Transformation of a MATLAB Function.

I have a function defined as,

f_xw   = @(x,w) [3.*x(1) - x(1).^2/7 + w(1);
              -2.*x(2) + w(2)];

I want to transform this from x coordinate system to \eta coordinate system which would look like

f_etaw = @(eta,w) [3.*(c1+G1*eta) - (c1+G1*eta).^2/7 + w(1);...
                -2.*(c2+G2*eta) + w(2)];

where i define eta as symbolic variables

eta = sym('eta',[2 1]);

and c's are constants numbers (1x1) and G's are constant row vectors (1x2) which i can define globally.

Is there a way to do this transformation using matlabFunction command? And can this transformation be made general for all functions with n states?

Answer 1

[Steven Lord]

f_xw   = @(x,w) [3.*x(1) - x(1).^2/7 + w(1);
              -2.*x(2) + w(2)];
f_etaw = @(eta,w) [3.*(c1+G1*eta) - (c1+G1*eta).^2/7 + w(1);...
                -2.*(c2+G2*eta) + w(2)];

So instead of x(1) you want to use c1+G1*eta and instead of x(2) you want to use c2+G2*eta?

% assuming c1, c2, G1, and G2 already exist
f_etaw = @(eta, w) f_xw([c1+G1*eta, c2+G2*eta], w);

And can this transformation be made general for all functions with n states?

Assuming c and G are vectors that are the same size as the x input with which f_xw expects to be called:

% assuming c and G already exist
f_etaw = @(eta, w) f_xw(c+G*eta, w);

[Fawad Khan]

Thank you so much. It works.

I still need a bit of help here.

After I get f_etaw using this. Considering this case, my original function had 2 equations. Can I get two separate function handles for each of them. I'll try to explain this.

I have a function handle which has two equations (the number of equations may vary, thats why I wanted to generalize it)

f_xw   = @(x,w) [3.*x(1) - x(1).^2/7 + w(1);
                -2.*x(2) + w(2)];

Basically I want separate function handles for each of the equations. I was unable to extract them in this form so I manually transformed them as used a cell array as

f_etaw = {@(eta,w) 3.*(c1+G1*eta) - (c1+G1*eta).^2/7 + w(1);
          @(eta,w) -2.*(c2+G2*eta) + w(2)};

This way I can use my eqiuations as f_etaw{1,1} and f_etaw{2,1}. I wanted to generalize this for any example with as many states/equations as required.

[Fawad Khan]

I've tried to do this in the following way. Is this correct?

f_xw   = @(x,w) [3.*x(1) - x(1).^2/7 + w(1);
                -2.*x(2) + w(2)];

c, G and w are defined. Here I removed w from f_etaw. I want to fix w by defining it globally.

eta    = sym('eta',[size(G,2) 1]);

f_eta = @(eta) f_xw(c+G*eta,w);
f_eta = f_etaw(eta);

f_etas = cell(1,size(f_eta,1));
for m = 1:size(f_eta,1)
        f_etas{m} = matlabFunction(f_eta(m,:),'Vars',{eta});
end

Does this seem alright?