quadc.m

工具箱 (数值积分工具箱) matlab 中使用

function int = quadc(fun,xlow,xhigh,tol,trace,p1,p2,p3,p4,p5,p6,p7,p8,p9)
%usage:  int = quadc('Fun',xlow,xhigh)
%or
%        int = quadc('Fun',xlow,xhigh,tol)
%or
%        int = quadc('Fun',xlow,xhigh,tol,trace,p1,p2,....)
%
%This function works just like QUAD or QUAD8 but uses a Gaussian-Chebyshev
%quadrature integration scheme.
%
%  The Gauss-Chebyshev Quadrature integrates an integral of the form
%     xhigh
%  Int ((1/sqrt(1-x^2)) fun(x)) dx
%    -xhigh
%This routine ignores xlow

global cb2
global cw2

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

xlow=-xhigh;

%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('cb2')~=1,
  [cb2,cw2]=crule(2);
end

x=(cb2+1)*jacob+xlow;
eval(exec_string);
int_old=sum(cw2.*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(['cb',gnum])~=1,
    eval(['[cb',gnum,',cw',gnum,']=crule(',gnum,');']);
    eval(['global cb',gnum,',cw',gnum,';']);
  end
  eval(['x=(cb',gnum,'+1)*jacob+xlow;']);
  x=x(:);
  eval(exec_string);
  eval(['int=sum(cw',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