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toolsf.f
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toolsf.f
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! subroutines to determine optimal biomarker from longitudinal data
! la,lrc,dx2,info=evec(lx,lp) - approximates the second eigenvector by a linear combination of variables - unsupervised determination of optimal biomarker
! la,lrc,dx2,info=committor(lx,lp,bval,skip) -. determines the commitor function by a linear combination of variables - supervised determination of optimal biomarker
! lrc,dx2,info=npevec(lx,lp) - finds an approximation to the second eigenvector by non-parametric optimization of variables - nonparametric unsupervised determination of optimal biomarker
! lrc,dx2,info=npcommittor(lx,lp,bval) - finds an approximation to the committor function by non-parametric optimization of variables - nonparametric upervised determination of optimal biomarker
! INPUT
! np -number of patients, nt - the total number of samples, summed over all patients, nx -number of variables in a sample
! lx(nx,nt) - variables in the samples, input
! lp(nt) - patient to whom the sample belongs, should look like 1,1,1, ...,1,2,2..
! bval(nt) - bounary value for the sample, to perform the supervised biomarker discovery. it is 0 for all samples but the last sample of a patient. 1 it means that the pation belongs to first group, -1 patient belongs to the second group, 2 - no information about the group.
! skip(nt) - if nonzero, then point is skipped from optimization, while the rc is still computed for the point. used for cross-validations.
! OUTPUT
! la(nx+1) - coefficients of the linear combination of the variables, the last coefficient, la(nx+1) is that before 1.
! lrc(nt) - values of the optimal biomarker for each sample
subroutine committor(lx,lp,bval,skip,la,lrc,dx2,lmb,info,nx,nt)
! la,lrc,dx2,info=committor(lx,lp,bval) -. determines the commitor function by a linear combination of variables - supervised determination of optimal biomarker
implicit none
integer nt,nx,info
real*8 lx(nx,nt),lrc(nt),dx2,la(nx+1),lmb
integer lp(nt),bval(nt),skip(nt)
integer i,iset
real*8 compdx2
real*8 y(nx+1,nt)
Cf2py intent(out):: la,lrc,dx2,info
do iset=1,nt
do i=1,nx
y(i,iset)=lx(i,iset)
enddo
y(nx+1,iset)=1
enddo
call optimdx2lc(y,bval,skip,nx+1,nt,la,lrc,lmb,info)
dx2=compdx2(lrc,bval,nt)
end
subroutine evecs(lx,lp,lrc,skip,info,nx,nt,lmb)
! lrc,info=evecs(lx,lp) - approximates eigenvectors higher than second by a linear combination of variables - unsupervised determination of optimal biomarker
implicit none
integer nt,nx,info
real*8 lx(nx,nt),lrc(nx,nt),dx2,lmb
integer lp(nt),skip(nt)
integer i,iset
real*8 compdx2evec
real*8 y(nx+1,nt)
Cf2py intent(out):: lrc,dx2,info
