function?legendre_rule?（?order?a?b?filename?）

%*****************************************************************************80
%?可直接在函數名前設置輸出為??[xw]=??其中x為積分點，w為權重，此處為求積分，因此w之和可能不為1。
%%?LEGENDRE_RULE?generates?a?Gauss-Legendre?rule.
%
%??Discussion:
%
%????This?program?computes?a?standard?Gauss-Legendre?quadrature?rule
%????and?writes?it?to?a?file.
%
%????The?user?specifies:
%????*?the?ORDER?（number?of?points）?in?the?rule;
%????*?A?the?left?endpoint;
%????*?B?the?right?endpoint;
%????*?FILENAME?the?root?name?of?the?output?files.
%
%??Licensing:
%
%????This?code?is?distributed?under?the?GNU?LGPL?license.
%
%??Modified:
%
%????08?February?2014
%
%??Author:
%
%????John?Burkardt
%
??timestamp?（?）;
??fprintf?（?1?‘\n‘?）;
??fprintf?（?1?‘LEGENDRE_RULE\n‘?）;
??fprintf?（?1?‘??MATLAB?version\n‘?）;
??fprintf?（?1?‘\n‘?）;
??fprintf?（?1?‘??Compute?a?Gauss-Legendre?rule?for?approximating\n‘?）;
??fprintf?（?1?‘????Integral?（?A?<=?x?<=?B?）?f（x）?dx\n‘?）;
??fprintf?（?1?‘??of?order?ORDER.\n‘?）;
??fprintf?（?1?‘\n‘?）;
??fprintf?（?1?‘??The?user?specifies?ORDER?A?B?and?FILENAME.\n‘?）;
??fprintf?（?1?‘\n‘?）;
??fprintf?（?1?‘??ORDER?is?the?number?of?points;\n‘?）;
??fprintf?（?1?‘??A?is?the?left?endpoint;\n‘?）;
??fprintf?（?1?‘??B?is?the?right?endpoint;\n‘?）;
??fprintf?（?1?‘??FILENAME?is?used?to?generate?3?files:\n‘?）;
??fprintf?（?1?‘????filename_w.txt?-?the?weight?file\n‘?）;
??fprintf?（?1?‘????filename_x.txt?-?the?abscissa?file.\n‘?）;
??fprintf?（?1?‘????filename_r.txt?-?the?region?file.\n‘?）;
%
%??Initialize?the?parameters.
%
??alpha?=?0.0;
??beta?=?0.0;
%
%??Get?ORDER.
%
??if?（?nargin?????order?=?input?（?‘??Enter?the?rule?order?ORDER.‘?）;
??elseif?（?ischar?（?order?）?）
????order?=?str2num?（?order?）;
??end
%
%??Get?A.
%
??if?（?nargin?????a?=?input?（?‘??Enter?A.‘?）;
??elseif?（?ischar?（?a?）?）
????a?=?str2num?（?a?）;
??end
%
%??Get?B.
%
??if?（?nargin?????b?=?input?（?‘??Enter?B.‘?）;
??elseif?（?ischar?（?b?）?）
????b?=?str2num?（?b?）;
??end
%
%??Get?FILENAME.
%
??if?（?nargin?????fprintf?（?1??‘\n‘?）;
????fprintf?（?1??‘??FILENAME?specifies?the?‘‘root?name‘‘?of?the?quadrature?files）.\n‘?）;
????filename?=?input?（?‘??Enter?the?value?of?FILENAME?as?a?quoted?string:‘?）;
??end
%
%??Input?summary.
%
??fprintf?（?1?‘\n‘?）;
??fprintf?（?1?‘??ORDER?=?%d\n‘?order?）;
??fprintf?（?1?‘??A?=?%f\n‘?a?）;
??fprintf?（?1?‘??B?=?%f\n‘?b?）;
??fprintf?（?1?‘??FILENAME?=?“%s“.\n‘?filename?）;
%
%??Construct?the?rule.
%
??kind?=?1;
??[?x?w?]?=?cgqf?（?order?kind?alpha?beta?a?b?）;
%
%??Write?the?rule.
%
??r?=?[?a?b?]‘;
??rule_write?（?order?filename?x?w?r?）;
%
%??Terminate.
%
??fprintf?（?1??‘\n‘?）;
??fprintf?（?1??‘LEGENDRE_RULE:\n‘?）;
??fprintf?（?1??‘??Normal?end?of?execution.\n‘?）;
??fprintf?（?1??‘\n‘?）;
??timestamp?（?）;

??return
end
function?[?t?wts?]?=?cdgqf?（?nt?kind?alpha?beta?）

%******************************************