README0100644001204700017620000000252210562653115012016 0ustar jphughesfacultyCENSRE2 - Mixed effects models for censored data. See censre2.s for arguments and calling structure Reference: Hughes JP: Mixed effects models with censored data with application to HIV RNA levels. Biometrics, 55:625-629, 1999. 2-Feb-2007 To install this software, do the following: 1) Compile the fortran code (need to do only once): e.g. % f77 -c censre2.f or % Splus SHLIB -o censre2.so censre2.f or ... 2) In Splus, source the function censre2() (need to do only once): > source("censre2.s") 3) In Splus, load the compiled fortran code (need to do everytime Splus is started): e.g. > dyn.load("censre2.o") or > dyn.load2("censre2.o") or > dyn.load.shared("censre2.so") or ... 4) Run the test dataset source("censre.test") 5) Compare the output with censre.test.out Report problems to Jim Hughes (jphughes@u.washington.edu) KNOWN BUGS: 1) Values in the extreme tails of the normal distribution can cause numerical problems which lead to a NaN in the fortran routines. Such values sometimes arise during the gibbs sampling procedure. The program cannot recover and all parameter estimates and the loglikelihood become NaN's (printed as "NA"). If this occurs, try rerunning the program with a different random seed or different initial values. censre2.s0100700001204700017620000000600610562654147012663 0ustar jphughesfacultycensre2 <- function(id,C,Q,X,Z,alpha,D,sigma,eps=.001,nsize=500,burnin=25, silent=F,iseed){ # Purpose: Implements Monte Carlo EM estimator for mixed effects model with # left and/or right censored data. Assumes normal errors and # normal distributions for random effects. # # Required: # id = unique identifier for each individual/unit # # C = censoring indicator; C = -1 means left censored, C = 0 means # uncensored, C = 1 means right censored # # Q = response variable; if C = 0, Q is the uncensored observation; if # C != 0, Q is the censoring level # # X = design matrix for fixed effects; generate using model.matrix or # by hand # # Z = design matrix for random effects; generate using model.matrix or # by hand # # alpha = initial values for fixed effects (optional) # # D = initial guess for the covariance matrix of the random effects # # S = initial guess for the within-subject residual variance # # Optional: # eps = max. relative change in parameters between successive iterates # to achieve convergence; typically this will be larger than one # might use in a deterministic algorithm # # nsize = starting number of Monte Carlo samples to compute expected # sufficient statistics on each person during E-step; this # number is doubled if the absolute change in any parameter is # less than the estimated Monte Carlo standard error for that # parameter # # burnin = number of Monte Carlo samples to discard during Gibbs # sampling; the sampler typically burns in quite rapidly # in this application # # silent = if T, do not display intermediate results # # iseed = random number seed (a negative integer) # # Reference: Hughes JP. Mixed effects models with censored data with # application to HIV RNA levels. Biometrics 55:625-629, 1999. # nsubj <- length(unique(id)) n <- rle(id)$lengths p <- ncol(X) q <- ncol(Z) sumn <- sum(n) if (missing(alpha)) alpha <- solve(t(X)%*%X)%*%t(X)%*%Q info <- matrix(0,p,p) storage.mode(X) <- "double" storage.mode(Z) <- "double" storage.mode(D) <- "double" storage.mode(info) <- "double" zzz <- .Fortran("censre2", as.integer(burnin), as.integer(nsize), as.integer(nsubj), as.integer(sumn), as.integer(n), as.integer(p), as.integer(q), X, Z, as.double(Q), as.integer(C), alpha=as.double(alpha), D=D, sigma=as.double(sigma), info=info, as.integer(silent), as.double(eps), as.integer(iseed)) var.alpha <- solve(zzz$info) list(alpha=zzz$alpha,D=zzz$D,sigma=zzz$sigma,var=var.alpha) # list(alpha=zzz$alpha,D=zzz$D,sigma=zzz$sigma) } censre2.f0100700001204700017620000012026010562652343012641 0ustar jphughesfaculty subroutine censre2(burnin,nsize,nsubj,sumn,n,p,q,X,Z,YQ,YC, * alpha,D,S,info,silent,eps,iseed) c c Routine to implement EM algorithm to estimate parameters of mixed c effects linear model in the presence of right and/or left censored c data. c c Arguments: c c burnin (I) = number of Monte Carlo samples to discard during Gibbs c sampling; the sampler typically burns in quite rapidly c in this application c nsize (I) = starting number of Monte Carlo samples to compute expected c sufficient statistics on each person during E-step; this c number is doubled if the absolute change in any parameter c is less than the estimated Monte Carlo standard error of that c parameter c nsubj (I) = number of subjects/clusters in the data set c sumn (I) = total number of observations c n (I) = vector of length nsubj giving the number of observations c per subject/cluster c p (I) = number of fixed effects (columns of design matrix) c q (I) = number of random effects (columns of design matrix) c X (I) = design matrix for fixed effects c Z (I) = design matrix for random effects c Q (I) = response (see censre2.s) c C (I) = sensoring indicator (see censre2.s) c alpha (IO) = on input, initial values for fixed effects; on output, c the final fitted values c D (IO) = on input, initial values for covariance matrix of random effects; c on output, the final fitted values c S (IO) = on input, initial value for within-subject residual variance; c on output, the final fitted value c info (O) = information matrix for the fixed effects c silent (I) = if 0, print out intermediate results; otherwise, don't print c intermediate results c eps (I) = max. relative change in parameters between successive iterates c to achieve convergence; typically this will be larger than one c might use in a deterministic algorithm c iseed (I) = (negative) seed for random number generator c c Author: c Jim Hughes (jphughes@u.washington.edu) c Dept. of Biostat. c Univ. of WA c c Revision history c 4/28/99 - Fixed computation of the likelihood; incorrect computation c caused the gibbs sample size to increase beyond necessity c in some situations. c c 2/6/07 - Added common block to ran1 and changed name of sumX to mysumX c to avoid apparent conflict with Splus 7.x c