### Copyright (C) 1996 John W. Eaton
###
### This file is part of Octave.
###
### Octave is free software; you can redistribute it and/or modify it
### under the terms of the GNU General Public License as published by
### the Free Software Foundation; either version 2, or (at your option)
### any later version.
###
### Octave is distributed in the hope that it will be useful, but
### WITHOUT ANY WARRANTY; without even the implied warranty of
### MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
### General Public License for more details.
###
### You should have received a copy of the GNU General Public License
### along with Octave; see the file COPYING.  If not, write to the Free
### Software Foundation, 59 Temple Place - Suite 330, Boston, MA
### 02111-1307, USA.

## usage:  polyfit (x, y, n)
##
## Returns the coefficients of a polynomial p(x) of degree n that
## minimizes sumsq (p(x(i)) - y(i)), i.e., that best fits the data 
## in the least squares sense.

function p = polyfit (x, y, n)
  
  ## Written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 13, 1994
  ## Copyright Dept of Statistics and Probability Theory TU Wien
  
  if (nargin != 3)
    usage ("polyfit (x, y, n)");
  endif
  
  if (! (is_vector (x) && is_vector (y) && size (x) == size (y)))
    error ("polyfit: x and y must be vectors of the same size");
  endif
  
  if (! (is_scalar (n) && n >= 0 && ! isinf (n) && n == round (n)))
    error ("polyfit: n must be a nonnegative integer");
  endif
  
  l = length (x);
  x = reshape (x, l, 1);
  y = reshape (y, l, 1);
  
  X = ones (l, 1);

  if (n > 0)
    tmp = (x * ones (1, n)) .^ (ones (l, 1) * (1 : n));
    X = [X, tmp];
  endif

  ## Compute polynomial coeffients, making returned value compatible
  ## with Matlab.

  [Q, R] = qr (X, 0);

  p = flipud (R \ (Q' * y));

  if (! prefer_column_vectors)
    p = p';
  endif

endfunction