function?[abcn]?=?agm（a0b0c0tol）
%?AGM?calculates?the?Artihmetic?Geometric?Mean?of?A?and?B?（see?[1]）.?
%?The?function?is?used?in?routines?ELLIPJ?and?ELLIPTIC12.
%
%???[ABCN]?=?AGM（A0B0C0TOL）?carry?out?the?process?of?the?arithmetic?geometric?
%???mean?starting?with?a?given?positive?numbers?triple?（A0B0C0）?and?returns?in?
%???（ABC）?the?generated?sequence.?N?is?a?number?of?steps?（returns?in?the?type?uint32）.
%
%???The?general?scheme?of?the?process:
%???????A（i）?=?1/2*（?A（i-1）+B（i-1）?）;?????A（0）?=?A0;
%???????B（i）?=?sqrt（A（i-1）*B（i-1））;???????B（0）?=?B0;
%???????C（i）?=?1/2*（?A（i-1）+B（i-1）?）;?????C（0）?=?C0;
%???Stop?at?the?N-th?step?when?A（N）?=?B（N）?i.e.?when?C（N）?=?0.
%
%???See?also?ELLIPKE?ELLIPJ?ELLIPTIC12?ELLIPTIC3?THETA.
%
%???References:
%???[1]?M.?Abramowitz?and?I.A.?Stegun?“Handbook?of?Mathematical
%???????Functions“?Dover?Publications“?1965?Ch.?17.1?-?17.6.


if?nargin<4?tol?=?eps;?end
if?nargin<3?error（‘Not?enough?input?arguments.‘）;?end

%?pre-allocate?space?and?augment?if?needed
chunk?=?8;?mmax?=?prod（size（a0））;
a?=?zeros（chunkmmax）;
c?=?a;
b?=?a;
a（1:）?=?a0;
b（1:）?=?b0;
c（1:）?=?c0;
n?=?uint32（?zeros（1mmax）?）;
i?=?1;
while?any（abs（c（i:））?>?tol）
????i?=?i?+?1;
????if?i?>?size（a1）
??????a?=?[a;?zeros（chunkmmax）];
??????b?=?[b;?zeros（chunkmmax）];
??????c?=?[c;?zeros（chunkmmax）];
????end
????a（i:）?=?0.5?*?（a（i-1:）?+?b（i-1:））;
????b（i:）?=?sqrt（a（i-1:）?.*?b（i-1:））;
????c（i:）?=?0.5?*?（a（i-1:）?-?b（i-1:））;
????in?=?uint32（?find（（abs（c（i:））?<=?tol）?&?（abs（c（i-1:））?>?tol））?）;
????if?~isempty（in）
??????[mini]?=?size（in）;
??????n（in）?=?ones（mini）*（i-1）;
????end
end

%?END?FUNCTION?AGM（）

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件????????1657??2007-10-23?18:04??agm.m
?????文件????????3415??2007-10-25?02:17??ellipj.m
?????文件????????2439??2009-06-20?17:33??ellipji.m
?????文件????????4888??2009-06-20?17:34??elliptic12.m
?????文件????????3727??2009-06-20?17:34??elliptic12i.m
?????文件????????2971??2005-10-08?14:29??elliptic3.m
?????文件????????2537??2009-06-20?17:35??inversenomeq.m
?????文件????????4837??2009-06-20?17:35??jacobiThetaEta.m
?????文件?????????968??2009-06-20?17:36??nomeq.m
?????文件????????2569??2009-06-20?17:36??theta.m
?????文件????????1312??2014-02-12?12:51??license.txt