Parameter(MAXP=20,MAXQ=20,MAXN=100) Parameter(MAXPQ=MAXP+(MAXQ*(MAXQ+1))/2+1) implicit double precision(A-H,O-Z) integer burnin,nsize,nsubj,n(*),p,q,YC(*),sumn,ind,silent integer npar,iseed real junk, ran1 real*8 X(sumn,*),Z(sumn,*),YQ(*) real*8 alpha(*),D(q,*),S,info(p,*),eps real*8 Eee,Ebb(MAXQ,MAXQ),XWY(MAXP),ui(MAXN),Vcc(MAXP,MAXP) real*8 Wi(MAXN,MAXN),DZW(MAXQ,MAXN),DZ(MAXQ,MAXN),XWX(MAXP,MAXP) real*8 XW(MAXP,MAXN),r(MAXN),rr(MAXN,MAXN),Vmc(MAXP,MAXP) real*8 y(MAXN),vy(MAXN,MAXN),det(2),va(MAXP) real*8 newa(MAXP),newD(MAXQ,MAXQ),newS,mcdel,delmx real*8 delta(MAXPQ),rWr,rlogl,llogl,ln10,ldetV,ldetD data ln10/2.302585/ junk = ran1(iseed) iseed = 0 npar = p + (q*(q+1))/2 + 1 1 ind = 0 c c Following loop does the matrix operations which constitute the c E step of the EM algorithm c Eee = 0.0D0 call veczero(p,XWY) call matzero(MAXQ,q,q,Ebb) call matzero(MAXP,p,p,XWX) call matzero(MAXP,p,p,Vcc) call matzero(MAXP,p,p,Vmc) c do 100 i = 1,nsubj c call INTPR("i",1,i,1) call makeui(sumn,p,ind,X,n(i),alpha,ui) c call DBLEPR("ui",2,ui,n(i)) call makeVi(MAXN,sumn,q,ind,Z,D,S,n(i),Wi) call gibbs(MAXN,burnin,nsize,ui,Wi,n(i),YQ(ind+1),YC(ind+1), * iseed,r,rr,y,vy) c call DBLEPR("r",1,r,n(i)) c r = E(Y - X%*%alpha | YQ,YC,alpha) c rr = E((Y-X%*%alpha)(Y-X%*%alpha)^T | YQ,YC,alpha) c y = E(Y | YQ,YC,alpha) call invert(MAXN,n(i),Wi,det,ierr) ldetV = det(2)*ln10 + log(det(1)) c call DBLEPR("ldetV",5,ldetV,1) call makeDZW(MAXN,MAXQ,sumn,q,n(i),ind,D,Z,Wi,DZW,DZ) c call DBLEPR("DZW",3,DZW(1,1),q) call makeXW(MAXN,MAXP,sumn,p,n(i),ind,X,Wi,XW) c call DBLEPR("XW",2,XW(1,1),p) call mysumX(MAXN,MAXP,sumn,p,n(i),ind,X,XW,y,vy,r,rr,XWY,XWX, * Vcc,Vmc) c call DBLEPR("XWX",3,XWX(1,1),p) call sumEbb(MAXN,MAXQ,q,n(i),DZW,rr,D,DZ,Ebb) call sumEee(MAXN,MAXQ,sumn,q,n(i),ind,rr,Z,DZW,S,Wi,Eee) ind = ind + n(i) 100 continue c call makeinfo(MAXP,p,XWX,Vcc,info) call invert(MAXP,p,XWX,det,ierr) c c M-step c call mstep(MAXP,MAXQ,nsubj,p,q,sumn,XWX,XWY,Ebb,Eee, * newa,newD,newS) c c compute monte Carlo uncertainty in estimate of alpha c call varmc(MAXP,p,XWX,Vmc,va) c c check for convergence c call pctchg(MAXQ,p,q,alpha,D,S,newa,newD,newS,va,delta,mcdel) if (silent.eq.0) then call DBLEPR("newa",4,newa,p) do 3 i = 1,q 3 call DBLEPR("newD",4,newD(1,i),q) call DBLEPR("newS",4,newS,1) call DBLEPR("Relative change in parameters",29,delta,npar) endif c delmx = delta(1) do 300 i = 1,npar 300 if (delta(i).gt.delmx) delmx=delta(i) if (delmx.le.eps) goto 999 if (mcdel.lt.1.0) then nsize=nsize*2 call intpr("Monte Carlo sample size increased to ",37,nsize,1) else if (mcdel.ge.20) then nsize=nsize/2 call intpr("Monte Carlo sample size decreased to ",37,nsize,1) endif c call copy(MAXQ,p,q,newa,newD,newS,alpha,D,S) goto 1 999 return end subroutine makeui(lda,p,ind,X,n,alpha,ui) implicit double precision(A-H,O-Z) integer lda,p,ind,n real*8 X(lda,*),alpha(*),ui(*) do 10 i = 1,n ui(i) = 0.0 do 10 j = 1,p ui(i) = ui(i) + X(ind+i,j)*alpha(j) 10 continue return end subroutine makeVi(ldn,lda,q,ind,Z,D,S,n,Vi) implicit double precision(A-H,O-Z) integer ldq,lda,q,ind,n real*8 Z(lda,*),D(q,*),S,Vi(ldn,*) c do 5 i = 1,n do 5 l = 1,n Vi(i,l) = 0.0D0 5 continue c do 10 i = 1,n Vi(i,i) = S do 10 l = 1,n do 10 j = 1,q do 10 k = 1,q Vi(i,l) = Vi(i,l) + Z(ind+i,k)*D(k,j)*Z(ind+l,j) 10 continue return end subroutine makeDZW(ldn,ldq,lda,q,n,ind,D,Z,Wi,DZW,DZ) implicit double precision(A-H,O-Z) integer ldn,ldq,lda,q,ind,n real*8 Wi(ldn,*),DZW(ldq,*),DZ(ldq,*) real*8 Z(lda,*),D(q,*) do 10 i = 1,q do 10 j = 1,n DZW(i,j) = 0.0 DZ(i,j) = 0.0 do 10 k = 1,q DZ(i,j) = DZ(i,j) + D(i,k)*Z(ind+j,k) do 10 l = 1,n DZW(i,j) = DZW(i,j) + D(i,k)*Z(ind+l,k)*Wi(l,j) 10 continue return end subroutine makeXW(ldn,ldp,lda,p,n,ind,X,Wi,XW) implicit double precision(A-H,O-Z) integer ldn,ldp,lda,p,n,ind real*8 X(lda,*),Wi(ldn,*),XW(ldp,*) do 10 i = 1,p do 10 j = 1,n XW(i,j) = 0.0 do 10 k = 1,n XW(i,j) = XW(i,j) + X(ind+k,i)*Wi(k,j) 10 continue return end subroutine mysumX(ldn,ldp,lda,p,n,ind,X,XW,y,vy,r,rr,XWY,XWX, * Vcc,Vmc) implicit double precision(A-H,O-Z) integer ldn,ldp,lda,p,n,ind real*8 X(lda,*),XWX(ldp,*),XW(ldp,*),XWY(*) real*8 Vcc(ldp,*),y(*),r(*),rr(ldn,*),vy(ldn,*),Vmc(ldp,*) do 10 i = 1,p do 10 j = 1,n XWY(i) = XWY(i) + XW(i,j)*y(j) 10 continue do 20 i = 1,p do 20 j = 1,p do 20 k = 1,n XWX(i,j) = XWX(i,j) + XW(i,k)*X(ind+k,j) 20 continue do 40 i = 1,p do 40 j = 1,p do 40 k = 1,n do 40 l = 1,n Vcc(i,j) = Vcc(i,j) + XW(i,k)*(rr(k,l)-r(k)*r(l))*XW(j,l) Vmc(i,j) = Vmc(i,j) + XW(i,k)*vy(k,l)*XW(j,l) 40 continue return end subroutine sumEbb(ldn,ldq,q,n,DZW,rr,D,DZ,Ebb) implicit double precision(A-H,O-Z) integer ldn,ldq,q,n real*8 DZW(ldq,*),rr(ldn,*),D(q,*),DZ(ldq,*),Ebb(ldq,*) do 10 i = 1,q do 10 j = 1,q Ebb(i,j) = Ebb(i,j) + D(i,j) do 10 k = 1,n do 20 l = 1,n Ebb(i,j) = Ebb(i,j) + DZW(i,k)*rr(k,l)*DZW(j,l) 20 continue Ebb(i,j) = Ebb(i,j) - DZW(i,k)*DZ(j,k) 10 continue return end subroutine sumEee(ldn,ldq,lda,q,n,ind,rr,Z,DZW,S,Wi,Eee) Parameter(MAXP=20,MAXQ=20,MAXN=100) implicit double precision(A-H,O-Z) integer lad,ldn,ldq,q,n,ind real*8 rr(ldn,*),Wi(ldn,*),DZW(ldq,*),S,Eee,Z(lda,*) real*8 A(MAXN,MAXN),sumW,sumrr do 2 i = 1,n A(i,i) = 1.0 do 2 j = i+1,n A(i,j) = 0.0 A(j,i) = 0.0 2 continue do 5 i = 1,n do 5 j = 1,n do 5 k = 1,q A(i,j) = A(i,j) - Z(ind+i,k)*DZW(k,j) 5 continue c call DBLEPR("A",1,A,n) sumW = 0.0 do 10 i = 1,n 10 sumW = sumW + Wi(i,i) c call DBLEPR("sumW",4,sumW,1) sumrr = 0.0 do 20 i = 1,n do 20 j = 1,n do 20 k = 1,n 20 sumrr = sumrr + rr(i,j)*A(k,i)*A(k,j) c call DBLEPR("sumrr",5,sumrr,1) Eee = Eee + sumrr + S*(n-S*sumW) return end subroutine makeinfo(ldp,p,XWX,Vcc,info) implicit double precision(A-H,O-Z) integer ldp,p real*8 XWX(ldp,*),Vcc(ldp,*),info(p,*) do 10 i = 1,p do 10 j = 1,p 10 info(i,j) = XWX(i,j)-Vcc(i,j) return end subroutine gibbs(ldn,burnin,nsize,mean,W,m,YQ,YC,iseed,r,rr,Z,vy) Parameter(MAXP=20,MAXQ=20,MAXN=100) implicit double precision(A-H,O-Z) integer ldn,burnin,nsize,m,iseed integer i1,i2,one,YC(*) real*8 mean(*),W(ldn,*),YQ(*),r(*),rr(ldn,*),vy(ldn,*) real*8 mwt(MAXN,MAXN),cvar(MAXN),u,p(MAXN),x(MAXN) real*8 Win(MAXN,MAXN),Z(MAXN),d(2) real pnorm,qnorm,zero real ran1 data one/1/,zero/0.0E0/ C do 10 i = 1,m Z(i) = YQ(i)-mean(i) p(i) = pnorm(sngl(Z(i)),zero,sngl(W(i,i))) c call DBLEPR("p",1,p(i),1) if (YC(i).eq.0) then