function?p?=?polyfitweighted2（xyznw）
%?polyfitweighted2.m?
%?-------------------
%
%?Find?a?least-squares?fit?of?2D?data?z（xy）?with?an?nth?order?
%?polynomial?weighted?by?w（xy）?.
%
%?By?S.S.?Rogers?（2006）
%
%?Usage
%?------
%
%?P?=?polyfitweighted2（XYZNW）?finds?the?coefficients?of?a?polynomial?
%?P（XY）?of?degree?N?that?fits?the?data?Z?best?in?a?least-squares?
%?sense.?P?is?a?row?vector?of?length?（N+1）*（N+2）/2?containing?the?
%?polynomial?coefficients?in?ascending?powers?0th?order?first.
%
%???P?=?[p00?p10?p01?p20?p11?p02?p30?p21?p12?p03...]
%
%?e.g.?For?a?3rd?order?fit?
%?the?regression?problem?is?formulated?in?matrix?format?as:
%
%???wZ?=?V*P????or
%
%??????????????????????2???????2???3???2?????2??????3
%???wZ?=?[w??wx??wy??wx??xy??wy??wx??wx?y??wx?y???wy?]??[p00
%????????????????????????????????????????????????????????p10
%????????????????????????????????????????????????????????p01
%????????????????????????????????????????????????????????p20
%????????????????????????????????????????????????????????p11
%????????????????????????????????????????????????????????p02
%????????????????????????????????????????????????????????p30
%????????????????????????????????????????????????????????p21
%????????????????????????????????????????????????????????p12
%????????????????????????????????????????????????????????p03]
%
%?*Note:*?P?is?not?in?the?format?of?standard?Matlab?1D?polynomials.?Use
%?polval2.m?to?evaluate?the?polynomial?in?this?format?at?given?values?of
%?xy.
%
%?XY?must?be?vectors
%?ZW?must?be?2D?arrays?of?size?[length（X）?length（Y）]
%
%?based?on?polyfit.m?by?The?Mathworks?Inc.?-?see?doc?polyfit?for?more?details
%
%?Class?support?for?inputs?XYZW:
%??????float:?double?single

x?=?x（:）;
y?=?y（:）;

lx=length（x）;
ly=length（y）;

if?~isequal（size（z）size（w）[ly?lx]）
????error（‘polyfitweighted2:XYSizeMismatch‘...
?????????[‘?XY?*must*?be?vectors‘?...
??????????‘??ZW?*must*?be?2D?arrays?of?size?[length（X）?length（Y）]‘]）
end

y=y*ones（1lx）;
x=ones（ly1）*x‘;
x?=?x（:）;
y?=?y（:）;
z?=?z（:）;
w?=?w（:）;

pts=length（z）;

%?Construct?weighted?Vandermonde?matrix.
V=zeros（pts（n+1）*（n+2）/2）;
V（:1）?=?w;
%V（:1）?=?ones（pts1）;
ordercolumn=1;
for?order?=?1:n
????for?ordercolumn=ordercolumn+（1:order）
????????V（:ordercolumn）?=?x.*V（:ordercolumn-order）;
????end
????ordercolumn=ordercolumn+1;
????V（:ordercolumn）?=?y.*V（:ordercolumn-order-1）;
end

%?Solve?least?squares?problem.
[QR]?=?qr（V0）;
ws?=?warning（‘off‘‘all‘）;?
p?=?R\（Q‘*（w.*z））;????%?Same?as?p?=?V\（w.*z）;
warning（ws）;
if?size（R2）?>?size（R1）
???warning（‘polyfitweighted2:PolyNotUnique‘?...
???????‘Polynomial?is?not?unique;?degree?>=?number?of?data?points.‘）
elseif?condest（R）?>?1.0e10
????????warning（‘polyfitweighted2:RepeatedPointsOrRescale‘?...
????????????[‘Polynomial?is?badly?conditioned.?Remove?repeated?data?points\n‘?...
????????????‘?????????or?try?centering?and?scaling?as?described?in?HELP?POLYFIT.‘]）
end
%r?=?z?-?（V*p）./w;
p?=?p.‘;??????????%?Polynomial?coefficients?are?row?vect

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????3019??2006-12-28?15:11??polyfitweighted2\polyfitweighted2.m
?????文件????????2023??2006-12-28?15:04??polyfitweighted2\polyval2.m
?????文件????????9907??2006-12-28?15:47??polyfitweighted2\publishpolyfitweighted2.html
?????文件????????3166??2006-12-28?15:12??polyfitweighted2\publishpolyfitweighted2.png
?????文件???????12406??2006-12-28?15:12??polyfitweighted2\publishpolyfitweighted2_01.png