How to use indexed function output as a function of original inputs?

Hello everyone,

I have a big code that pin down to a system of nonlinear equations which I want to solve using fsolve. I am facing an error message: "Dot indexing is not supported for variables of this type". A simplified version of the code is:

function out = equilibrium_F(par_n,tax_n,tar_n,init_n,...
                             par_m,tax_m,tar_m,init_m,...
                             par_z,tax_z,tar_z,init_z)

cons_n = @(Q) pd_cons(I(Q(115:129) , Q(160:174) , Q(205:207) , Q(214:217) ,...
                        Q(13)      , Q(14)      , Q(15)      , Q(16)      , Q(17)  , Q(18) ,...
                        Q(10)      , Q(1)       , init_n)    ,...
                      Q(7)         , ...
                      Q(19:33)     , Q(34:48)   , Q(49:63)   ,...
                      Q(64)        , ...
                      par_n        , tax_n      , tar_n      ,...
                      par_m        , tax_m      , tar_m      ,...
                      par_z        , tax_z      , tar_z);
                  
XA_i_n           = @(Q) cons_n.XA_i(Q);                 
INV_i_n          = @(Q) cons_n.INV_i(Q);
XMT_i_nm         = @(Q) cons_n.XMT_i_nm(Q);
XMT_i_nz         = @(Q) cons_n.XMT_i_nz(Q);
Tax_rev_cons_n   = @(Q) cons_n.Tax_rev_cons(Q);
F1 = @(Q) (XA_i_n(Q),INV_i_n(Q), ...)
F2 = @(Q) (XMT_i_nm(Q), XMT_i_nz(Q), ...)
.
.
F42
F =@(Q)  [F1(Q);F2(Q);F3(Q);F4(Q);F5(Q);F6(Q);F7(Q);F8(Q);F9(Q);F10(Q);...
     F11(Q);F12(Q);F13(Q);F14(Q);F15(Q);F16(Q);F17(Q);F18(Q);F19(Q);F20(Q);...
     F21(Q);F22(Q);F23(Q);F24(Q);F25(Q);F26(Q);F27(Q);F28(Q);F29(Q);F30(Q);...
     F31(Q);F32(Q);F33(Q);F34(Q);F35(Q);F36(Q);F37(Q);F38(Q);F39(Q);F40(Q);...
     F41(Q);F42(Q)];
options = optimoptions('fsolve','Algorithm','trust-region');
 
 x0 =  ones(1,225);
 x0(1,1:3) = 0;
 x0(1,7:9) = 0;
 
 [out,fval,exitflag,output] = fsolve(F,x0,options);
 
end

I get this error message:

Dot indexing is not supported for variables of this type.

Error in equilibrium_F>@(Q)cons_n.Tax_rev_cons(Q) (line 129)

Tax_rev_cons_n = @(Q) cons_n.Tax_rev_cons(Q);

I have have two questions with regard to this:

1. How can I solve the issue of using an indexed function output as a function of original inputs.
2. Using fsolve needs initial values but the number of variables and the system complexity is very high to be able to provides these. Is there a way to get these somehow generically? or is there another way to sovle such large system of nonlinear equations other than fsolve?

Many thanks in advance for your help.

Answer 1

[Steven Lord]

Dot notation is indeed not defined for function handles. You can't do:

f = @sin;
% Commenting this code that would error so the block of code later in this answer can run
%{
g = f.x 
%}

If your function handle returns a struct array and you're using a fairly recent release of MATLAB (I don't remember which one introduced this behavior) you could index directly into the result of evaluating the function handle.

q = @whos;
names = {q().name}

names = 1x2 cell array
    {'f'}    {'q'}

But that would require your cons_n to return a struct array and for you to call it then index into the output.

%{
XA_i_n = @(Q) cons_n(Q).XA_i;
%}

[Steven Lord]

I went to the Release Notes to check and this functionality was introduced in release R2019b.

[Moutaz Altaghlibi]

I updated my matlab to 2020b release and it worked. Thank you so much Steven!