x(i)=Z(i) elseif (YC(i).lt.0) then u = p(i)*ran1(iseed) x(i) = qnorm(sngl(u),zero,sngl(W(i,i))) else u = p(i)+(1.0-p(i))*ran1(iseed) x(i) = qnorm(sngl(u),zero,sngl(W(i,i))) endif call dropi(MAXN,m,W,i,Win) if (m.gt.1) call invert(MAXN,m-1,Win,d,ierr) cvar(i) = W(i,i) i1 = 0 do 10 j = 1,m mwt(i,j) = 0.0D0 if (j.ne.i) then i1 = i1+1 i2 = 0 do 20 l = 1,m if (l.ne.i) then i2 = i2+1 mwt(i,j) = mwt(i,j) + W(i,l)*Win(i2,i1) endif 20 continue cvar(i) = cvar(i) - mwt(i,j)*W(j,i) endif 10 continue c c call DBLEPR("mwt",3,mwt,m) c call DBLEPR("cvar",4,cvar,m) call gsample(ldn,burnin,m,mwt,cvar,Z,YC,x,r,rr,vy,iseed) call matzero(MAXN,m,m,rr) call veczero(m,r) call gsample(ldn,nsize,m,mwt,cvar,Z,YC,x,r,rr,vy,iseed) do 30 i = 1,m 30 Z(i) = r(i)+mean(i) return end subroutine dropi(ldn,n,W,i,V) implicit double precision(A-H,O-Z) integer ldn,n,i,i1,i2 real*8 W(ldn,*),V(ldn,*) i1 = 0 do 15 j=1,n if (j.eq.i) goto 15 i1 = i1+1 i2 = 0 do 10 l=1,n if (l.eq.i) goto 10 i2 = i2+1 V(i1,i2) = W(j,l) 10 continue 15 continue return end subroutine invert(lda,n,a,d,info) implicit double precision(A-H,O-Z) PARAMETER(MAXN=100) integer lda,n,ipvt(MAXN) integer job,info real*8 a(lda,*),d(2),work(MAXN) data job/11/ c call DGEFA(a,lda,n,ipvt,info) if (info.gt.0) call intpr("info = ",7,info,1) call DGEDI(a,lda,n,ipvt,d,work,job) return end subroutine mstep(ldp,ldq,nsubj,p,q,sumn,XWX,XWY,Ebb,Eee, * newa,newD,newS) implicit double precision(A-H,O-Z) integer ldp,ldq,nsubj,p,q,sumn real*8 XWX(ldp,*),XWY(*),Ebb(ldq,*),Eee real*8 newa(*),newD(ldq,*),newS c c update u do 400 i = 1,p newa(i) = 0.0 do 400 j = 1,p newa(i) = newa(i) + XWX(i,j)*XWY(j) 400 continue c update D and S do 300 i = 1,q do 300 j = i,q newD(i,j) = Ebb(i,j)/nsubj newD(j,i) = newD(i,j) 300 continue newS = Eee/sumn return end subroutine varmc(ldp,p,XWX,Vmc,a) implicit double precision(A-H,O-Z) integer ldp,p real*8 XWX(ldp,*),Vmc(ldp,*),a(*) c do 400 i = 1,p a(i) = 0.0D0 do 400 j = 1,p do 400 k = 1,p a(i) = a(i) + XWX(i,j)*Vmc(j,k)*XWX(k,i) 400 continue return end subroutine copy(ldq,p,q,newa,newD,newS,a,D,S) implicit double precision(A-H,O-Z) integer ldq,p,q real*8 a(*),D(q,*),S real*8 newa(*),newD(ldq,*),newS c do 10 i = 1,p 10 a(i) = newa(i) do 20 i = 1,q do 20 j = 1,q D(i,j) = newD(i,j) 20 continue S = newS return end subroutine matzero(lda,p,q,A) implicit double precision(A-H,O-Z) integer lda,p,q real*8 A(lda,*) do 10 i = 1,p do 10 j = 1,q 10 A(i,j) = 0.0 return end subroutine veczero(n,A) implicit double precision(A-H,O-Z) integer n real*8 A(*) do 10 i = 1,n 10 A(i) = 0.0 return end subroutine matcopy(lda,a,b,from,to) integer lda,a,b real*8 from(lda,*),to(lda,*) c do 10 i = 1,a do 10 j = 1,b 10 to(i,j) = from(i,j) return end subroutine pctchg(lpq,p,q,a,D,S,newa,newD,newS,va,delta,mcdel) implicit double precision(A-H,O-Z) integer lpq,p,q real*8 a(*),D(q,*),S,delta(*),va(*),mcdel,temp real*8 newa(*),newD(lpq,*),newS real*8 ulim data ulim/40.0D0/ c ijk = 0 mcdel = ulim do 10 i = 1,p ijk = ijk+1 if (va(i).gt.0.0D0) then temp = abs(a(i)-newa(i))/sqrt(va(i)) else temp = ulim endif if (temp.lt.mcdel) mcdel=temp 10 delta(ijk) = abs((a(i)-newa(i))/a(i)) do 20 i = 1,q do 20 j = i,q ijk=ijk+1 20 delta(ijk) = abs((D(i,j)-newD(i,j))/D(i,j)) ijk=ijk+1 delta(ijk) = abs(S-newS)/S return end real function ran1(idum) dimension r(97) parameter (m1=259200,ia1=7141,ic1=54773,rm1=1./m1) parameter (m2=134456,ia2=8121,ic2=28411,rm2=1./m2) parameter (m3=243000,ia3=4561,ic3=51349) common /rstate/ r,ix1,ix2,ix3 data iff/0/ c if (idum.lt.0 .or. iff.eq.0) then iff=1 ix1=mod(ic1-idum,m1) ix1=mod(ia1*ix1+ic1,m1) ix2=mod(ix1,m2) ix1=mod(ia1*ix1+ic1,m1) ix3=mod(ix1,m3) do 11 j=1,97 ix1=mod(ia1*ix1+ic1,m1) ix2=mod(ia2*ix2+ic2,m2) r(j)=(float(ix1)+float(ix2)*rm2)*rm1 11 continue idum=1 endif ix1=mod(ia1*ix1+ic1,m1) ix2=mod(ia2*ix2+ic2,m2) ix3=mod(ia3*ix3+ic3,m3) j=1+(97*ix3)/m3 c if (j.gt.97 .or. j.lt.1) pause ran1=r(j) r(j)=(float(ix1)+float(ix2)*rm2)*rm1 return end real function pnorm(X,u,v) real X,u,v c Adapted from ERFCC in Numerical Recipes, Press et al. 1986 data sqrt2/1.4142136/ Z=ABS((X-u)/sqrt(v))/sqrt2 T=1./(1.+0.5*Z) ERFCC=1. - (T*EXP(-Z*Z-1.26551223+T*(1.00002368+T*(.37409196+ * T*(.09678418+T*(-.18628806+T*(.27886807+T*(-1.13520398+ * T*(1.48851587+T*(-.82215223+T*.17087277))))))))))/2. IF (X.LT.u) ERFCC=1.-ERFCC pnorm=erfcc RETURN END real function qnorm(p,u,v) real p,u,v data p0/-0.322232431088/,p1/-1.0/,p2/-0.342242088547/ data p3/-0.0204231210245/,p4/-0.453642210148e-4/ data q0/0.0993484626060/,q1/0.588581570495/,q2/0.531103462366/ data q3/0.103537752850/,q4/0.38560700634e-2/ c if (p.eq.0.5) then qnorm = u return endif z=0.0 pp = p if (p.gt.0.5) pp = 1-p y = sqrt(log(1./pp**2)) z = y + ((((y*p4 + p3)*y + p2)*y + p1)*y + p0)/ * ((((y*q4 + q3)*y + q2)*y + q1)*y + q0) if (p.lt.0.5) z = -z qnorm = sqrt(v)*z + u return end subroutine gsample(ldn,n,m,mwt,cvar,q,cens,x,r,rr,vy,iseed) implicit double precision(A-H,O-Z) integer ldn,n,m,cens(*),iseed real*8 mwt(ldn,*),cvar(*),q(*),r(*),x(*),rr(ldn,*),vy(ldn,*) real pnorm,qnorm,ran1,eps data eps/1.e-8/ c do 100 i1 = 1,n do 50 i = 1,m if (cens(i).eq.0) then x(i) = q(i) else cmu = 0.0 do 10 l = 1,m c Note that mwt(i,i) = 0 10 cmu = cmu + mwt(i,l)*x(l) p = pnorm(sngl(q(i)),sngl(cmu),sngl(cvar(i))) rmin=0.0 rmax=p if (cens(i).gt.0) then rmin=p rmax=1.0 endif u = rmin + ran1(iseed)*(rmax-rmin) if (u.lt.eps.or.u.gt.1.0-eps) then x(i) = q(i) else x(i) = qnorm(sngl(u),sngl(cmu),sngl(cvar(i))) endif endif 50 continue do 60 i = 1,m r(i) = r(i) + x(i) do 60 j = 1,m rr(i,j) = rr(i,j) + x(i)*x(j) 60 continue 100 continue do 30 j = 1,m r(j) = r(j)/n do 30 k = 1,j rr(j,k) = rr(j,k)/n rr(k,j) = rr(j,k) c vy is meant to be an estimate of the Monte Carlo variance of E(r) = E(Y); c It is not quite right since the generated x's were not independent; fix this c in a later version vy(j,k) = (rr(j,k) - r(j)*r(k))/n vy(k,j) = vy(j,k) 30 continue return end ccccccc Routines from CMLIB ccccccccccccccc double precision function dasum(n,dx,incx) c c takes the sum of the absolute values. