Re: fsolve() not adjusting all function variables

[Kai Torben Ohlhus]

On Mon, Aug 25, 2014 at 9:24 PM, gerritb <address@hidden> wrote:

I am an Octave novice and a new user of fsolve(), which I am using to fit a
formula to complex data.  I am generating a set of complex electrical
impedance data here (phase shift caused by capacitance C and inductance L)
and I want to fit an impedance formula to it.  My problem is that fsolve()
seems to adjust only some of the input variables to the function 'fit'.  In
the example below it does not change my initial guess of R (100), even
though changing it would result in a better fit to the data.  What am I
doing wrong?

Many thanks,
Gerrit
---------------------------------------------------
clear all; clf;
% To enable use of 'fsolve':
pkg load optim

function F = Zl (L, f)
  F = j*2*pi*f*L;
endfunction

function F = Zc (C, f)
  F = 1./(j*2*pi*f*C);
endfunction

% Define a function to drive to zero. Input arg is the independent vars.
function F = fit(vin)
  % Need global access to data for fitting
  global f;
  global Vc;
  % Can redefine independent vars for more meaningful names
  R = vin(1);
  C = vin(2);
  L = vin(3);
  % Return function evaluation at input vin, column vector.
  % Arrange so function = zero (ie. subtract eqn left side from right)
  F = Vc - (Zc(C, f) ./ (R + Zl(L, f) + Zc(C, f)));
  % Separate real/imag columns so both are driven to zero
  F = [real(F), imag(F)];
endfunction

% This section creates a noisy curve to fit the function to: ========
% Here are the pre-noise exact values which fsolve will approximate:
R = 50;
C = 1e-9;
L = 1e-5;
% Store input f and Z as two separate vectors
% Column vector of f values
global f = logspace(4, 8, 100)';
% Create a noisy complex curve in Vc
global Vc = Zc(C, f) ./ (R + Zl(L, f) + Zc(C, f));
rn = real(Vc) .* (1 + .05*randn(size(f)));
in = imag(Vc) .* (1 + .05*randn(size(f)));
Vc = rn + j*in;
% ===================================================================

% Initial solution guess (column vector)
vin = [100; 2e-9; 1.2e-5];
% Display, TolFun, and TolX options don't seem to have an effect:
% options = optimset('Display', 'iter', 'TolFun', 1e-12);
[vout, fval, info, output]=fsolve('fit', vin);

% Print out the results
% 'vout' is the solution vector
% 'fval' is the final function evaluation (can be used to evaluate how
%    good the fit is)
% 'info = 1' means solution converged, but 2 and 3 seem to be okay too
% 'output' lists some statistics about the process
vout
info
output

% Plot input data & best fit curve
fitVc = Zc(vout(2), f) ./ (vout(1) + Zl(vout(3), f) + Zc(vout(2), f));
inVc = Vc;
subplot(2, 1, 1);
hold;
semilogx (f, abs(inVc), 'r.');
semilogx (f, abs(fitVc), 'b');
subplot(2, 1, 2);
hold;
semilogx (f, arg(inVc)*180/pi, 'r.');
semilogx (f, arg(fitVc)*180/pi, 'b');



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Hello Gerrit,

I tried your program and you should definitely be more careful with using nested functions, global variables and alike. It seems your values for R were simply ignored. In general it is a good idea to make more smaller functions and pass the required variables. This makes the code much clearer, the variable scope as small as it is required.

HTH, Kai

fit.m
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prog.m
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