static gdouble X1(gint n,gint l1,gint l2,gdouble A, gdouble B,gdouble g)
{
gint i,r,l;
gint imin,imax;
gdouble X=0.0;
gdouble fourg=4*g;
l=l1+l2;
imin=n;
if(n%2 == 0)
{
if( l%2==0) imax = l;
else imax = l-1;
}
else
{
if( l%2==0) imax = l-1;
else imax = l;
}
for(i=imin;i<=imax;i+=2)
{
r = (i-n)/2;
/* printf("n=%d i=%d r=%d \n",n,i,r);*/
/* printf("CI2J=%f f=%f \n",binomial2(i,r),f(i,l1,l2,A,B));*/
X+=binomial2(i,r)/dpn(fourg,i-r)*f(i,l1,l2,A,B);
}
/* printf("g=%f X=%f\n",g,X);*/
return X;
}
static gdouble X2(gint n,gint l1,gint l2,gdouble A, gdouble B,gdouble g)
{
gint i,r,l;
gint imin,imax;
gdouble X=0.0;
gdouble fourg=4*g;
l=l1+l2;
imin=n;
if(n%2 == 0)
{
if( l%2==0) imax = l;
else imax = l-1;
}
else
{
if( l%2==0) imax = l-1;
else imax = l;
}
for(i=imin;i<=imax;i+=2)
{
r = (i-n)/2;
X+=m1p(i)*binomial2(i,r)/dpn(fourg,i-r)*f(i,l1,l2,A,B);
}
return X;
}
static gdouble f(gint i,gint l,gint m,gdouble A,gdouble B)
{
gint j,jmin,jmax;
gdouble sum=0.0;
jmin = 0;
if(jmin<i-m) jmin =i-m;
jmax = i;
if(jmax>l) jmax = l;
for( j=jmin;j<=jmax;j++)
{
sum += binomial(l,j)*binomial(m,i-j)*
dpn(-A,l-j)*dpn(-B,m-i+j);
}
return sum;
}
//---------------------------------------------------------------------------
//用于生成高斯点序列
int Gauss::Generate_gauss_array(vector<double> &gauss, vector<double> &weight)const
{
//开始计算
int n = precision;
int iter = 10; //迭代次数
int m=int((n+1)/2);
int e1=n*(n+1);
int mm=4*m-1;
vector<long double> t;
for(int i=3; i<=mm; i=i+4)
{
t.push_back((PI/(4*n+2))*i);
}
int nn=(1-(1-1/n)/(8*n*n));
vector<long double> xo;
for(int i=0; i<m; i++)
{
xo.push_back(nn*cos(t[i]));
}
vector<long double> pk;
vector<long double> den(m);
vector<long double> d1(m);
vector<long double> dpn(m);
vector<long double> d2pn(m);
vector<long double> d3pn(m);
vector<long double> d4pn(m);
vector<long double> u(m);
vector<long double> v(m);
vector<long double> h(m);
vector<long double> p(m);
vector<long double> dp(m);
for(int j=1; j<=iter; j++)
{
vector<long double> pkm1(m, 1.0);
pk=xo;
for(int k=2; k<=n; k++)
{
vector<long double> t1(m);
vector<long double> pkp1(m);
for(int i=0; i<m; i++)
{
t1[i]=xo[i]*pk[i];
pkp1[i]=t1[i]-pkm1[i]-(t1[i]-pkm1[i])/k+t1[i];
}
pkm1=pk;
pk=pkp1;
}
for(int i=0; i<m; i++)
{
den[i]=1.0-xo[i]*xo[i];
d1[i]=n*(pkm1[i]-xo[i]*pk[i]);
dpn[i]=d1[i]/den[i];
d2pn[i]=(2.0*xo[i]*dpn[i]-e1*pk[i])/den[i];
d3pn[i]=(4*xo[i]*d2pn[i]+(2-e1)*dpn[i])/den[i];
d4pn[i]=(6*xo[i]*d3pn[i]+(6-e1)*d2pn[i])/den[i];
u[i]=pk[i]/dpn[i];
v[i]=d2pn[i]/dpn[i];
h[i]=-u[i]*(1+(0.5*u[i])*(v[i]+u[i]*(v[i]*v[i]-u[i]*d3pn[i]/(3*dpn[i]))));
p[i]=pk[i]+h[i]*(dpn[i]+(0.5*h[i])*(d2pn[i]+(h[i]/3)*(d3pn[i]+0.25*h[i]*d4pn[i])));
dp[i]=dpn[i]+h[i]*(d2pn[i]+(0.5*h[i])*(d3pn[i]+h[i]*d4pn[i]/3));
h[i]=h[i]-p[i]/dp[i];
xo[i]=xo[i]+h[i];
}
}
vector<long double> bp(m);
vector<long double> fx(m);
vector<long double> wf(m);
for(int i=0; i<m; i++)
{
bp[i]=-xo[i]-h[i];
fx[i]=d1[i]-h[i]*e1*(pk[i]+(h[i]/2)*(dpn[i]+(h[i]/3)*(d2pn[i]+(h[i]/4)*(d3pn[i]+(0.2*h[i])*d4pn[i]))));
wf[i]=2*(1-bp[i]*bp[i])/(fx[i]*fx[i]);
}
if((m+m)>n) bp[m-1]=0;
if((m+m) != n) m=m-1;
for(int i=m-1; i>=0; i--)
{
bp.push_back(-bp[i]);
wf.push_back(wf[i]);
}
for(int i=0; i<n; i++)
{
gauss.push_back(bp[i]);
weight.push_back(wf[i]);
}
//cout << "bp=" << endl;
//for(int i=0; i<n; i++)
//{
// cout << setprecision(20) << bp[i] << endl;
//}
//cout << "wf=" << endl;
//long double sum=0.0;
//for(int i=0; i<n; i++)
//{
// sum += wf[i];
// cout << setprecision(20) << wf[i] << endl;
//}
//cout << setprecision(20) << "sum=" << sum << endl;
return 1;
}