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dtemp integer i,incx,m,mp1,n,nincx c dasum = 0.0d0 dtemp = 0.0d0 if(n.le.0)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c nincx = n*incx do 10 i = 1,nincx,incx dtemp = dtemp + dabs(dx(i)) 10 continue dasum = dtemp return c c code for increment equal to 1 c c c clean-up loop c 20 m = mod(n,6) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dtemp + dabs(dx(i)) 30 continue if( n .lt. 6 ) go to 60 40 mp1 = m + 1 do 50 i = mp1,n,6 dtemp = dtemp + dabs(dx(i)) + dabs(dx(i + 1)) + dabs(dx(i + 2)) * + dabs(dx(i + 3)) + dabs(dx(i + 4)) + dabs(dx(i + 5)) 50 continue 60 dasum = dtemp return end subroutine daxpy(n,da,dx,incx,dy,incy) c c constant times a vector plus a vector. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dy(*),da integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if (da .eq. 0.0d0) return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dy(iy) = dy(iy) + da*dx(ix) ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,4) if( m .eq. 0 ) go to 40 do 30 i = 1,m dy(i) = dy(i) + da*dx(i) 30 continue if( n .lt. 4 ) return 40 mp1 = m + 1 do 50 i = mp1,n,4 dy(i) = dy(i) + da*dx(i) dy(i + 1) = dy(i + 1) + da*dx(i + 1) dy(i + 2) = dy(i + 2) + da*dx(i + 2) dy(i + 3) = dy(i + 3) + da*dx(i + 3) 50 continue return end double precision function ddot(n,dx,incx,dy,incy) c c forms the dot product of two vectors. c uses unrolled loops for increments equal to one. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dy(*),dtemp integer i,incx,incy,ix,iy,m,mp1,n c ddot = 0.0d0 dtemp = 0.0d0 if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments c not equal to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = dtemp + dx(ix)*dy(iy) ix = ix + incx iy = iy + incy 10 continue ddot = dtemp return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dtemp + dx(i)*dy(i) 30 continue if( n .lt. 5 ) go to 60 40 mp1 = m + 1 do 50 i = mp1,n,5 dtemp = dtemp + dx(i)*dy(i) + dx(i + 1)*dy(i + 1) + * dx(i + 2)*dy(i + 2) + dx(i + 3)*dy(i + 3) + dx(i + 4)*dy(i + 4) 50 continue 60 ddot = dtemp return end SUBROUTINE DGECO(A,LDA,N,IPVT,RCOND,Z) INTEGER LDA,N,IPVT(*) DOUBLE PRECISION A(LDA,*),Z(*) DOUBLE PRECISION RCOND C C DGECO FACTORS A DOUBLE PRECISION MATRIX BY GAUSSIAN ELIMINATION C AND ESTIMATES THE CONDITION OF THE MATRIX. C C IF RCOND IS NOT NEEDED, DGEFA IS SLIGHTLY FASTER. C TO SOLVE A*X = B , FOLLOW DGECO BY DGESL. C TO COMPUTE INVERSE(A)*C , FOLLOW DGECO BY DGESL. C TO COMPUTE DETERMINANT(A) , FOLLOW DGECO BY DGEDI. C TO COMPUTE INVERSE(A) , FOLLOW DGECO BY DGEDI. C C ON ENTRY C C A DOUBLE PRECISION(LDA, N) C THE MATRIX TO BE FACTORED. C C LDA INTEGER C THE LEADING DIMENSION OF THE ARRAY A . C C N INTEGER C THE ORDER OF THE MATRIX A . C C ON RETURN C C A AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS C WHICH WERE USED TO OBTAIN IT. C THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE C L IS A PRODUCT OF PERMUTATION AND UNIT LOWER C TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR. C C IPVT INTEGER(N) C AN INTEGER VECTOR OF PIVOT INDICES. C C RCOND DOUBLE PRECISION C AN ESTIMATE OF THE RECIPROCAL CONDITION OF A . C FOR THE SYSTEM A*X = B , RELATIVE PERTURBATIONS C IN A AND B OF SIZE EPSILON MAY CAUSE C RELATIVE PERTURBATIONS IN X OF SIZE EPSILON/RCOND . C IF RCOND IS SO SMALL THAT THE LOGICAL EXPRESSION C 1.0 + RCOND .EQ. 1.0 C IS TRUE, THEN A MAY BE SINGULAR TO WORKING C PRECISION. IN PARTICULAR, RCOND IS ZERO IF C EXACT SINGULARITY IS DETECTED OR THE ESTIMATE C UNDERFLOWS. C C Z DOUBLE PRECISION(N) C A WORK VECTOR WHOSE CONTENTS ARE USUALLY UNIMPORTANT. C IF A IS CLOSE TO A SINGULAR MATRIX, THEN Z IS C AN APPROXIMATE NULL VECTOR IN THE SENSE THAT C NORM(A*Z) = RCOND*NORM(A)*NORM(Z) . C C LINPACK. THIS VERSION DATED 08/14/78 . C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. C C SUBROUTINES AND FUNCTIONS C C LINPACK DGEFA C BLAS DAXPY,DDOT,DSCAL,DASUM C FORTRAN DABS,DMAX1,DSIGN C C INTERNAL VARIABLES C DOUBLE PRECISION DDOT,EK,T,WK,WKM DOUBLE PRECISION ANORM,S,DASUM,SM,YNORM INTEGER INFO,J,K,KB,KP1,L C C C COMPUTE 1-NORM OF A C ANORM = 0.0D0 DO 10 J = 1, N ANORM = DMAX1(ANORM,DASUM(N,A(1,J),1)) 10 CONTINUE C C FACTOR C CALL DGEFA(A,LDA,N,IPVT,INFO) C C RCOND = 1/(NORM(A)*(ESTIMATE OF NORM(INVERSE(A)))) . C ESTIMATE = NORM(Z)/NORM(Y) WHERE A*Z = Y AND TRANS(A)*Y = E . C TRANS(A) IS THE TRANSPOSE OF A . THE COMPONENTS OF E ARE C CHOSEN TO CAUSE MAXIMUM LOCAL GROWTH IN THE ELEMENTS OF W WHERE C TRANS(U)*W = E . THE VECTORS ARE FREQUENTLY RESCALED TO AVOID C OVERFLOW. C C SOLVE TRANS(U)*W = E C EK = 1.0D0 DO 20 J = 1, N Z(J) = 0.0D0 20 CONTINUE DO 100 K = 1, N IF (Z(K) .NE. 0.0D0) EK = DSIGN(EK,-Z(K)) IF (DABS(EK-Z(K)) .LE. DABS(A(K,K))) GO TO 30 S = DABS(A(K,K))/DABS(EK-Z(K)) CALL DSCAL(N,S,Z,1) EK = S*EK 30 CONTINUE WK = EK - Z(K) WKM = -EK - Z(K) S = DABS(WK) SM = DABS(WKM) IF (A(K,K) .EQ. 0.0D0) GO TO 40 WK = WK/A(K,K) WKM = WKM/A(K,K) GO TO 50 40 CONTINUE WK = 1.0D0 WKM = 1.0D0 50 CONTINUE KP1 = K + 1 IF (KP1 .GT. N) GO TO 90 DO 60 J = KP1, N SM = SM + DABS(Z(J)+WKM*A(K,J)) Z(J) = Z(J) + WK*A(K,J) S = S + DABS(Z(J)) 60 CONTINUE IF (S .GE. SM) GO TO 80 T = WKM - WK WK = WKM DO 70 J = KP1, N Z(J) = Z(J) + T*A(K,J) 70 CONTINUE 80 CONTINUE 90 CONTINUE Z(K) = WK 100 CONTINUE S = 1.0D0/DASUM(N,Z,1) CALL DSCAL(N,S,Z,1) C C SOLVE TRANS(L)*Y = W C DO 120 KB = 1, N K = N + 1 - KB IF (K .LT. N) Z(K) = Z(K) + DDOT(N-K,A(K+1,K),1,Z(K+1),1) IF (DABS(Z(K)) .LE. 1.0D0) GO TO 110 S = 1.0D0/DABS(Z(K)) CALL DSCAL(N,S,Z,1) 110 CONTINUE L = IPVT(K) T = Z(L) Z(L) = Z(K) Z(K) = T 120 CONTINUE S = 1.0D0/DASUM(N,Z,1) CALL DSCAL(N,S,Z,1) C YNORM = 1.0D0 C C SOLVE L*V = Y C DO 140 K = 1, N L = IPVT(K) T = Z(L) Z(L) = Z(K) Z(K) = T IF (K .LT. N) CALL DAXPY(N-K,T,A(K+1,K),1,Z(K+1),1) IF (DABS(Z(K)) .LE. 1.0D0) GO TO 130 S = 1.0D0/DABS(Z(K)) CALL DSCAL(N,S,Z,1) YNORM = S*YNORM 130 CONTINUE 140 CONTINUE S = 1.0D0/DASUM(N,Z,1) CALL DSCAL(N,S,Z,1) YNORM = S*YNORM C C SOLVE U*Z = V C DO 160 KB = 1, N K = N + 1 - KB IF (DABS(Z(K)) .LE. DABS(A(K,K))) GO TO 150 S = DABS(A(K,K))/DABS(Z(K)) CALL DSCAL(N,S,Z,1) YNORM = S*YNORM 150 CONTINUE IF (A(K,K) .NE. 0.0D0) Z(K) = Z(K)/A(K,K) IF (A(K,K) .EQ. 0.0D0) Z(K) = 1.0D0 T = -Z(K) CALL DAXPY(K-1,T,A(1,K),1,Z(1),1) 160 CONTINUE C MAKE ZNORM = 1.0 S = 1.0D0/DASUM(N,Z,1) CALL DSCAL(N,S,Z,1) YNORM = S*YNORM C IF (ANORM .NE. 0.0D0) RCOND = YNORM/ANORM IF (ANORM .EQ. 0.0D0) RCOND = 0.0D0 RETURN END SUBROUTINE DGEDI(A,LDA,N,IPVT,DET,WORK,JOB) INTEGER