How to use fsolve with a system of 2 nonlinear equations in a for that changes a parameter at each iteration

Hi everyone, thanks in advance for any help or tip you will give me.

I have a problem about solving a system of 2 nonlinear equation of 2 variables and 1 parameters, the one which would change during every iteraction (I tried to search in other questions opened before mine but it seems i couldn't find anything relatable or solvable for my case).

The problem at the beginning of my matlab code is to find self-consistent solutions of a a system of 2 nonlin. equation in 2 variables, but one of these equations with a parameter that is the components of a given vector V. The result i need is a matrix with the 2 solutions in the rows, and column based on V dimension.

My thought was to use this kind of code, but i dont understand the source of the error "Unable to perform assignment because dot indexing is not supported for variables of this type.".

Am i just using a bad code, or what i need is not solvable by fsolve, and i need another approach?

(Sorry for any mistake, english in not my mother tongue)

Code:

function F(Cq,Vch,V)        %%variables are Cq and Vch, V should be the parameter
    %%...
    %%constants definitions
    %%..

    F(1)= Cq-(K*kB*T)*log(2*(1+cosh((q*Vch))/(kB*T))));
    F(2)= Vch -(Vgstop-V)*(Cox/(Cox+0.5*Cq));
end

%%different file
%...
% constant definitions
%...
V=-1:0.01:1;            %%vector of parameters
Cq0=0;                    %initial guess
Vch0=0;                    %initial guess
for i=1:length(V)
    iterfun=@(Cq,Vch) F(Cq,Vch,V(i)});
    ans(i,:)=fsolve(iterfun,Cq0,Vch0);
end

[Walter Roberson]

Do not use ans as a variable name in your code.

Answer 1

[madhan ravi]

Note: Lots of parameters were not defined so please take care of it.

%%different file
%...
% constant definitions
%...
V=-1:0.01:1;            %%vector of parameters
Cq0=0;                    %initial guess
Vch0=0;                    %initial guess
Roots=cell(1,numel(V));   % preallocate!
for i=1:length(V)
    iterfun=@(x)Fdd(x,V(i));
  Roots{i}=fsolve(iterfun,[Cq0;Vch0]);  % don't name variable as ans
end
celldisp(Roots)
Roots= [Roots{:}] % double array

function F=Fdd(x,V)        %%variables are Cq and Vch, V should be the parameter
    %%...
    %%constants definitions
    %%..
    Cq=x(1);
    Vch=x(2);
    K=6; % your value
    kB=8; % your value
    q=10; % your value
    T=2; % your value 
    Vgstop=3; % your value
    Cox=4; % your value
    F(1)= Cq-(K.*kB.*T).*log(2.*(1+cosh((q.*Vch))./(kB.*T)));
    F(2)= Vch -(Vgstop-V).*(Cox./(Cox+0.5.*Cq));
end

[Pietro Rinaudo]

Thank you for the answer, but unfortunately it seems to be not working, in fact i get the error

Error using Fdd
Too many output arguments.     

I dont know what could cause this to happen :/ tried with different layouts of cell and arguments, but nothing worked

[madhan ravi]

Wierd this is what I got (although with an error message):

Roots =

  Columns 1 through 7

    1.2626    1.2238    1.2237    1.2236    1.2235    1.2234    1.2234
    0.0043   -0.0007   -0.0007   -0.0007   -0.0007   -0.0007   -0.0007

  Columns 8 through 14

    1.2234    1.2234    1.2234    1.2235    1.2236    1.2237    1.2238
   -0.0007   -0.0007   -0.0007   -0.0007   -0.0007   -0.0007   -0.0007
 
   ...... lot of lines here

  Columns 106 through 112

    1.2304    1.2251    1.2264    1.2437    1.2438    1.2262    1.2248
    0.0046   -0.0024   -0.0024   -0.0024    0.0025    0.0025   -0.0075

  Columns 113 through 119

    1.2255    1.2625    1.3013    1.2543    1.2256    1.2245    1.2299
    0.0025   -0.0044    0.0045   -0.0006   -0.0024   -0.0024    0.0046

  Columns 120 through 126

    1.2378    1.2322    1.2394    1.2209    1.2207    1.2206    1.2206
    0.0045    0.0007    0.0024    0.0008    0.0008    0.0008    0.0008

  Columns 197 through 201

    1.2260    1.2272    1.2456    1.2442    1.2411
    0.0025    0.0025    0.0025   -0.0006    0.0025

Upload the code that you are trying.