do iset=1,nt
do i=1,nx
y(i,iset)=lx(i,iset)
enddo
y(nx+1,iset)=1
enddo
call optimeveclc(y,lp,skip,nx+1,nt,lrc,lmb,info)
end
subroutine npcommittor(lx,lp,bval,lrc,dx2,info,nx,nt,np,eps,miter)
! lrc,dx2,info=npcommittor(lx,lp,bval,...) - finds an approximation to the committor function by non-parametric optimization of variables - nonparametric upervised determination of optimal biomarker
! np - the degree of the polynomial
! eps - accuracy of optimization
! miter - maximal number of iterations
implicit none
integer nt,nx,info,np,miter
real*8 lx(nx,nt),lrc(nt),dx2,eps
integer lp(nt),bval(nt)
integer iter,i,j
real*8 y(nt)
real*8 compdx2,dx2last
Cf2py intent(out):: lrc,dx2,info
lrc=0
dx2=compdx2(lrc,bval,nt)
dx2last=dx2
do iter=1,miter
i=rand()*nx+1
i=min(i,nx)
do j=1,nt
y(j)=lx(i,j)
enddo
if (iter==1)then
call optimdx2np(1,1,lrc,y,bval,nt,info,dx2)
else
call optimdx2np(np,np,lrc,y,bval,nt,info,dx2)
endif
c if (info/=0)return
if (mod(iter,10)==0 .and. info==0)then
if (abs(dx2last-dx2)<eps) return
dx2last=dx2
endif
if (mod(iter,5)==0)call optimdx2np(6,0,lrc,y,bval,nt,info,dx2)
enddo
end
subroutine optimdx2lc(y,bval,skip,ny,nt,la,rc,lmb,info)
! optimal linear combination of yi
!!!! minimum of [x(t)-x(t+dt)]^2 +[x(t)-x_A]^2+[x(t)-x_B]^2 where x_A=-1 and x_B=1
implicit none
integer ny,nt,bval(nt),skip(nt)
real*8 rc(nt),y(ny,nt),la(ny),lmb
real*8 drdr(ny, ny),dind
real*8 al(ny),alal,rhs(ny)
integer i,j,i1,iset,k,isize
real*8 r
integer info,ipiv(ny)
integer i12(ny),i21(ny),nij2
real*8 dfij(ny)
isize=ny
do i=1,isize
al(i)=0
do j=1,i
drdr(i,j)=0
enddo
enddo
alal=0
do iset=1,nt
if (skip(iset)/=0)cycle ! do not consider points
if (bval(iset)==0)then ! not a boundary point
do i=1,ny
dfij(i)=y(i,iset+1)-y(i,iset)
enddo
do j=1,ny
do k=1,j
drdr(j,k)=drdr(j,k)+dfij(k)*dfij(j)
enddo
enddo
else
if (bval(iset)/=2)then ! a boundary point connected to +1 or -1
dind=-bval(iset)
do i=1,ny
dfij(i)=y(i,iset)
enddo
alal=alal+dind*dind
do j=1,ny
al(j)=al(j)+2*dind*dfij(j)
enddo
do j=1,ny
do k=1,j
drdr(j,k)=drdr(j,k)+dfij(k)*dfij(j)
enddo
enddo
endif
endif
enddo
nij2=0
do i=1,isize
i21(i)=0
enddo
do i=1,isize ! select only non zero
if (drdr(i,i)<1e-7)cycle
nij2=nij2+1
i12(nij2)=i
i21(i)=nij2
drdr(i,i)=drdr(i,i)+lmb
enddo
do i=1,nij2
do j=1,i
drdr(i,j)=drdr(i12(i),i12(j))
drdr(j,i)=drdr(i,j)
enddo
al(i)=al(i12(i))
rhs(i)=-al(i)/2
enddo
call dgetrf(nij2,nij2,drdr,isize,ipiv,info)
if(info/=0)then
write(*,*)'dgetrf info=',info
return
stop'info/=0'
endif
call dgetrs('N',nij2,1,drdr,isize,ipiv,rhs,isize,info)
if(info/=0)then
write(*,*)'dgetrs info=',info
return
stop'info/=0'
endif
do iset=1,nt
do i=1,ny
dfij(i)=y(i,iset)
enddo
r=0
do i=1,nij2
i1=i12(i)
r=r+rhs(i)*dfij(i1)
enddo
c if (r>1)r=1 ! impose boundaries 0<q<1
c if (r<-1)r=-1
rc(iset)=r
enddo
la=0