LDA,N,IPVT(*),JOB DOUBLE PRECISION A(LDA,*),DET(2),WORK(*) C C DGEDI COMPUTES THE DETERMINANT AND INVERSE OF A MATRIX C USING THE FACTORS COMPUTED BY DGECO OR DGEFA. C C ON ENTRY C C A DOUBLE PRECISION(LDA, N) C THE OUTPUT FROM DGECO OR DGEFA. C C LDA INTEGER C THE LEADING DIMENSION OF THE ARRAY A . C C N INTEGER C THE ORDER OF THE MATRIX A . C C IPVT INTEGER(N) C THE PIVOT VECTOR FROM DGECO OR DGEFA. C C WORK DOUBLE PRECISION(N) C WORK VECTOR. CONTENTS DESTROYED. C C JOB INTEGER C = 11 BOTH DETERMINANT AND INVERSE. C = 01 INVERSE ONLY. C = 10 DETERMINANT ONLY. C C ON RETURN C C A INVERSE OF ORIGINAL MATRIX IF REQUESTED. C OTHERWISE UNCHANGED. C C DET DOUBLE PRECISION(2) C DETERMINANT OF ORIGINAL MATRIX IF REQUESTED. C OTHERWISE NOT REFERENCED. C DETERMINANT = DET(1) * 10.0**DET(2) C WITH 1.0 .LE. DABS(DET(1)) .LT. 10.0 C OR DET(1) .EQ. 0.0 . C C ERROR CONDITION C C A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS C A ZERO ON THE DIAGONAL AND THE INVERSE IS REQUESTED. C IT WILL NOT OCCUR IF THE SUBROUTINES ARE CALLED CORRECTLY C AND IF DGECO HAS SET RCOND .GT. 0.0 OR DGEFA HAS SET C INFO .EQ. 0 . C C LINPACK. THIS VERSION DATED 08/14/78 . C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. C C SUBROUTINES AND FUNCTIONS C C BLAS DAXPY,DSCAL,DSWAP C FORTRAN DABS,MOD C C INTERNAL VARIABLES C DOUBLE PRECISION T DOUBLE PRECISION TEN INTEGER I,J,K,KB,KP1,L,NM1 C C C COMPUTE DETERMINANT C IF (JOB/10 .EQ. 0) GO TO 70 DET(1) = 1.0D0 DET(2) = 0.0D0 TEN = 10.0D0 DO 50 I = 1, N IF (IPVT(I) .NE. I) DET(1) = -DET(1) DET(1) = A(I,I)*DET(1) C ...EXIT IF (DET(1) .EQ. 0.0D0) GO TO 60 10 IF (DABS(DET(1)) .GE. 1.0D0) GO TO 20 DET(1) = TEN*DET(1) DET(2) = DET(2) - 1.0D0 GO TO 10 20 CONTINUE 30 IF (DABS(DET(1)) .LT. TEN) GO TO 40 DET(1) = DET(1)/TEN DET(2) = DET(2) + 1.0D0 GO TO 30 40 CONTINUE 50 CONTINUE 60 CONTINUE 70 CONTINUE C C COMPUTE INVERSE(U) C IF (MOD(JOB,10) .EQ. 0) GO TO 150 DO 100 K = 1, N A(K,K) = 1.0D0/A(K,K) T = -A(K,K) CALL DSCAL(K-1,T,A(1,K),1) KP1 = K + 1 IF (N .LT. KP1) GO TO 90 DO 80 J = KP1, N T = A(K,J) A(K,J) = 0.0D0 CALL DAXPY(K,T,A(1,K),1,A(1,J),1) 80 CONTINUE 90 CONTINUE 100 CONTINUE C C FORM INVERSE(U)*INVERSE(L) C NM1 = N - 1 IF (NM1 .LT. 1) GO TO 140 DO 130 KB = 1, NM1 K = N - KB KP1 = K + 1 DO 110 I = KP1, N WORK(I) = A(I,K) A(I,K) = 0.0D0 110 CONTINUE DO 120 J = KP1, N T = WORK(J) CALL DAXPY(N,T,A(1,J),1,A(1,K),1) 120 CONTINUE L = IPVT(K) IF (L .NE. K) CALL DSWAP(N,A(1,K),1,A(1,L),1) 130 CONTINUE 140 CONTINUE 150 CONTINUE RETURN END SUBROUTINE DGEFA(A,LDA,N,IPVT,INFO) INTEGER LDA,N,IPVT(*),INFO DOUBLE PRECISION A(LDA,*) C C DGEFA FACTORS A DOUBLE PRECISION MATRIX BY GAUSSIAN ELIMINATION. C C DGEFA IS USUALLY CALLED BY DGECO, BUT IT CAN BE CALLED C DIRECTLY WITH A SAVING IN TIME IF RCOND IS NOT NEEDED. C (TIME FOR DGECO) = (1 + 9/N)*(TIME FOR DGEFA) . C C ON ENTRY C C A DOUBLE PRECISION(LDA, N) C THE MATRIX TO BE FACTORED. C C LDA INTEGER C THE LEADING DIMENSION OF THE ARRAY A . C C N INTEGER C THE ORDER OF THE MATRIX A . C C ON RETURN C C A AN UPPER TRIANGULAR MATRIX AND THE MULTIPLIERS C WHICH WERE USED TO OBTAIN IT. C THE FACTORIZATION CAN BE WRITTEN A = L*U WHERE C L IS A PRODUCT OF PERMUTATION AND UNIT LOWER C TRIANGULAR MATRICES AND U IS UPPER TRIANGULAR. C C IPVT INTEGER(N) C AN INTEGER VECTOR OF PIVOT INDICES. C C INFO INTEGER C = 0 NORMAL VALUE. C = K IF U(K,K) .EQ. 0.0 . THIS IS NOT AN ERROR C CONDITION FOR THIS SUBROUTINE, BUT IT DOES C INDICATE THAT DGESL OR DGEDI WILL DIVIDE BY ZERO C IF CALLED. USE RCOND IN DGECO FOR A RELIABLE C INDICATION OF SINGULARITY. C C LINPACK. THIS VERSION DATED 08/14/78 . C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. C C SUBROUTINES AND FUNCTIONS C C BLAS DAXPY,DSCAL,IDAMAX C C INTERNAL VARIABLES C DOUBLE PRECISION T INTEGER IDAMAX,J,K,KP1,L,NM1 C C C GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING C INFO = 0 NM1 = N - 1 IF (NM1 .LT. 1) GO TO 70 DO 60 K = 1, NM1 KP1 = K + 1 C C FIND L = PIVOT INDEX C L = IDAMAX(N-K+1,A(K,K),1) + K - 1 IPVT(K) = L C C ZERO PIVOT IMPLIES THIS COLUMN ALREADY TRIANGULARIZED C IF (A(L,K) .EQ. 0.0D0) GO TO 40 C C INTERCHANGE IF NECESSARY C IF (L .EQ. K) GO TO 10 T = A(L,K) A(L,K) = A(K,K) A(K,K) = T 10 CONTINUE C C COMPUTE MULTIPLIERS C T = -1.0D0/A(K,K) CALL DSCAL(N-K,T,A(K+1,K),1) C C ROW ELIMINATION WITH COLUMN INDEXING C DO 30 J = KP1, N T = A(L,J) IF (L .EQ. K) GO TO 20 A(L,J) = A(K,J) A(K,J) = T 20 CONTINUE CALL DAXPY(N-K,T,A(K+1,K),1,A(K+1,J),1) 30 CONTINUE GO TO 50 40 CONTINUE INFO = K 50 CONTINUE 60 CONTINUE 70 CONTINUE IPVT(N) = N IF (A(N,N) .EQ. 0.0D0) INFO = N RETURN END SUBROUTINE DGESL(A,LDA,N,IPVT,B,JOB) INTEGER LDA,N,IPVT(*),JOB DOUBLE PRECISION A(LDA,*),B(*) C C DGESL SOLVES THE DOUBLE PRECISION SYSTEM C A * X = B OR TRANS(A) * X = B C USING THE FACTORS COMPUTED BY DGECO OR DGEFA. C C ON ENTRY C C A DOUBLE PRECISION(LDA, N) C THE OUTPUT FROM DGECO OR DGEFA. C C LDA INTEGER C THE LEADING DIMENSION OF THE ARRAY A . C C N INTEGER C THE ORDER OF THE MATRIX A . C C IPVT INTEGER(N) C THE PIVOT VECTOR FROM DGECO OR DGEFA. C C B DOUBLE PRECISION(N) C THE RIGHT HAND SIDE VECTOR. C C JOB INTEGER C = 0 TO SOLVE A*X = B , C = NONZERO TO SOLVE TRANS(A)*X = B WHERE C TRANS(A) IS THE TRANSPOSE. C C ON RETURN C C B THE SOLUTION VECTOR X . C C ERROR CONDITION C C A DIVISION BY ZERO WILL OCCUR IF THE INPUT FACTOR CONTAINS A C ZERO ON THE DIAGONAL. TECHNICALLY THIS INDICATES SINGULARITY C BUT IT IS OFTEN CAUSED BY IMPROPER ARGUMENTS OR IMPROPER C SETTING OF LDA . IT WILL NOT OCCUR IF THE SUBROUTINES ARE C CALLED CORRECTLY AND IF DGECO HAS SET RCOND .GT. 0.0 C OR DGEFA HAS SET INFO .EQ. 0 . C C TO COMPUTE INVERSE(A) * C WHERE C IS A MATRIX C WITH P COLUMNS C CALL DGECO(A,LDA,N,IPVT,RCOND,Z) C IF (RCOND IS TOO SMALL) GO TO ... C DO 10 J = 1, P C CALL DGESL(A,LDA,N,IPVT,C(1,J),0) C 10 CONTINUE C C LINPACK. THIS VERSION DATED 08/14/78 . C CLEVE MOLER, UNIVERSITY OF NEW MEXICO, ARGONNE NATIONAL LAB. C C SUBROUTINES AND FUNCTIONS C C BLAS DAXPY,DDOT C C INTERNAL VARIABLES C DOUBLE PRECISION DDOT,T INTEGER K,KB,L,NM1 C NM1 = N - 1 IF (JOB .NE. 0) GO TO 50 C C JOB = 0 , SOLVE A * X = B C FIRST SOLVE L*Y = B C IF (NM1 .LT. 1) GO TO 30 DO 20 K = 1, NM1 L = IPVT(K) T = B(L) IF (L .EQ. K) GO TO 10 B(L) = B(K) B(K) = T 10 CONTINUE CALL