swh:1:snp:16c54c84bc54885e783d4424d714e5cc82f479a1
Tip revision: 2edc14079ceb44ef9b54b820472a1e73f79989f5 authored by Roger Koenker on 08 August 1977, 00:00:00 UTC
version 3.31
version 3.31
Tip revision: 2edc140
rqfn.f
subroutine rqfn(n,p,a,y,rhs,d,u,beta,eps,wn,wp,aa,nit,info)
integer n,p,info,nit(3)
double precision a(p,n),y(n),rhs(p),d(n),u(n),wn(n,10),wp(p,p+3),
& aa(p,p)
double precision one,beta,eps
data one/1.0d0/
call fna(n,p,a,y,rhs,d,u,beta,eps,wn(1,1),wn(1,2),wp(1,1),wn(1,3),
& wn(1,4),wn(1,5), wn(1,6),wp(1,2),wn(1,7),wn(1,8),wn(1,9),wn(1,10),
& wp(1,3), wp(1,4),aa,nit,info)
return
end
subroutine fna(n,p,a,c,b,d,u,beta,eps,x,s,y,z,w,dx,ds,dy,dz,dw,
& dsdw,dxdz,rhs,ada,aa,nit,info)
integer n,p,pp,i,info,nit(3)
double precision a(p,n),c(n),b(p)
double precision zero,one,mone,big,ddot,dmax1,dmin1,dasum
double precision deltap,deltad,beta,eps,cx,by,uw,uz,mu,mua,acomp,
& rdg,g
double precision x(n),u(n),s(n),y(p),z(n),w(n),d(n),rhs(p),ada(p,
& p)
double precision aa(p,p),dx(n),ds(n),dy(p),dz(n),dw(n),dxdz(n),
& dsdw(n)
data zero /0.0d0/
data half /0.5d0/
data one /1.0d0/
data mone /-1.0d0/
data big /1.0d+20/
nit(1)=0
nit(2)=0
nit(3)=n
pp=p*p
call dgemv('N',p,n,one,a,p,c,1,zero,y,1)
call stepy(n,p,a,d,y,aa,info)
if(.not.(info .ne. 0))goto 23000
return
23000 continue
do 23002 i=1,p
do 23004 j=1,p
ada(i,j)=zero
23004 continue
ada(i,i)=one
23002 continue
call dtrtrs('U','T','N',p,p,aa,p,ada,p,info)
call dcopy(pp,ada,1,aa,1)
call dcopy(n,c,1,s,1)
call dgemv('T',p,n,mone,a,p,y,1,one,s,1)
do 23006 i=1,n
d(i)=one
if(.not.(dabs(s(i)) .lt. eps))goto 23008
z(i) = dmax1( s(i),zero) + eps
w(i) = dmax1(-s(i),zero) + eps
goto 23009
23008 continue
z(i) = dmax1( s(i),zero)
w(i) = dmax1(-s(i),zero)
23009 continue
s(i)=u(i)-x(i)
23006 continue
cx = ddot(n,c,1,x,1)
by = ddot(p,b,1,y,1)
uw = dasum(n,w,1)
uz = dasum(n,z,1)
rdg = (cx - by + uw)
23010 if(.not.(rdg .gt. eps))goto 23011
nit(1)=nit(1)+1
do 23012 i =1,n
d(i) = one/(z(i)/x(i) + w(i)/s(i))
ds(i)=z(i)-w(i)
dx(i)=d(i)*ds(i)
23012 continue
call dgemv('N',p,n,one,a,p,dx,1,zero,dy,1)
call dcopy(p,dy,1,rhs,1)
call stepy(n,p,a,d,dy,ada,info)
if(.not.(info .ne. 0))goto 23014
return
23014 continue
call dgemv('T',p,n,one,a,p,dy,1,mone,ds,1)
deltap=big
deltad=big
do 23016 i=1,n
dx(i)=d(i)*ds(i)
ds(i)=-dx(i)
dz(i)=-z(i)*(dx(i)/x(i) + one)
dw(i)=w(i)*(dx(i)/s(i) - one)
dxdz(i)=dx(i)*dz(i)
dsdw(i)=ds(i)*dw(i)
if(.not.(dx(i).lt.0))goto 23018
deltap=dmin1(deltap,-x(i)/dx(i))
23018 continue
if(.not.(ds(i).lt.0))goto 23020
deltap=dmin1(deltap,-s(i)/ds(i))
23020 continue
if(.not.(dz(i).lt.0))goto 23022
deltad=dmin1(deltad,-z(i)/dz(i))
23022 continue
if(.not.(dw(i).lt.0))goto 23024
deltad=dmin1(deltad,-w(i)/dw(i))
23024 continue
23016 continue
deltap=dmin1(beta*deltap,one)
deltad=dmin1(beta*deltad,one)
if(.not.(deltap*deltad.lt.one))goto 23026
nit(2)=nit(2)+1
acomp=ddot(n,x,1,z,1)+ddot(n,s,1,w,1)
g=acomp+deltap*ddot(n,dx,1,z,1)+deltad*ddot(n,dz,1,x,1)+deltap*
& deltad*ddot(n,dz,1,dx,1)+deltap*ddot(n,ds,1,w,1)+deltad*ddot(n,dw,
& 1,s,1)+deltap*deltad*ddot(n,ds,1,dw,1)
mu=acomp/dfloat(2*n)
mua=g/dfloat(2*n)
mu=mu*(mua/mu)**3
do 23028 i=1,n
dz(i)=d(i)*(mu*(1/s(i)-1/x(i))+dx(i)*dz(i)/x(i)-ds(i)*dw(i)/s(i))
23028 continue
call dswap(p,rhs,1,dy,1)
call dgemv('N',p,n,one,a,p,dz,1,one,dy,1)
call dpotrs('U',p,1,ada,p,dy,p,info)
call daxpy(p,mone,dy,1,rhs,1)
call dgemv('T',p,n,one,a,p,rhs,1,zero,dw,1)
deltap=big
deltad=big
do 23030 i=1,n
dx(i)=dx(i)-dz(i)-d(i)*dw(i)
ds(i)=-dx(i)
dz(i)=mu/x(i) - z(i)*dx(i)/x(i) - z(i) - dxdz(i)/x(i)
dw(i)=mu/s(i) - w(i)*ds(i)/s(i) - w(i) - dsdw(i)/s(i)
if(.not.(dx(i).lt.0))goto 23032
deltap=dmin1(deltap,-x(i)/dx(i))
goto 23033
23032 continue
deltap=dmin1(deltap,-s(i)/ds(i))
23033 continue
if(.not.(dz(i).lt.0))goto 23034
deltad=dmin1(deltad,-z(i)/dz(i))
23034 continue
if(.not.(dw(i).lt.0))goto 23036
deltad=dmin1(deltad,-w(i)/dw(i))
23036 continue
23030 continue
deltap=dmin1(beta*deltap,one)
deltad=dmin1(beta*deltad,one)
23026 continue
call daxpy(n,deltap,dx,1,x,1)
call daxpy(n,deltap,ds,1,s,1)
call daxpy(p,deltad,dy,1,y,1)
call daxpy(n,deltad,dz,1,z,1)
call daxpy(n,deltad,dw,1,w,1)
cx=ddot(n,c,1,x,1)
by=ddot(p,b,1,y,1)
uw = dasum(n,w,1)
uz = dasum(n,z,1)
rdg=(cx-by+uw)
goto 23010
23011 continue
call daxpy(n,mone,w,1,z,1)
call dswap(n,z,1,x,1)
return
end