How to delete some of anonymous variables randomly?

Hello Everyone,

I have a anonymous nonlinear function with 47 variables (f=x(:,1)+x(:2).*x(:,3)./x(:,4)+...x(:,47)). In each iteration, I need some of the variables, randomly (for example x(:,1), x(:.25), and x(:,34) in the first iteration), and f should be calculated only according to these variables. Also, the number of the selected variables is important, and I need to delete the other variables (not putting zero) in each iteration.

How can I do that?

[Jeff Miller]

What does it mean to compute a function of 47 variables based on (say) 3 of them and deleting the others?

It sounds like the function changes depending on which variables are used. For example, with x(:,1), x(:.25), and x(:,34) it is only a function of 3 variables, not 47.

[Asghar AmaniDashlejeh]

Exactly!

The complete function relation has 47 variables. At each iteration, the f(x) obtained by some of the variables are needed. In other words, the function relation is the part of complete relation, and it changes at each iteration. The selection of the variables is implemented in the previous section of my code.

It is similar to the subsets of the set with 47 members in each iteration. It is so easy to do that for double arrays. But, I couldn't find any way to function.

[Walter Roberson]

Would it be correct that your f is a sum of subexpressions, and that at any particular time you want to randomly select a subset of variables, and you want to create a new related function that removes from the sum any term that involves a variable that is not selected?

This would be different than setting the variables to 0 because you show us an example where you divide by x(:,4) . If I understand correctly, if x(2) and x(3) happened to be selected by x(:,4) did not happen to be selected, then you would want to delete the entire term x(:,2).*x(:,3)./x(:,4) ?

If so... then do you have access to the Symbolic toolbox? And can all terms of f() be evaluated symbolically?

[Walter Roberson]

Also, is this always going to be one specific equation that could be analyzed by hand?

nrow = size(x,1);
involves = {[1], [2 3 4], [5 8], ...}   %hardcoded analysis!
subexpr = zeros(nrow,length(involves));
if all(active(involves{1}))
  subexpr(:,1) = x(:,1);
end
if all(active(invokes{2}))
  subexpr(:,2) = x(:,2).*x(:,3)./x(:,4);
end
...
etc

output = sum(subexpr,2);

Answer 1

[Jeff Miller]

One way to approach the problem is to write a function f(x) where x is a vector with 47 positions. When you call f, put numerical values in the positions corresponding to the x's that you want to use, and put nan's in the positions corresponding to the x's that you want to leave out.

The tricky part is that the function f will need some logic to figure out how to compute its final value from the x's that are supplied, ignoring the x's that are specified as nan. That logic could be pretty simple or extremely complex, depending on exactly how each of the different x's is (potentially) used to compute the function. If it is a sum of subexpressions, as Walter suggested, then it should not be too bad.

Answer 2

[KSSV]

Multiply each variable with a constant array, and assign this contant array with 0 and 1. See to it that, randomly only three 1's are present and rest are zero, so that thought you substitue the variables, the respective contribution will be zero.

Example:

K = zeros(1,4) ;  % initiate K
idx = randperm(4,2) ;  % Make randomly one
K(idx) = 1 ; 
f = K(1)*X1+K(2)*X2+K(3)*X3/X4+K(4)*X5 ; 

[Asghar AmaniDashlejeh]

This method does not work. All numbers of the variables (47) are accounted for solving. For example, when 7 variables are selected, this error occurs:

"Index in position 2 exceeds array bounds (must not exceed 7)."

[KSSV]

Show the code which gave you this error.

[Asghar AmaniDashlejeh]

The problem was solved by putting i in x(i) depending on double array in addition to multiplying double array to variables as shown below:

h_ctff=@(x) 0; h_ctfff=@(x) 0; h_ctf=@(x) 0; h_ccff=@(x) 0; h_ccfff=@(x) 0; h_ccf=@(x) 0; g=@(x) 0;

aa=0; a=1; bb=0; b=1; cc=0; c=1; dd=0; d=1; ee=0; e=1; ff=0; f=1; hh=0; h=1;

ll=0; l=1;

for iii=1:l_uu

switch uu(iii)

case 8

aa=1;

a=iii;

case 14

bb=1;

b=iii;

case 19

cc=1;

c=iii;

case 24

dd=1;

d=iii;

case 28

ee=1;

e=iii;

case 34

ff=1;

f=iii;

case 39

hh=1;

h=iii;

case 44

ll=1;

l=iii;

end

end

h_ctff=@(x) h_ctff(x)+(-((aa.*x(:,a+2).*(aa.*x(:,a).*aa.*x(:,a+1))+bb.*x(:,b+2).*bb.*(x(:,b).*bb.*x(:,b+1))+cc.*x(:,c+1).*...

