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## 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: [p, yf] = 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.
##
## If two outputs are requested, also return the values of the
## polynomial for each value of x.
## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
## Created: 13 December 1994
## Adapted-By: jwe
function [p, yf] = polyfit (x, y, n)
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
y_is_row_vector = (rows (y) == 1);
l = length (x);
x = reshape (x, l, 1);
y = reshape (y, l, 1);
## Unfortunately, the economy QR factorization doesn't really save
## memory doing the computation -- the returned values are just
## smaller.
## [Q, R] = qr (X, 0);
## p = flipud (R \ (Q' * y));
## XXX FIXME XXX -- this is probably not so good for extreme values of
## N or X...
X = (x * ones (1, n+1)) .^ (ones (l, 1) * (0 : n));
p = (X' * X) \ (X' * y);
if (nargout == 2)
yf = X * p;
if (y_is_row_vector)
yf = yf';
endif
endif
p = flipud (p);
if (! prefer_column_vectors)
p = p';
endif
endfunction
These are the contents of the former NiCE NeXT User Group NeXTSTEP/OpenStep software archive, currently hosted by Netfuture.ch.