DAXPY(N-K,T,A(K+1,K),1,B(K+1),1) 20 CONTINUE 30 CONTINUE C C NOW SOLVE U*X = Y C DO 40 KB = 1, N K = N + 1 - KB B(K) = B(K)/A(K,K) T = -B(K) CALL DAXPY(K-1,T,A(1,K),1,B(1),1) 40 CONTINUE GO TO 100 50 CONTINUE C C JOB = NONZERO, SOLVE TRANS(A) * X = B C FIRST SOLVE TRANS(U)*Y = B C DO 60 K = 1, N T = DDOT(K-1,A(1,K),1,B(1),1) B(K) = (B(K) - T)/A(K,K) 60 CONTINUE C C NOW SOLVE TRANS(L)*X = Y C IF (NM1 .LT. 1) GO TO 90 DO 80 KB = 1, NM1 K = N - KB B(K) = B(K) + DDOT(N-K,A(K+1,K),1,B(K+1),1) L = IPVT(K) IF (L .EQ. K) GO TO 70 T = B(L) B(L) = B(K) B(K) = T 70 CONTINUE 80 CONTINUE 90 CONTINUE 100 CONTINUE RETURN END subroutine dscal(n,da,dx,incx) c c scales a vector by a constant. c uses unrolled loops for increment equal to one. c jack dongarra, linpack, 3/11/78. c double precision da,dx(*) integer i,incx,m,mp1,n,nincx c if(n.le.0)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c nincx = n*incx do 10 i = 1,nincx,incx dx(i) = da*dx(i) 10 continue return c c code for increment equal to 1 c c c clean-up loop c 20 m = mod(n,5) if( m .eq. 0 ) go to 40 do 30 i = 1,m dx(i) = da*dx(i) 30 continue if( n .lt. 5 ) return 40 mp1 = m + 1 do 50 i = mp1,n,5 dx(i) = da*dx(i) dx(i + 1) = da*dx(i + 1) dx(i + 2) = da*dx(i + 2) dx(i + 3) = da*dx(i + 3) dx(i + 4) = da*dx(i + 4) 50 continue return end subroutine dswap (n,dx,incx,dy,incy) c c interchanges two vectors. c uses unrolled loops for increments equal one. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dy(*),dtemp integer i,incx,incy,ix,iy,m,mp1,n c if(n.le.0)return if(incx.eq.1.and.incy.eq.1)go to 20 c c code for unequal increments or equal increments not equal c to 1 c ix = 1 iy = 1 if(incx.lt.0)ix = (-n+1)*incx + 1 if(incy.lt.0)iy = (-n+1)*incy + 1 do 10 i = 1,n dtemp = dx(ix) dx(ix) = dy(iy) dy(iy) = dtemp ix = ix + incx iy = iy + incy 10 continue return c c code for both increments equal to 1 c c c clean-up loop c 20 m = mod(n,3) if( m .eq. 0 ) go to 40 do 30 i = 1,m dtemp = dx(i) dx(i) = dy(i) dy(i) = dtemp 30 continue if( n .lt. 3 ) return 40 mp1 = m + 1 do 50 i = mp1,n,3 dtemp = dx(i) dx(i) = dy(i) dy(i) = dtemp dtemp = dx(i + 1) dx(i + 1) = dy(i + 1) dy(i + 1) = dtemp dtemp = dx(i + 2) dx(i + 2) = dy(i + 2) dy(i + 2) = dtemp 50 continue return end integer function idamax(n,dx,incx) c c finds the index of element having max. absolute value. c jack dongarra, linpack, 3/11/78. c double precision dx(*),dmax integer i,incx,ix,n c idamax = 0 if( n .lt. 1 ) return idamax = 1 if(n.eq.1)return if(incx.eq.1)go to 20 c c code for increment not equal to 1 c ix = 1 dmax = dabs(dx(1)) ix = ix + incx do 10 i = 2,n if(dabs(dx(ix)).le.dmax) go to 5 idamax = i dmax = dabs(dx(ix)) 5 ix = ix + incx 10 continue return c c code for increment equal to 1 c 20 dmax = dabs(dx(1)) do 30 i = 2,n if(dabs(dx(i)).le.dmax) go to 30 idamax = i dmax = dabs(dx(i)) 30 continue return end test.dump0100700001204700017620000012110106617643307013000 0ustar jphughesfacultytest structure 3 .Data list 9 id integer 500 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16 16 16 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 19 19 19 19 19 19 19 19 19 19 20 20 20 20 20 20 20 20 20 20 21 21 21 21 21 21 21 21 21 21 22 22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 24 24 24 24 24 24 24 24 24 24 25 25 25 25 25 25 25 25 25 25 26 26 26 26 26 26 26 26 26 26 27 27 27 27 27 27 27 27 27 27 28 28 28 28 28 28 28 28 28 28 29 29 29 29 29 29 29 29 29 29 30 30 30 30 30 30 30 30 30 30 31 31 31 31 31 31 31 31 31 31 32 32 32 32 32 32 32 32 32 32 33 33 33 33 33 33 33 33 33 33 34 34 34 34 34 34 34 34 34 34 35 35 35 35 35 35 35 35 35 35 36 36 36 36 36 36 36 36 36 36 37 37 37 37 37 37 37 37 37 37 38 38 38 38 38 38 38 38 38 38 39 39 39 39 39 39 39 39 39 39 40 40 40 40 40 40 40 40 40 40 41 41 41 41 41 41 41 41 41 41 42 42 42 42 42 42 42 42 42 42 43 43 43 43 43 43 43 43 43 43 44 44 44 44 44 44 44 44 44 44 45 45 45 45 45 45 45 45 45 45 46 46 46 46 46 46 46 46 46 46 47 47 47 47 47 47 47 47 47 47 48 48 48 48 48 48 48 48 48 48 49 49 49 49 49 49 49 49 49 49 50 50 50 50 50 50 50 50 50 50 X.1 numeric 500 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X.2 numeric 500 0 1.9689124338328838 3.9851707872003317 5.2258632853627205 7.1674287179484963 10.992215045727789 12.759576045908034 14.868322405032814 16.215922550298274 17.160177292302251 0 1.1180776990950108 3.7420181483030319 6.6504926681518555 7.9738349597901106 10.652843913063407 11.146777094341815 14.00282078050077 15.114966799505055 17.643045781180263 0 2.6157550383359194 4.9887275984510779 6.1209687292575836 8.190641070716083 9.0764763746410608 12.199556766077876 13.84231318347156 16.444741952233016 18.053332454524934 0 1.2892928551882505 3.6986844511702657 5.9273072453215718 7.1491304393857718 10.831002705730498 11.888625879772007 13.570421258918941 16.864924718625844 18.895327731966972 0 2.9121254319325089 3.0053639654070139 5.7506635021418333 7.2543407268822193 9.1558698965236545 11.360657296143472 14.252251814119518 16.743367013521492 18.880199159495533 0 2.3407840095460415 3.3130730027332902 5.0747368624433875 7.4800448212772608 9.3947643572464585 12.055539139546454 13.989902251400054 15.916238159872591 18.129315882921219 0 1.2336910320445895 4.7424402423202991 6.0648756669834256 8.6593224443495274 10.661516055464745 12.438015083782375 13.637957754544914 15.606641876511276 18.839579591527581 0 1.4687451329082251 3.2023602798581123 6.0823120027780533 8.6367837833240628 9.9385820282623172 12.418768612667918 14.199422631412745 15.917527468875051 17.773107293061912 0 1.5287178298458457 4.4930853769183159 5.1911247251555324 8.1195585429668427 10.268292058259249 12.25794911198318 13.203350902535021 15.380376574583352 18.342003718949854 0 2.0708286920562387 4.2102315481752157 6.353276920504868 8.8592384736984968 10.806047464720905 11.275565613992512 14.278815606608987 16.384894417598844 18.611997782252729 0 2.6033290196210146 4.2297188322991133 5.6787429787218571 7.5193258626386523 9.7193115772679448 12.919807003811002 14.802221409976482 15.231553827412426 18.204322317615151 0 1.8918464789167047 3.553384336642921 6.6226537618786097 8.1203931905329227 9.3228516923263669 11.272839759476483 13.21973573230207 16.277270780876279 17.594885515980422 0 1.8045781198889017 3.345475759357214 