do i=1,nij2
la(i12(i))=rhs(i) ! assign coefficients
enddo
end
subroutine optimeveclc(y,lp,skip,ny,nt,rc,lmb,info)
! optimal linear combination of yi
!!!! minimum of [x(t)-x(t+dt)]^2 under constraint sum_t x^2(t)=1
implicit none
integer ny,nt,lp(nt),skip(nt)
real*8 rc(ny-1,nt),y(ny,nt),lmb
real*8 drdr(ny, ny),rr(ny,ny)
integer i,j,iset,k
real*8 r
integer info,lwork
real*8 work(ny*10),w(ny)
integer nij2,i12(ny),i21(ny),iev
real*8 dfij(ny)
drdr=0
rr=0
lwork=ny*10
do iset=1,nt
if (skip(iset)/=0)cycle ! do not consider points
do i=1,ny
dfij(i)=y(i,iset)
enddo
do j=1,ny
do k=1,j
rr(j,k)=rr(j,k)+dfij(k)*dfij(j)
enddo
enddo
enddo
do iset=1,nt-1
if (skip(iset)/=0)cycle ! do not consider points
if (lp(iset)==lp(iset+1))then ! the same patient
do i=1,ny
dfij(i)=y(i,iset+1)-y(i,iset)
enddo
do j=1,ny
do k=1,j
drdr(j,k)=drdr(j,k)+dfij(k)*dfij(j)
enddo
enddo
endif
enddo
nij2=0
i21=0
do i=1,ny ! select only non zero
if (drdr(i,i)<1e-5 .and. i<ny)cycle
nij2=nij2+1
i12(nij2)=i
i21(i)=nij2
drdr(i,i)=drdr(i,i)+lmb
rr(i,i)=rr(i,i)+lmb
enddo
do i=1,nij2
do j=1,i
drdr(i,j)=drdr(i12(i),i12(j))
drdr(j,i)=drdr(i,j)
rr(i,j)=rr(i12(i),i12(j))
rr(j,i)=rr(i,j)
enddo
enddo
call dsygv(1,'V','U',nij2,drdr,ny,rr,ny,w,work,lwork,info)
if (info/=0)then
write(*,*)'info=',info
write(*,*)'ny,nij2=',ny,nij2
return
endif
do i=1,ny
write(*,*)i,w(i)
enddo
do iev=1,ny-1
do iset=1,nt
r=0
do i=1,nij2
r=r+y(i12(i),iset)*drdr(i,iev)
enddo
rc(iev,iset)=r
enddo
enddo
end
real*8 function compdx2(rc,rcbd,nsets)
implicit none
integer nsets,rcbd(nsets)
real*8 rc(nsets)
integer iset,dt
real*8 r
r=0
dt=1
do iset=1,nsets
if (rcbd(iset)==0)then
r=r+(rc(iset+dt)-rc(iset))**2
else
if (rcbd(iset)/=2) r=r+(rcbd(iset)-rc(iset))**2
endif
enddo
compdx2=r
end
real*8 function compdx2evec(rc,lp,nsets)
implicit none
integer nsets,lp(nsets)
real*8 rc(nsets)
integer iset
real*8 r
r=0
do iset=1,nsets-1
if (lp(iset)==lp(iset+1))then
r=r+(rc(iset+1)-rc(iset))**2
endif
enddo
compdx2evec=r
end
subroutine optimdx2np(nr,ny,rc,y,bval,nt,info,dx2)
implicit none
integer nr,ny,nt,info,bval(nt)
real*8 rc(nt),y(nt),dx2
!!!! minimum of [x(t)-x(t+dt)]^2 +[x(t)-x_A]^2+[x(t)-x_B]^2 where x_A=-1 and x_B=1
!!!! for all i: \sum_j al_j[<dx_idx_j>_t+<x_ix_j>_AB] = x_AB <x_i>_AB
real*8 dxdx((ny+1)*(ny+1)+nr-ny,(ny+1)*(ny+1)+nr-ny)
real*8 al((ny+1)*(ny+1)+nr-ny),alal
real*8 rhs((ny+1)*(ny+1)+nr-ny)
integer i,j,i1,nij,iset,isize
real*8 r
integer ipiv((ny+1)*(ny+1)+nr-ny)
real*8 sval((ny+1)*(ny+1)+nr-ny),work(((ny+1)*(ny+1)+nr-ny)*10)
integer rank,lwork,iwork(((ny+1)*(ny+1)+nr-ny)*10)
integer i12((ny+1)*(ny+1)+nr-ny)
integer i21((ny+1)*(ny+1)+nr-ny),nij2
real*8 compdx2,dx2n
real*8 rcn(nt)
real*8 rcp1,yp1,dfij((ny+1)*(ny+1)+nr-ny)
isize=(ny+1)*(ny+1)+nr-ny
lwork=isize*10
al=0
alal=0
dxdx=0
call compxxnp(nr,ny,rc,y,bval,nt,alal,al,dxdx,isize)