[Pietro Rinaudo]

function Fdd(x,V)
q= 1.6e-19;                                   %% carica elettrica elementare  [C]
vf=1e6;                                 %% velocità fermi               [m/s]
kB=8.617e-5;                            %% boltzmann costante           [eV/K]
ht=(4.136e-15)/(2*pi);                  %% h tagliato                   [eV*s]
T=300;                                  %%Temperature                   [K]

K=2*(q*2)/(pi*(ht*vf)^2);             %% costante pre_integrale       [C/(eV*m)^2]

tox=15e-9;                              %%spessore ossido              [m]
e0=8.854e-12;                           %% permettività vuoto          [F/m]
er=16;                                  %% permettività ossido rel     [adim]
eox=e0*er;                              %% permettività assoluta       [F/m]
Vgstop=1;                               %% tensione gs Mos             [V]    no backgate  
Cox=eox/tox;

    Cq=x(1);
    Vch=x(2);
   
    F(1)= Cq-(K.*kB.*T).*log(2.*(1+cosh((q.*Vch))./(kB.*T)));
    F(2)= Vch -(Vgstop-V).*(Cox./(Cox+0.5.*Cq));
end

%%main file
q= 1.6e-19;                                   %% carica elettrica elementare  [C]
vf=1e6;                                 %% velocità fermi               [m/s]
kB=8.617e-5;                            %% boltzmann costante           [eV/K]
ht=(4.136e-15)/(2*pi);                  %% h tagliato                   [eV*s]
T=300;                                  %%Temperature                   [K]

K=2*(q*2)/(pi*(ht*vf)^2);             %% costante pre_integrale       [C/(eV*m)^2]


tox=15e-9;                              %%spessore ossido              [m]
e0=8.854e-12;                           %% permettività vuoto          [F/m]
er=16;                                  %% permettività ossido rel     [adim]
eox=e0*er;                              %% permettività assoluta       [F/m]
Vgstop=1;                               %% tensione gs Mos             [V]    no backgate  
Cox=eox/tox;


V=-1:0.01:1;            %%vector of parameters
Cq0=0;                    %initial guess
Vch0=0;                    %initial guess
Roots=cell(1,numel(V));   % preallocate!
for i=1:length(V)
    iterfun=@(x)Fdd(x,V(i));
  Roots{i}=fsolve(iterfun,[Cq0;Vch0]);  % don't name variable as ans
end
celldisp(Roots)
Roots= [Roots{:}] % double array

This is the code i'm using, i literaly pasted your files in mine. Complete error is

Error using Fdd
Too many output arguments.

Error in test_fsolve>@(x)Fdd(x,V(i))

Error in fsolve (line 242)
            fuser = feval(funfcn{3},x,varargin{:});

Error in test_fsolve (line 24)
  Roots{i}=fsolve(iterfun,[Cq0;Vch0]);  % don't name variable as ans

Caused by:
    Failure in initial objective function evaluation. FSOLVE cannot continue.
 

[madhan ravi]

See you have some problems with copying!!!

function Fdd(x,V) % your code

function F = Fdd(x,V) % my code!

First you need to realise that a function should be placed at the end of a script file if and only if your using 2016b or later else you need to store the function in a separate file named as the same name of a function . Rename or delete if you have any file named Fdd.m.

[Pietro Rinaudo]

Ahhh that's the point, i didnt noticed the F= declaration because i was using a different file for Fdd function, so i didnt pay attention on that little detail. So from 2016b you should always include function in the script file, and no more in a different one? Anyway thank you so much for the patience and your help, now i understand my mistakes!

[madhan ravi]

Anytime :) , yes you are right .

[Walter Roberson]

So from 2016b you should always include function in the script file, and no more in a different one?

No, R2016b increases your options. It is often still a good idea to put functions into seperate files. Makes it easier to use source code control systems, for example.

[madhan ravi]

Thank you sir Walter :)