C Output from Public domain Ratfor, version 1.05 subroutine rqfnc(n1,n2,p,a1,y,a2,r,rhs,d1,d2,u,beta,eps,wn1,wn2,wp *,nit,info) integer n1,n2,p,info,nit(3) double precision a1(p,n1),a2(p,n2),y(n1),r(n2),rhs(p),d1(n1),d2(n2 *),u(n1) double precision wn1(n1,9),wn2(n2,6),wp(p,p+3) double precision one,beta,eps parameter(one = 1.0d0) call lpfnc(n1,n2,p,a1,y,a2,r,rhs,d1,d2,u,beta,eps,wn1(1,1),wn2(1,1 *),wn1(1,2), wp(1,1),wn1(1,3),wn2(1,2),wn1(1,4),wn1(1,5),wn2(1,3),w *n1(1,6), wp(1,2),wn1(1,7),wn2(1,4),wn1(1,8),wn1(1,9),wn2(1,5),wn2( *1,6), wp(1,3),wp(1,4),nit,info) return end subroutine lpfnc(n1,n2,p,a1,c1,a2,c2,b,d1,d2,u,beta,eps,x1,x2,s, y *,z1,z2,w,dx1,dx2,ds,dy,dz1,dz2,dw,dr1,dr2,r2, rhs,ada,nit,info) integer n1,p,i,info,nit(3),maxit double precision a1(p,n1),a2(p,n2),c1(n1),c2(n2),b(p) double precision zero,one,mone,big,ddot,dmax1,dmin1,dxdz1,dxdz2,ds *dw double precision deltap,deltad,beta,eps,mu,gap,g double precision x1(n1),x2(n2),u(n1),s(n1),y(p),z1(n1),z2(n2),w(n1 *) double precision d1(n1),d2(n2),rhs(p),ada(p,p) double precision dx1(n1),dx2(n2),ds(n1),dy(p),dz1(n1),dz2(n2),dw(n *1) double precision dr1(n1),dr2(n2),r2(n2) parameter(zero = 0.0d0) parameter(one = 1.0d0) parameter(mone = -1.0d0) parameter(big = 1.0d+20) parameter(maxit = 500) nit(1)=0 nit(2)=0 nit(3)=n1 call dgemv('N',p,n1,one,a1,p,c1,1,zero,y,1) do23000 i=1,n1 d1(i)=one 23000 continue 23001 continue do23002 i=1,n2 d2(i)=zero z2(i)=one 23002 continue 23003 continue call stepy2(n1,n2,p,a1,d1,a2,d2,y,ada,info) if(info .ne. 0)then return endif call dcopy(n1,c1,1,s,1) call dgemv('T',p,n1,mone,a1,p,y,1,one,s,1) do23006 i=1,n1 if(dabs(s(i)) .lt. eps)then z1(i)=dmax1(s(i),zero)+eps w(i)=dmax1(-s(i),zero)+eps else z1(i)=dmax1(s(i),zero) w(i)=dmax1(-s(i),zero) endif s(i)=u(i)-x1(i) 23006 continue 23007 continue gap = ddot(n1,z1,1,x1,1)+ddot(n2,z2,1,x2,1)+ddot(n1,w,1,s,1) 23010 if(gap .gt. eps .and. nit(1).lt.maxit)then nit(1)=nit(1)+1 call dcopy(n2,c2,1,r2,1) call dgemv('T',p,n2,mone,a2,p,y,1,one,r2,1) call dcopy(p,b,1,dy,1) call dgemv('N',p,n1,mone,a1,p,x1,1,one,dy,1) call dgemv('N',p,n2,mone,a2,p,x2,1,one,dy,1) do23012 i = 1,n1 d1(i)=one/(z1(i)/x1(i) + w(i)/s(i)) ds(i)=z1(i)-w(i) dz1(i)=d1(i)*ds(i) 23012 continue 23013 continue do23014 i = 1,n2 d2(i)=x2(i)/z2(i) dz2(i)=d2(i)*r2(i) 23014 continue 23015 continue call dgemv('N',p,n1,one,a1,p,dz1,1,one,dy,1) call dgemv('N',p,n2,one,a2,p,dz2,1,one,dy,1) call dcopy(p,dy,1,rhs,1) call stepy2(n1,n2,p,a1,d1,a2,d2,dy,ada,info) if(info .ne. 0)then return endif call dgemv('T',p,n1,one,a1,p,dy,1,mone,ds,1) deltap=big deltad=big do23018 i=1,n1 dx1(i)=d1(i)*ds(i) ds(i)=-dx1(i) dz1(i)=-z1(i)*(dx1(i)/x1(i) + one) dw(i)=-w(i)*(ds(i)/s(i) + one) if(dx1(i).lt.0)then deltap=dmin1(deltap,-x1(i)/dx1(i)) endif if(ds(i).lt.0)then deltap=dmin1(deltap,-s(i)/ds(i)) endif if(dz1(i).lt.0)then deltad=dmin1(deltad,-z1(i)/dz1(i)) endif if(dw(i).lt.0)then deltad=dmin1(deltad,-w(i)/dw(i)) endif 23018 continue 23019 continue call