gaujac.for

Numerical Recipes一书中例子的源码所用到的函数集,William H. Press 和 Saul A. Teukolsky 所著

      SUBROUTINE gaujac(x,w,n,alf,bet)
      INTEGER n,MAXIT
      REAL alf,bet,w(n),x(n)
      DOUBLE PRECISION EPS
      PARAMETER (EPS=3.D-14,MAXIT=10)
CU    USES gammln
      INTEGER i,its,j
      REAL alfbet,an,bn,r1,r2,r3,gammln
      DOUBLE PRECISION a,b,c,p1,p2,p3,pp,temp,z,z1
      do 13 i=1,n
        if(i.eq.1)then
          an=alf/n
          bn=bet/n
          r1=(1.+alf)*(2.78/(4.+n*n)+.768*an/n)
          r2=1.+1.48*an+.96*bn+.452*an*an+.83*an*bn
          z=1.-r1/r2
        else if(i.eq.2)then
          r1=(4.1+alf)/((1.+alf)*(1.+.156*alf))
          r2=1.+.06*(n-8.)*(1.+.12*alf)/n
          r3=1.+.012*bet*(1.+.25*abs(alf))/n
          z=z-(1.-z)*r1*r2*r3
        else if(i.eq.3)then
          r1=(1.67+.28*alf)/(1.+.37*alf)
          r2=1.+.22*(n-8.)/n
          r3=1.+8.*bet/((6.28+bet)*n*n)
          z=z-(x(1)-z)*r1*r2*r3
        else if(i.eq.n-1)then
          r1=(1.+.235*bet)/(.766+.119*bet)
          r2=1./(1.+.639*(n-4.)/(1.+.71*(n-4.)))
          r3=1./(1.+20.*alf/((7.5+alf)*n*n))
          z=z+(z-x(n-3))*r1*r2*r3
        else if(i.eq.n)then
          r1=(1.+.37*bet)/(1.67+.28*bet)
          r2=1./(1.+.22*(n-8.)/n)
          r3=1./(1.+8.*alf/((6.28+alf)*n*n))
          z=z+(z-x(n-2))*r1*r2*r3
        else
          z=3.*x(i-1)-3.*x(i-2)+x(i-3)
        endif
        alfbet=alf+bet
        do 12 its=1,MAXIT
          temp=2.d0+alfbet
          p1=(alf-bet+temp*z)/2.d0
          p2=1.d0
          do 11 j=2,n
            p3=p2
            p2=p1
            temp=2*j+alfbet
            a=2*j*(j+alfbet)*(temp-2.d0)
            b=(temp-1.d0)*(alf*alf-bet*bet+temp*(temp-2.d0)*z)
            c=2.d0*(j-1+alf)*(j-1+bet)*temp
            p1=(b*p2-c*p3)/a
11        continue
          pp=(n*(alf-bet-temp*z)*p1+2.d0*(n+alf)*(n+bet)*p2)/(temp*
     *(1.d0-z*z))
          z1=z
          z=z1-p1/pp
          if(abs(z-z1).le.EPS)goto 1
12      continue
        pause 'too many iterations in gaujac'
1       x(i)=z
        w(i)=exp(gammln(alf+n)+gammln(bet+n)-gammln(n+1.)-gammln(n+
     *alfbet+1.))*temp*2.**alfbet/(pp*p2)
13    continue
      return
      END