how to solve rank deficiency warning problem?

I have written a code but it is showing some warnings due to which i m getting improper outputs.....the code is as follows:

any help would be appreciated....

clear
clc
clf
format compact
% the data 
     y=[9.64E-11 5.29E-11 5.34E-11 5.32E-11 5.34E-11 5.34E-11 5.36E-11 5.35E-11 5.29E-11 5.29E-11 5.29E-11 5.30E-11 5.28E-11 5.28E-11 5.29E-11 5.28E-11 5.28E-11 5.27E-11 5.27E-11 5.28E-11 5.27E-11 5.26E-11 5.27E-11 5.26E-11 5.27E-11 5.26E-11 5.26E-11 5.26E-11 5.26E-11];
     f=[1.00E+02 3.54E+03 6.99E+03 1.04E+04 1.39E+04 1.73E+04 2.08E+04 2.42E+04 2.77E+04 3.11E+04 3.45E+04 3.80E+04 4.14E+04 4.49E+04 4.83E+04 5.18E+04 5.52E+04 5.87E+04 6.21E+04 6.56E+04 6.90E+04 7.24E+04 7.59E+04 7.93E+04 8.28E+04 8.62E+04 8.97E+04 9.31E+04 9.66E+04];
w=(2*pi)*f;
% the proposed functionality (fh is a handle to the function)
fh=@(b,w) 1./(((b(1)+(b(2)./(1+(b(2).*w.*b(3)).^2))).^2)./((b(2).^2.*b(3))./(1+(b(2).*w.*b(3)).^2))+((b(2).^2.*w.*b(3))./(1+(b(2).*w.*b(3)).^2)));
% guess values for parameters (beta0)
    b0=[1,1,1];
% plot the raw data
plot(w,y,'s','markersize',5,'color',[0,0,0]);  
hold on
% determine best fit values for coefficient (bhat)
bhat=nlinfit(w,y,fh,b0);
% plot the fit
xf = linspace(w(1), w(length(w)));
plot(xf,fh(bhat,xf),'linewidth',1,'color',[1,0,0]);
legend('original data','fitdata','location','Best') % the result 
bhat(1)
bhat(2)
bhat(3)

the warnings are as follows:

Warning: Rank deficient, rank = 2,  tol =   1.7048e-020.

    > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   5.8195e-021.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   1.9867e-021.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   6.7835e-022.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   2.3173e-022.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.9252e-023.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   2.7174e-023.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   9.3744e-024.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   3.2799e-024.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   1.1852e-024.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   4.6048e-025.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   2.0921e-025.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   1.1485e-025.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   1.1485e-025.
  > In nlinfit>LMfit at 322
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   1.1485e-025.
  > In nlinfit>LMfit at 322
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.8466e-026.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.5760e-026.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.5760e-026.
  > In nlinfit>LMfit at 322
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.5760e-026.
  > In nlinfit>LMfit at 322
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.4567e-026.
  > In nlinfit>LMfit at 295
    In nlinfit at 167
    In neha_test1 at 17
  Warning: Rank deficient, rank = 2,  tol =   7.4567e-026.
  > In nlinfit>LMfit at 322
    In nlinfit at 167
    In neha_test1 at 17
  Warning: The Jacobian at the solution is ill-conditioned, and some
  model parameters may not be estimated well (they are not identifiable).
  Use caution in making predictions.
  > In nlinfit at 224
    In neha_test1 at 17

could anybody fix this problem...?

[shantanu]

hiii, i m also facing same problem did u fix it.please help me.

[shantanu]

hiii what does colour signify here thanks in advance.

[Kerry Hipps]

I too have questions about rank deficiency, in my case it is

Warning: Rank deficient, rank = 3, tol = 4.989138e-12.

> In nlinfit>LMfit (line 587)

In nlinfit>nlrobustfit (line 768)

In nlinfit (line 315)

In SPR_ODE45_P4x (line 58)

The last is my calling program

Answer 1

[Artur Hahn]

I too have a problem with the rank deficiency. I get "Warning: Rank deficient, rank = 1, tol = 1.666613e+04."

when trying to solve a system of linear equations c = A\y. Any help or explanation of the meaning/problem would be appreciated.

Answer 2

[Kerry Hipps]

No solution yet. I switched to lsqcurvefit. Would still like to find a solution.