Re: polyfit -> polyval problem

[Sergei Steshenko]

--- On Wed, 6/22/11, Ben Abbott <address@hidden> wrote:

> From: Ben Abbott <address@hidden>
> Subject: Re: polyfit -> polyval problem
> To: "Sergei Steshenko" <address@hidden>
> Cc: address@hidden
> Date: Wednesday, June 22, 2011, 6:21 AM
> 
> On Jun 22, 2011, at 9:16 AM, Sergei Steshenko wrote:
> 
> > Hello,
> > 
> > I can't figure out what I an doing wrong in the
> following example:
> > 
> > "
> > octave:42> [p, s, mu] = polyfit ((1:10)(:), 2 *
> (1:10)(:), 1);
> > octave:43> p
> > p =
> > 
> >    6.0553   11.0000
> > 
> > octave:44> polyval(p, 1:10)
> > ans =
> > 
> >   17.055   23.111   29.166   35.221   41.277   47.332   53.387   59.442   
> >65.498   71.553
> > 
> 
> I think the problem is with the syntax you're using for
> polyval. If "mu" is an output for polyfit(), then it must be
> used as an input for polval().
> 
> octave:3>  [p, s, mu] = polyfit ((1:10)(:), 2 *
> (1:10)(:), 1);
> octave:4> polyval(p, 1:10, [], mu)
> ans =
> 
>     2.0000    4.0000   
> 6.0000   
> 8.0000   10.0000   12.0000   14.0000   16.0000   18.0000   20.0000
> 
> Ben
> 
> 


Thanks.

Well, this:

"
octave:48> p = polyfit ((1:10)(:), 2 * (1:10)(:), 1);
octave:49> p
p =

   2.0000e+00   2.2753e-15

octave:50> polyval(p, 1:10)
ans =

    2.0000    4.0000    6.0000    8.0000   10.0000   12.0000   14.0000   
16.0000   18.0000   20.0000

octave:51>
"

also works.

Now, this is the documentation:

"
octave:47> help polyfit
 -- Function File: [P, S, MU] = polyfit (X, Y, N)
     Return the coefficients of a polynomial P(X) of degree N that
     minimizes the least-squares-error of the fit.

     The polynomial coefficients are returned in a row vector.

     The second output is a structure containing the following fields:

    `R'
          Triangular factor R from the QR decomposition.

    `X'
          The Vandermonde matrix used to compute the polynomial
          coefficients.

    `df'
          The degrees of freedom.

    `normr'
          The norm of the residuals.

    `yf'
          The values of the polynomial for each value of X.

     The second output may be used by `polyval' to calculate the
     statistical error limits of the predicted values.

     When the third output, MU, is present the coefficients, P, are
     associated with a polynomial in XHAT = (X-MU(1))/MU(2).  Where
     MU(1) = mean (X), and MU(2) = std (X).  This linear transformation
     of X improves the numerical stability of the fit.

     See also: polyval, polyconf, residue.

/mnt/sdb8/sergei/AFSWD_debug/20110424/octave-3.0.5/share/octave/3.0.5/m/polynomial/polyfit.m

Additional help for built-in functions and operators is
available in the on-line version of the manual.  Use the command
`doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the address@hidden
mailing list.
"

- could you point exactly which part of the above documentation _clearly_
explains how to use 'polyval' with 'polyfit' results ?

I.e., for starters, I do not even see in the documentation that

p = polyfit(...);

is a legal form of usage.

Thanks,
  Sergei.