quadgold.m

工具箱 (数值积分工具箱) matlab 中使用

function int = quadg(fun,xlow,xhigh,tol,trace,p1,p2,p3,p4,p5,p6,p7,p8,p9)
%usage:  int = quadg('Fun',xlow,xhigh)
%or
%        int = quadg('Fun',xlow,xhigh,tol)
%or
%        int = quadg('Fun',xlow,xhigh,tol,trace,p1,p2,....)
%
%This function works just like QUAD or QUAD8 but uses a Gaussian quadrature
%integration scheme.  Use this routine instead of QUAD or QUAD8:
%	if higher accuracy is desired (this works best if the function, 
%		'Fun', can be approximated by a power series) 
%	or if many similar integrations are going to be done (I think less
%		function evaluations will typically be done, but the 
%		integration points and the weights must be calculated.
%		These are saved between integrations so when QUADG
%		is called again, the points and weights are all ready
%		known.)
%	or if the function evaluations are time consuming.
%Note that if there are discontinuities the integral should be broken up into separate 
%pieces.  And if there are singularities,  a more appropriate integration quadrature
%should be used (such as the Gauss-Chebyshev).

global b2
global w2

if exist('tol')~=1,
  tol=1e-3;
elseif tol==[],
  tol=1e-3;
end
if exist('trace')~=1,
  trace=0;
elseif trace==[],
  trace=0;
else,
  trace=1;
end

%setup string to call the function
exec_string=['y=',fun,'(x'];
num_parameters=nargin-5;
for i=1:num_parameters,
  exec_string=[exec_string,',p',int2str(i)];
end
exec_string=[exec_string,');'];

%setup mapping parameters
jacob=(xhigh-xlow)/2;

%generate the first two sets of integration points and weights
if exist('b2')~=1,
  [b2,w2]=grule(2);
end

x=(b2+1)*jacob+xlow;
eval(exec_string);
int_old=sum(w2.*y)*jacob;
if trace==1,
  x_trace=x(:);
  y_trace=y(:);
end

converge='n';
for i=1:7,
  gnum=int2str(2^(i+1));
  if exist(['b',gnum])~=1,
    eval(['[b',gnum,',w',gnum,']=grule(',gnum,');']);
    eval(['global b',gnum,',w',gnum,';']);
  end
  eval(['x=(b',gnum,'+1)*jacob+xlow;']);
  eval(exec_string);
  eval(['int=sum(w',gnum,'.*y)*jacob;']);

  if trace==1,
    x_trace=[x_trace;x(:)];
    y_trace=[y_trace;y(:)];
  end

  if abs(int_old-int) < abs(tol*int),
    converge='y';
    break;
  end
  int_old=int;
end

if converge=='n',
  disp('Integral did not converge--singularity likely')
end

if trace==1,
  plot(x_trace,y_trace,'+')
end

%gnum,i,length(x_trace)