6.9929611897096038 7.0821871645748615 9.3641818761825562 12.477375054731965 13.119392102584243 15.53038496337831 17.67184638325125 0 1.1166758229956031 3.0232084142044187 6.7322307368740439 8.894196530804038 10.479136193171144 12.561057085171342 13.840140363201499 16.918752593919635 17.702023610472679 0 2.8757903780788183 4.0582049330696464 5.9231369560584426 7.3588091051205993 10.798493202775717 12.318759481422603 14.481096520088613 15.306240260601044 18.650128553621471 0 1.5721898758783937 3.8613555459305644 5.5887738764286041 7.2778329961001873 9.827675056643784 11.820478511974216 14.338154599070549 16.994280310347676 18.233715553767979 0 1.2807146292179823 4.8919241167604923 5.3684282153844833 8.5878104418516159 9.4783446108922362 12.129691096954048 13.70334040094167 15.032174513675272 17.916667361743748 0 2.5555877462029457 3.604129015468061 5.0829665809869766 7.2813654104247689 9.1812652284279466 11.284365579485893 13.617285578511655 16.768424007110298 18.36014278139919 0 2.1741203395649791 3.0101366732269526 6.6151660736650229 7.4599655456840992 9.8096832493320107 11.468656807206571 14.353068009950221 16.543783824890852 18.821127272211015 0 2.1791580244898796 4.7304480001330376 5.0409424286335707 8.2918830933049321 10.908003649674356 11.92694238293916 14.06482667196542 15.932209787890315 17.008132207207382 0 2.6262495527043939 3.7507430305704474 6.358933481387794 8.3475173749029636 10.401890326291323 11.842144064605236 13.022438638843596 15.058043861761689 18.60377215500921 0 1.809678977355361 4.917498386465013 6.8914431612938643 8.1574069419875741 10.438654381781816 11.973373834975064 14.148001942783594 16.636669360101223 17.546317601576447 0 1.0423023207113147 4.0290499981492758 5.5629867278039455 8.6760052917525172 9.1285541243851185 12.272226702421904 14.170565657317638 15.354660981334746 18.430518949404359 0 2.423466308042407 3.3535511819645762 6.7522577680647373 8.7569912048056722 9.4486157735809684 12.054009068757296 14.860778861679137 16.990265962667763 17.024199220351875 0 2.215515810996294 3.4657079661265016 5.9856320451945066 7.3068176852539182 9.8892744174227118 12.75565876532346 13.735232448205352 15.436753281392157 18.776775634847581 0 2.0393614945933223 4.3317445814609528 5.2928142165765166 7.4077642122283578 10.659664806909859 12.564011367037892 13.248282447457314 15.570676101371646 17.578473378904164 0 1.7529070442542434 4.3389701535925269 6.9695288455113769 8.6332401102408767 10.672374618239701 11.50003045424819 13.995182902552187 15.126981330104172 18.192839995957911 0 1.1284796427935362 4.2302149785682559 6.9126932974904776 8.5164379319176078 10.190976861864328 11.863953927531838 13.451510051265359 15.253169786185026 18.89619215298444 0 2.9329490065574646 4.4710146943107247 5.9167258394882083 8.1357910139486194 10.804225729778409 12.687731130048633 14.810636078007519 16.490196762606502 18.492776746861637 0 2.9587348978966475 4.0055805025622249 6.3911269502714276 7.2781385285779834 9.7255313908681273 11.994256690144539 13.916450099088252 15.176978254690766 17.747132752090693 0 2.5378952194005251 4.3866067752242088 6.5426448248326778 7.5214484743773937 10.176104076206684 12.631151767447591 14.097834376618266 15.454911423847079 18.606160135008395 0 1.6250922549515963 3.4737294400110841 6.8210345953702927 7.217225318774581 10.280452241189778 12.625380312092602 14.542113339528441 16.444898443296552 18.908647120930254 0 2.6314144497737288 4.3333717286586761 5.8115262314677238 7.0242060637101531 9.6925689904019237 11.597383517771959 13.385339375585318 16.347461551427841 18.694630585610867 0 1.1254470851272345 4.2608036128804088 6.1903666844591498 7.7412815541028976 10.047761874273419 12.023606597445905 13.08100575953722 15.992623734287918 18.404131794348359 0 1.6285012792795897 3.9703527633100748 5.8972154948860407 8.0110588883981109 10.339680716395378 11.974855206906796 14.220517647452652 15.524232708849013 17.85230175871402 0 1.5714943530037999 4.1849299520254135 5.8003812804818153 8.1572088580578566 10.281901731155813 12.588701984845102 13.462191901169717 16.540073338896036 17.606435546651483 0 1.8544381996616721 3.25537427701056 6.9293172899633646 7.3276684917509556 9.1057603787630796 11.824375408701599 13.998349261470139 15.222485393285751 18.261204995214939 0 2.4665987491607666 4.3272526795044541 6.8326859781518579 7.5558599112555385 9.2292511183768511 11.452494620345533 13.265990369021893 15.554199830628932 17.047022673301399 0 2.212244869209826 4.6400311021134257 6.5332748014479876 8.7579363128170371 10.34065430611372 11.158647477626801 13.234115516766906 15.431289506144822 17.411710163578391 0 2.9495928781107068 3.6753023341298103 6.6704428642988205 8.3609637059271336 10.654623507522047 11.133884680457413 13.041667654179037 16.618442621082067 17.808704631403089 0 2.1841458594426513 4.2661936609074473 5.7829288579523563 7.2203010069206357 10.898205507546663 12.862244005315006 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458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 class character 1 data.frame censre.test0100700001204700017620000000066010322764730013310 0ustar jphughesfacultydata.restore("test.dump") source("censre2.s") #dyn.load.shared("censre2.so") temp <- censre2(test$id, test$c, test$q, cbind(test$X.1,test$X.2,test$X.3), cbind(test$Z.1,test$Z.2), eps=.005, nsize=500, D=matrix(c(1,.095,.095,.1),2,2), sigma=1.0, silent=F, iseed=(-11)) temp censre.test.out0100700001204700017620000001656306720025001014113 0ustar jphughesfacultyS-PLUS : Copyright (c) 1988, 1995 MathSoft, Inc. S : Copyright AT&T. Version 3.3 Release 1 for DEC alpha, OSF1 V3.2 : 1995 Working data will be in .Data Current search list is: [1] ".Data" "/t0/hughes/.Data" [3] "/usr/local/splus/splus/.Functions" "/usr/local/splus/stat/.Functions" [5] "/usr/local/splus/s/.Functions" "/usr/local/splus/s/.Datasets" [7] "/usr/local/splus/stat/.Datasets" "/usr/local/splus/splus/.Datasets" [9] "/t2/courtois/library/fexact/.Data" > data.restore("test.dump") [1] "test.dump" > source("censre2.s") > censre2 <- function(id, C, Q, X, Z, alpha, D, sigma, eps = 0.001, nsize = 500, burnin = 25, silent = F, iseed) { # Purpose: Implements Monte Carlo EM estimator for mixed effects model with # left and/or right censored data. Assumes normal errors