[ fminsearch ] Assignment has more non-singleton rhs dimensions than non-singleton subscripts - where is the error?

Hello everybody,

so I have 50 sets of measured data in the first column of y. Now I want to fit a linear combination of polynomials of second order to these sets of data. With fminsearch, I want to find the optimum coefficients of the polynomials, so that the linear combination of the polynomials fits my data best. Each polynomial depends on the k-coefficients (of course) and some other input parameters that are related on the experimental setup. These parameters are summarized in matrix A. In total I have 7 parameters that define my setup, so if I want to fit one second-order polynomial for each parameter, I need 7*3=21 coefficients that have to be optimized through fminsearch. The coefficients are called k.

So here's my code:

///////////////////////

% size(y) = 50   1 (just FYI, not really executed in the programme like this)

% size(A) = 50   7 (just FYI, not really executed in the programme like this)

pol = @(k) ((-y(:,1) + k(1)*A(:,1).^0 + k(2)*A(:,1).^1 + k(3)*A(:,1).^2 + k(4)*A(:,2).^0 + k(5)*A(:,2).^1 + k(6)*A(:,2).^2 + ............. + k(19)*A(:,7).^0 + k(20)*A(:,7).^1 + k(21)*A(:,7).^2).^2);

k0 = zeros(1,21);         % I expect the coefficients to be really small

k_opt = fminsearch(pol,k0);

/////////////////////// 

Unfortunately, this is the result:

///////////////////////

Assignment has more non-singleton rhs dimensions than non-singleton subscripts

Error in fminsearch (line 200)
fv(:,1) = funfcn(x,varargin{:});

Error in cocacola_script (line 63)
k_opt = fminsearch(pol, k0);

////////////////////////

I guess I am overlooking something, does anybody see the problem here? Any assumptions are welcome!

[Stephen23]

Does pol return a scalar?

[T Webert]

Hello Stephen,

thank you for your reply.

Here's the output:

pol =

function_handle with value:
@(k) ((-y(:,1) + k(1)*A(:,1).^0 + k(2)*A(:,1).^1 + k(3)*A(:,1).^2 + k(4)*A(:,2).^0 + k(5)*A(:,2).^1 + k(6)*A(:,2).^2 + ............. + k(19)*A(:,7).^0 + k(20)*A(:,7).^1 + k(21)*A(:,7).^2).^2);

[Ameer Hamza]

Show the output of pol with an input e.g.

pol(zeros(1,21))

[T Webert]

Hello Ameer,

sure, here you go:

>> pol(zeros(1,21))

ans =

    0.1045
    0.0791
    0.0714
    0.1411
    0.1201
    0.2220
    0.1560
    0.0714
    0.0649
    0.1859
    0.0939
    0.0516
    0.0620
    0.0714
    0.1382
    0.1411
    0.1172
    0.1592
    0.0939
    0.1049
    0.1411

(note that these are only 21 rows now because I tried another set of data which has only 21 entries instead of 50.... so size(y) and size(A) are both 21 here aswell, not 50 as stated in the first post)

[Stephen23]

@T Webert: the fminsearch documentation clearly states that the function being optimized has to return a scalar. Is a 21x1 vector a scalar?

Answer 1

[Ameer Hamza]

As pointed out by Walter, the function handle to fminsearch() need to return a scalar. Without any prior knowledge about your function, I would suggest minimizing the sum of the square of vector elements. For example, try

k_opt = fminsearch(@(x) sum(pol(x).^2), k0);

[T Webert]

Ameer,

excellent, this works exactly the way I want it to work. I feel a little embarrassed that I have not been thinking about this in the first place. Thank you very much for your help. Have a great day!

[Ameer Hamza]

You are welcome.

Answer 2

[Walter Roberson]

You are using y(:,1) and so on, so your function is producing a vector result. Functions you use for fminsearch need to return a scalar.

See https://www.mathworks.com/matlabcentral/answers/405790-genetic-algorithm-calculated-values-compared-to-measured#comment_579222

[T Webert]

Hello Walter,

thank you very much, that makes sense to me.

I thought, because I would use y(:,1), it would not return a vector, but rather sum all 50 rows together in one row.

This is what I would like to do actually! I guess, I took the wrong turn before.

So the next question is: How can I put all rows of pol together in one big sum, so that I can feed this sum into fminsearch? (if I understand the problem here, this should be the solution to my problem)

Earlier today, I tried something like this:

///////////////////////////////

pol_sum = 0;

for i = 1:size(A,1)

pol{i} = @(k) ((-y(i,1)+k(1)*A(i,1)^0 + ..... + k(21)*A(i,7)^2)^2 );

pol_sum = @(k) (pol_sum + pol{i});

end

k_opt = fminsearch(pol_sum, k0)

/////////////////////////

This did not work however, because:

/////////////////

Undefined operator '+' for input arguments of type 'function_handle'.

Error in cocacola_script>@(k) (pol_sum + pol{i})

Error in fminsearch (line 200)

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

Error in cocacola_script (line 70)

k_opt = fminsearch(pol_sum,cL0);