(nb_btf.*pi.*cc.*x(:,c).^2./4)+dd.*x(:,d+1).*(nb_bcf.*pi.*dd.*x(:,d).^2./4)+ee.*x(:,e+2).*ee.*...

(x(:,e).*ee.*x(:,e+1))+ff.*x(:,f+2).*ff.*(x(:,f).*ff.*x(:,f+1))+hh.*x(:,h+1).*(nb_bts.*pi.*hh.*...

x(:,h).^2./4)+ll.*x(:,l+1).*(nb_bcs.*pi.*ll.*x(:,l).^2./4)).*alpha.*(x(:,7)./x(:,5))+(x(:,5).*...

((x(:,1).*n_h).*(x(:,2).*n_v)).*(alpha.^2.*(x(:,7)./x(:,5)).^2+(1-mmm).*(x(:,6)./x(:,5)).*(alpha...

.*(x(:,7)./x(:,5))+(x(:,6)./x(:,5)))))/((alpha.*(x(:,7)./x(:,5)))))+ sqrt(((aa.*x(:,a+2).*(aa.*x(:,a)...

.*aa.*x(:,a+1))+bb.*x(:,b+2).*bb.*(x(:,b).*bb.*x(:,b+1))+cc.*x(:,c+1).*(nb_btf.*pi.*cc.*x(:,c).^2./4)...

+dd.*x(:,d+1).*(nb_bcf.*pi.*dd.*x(:,d).^2./4)+ee.*x(:,e+2).*(ee.*x(:,e).*ee.*x(:,e+1))+ff.*x(:,f+2)...

.*ff.*(x(:,f).*ff.*x(:,f+1))+hh.*x(:,h+1).*(nb_bts.*pi.*hh.*x(:,h).^2./4)+ll.*x(:,l+1).*(nb_bcs.*pi...

.*ll.*x(:,l).^2./4)).*alpha.*(x(:,7)./x(:,5))+(x(:,5).*((x(:,1).*n_h).*(x(:,2).*n_v)).*(alpha...

.^2.*(x(:,7)./x(:,5)).^2+(1-mmm).*(x(:,6)./x(:,5)).*(alpha.*(x(:,7)./x(:,5))+(x(:,6)./x(:,5)))))./...

((alpha.*(x(:,7)./x(:,5))))).^2-4.*((x(:,5).*((x(:,1).*n_h).*(x(:,2).*n_v)).*(mmm-1).*((alpha...

.*(x(:,7)./x(:,5))+(x(:,6)./x(:,5)))).^2)./(2.*alpha.*(x(:,7)./x(:,5)).*(x(:,2).*n_v))).*(-((aa.*...

x(:,a+2).*(aa.*x(:,a).*aa.*x(:,a+1)).*aa.*x(:,a+4))+(bb.*x(:,b+2).*bb.*(x(:,b).*bb.*x(:,b+1)).*bb.*x(:,b+4))+...

(cc.*x(:,c+1).*(nb_btf.*pi.*cc.*x(:,c).^2./4).*cc.*x(:,c+3))+(dd.*x(:,d+1).*(nb_bcf.*pi.*dd.*x(:,d)...

.^2./4).*dd.*x(:,d+3))+(ee.*x(:,e+2).*ee.*(x(:,e).*ee.*x(:,e+1)).*ee.*x(:,e+4))+(ff.*x(:,f+2).*(ff.*...

x(:,f).*ff.*x(:,f+1)).*ff.*x(:,f+4))+(hh.*x(:,h+1).*(nb_bts.*pi.*hh.*x(:,h).^2./4).*hh.*x(:,h+3))+(...

ll.*x(:,l+1).*(nb_bcs.*pi.*ll.*x(:,l).^2./4).*ll.*x(:,l+3))).*alpha.*(x(:,7)./x(:,5))+(x(:,5).*(...

(x(:,1).*n_h).*(x(:,2).*n_v)).*(x(:,2).*n_v).*((mmm-1).*(x(:,6)./x(:,5)).^2-alpha.^2.*(x(:,7)./...

x(:,5)).^2))./(2.*alpha.*(x(:,7)./x(:,5))))))./(2.*((x(:,5).*((x(:,1).*n_h).*(x(:,2).*n_v)).*...

(mmm-1).*((alpha.*(x(:,7)./x(:,5))+(x(:,6)./x(:,5)))).^2)./(2.*alpha.*(x(:,7)./x(:,5)).*(x(:,2).*...

n_v))));