dcopy(n2,r2,1,dx2,1) call dgemv('T',p,n2,one,a2,p,dy,1,mone,dx2,1) do23028 i=1,n2 dx2(i)=d2(i)*dx2(i) dz2(i)=-z2(i)*(dx2(i)/x2(i) + one) if(dx2(i).lt.0)then deltap=dmin1(deltap,-x2(i)/dx2(i)) endif if(dz2(i).lt.0)then deltad=dmin1(deltad,-z2(i)/dz2(i)) endif 23028 continue 23029 continue deltap=dmin1(beta*deltap,one) deltad=dmin1(beta*deltad,one) if(min(deltap,deltad) .lt. one)then nit(2)=nit(2)+1 mu = ddot(n1,x1,1,z1,1)+ddot(n2,x2,1,z2,1)+ddot(n1,s,1,w,1) g = mu + deltap*ddot(n1,dx1,1,z1,1)+ deltad*ddot(n1,dz1,1,x1,1)+ d *eltap*deltad*ddot(n1,dz1,1,dx1,1)+ deltap*ddot(n2,dx2,1,z2,1)+ del *tad*ddot(n2,dz2,1,x2,1)+ deltap*deltad*ddot(n2,dz2,1,dx2,1)+ delta *p*ddot(n1,ds,1,w,1)+ deltad*ddot(n1,dw,1,s,1) + deltap*deltad*ddot *(n1,ds,1,dw,1) mu = mu * ((g/mu)**3) /(dfloat(2*n1)+dfloat(n2)) do23036 i=1,n1 dsdw = ds(i)*dw(i) dr1(i)=d1(i)*(mu*(one/s(i)-one/x1(i))+ dx1(i)*dz1(i)/x1(i)-dsdw/s( *i)) 23036 continue 23037 continue do23038 i=1,n2 dr2(i)=d2(i)*(dx2(i)*dz2(i)/x2(i)-mu/x2(i)) 23038 continue 23039 continue call dswap(p,rhs,1,dy,1) call dgemv('N',p,n1,one,a1,p,dr1,1,one,dy,1) call dgemv('N',p,n2,one,a2,p,dr2,1,one,dy,1) call dpotrs('U',p,1,ada,p,dy,p,info) call dgemv('T',p,n1,one,a1,p,dy,1,zero,u,1) deltap=big deltad=big do23040 i=1,n1 dsdw = ds(i)*dw(i) dxdz1 = dx1(i)*dz1(i) dx1(i) = d1(i)*(u(i)-z1(i)+w(i))-dr1(i) ds(i) = -dx1(i) dz1(i) = -z1(i)+(mu - z1(i)*dx1(i) - dxdz1)/x1(i) dw(i) = -w(i)+(mu - w(i)*ds(i) - dsdw)/s(i) if(dx1(i).lt.0)then deltap=dmin1(deltap,-x1(i)/dx1(i)) endif if(ds(i).lt.0)then deltap=dmin1(deltap,-s(i)/ds(i)) endif if(dz1(i).lt.0)then deltad=dmin1(deltad,-z1(i)/dz1(i)) endif if(dw(i).lt.0)then deltad=dmin1(deltad,-w(i)/dw(i)) endif 23040 continue 23041 continue call dgemv('T',p,n2,one,a2,p,dy,1,zero,u,1) do23050 i=1,n2 dxdz2 = dx2(i)*dz2(i) dx2(i) = d2(i)*(u(i)-r2(i))-dr2(i) dz2(i) = -z2(i)+(mu - z2(i)*dx2(i) - dxdz2)/x2(i) if(dx2(i).lt.0)then deltap=dmin1(deltap,-x2(i)/dx2(i)) endif if(dz2(i).lt.0)then deltad=dmin1(deltad,-z2(i)/dz2(i)) endif 23050 continue 23051 continue deltap=dmin1(beta*deltap,one) deltad=dmin1(beta*deltad,one) endif call daxpy(n1,deltap,dx1,1,x1,1) call daxpy(n2,deltap,dx2,1,x2,1) call daxpy(n1,deltap,ds,1,s,1) call daxpy(p,deltad,dy,1,y,1) call daxpy(n1,deltad,dz1,1,z1,1) call daxpy(n2,deltad,dz2,1,z2,1) call daxpy(n1,deltad,dw,1,w,1) gap = ddot(n1,z1,1,x1,1)+ddot(n2,z2,1,x2,1)+ddot(n1,w,1,s,1) goto 23010 endif 23011 continue call daxpy(n1,mone,w,1,z1,1) call dswap(n1,z1,1,x1,1) return end subroutine stepy2(n1,n2,p,a1,d1,a2,d2,b,ada,info) integer n1,n2,p,i,j,k,info double precision a1(p,n1),a2(p,n2),b(p),d1(n1),d2(n2),ada(p,p),zer *o parameter(zero = 0.0d0) do23056 j=1,p do23058 k=1,p ada(j,k)=zero 23058 continue 23059 continue 23056 continue 23057 continue do23060 i=1,n1 call dsyr('U',p,d1(i),a1(1,i),1,ada,p) 23060 continue 23061 continue do23062 i=1,n2 call dsyr('U',p,d2(i),a2(1,i),1,ada,p) 23062 continue 23063 continue call dposv('U',p,1,ada,p,b,p,info) return end