and # normal distributions for random effects. # # Required: # id = unique identifier for each individual/unit # # C = censoring indicator; C = -1 means left censored, C = 0 means # uncensored, C = 1 means right censored # # Q = response variable; if C = 0, Q is the uncensored observation; if # C != 0, Q is the censoring level # # X = design matrix for fixed effects; generate using model.matrix or # by hand # # Z = design matrix for random effects; generate using model.matrix or # by hand # # alpha = initial values for fixed effects (optional) # # D = initial guess for the covariance matrix of the random effects # # S = initial guess for the within-subject residual variance # # Optional: # eps = max. relative change in parameters between successive iterates # to achieve convergence; typically this will be larger than one # might use in a deterministic algorithm # # nsize = starting number of Monte Carlo samples to compute expected # sufficient statistics on each person during E-step; this # number is doubled if the absolute change in any parameter is # less than the estimated Monte Carlo standard error for that # parameter # # burnin = number of Monte Carlo samples to discard during Gibbs # sampling; the sampler typically burns in quite rapidly # in this application # # silent = if T, do not display intermediate results # # iseed = random number seed (a negative integer) # # Reference: Hughes JP. Mixed effects models with censored data with # application to HIV RNA levels. Biometrics, in press, 1999. # nsubj <- length(unique(id)) n <- rle(id)$lengths p <- ncol(X) q <- ncol(Z) sumn <- sum(n) if(missing(alpha)) alpha <- solve(t(X) %*% X) %*% t(X) %*% Q info <- matrix(0, p, p) storage.mode(X) <- "double" storage.mode(Z) <- "double" storage.mode(D) <- "double" storage.mode(info) <- "double" zzz <- .Fortran("censre2", as.integer(burnin), as.integer(nsize), as.integer(nsubj), as.integer(sumn), as.integer(n), as.integer(p), as.integer(q), X, Z, as.double(Q), as.integer(C), alpha = as.double(alpha), D = D, sigma = as.double(sigma), info = info, as.integer(silent), as.double(eps), as.integer(iseed)) var.alpha <- solve(zzz$info) list(alpha = zzz$alpha, D = zzz$D, sigma = zzz$sigma, var = var.alpha) # list(alpha=zzz$alpha,D=zzz$D,sigma=zzz$sigma) } Warning messages: assigning "censre2" masks an object of the same name on database 3 > dyn.load.shared("censre2.so") > temp <- censre2(test$id, + test$c, + test$q, + cbind(test$X.1,test$X.2,test$X.3), + cbind(test$Z.1,test$Z.2), + eps=.005, + nsize=500, + D=matrix(c(1,.095,.095,.1),2,2), + sigma=1.0, + silent=F, + iseed=(-11)) newa [1] 3.0220344 -0.1311881 0.8583855 newD [1] 1.11986723 0.04069861 newD [1] 0.04069861 0.06293572 newS [1] 1.021475 Relative change in parameters [1] 0.05573236 0.89984646 0.14206662 0.11986723 0.57159358 0.37064281 0.02147471 Monte Carlo sample size decreased to [1] 250 newa [1] 3.0109581 -0.1315123 0.8888658 newD [1] 1.23332486 0.03377116 newD [1] 0.03377116 0.05022267 newS [1] 1.017916 Relative change in parameters [1] 0.003665177 0.002471276 0.035508838 0.101313470 0.170213536 0.202000534 [7] 0.003484021 Monte Carlo sample size increased to [1] 500 newa [1] 3.0102804 -0.1313255 0.8980813 newD [1] 1.30340202 0.03741478 newD [1] 0.03741478 0.05056121 newS [1] 1.018999 Relative change in parameters [1] 0.0002250709 0.0014202551 0.0103677550 0.0568197032 0.1078916268 [6] 0.0067407104 0.0010643857 Monte Carlo sample size increased to [1] 1000 newa [1] 3.0076149 -0.1316037 0.9006580 newD [1] 1.34183216 0.03286326 newD [1] 0.03286326 0.04888073 newS [1] 1.017061 Relative change in parameters [1] 0.0008854958 0.0021181347 0.0028690879 0.0294844889 0.1216502151 [6] 0.0332365390 0.0019020244 newa [1] 3.0100645 -0.1311949 0.8976917 newD [1] 1.36681383 0.03140379 newD [1] 0.03140379 0.04811899 newS [1] 1.016042 Relative change in parameters [1] 0.000814473 0.003106279 0.003293431 0.018617585 0.044410417 0.015583673 [7] 0.001002118 newa [1] 3.0049568 -0.1306040 0.9061026 newD [1] 1.37709300 0.03092927 newD [1] 0.03092927 0.04778201 newS [1] 1.016735 Relative change in parameters [1] 0.0016968793 0.0045036345 0.0093694241 0.0075205295 0.0151103894 [6] 0.0070030158 0.0006816457 newa [1] 3.0071872 -0.1304387 0.9014636 newD [1] 1.38589448 0.03092932 newD [1] 0.03092932 0.04765308 newS [1] 1.016623 Relative change in parameters [1] 7.422518e-04 1.265985e-03 5.119683e-03 6.391353e-03 1.528402e-06 [6] 2.698268e-03 1.094499e-04 Monte Carlo sample size increased to [1] 2000 newa [1] 3.0076129 -0.1303791 0.8995032 newD [1] 1.39082297 0.03121465 newD [1] 0.03121465 0.04779050 newS [1] 1.014485 Relative change in parameters [1] 0.0001415517 0.0004566340 0.0021747195 0.0035561801 0.0092254247 [6] 0.0028837511 0.0021028907 Monte Carlo sample size increased to [1] 4000 newa [1] 3.0081752 -0.1307085 0.9020637 newD [1] 1.38928681 0.03154907 newD [1] 0.03154907 0.04809893 newS [1] 1.014443 Relative change in parameters [1] 1.869740e-04 2.526156e-03 2.846525e-03 1.104501e-03 1.071350e-02 [6] 6.453837e-03 4.178802e-05 Monte Carlo sample size increased to [1] 8000 newa [1] 3.0070910 -0.1306663 0.9023662 newD [1] 1.3885809 0.0313066 newD [1] 0.03130660 0.04791235 newS [1] 1.014583 Relative change in parameters [1] 0.0003604330 0.0003226702 0.0003353217 0.0005081180 0.0076855589 [6] 0.0038790285 0.0001380574 Monte Carlo sample size increased to [1] 16000 newa [1] 3.0074398 -0.1306152 0.9018959 newD [1] 1.38911511 0.03155595 newD [1] 0.03155595 0.04792641 newS [1] 1.014358 Relative change in parameters [1] 0.0001160009 0.0003912374 0.0005211302 0.0003847268 0.0079649192 [6] 0.0002933256 0.0002223062 Monte Carlo sample size increased to [1] 32000 newa [1] 3.0071304 -0.1305670 0.9019944 newD [1] 1.38920770 0.03143713 newD [1] 0.03143713 0.04794335 newS [1] 1.014723 Relative change in parameters [1] 1.028720e-04 3.690885e-04 1.092170e-04 6.665699e-05 3.765607e-03 [6] 3.535322e-04 3.608023e-04 > temp $alpha: [1] 3.0074398 -0.1306152 0.9018959 $D: [,1] [,2] [1,] 1.38911511 0.03155595 [2,] 0.03155595 0.04792641 $sigma: [1] 1.014358 $var: [,1] [,2] [,3] [1,] 0.0712484026 -1.184542e-04 -7.123083e-02 [2,] -0.0001184542 1.090985e-03 -4.339122e-05 [3,] -0.0712308302 -4.339122e-05 1.435767e-01 > q() # end-of-file