matlab quad 函数代码中的y(1) ,跟数值积分分成的n个节点有什么关系,

matlab quad 函数代码中的y(1) ,跟数值积分分成的n个节点有什么关系,
function [Q,fcnt] = quad(funfcn,a,b,tol,trace,varargin)
%QUAD Numerically evaluate integral,adaptive Simpson quadrature.
% Q = QUAD(FUN,A,B) tries to approximate the integral of scalar-valued
% function FUN from A to B to within an error of 1.e-6 using recursive
% adaptive Simpson quadrature.FUN is a function handle.The function
% Y=FUN(X) should accept a vector argument X and return a vector result
% Y,the integrand evaluated at each element of X.
%
% Q = QUAD(FUN,A,B,TOL) uses an absolute error tolerance of TOL
% instead of the default,which is 1.e-6.Larger values of TOL
% result in fewer function evaluations and faster computation,
% but less accurate results.The QUAD function in MATLAB 5.3 used
% a less reliable algorithm and a default tolerance of 1.e-3.
%
% Q = QUAD(FUN,A,B,TOL,TRACE) with non-zero TRACE shows the values
% of [fcnt a b-a Q] during the recursion.Use [] as a placeholder to
% obtain the default value of TOL.
%
% [Q,FCNT] = QUAD(...) returns the number of function evaluations.
%
% Use array operators .*,./ and .^ in the definition of FUN
% so that it can be evaluated with a vector argument.
%
% Notes:
% Function QUADL may be more efficient with high accuracies and smooth
% integrands.
% Function QUADV vectorizes QUAD for array-valued FUN.
%
% Example:
% Q = quad(@myfun,0,2);
% where myfun.m is the M-file function:
% %-------------------%
% function y = myfun(x)
% y = 1./(x.^3-2*x-5);
% %-------------------%
%
% or,use a parameter for the constant:
% Q = quad(@(x)myfun2(x,5),0,2);
% where myfun2 is the M-file function:
% %----------------------%
% function y = myfun2(x,c)
% y = 1./(x.^3-2*x-c);
% %----------------------%
%
% Class support for inputs A,B,and the output of FUN:
% float:double,single
%
% See also QUADV,QUADL,DBLQUAD,TRIPLEQUAD,TRAPZ,FUNCTION_HANDLE.
% Based on "adaptsim" by Walter Gander.
%
% Reference:
% [1] W.Gander and W.Gautschi,Adaptive Quadrature - Revisited,
% BIT Vol.40,No.1,March 2000,pp.84-101.
%
% Copyright 1984-2006 The MathWorks,Inc.
% $Revision:5.26.4.7 $ $Date:2006/04/03 17:10:41 $
f = fcnchk(funfcn);
if nargin < 4 || isempty(tol),tol = 1.e-6; end;
if nargin < 5 || isempty(trace),trace = 0; end;
if isscalar(a) || isscalar(b)
error('MATLAB:quad:scalarLimits',...
'The limits of integration must be scalars.');
end
% Initialize with three unequal subintervals.
h = 0.13579*(b-a);
x = [a a+h a+2*h (a+b)/2 b-2*h b-h b];
y = f(x,varargin{:});
fcnt = 7;
% Fudge endpoints to avoid infinities.
if isfinite(y(1))
y(1) = f(a+eps(superiorfloat(a,b))*(b-a),varargin{:});
fcnt = fcnt+1;
end
if isfinite(y(7))
y(7) = f(b-eps(superiorfloat(a,b))*(b-a),varargin{:});
fcnt = fcnt+1;
end

这个是按着辛普森公式在计算,辛普森公式跟节点有关的,Y1应该是Y的第一个值,就是说第一次算出来的值,Y7是Y积分结果矩阵的第七个值,这个值都跟节点有关系.不好意思.这个辛普森公式在计算方法（或者数值分析里有详细介绍）,我给忘记了!所以只能回答这么多!