you for you answer. I know I do not really need to use i in the above example. However, in the real life, i=1:1:300, then how are you going to deal with this? To me, sum_A=@(i,x) sum(fun(2:300,x)); just has one input argument which is x since i has been assigned with a specific number. Could you provide any further precious help please?

Thank you

Answer 3

[Albert]

Thank everyone.

I finally got it work. Here is my solution. I apologize for my vague question. It was my bad to introduce i as a number instead of an index.

n=100;

dz=1;

A=@(X) sum((X(3:n)-2*X(2:n-1)+X(1:n-2)).^2/(dz)^3);

[exit,fval,exitflag]=fminsearch(A,initial);

Thanks the support and power of MATLAB community.

Answer 4

[John BG]

Hi Albert

1.

I have changed the syntax so it doesn't return error, could you please be so kind to confirm that this way is how you need to further process your data?

fun = @(x,i) 100*(x(2)-x(1)^2)^2+(i- x(1))^2;

   % MATLAB  comment // I have to do this summation in my real code

x0 = [-1.2,1];

N=10
sum_A=0
for k=1:1:N
    sum_A=sum_A+fun(x0,k)
end

2. I don't know if the following is what you need for the fminsearch, again I make it avoid error, please confirm it me be of use in your code

ni=[-10:.01:10]
fun2= @(x,s) 100*(x(2)-x(1)^2)^2+(s- x(1))^2;

for s=1:1:numel(ni)
    xmin = fminsearch(@(x) fun2(x,ni(s)),x0);
end

if you find this answer useful would you please be so kind to mark my answer as Accepted Answer?

To any other reader, please if you find this answer

please click on the thumbs-up vote link

thanks in advance

John BG

<mailto:[e-mail] [e-mail]>

[Albert]

Hi, John

Thank you very much for your answer. But your answer is not a little bit different from the original meaning of question.

Part 1 is alright.

Part 2 is not exactly what I want. In the code, you are trying to use fminsearch to find the x(2) and x(1) for each fun2 with different s. However, what I really want to do or have to do is to take the summation of the fun2 first then use fminsearch (sum_A) to find the unique x(2) and x(1) .

Could you please provide further help? Greatly appreciate your time and efforts.

Albert

[John BG]

Hi Albert

would it be possible for you to

1.

give an example of x, size, just an example

2.

is the expected of

 f1=@(i,x)sum(fun(2:3,x))

just 1 point, 2 points, or another vector?

3.

let me call the second function f2 instead of sum_A

f2=@(i,x) sum(fun(2:3,x));

Again I need a clear picture of the expected outcome of f2, the input to fminsearch

regards

John BG

<mailto:[e-mail] [e-mail]>

[Albert]

Hi, John

Again, thank you very much.

Here is what I am doing. I am trying to find the minimum curvature of a line in 3D space using fminsearch. the initial points (200 points) are known. Thus expected line is in the vicinity of initial line. x(1:200), y(200:400) denote X and Y coordinates of these 200 points. z=1:1:200, delta_z=1. The curvature at each points could be calculated by (x(i+1)-2x(i)+x(i-1))^2/(delta_z)^2+ (y(i+1)-2y(i)+y(i-1))^2/(delta_z)^2 , which is not the full formula here, but it could represent what I am trying to do . Thus I need to take summation of the curvature at each point, then use fminsearch to find the x and y coordinate of these 200 points.

Currently I can take summation of the function handle of curvature at each point, however, when I pass it to fminsearch, it throws me an error.

Thank you very very much.

[John BG]

the 'curvature' of a 2D array is the 2nd derivative, aka Laplacian.

In MATLAB it's calculated with command

del2

But as you very well point out, it all ends up in numeric approximations: some people approximate the laplacian or curvature with 5 points instead of the 1 point you have implemented.

N points meaning N points EACH SIDE of the shifting point.

Let's say you have for instance the following input 2D:

A=imread('lines_count00.jpg');imshow(A)

.

.

Let me simplify to just Red layer, the lowest value of the curvature of A1 is

A1=A(:,:,1);L=del2(double(A1));
min(min(A))
 =
  -113

The location of such min, the flattest point, is:

find(L==min(min(L)))
 =
      339189

or what's the same:

[nx,ny]=ind2sub(size(L),find(L==min(min(L))))
nx =
   389
ny =
   701

So, having said all this, please choose, do you want to carry on your development with linear expressions like

fun = @(x,i)100*(x(2) - x(1)^2)^2 + (i - x(1))^2;

or

(x(i+1)-2x(i)+x(i-1))^2+ (y(i+1)-2y(i)+y(i-1))^2

or you would consider using the points generated with a meshgrid, and the surface function, along with the Laplacian, or a numeric approximation of del2, like

delsq

introduced in

https://uk.mathworks.com/help/matlab/examples/finite-difference-laplacian.html

.

John BG

<mailto:[e-mail] [e-mail]>

[Albert]

Hi, John

I appreciate your help very much.

I apologize for any ambiguity in my description of question. Please allow me to restate my question: I am trying to find a curve in 3D space with the minimum integral curvature in the vicinity of a given curve instead of trying to find a single point with minimum curvature in a image.

My method is to discretize the given curve into 200 points, then take the summation of curvature at each point. Also the curvature at a point of 3D curve is not equal to the Laplacian value at that point. It is K=|(dr/ds) x (d^2r/ds^2)|/|(dr/ds)|^3 where r=[x(s);y(s);z(s)]; Then use fminsearch to find new 200 points with minimum integral curvature.

At the very beginning, I was trying pass a summation of function handles to fminsearch (a curvature at a given point was a function handle; 200 points yielded 200 curvatures and 200 function handles ), it didn't work and always threw me an error. Then I switched the order. I took summation of the curvature at the 200 points first and then pass this single function handle to fminsearch instead of passing summation of function handles. It woks in this way.

Even though it works now, honestly I don't understand why fminsearch doesn't accept summation of function handles. I don't see much difference between these two methods.

Thank John very much.