nij2=0
do i=1,isize
i21(i)=0
enddo
do i=1,isize ! select only non zero
if (dxdx(i,i)<1e-5)cycle
nij2=nij2+1
i12(nij2)=i
i21(i)=nij2
enddo
do i=1,nij2
do j=1,i
dxdx(i,j)=dxdx(i12(i),i12(j))
dxdx(j,i)=dxdx(i,j)
enddo
al(i)=al(i12(i))
rhs(i)=-al(i)/2
enddo
if (.true.)then !solving SLE
call dgetrf(nij2,nij2,dxdx,isize,ipiv,info)
if(info/=0)then
write(*,*)'dgetrf info=',info
return
stop'info/=0'
endif
call dgetrs('N',nij2,1,dxdx,isize,ipiv,rhs,isize,info)
if(info/=0)then
write(*,*)'dgetrs info=',info
stop'info/=0'
endif
else ! solving least square problem
call DGELSD(nij2,nij2,1,dxdx,isize,rhs,isize,sval,-1d-14, rank,
$ work,lwork,iwork,info)
if(info/=0)then
write(*,*)'DGELSD info=',info
stop'info/=0'
endif
endif
!$OMP PARALLEL default(none)
!$OMP& SHARED(nsets,nij2,ny,nr,y,rc,rcfix,rcn,rhs,i12)
!$OMP& PRIVATE(nij,rcp1,yp1,dfij,i1,r)
!$OMP DO
do iset=1,nt
rcn(iset)=rc(iset)
nij=0
rcp1=1
do i=0,ny
yp1=rcp1
do j=0,ny-i
nij=nij+1
c dfij(nij)=rc(iset)**i*y(iset)**j
dfij(nij)=yp1
yp1=yp1*y(iset)
enddo
rcp1=rcp1*rc(iset)
enddo
do i=ny+1,nr
nij=nij+1
c dfij(nij)=rc(iset)**i
dfij(nij)=rcp1
rcp1=rcp1*rc(iset)
enddo
r=0
do i=1,nij2
i1=i12(i)
r=r+rhs(i)*dfij(i1)
enddo
rcn(iset)=r
enddo
!$OMP END PARALLEL
dx2n=compdx2(rcn,bval,nt)
if (.not. (dx2n>1 .or. dx2n<1)) return ! check for nan
if (dx2n>dx2) return
rc=rcn
dx2=dx2n
end
subroutine compxxnp(nr,ny,rc,y,bval,nt,alal,al,dxdx,isize2)
implicit none
integer nt,isize2,nr,ny,bval(nt)
real*8 rc(nt),y(nt),alal,al(isize2),dxdx(isize2,isize2)
integer iset,nij,i,j
real*8 rcp1,rcp2,yp1,yp2,dfij(isize2)
real*8 dind
!$OMP PARALLEL default(none)
!$OMP& SHARED(nsets,dt,rcind,rcfix,ny,nr,y,rc)
!$OMP& PRIVATE(bi,b1,b2,dind,ix,nij,rcp2,rcp1,yp2,yp1,dfij)
!$OMP& reduction(+:alal,al,dxdx)
!$OMP DO
do iset=1,nt
! f(t)=2rcind(t)+(-1)**rcind(t)*rc(t)=k+b*rc
if (bval(iset)==0)then
nij=0
rcp2=1
rcp1=1
do i=0,ny
yp2=rcp2
yp1=rcp1
do j=0,ny-i
nij=nij+1
c dfij(nij)=rc(iset+dt)**i*y(iset+dt)**j
c $ -rc(iset)**i*y(iset)**j
dfij(nij)=yp2-yp1
yp2=yp2*y(iset+1)
yp1=yp1*y(iset)
enddo
rcp2=rcp2*rc(iset+1)
rcp1=rcp1*rc(iset)
enddo
do i=ny+1,nr
nij=nij+1
c dfij(nij)=rc(iset+dt)**i-rc(iset)**i
dfij(nij)=rcp2-rcp1
rcp2=rcp2*rc(iset+1)
rcp1=rcp1*rc(iset)
enddo
do i=1,nij
do j=1,i
dxdx(i,j)=dxdx(i,j)+dfij(i)*dfij(j)
enddo
enddo
else
if (bval(iset)==2)cycle ! no boundary value
dind=-bval(iset) ! distance offset
nij=0
rcp1=1
do i=0,ny
yp1=rcp1
do j=0,ny-i
nij=nij+1
c dfij(nij)=bi*rc(ix)**i*y(ix)**j
dfij(nij)=yp1
yp1=yp1*y(iset)
enddo
rcp1=rcp1*rc(iset)
enddo
do i=ny+1,nr
nij=nij+1
c dfij(nij)=bi*rc(ix)**i
dfij(nij)=rcp1
rcp1=rcp1*rc(iset)
enddo
alal=alal+dind*dind
do j=1,nij
al(j)=al(j)+2*dind*dfij(j)
enddo
do i=1,nij
do j=1,i
dxdx(i,j)=dxdx(i,j)+dfij(i)*dfij(j)
enddo
enddo
endif
enddo
!$OMP END PARALLEL
end