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GLMnet.f
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c
c GLMnet (5/17/08)
c
c
c Elastic net with squared-error loss
c
c dense predictor matrix:
c
c call elnet(ka,parm,no,ni,x,y,w,jd,vp,ne,nx,nlam,flmin,ulam,thr,isd,
c lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
c
c x(no,ni) = predictor data matrix flat file
c
c
c sparse predictor matrix:
c
c call spelnet(ka,parm,no,ni,x,ix,jx,y,w,jd,vp,ne,nx,nlam,flmin,ulam,thr,
c isd,lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
c
c x, ix, jx = predictor data matrix in compressed sparse column format
c
c
c other inputs:
c
c ka = algorithm flag
c ka=1 => covariance updating algorithm
c ka=2 => naive algorithm
c parm = family member index (0 <= parm <= 1)
c = 0.0 => ridge
c = 1.0 => lasso
c no = number of observations
c ni = number of predictor variables
c y(no) = response vector
c w(no)= observation weights
c jd(jd(1)+1) = predictor variable deletion flag
c jd(1) = 0 => use all variables
c jd(1) != 0 => do not use variables jd(2)...jd(jd(1)+1)
c vp(ni) = relative penalties for each predictor variable
c vp(j) = 0 => jth variable unpenalized
c ne = maximum number of variables allowed to enter largest model
c (stopping criterion)
c nx = maximum number of variables allowed to enter all models
c along path (memory allocation, nx > ne).
c nlam = (maximum) number of lamda values
c flmin = user control of lamda values (>=0)
c flmin < 1.0 => minimum lamda = flmin*(largest lamda value)
c flmin >= 1.0 => use supplied lamda values (see below)
c ulam(nlam) = user supplied lamda values (ignored if flmin < 1.0)
c thr = convergence threshold for each lamda solution.
c iterations stop when the maximum standardized coefficient
c change from the previous iteration is less than thr
c (suggested value, thr=1.0e-4)
c isd = standarization flag:
c isd = 0 => regression on original predictor variables
c isd = 1 => regression on standardized predictor variables
c Note: output solutions always reference original
c variables locations and scales.
c
c output:
c
c lmu = actual number of lamda values (solutions)
c a0(lmu) = intercept values for each solution
c ca(nx,lmu) = compressed coefficient values for each solution
c ia(nx) = pointers to compressed coefficients
c nin(lmu) = number of compressed coefficients for each solution
c rsq(lmu) = R**2 values for each solution
c alm(lmu) = lamda values corresponding to each solution
c nlp = total passes over the data summed over all lamda values
c jerr = error flag:
c jerr = 0 => no error
c jerr != 0 => fatal error - no output returned
c jerr < 7777 => memory allocation error
c jerr = 7777 => all used predictors have zero variance
c jerr = 10000 => maxval(vp) <= 0.0
c
c
c Note: x, y and w are overwritten by programs
c
c
c least-squares utility routines:
c
c uncompress coefficient vector for particular solution:
c
c call uncomp(ni,ca,ia,nin,a)
c
c input:
c
c ni = total number of predictor variables
c ca(nx) = compressed coefficient values for the solution
c ia(nx) = pointers to compressed coefficients
c nin = number of compressed coefficients for the solution
c
c output:
c
c a(ni) = uncompressed coefficient vector
c referencing original variables
c
c
c evaluate linear model from compressed coefficients and
c uncompressed predictor matrix:
c
c call modval(a0,ca,ia,nin,n,x,f);
c
c input:
c
c a0 = intercept
c ca(nx) = compressed coefficient values for a solution
c ia(nx) = pointers to compressed coefficients
c nin = number of compressed coefficients for solution
c n = number of predictor vectors (observations)
c x(n,ni) = full (uncompressed) predictor matrix
c
c output:
c
c f(n) = model predictions
c
c
c evaluate linear model from compressed coefficients and
c compressed predictor matrix:
c
c call cmodval(a0,ca,ia,nin,x,ix,jx,n,f);
c
c input:
c
c a0 = intercept
c ca(nx) = compressed coefficient values for a solution
c ia(nx) = pointers to compressed coefficients
c nin = number of compressed coefficients for solution
c x, ix, jx = predictor matrix in compressed sparse row format
c n = number of predictor vectors (observations)
c
c output:
c
c f(n) = model predictions
c
c
c
c
c Symmetric binomial/multinomial logistic elastic net
c
c
c dense predictor matrix:
c
c call lognet (parm,no,ni,nc,x,y,jd,vp,ne,nx,nlam,flmin,ulam,thr,isd,
c maxit,kopt,lmu,a0,ca,ia,nin,dev,alm,nlp,jerr)
c
c x(no,ni) = predictor data matrix flat file
c
c
c sparse predictor matrix:
c
c call splognet (parm,no,ni,nc,x,ix,jx,y,jd,vp,ne,nx,nlam,flmin,
c ulam,thr,isd,maxit,kopt,lmu,a0,ca,ia,nin,dev,alm,nlp,jerr)
c
c x, ix, jx = predictor data matrix in compressed sparse column format
c
c
c other inputs:
c
c parm, no, ni, jd, vp, ne, nx, nlam, flmin, ulam, thr, isd, same as above.
c
c nc = number of classes (distinct outcome values)
c nc=1 => binomial two-class logistic regression
c (all output references class 1)
c y(no,max(2,nc)) = number of each class at each design point(overwritten)
c maxit = maximum number of iterations allowed for any lamda value
c (suggested value, maxit = 100)
c kopt = optimization flag
c kopt = 0 => Newton-Raphson
c kpot = 1 => modified Newton-Raphson (recommended)
c
c
c output:
c
c lmu, ia, nin, alm, nlp, same as above
c
c a0(nc,lmu) = intercept values for each class at each solution
c ca(nx,nc,lmu) = compressed coefficient values for each class at
c each solution
c dev(lmu) = fraction of explained devience for each solution
c jerr = error flag
c jerr = 0 => no error
c jerr > 0 => fatal error - no output returned
c jerr < 7777 => memory allocation error
c jerr = 7777 => all used predictors have zero variance
c jerr = 8000 + k => null probability < 1.0e-5 for class k
c jerr = 9000 + k => null probability for class k
c > 1.0 - 1.0e-5
c jerr = 10000 => maxval(vp) <= 0.0
C jerr < 0 => non fatal error - partial output returned
c jerr = -k => convergence for kth lamda value not reached
c after maxit (see above) iterations. Solutions for
c larger lamdas returned
c jerr = -10000-k => number of non zero coefficients along path
c exceeds nx (see above) at kth lamda value. Solutions for
c larger lamdas returned
c
c
c
c logistic utilitity routines:
c
c uncompress coefficient vector for particular solution:
c
c call luncomp(ni,nx,nc,ca,ia,nin,a)
c
c input:
c
c ni, nx, nc = same as above
c ca(nx,nc) = compressed coefficient values (for each class)
c ia(nx) = pointers to compressed coefficients
c nin = number of compressed coefficients
c
c output:
c
c a(ni,nc) = uncompressed coefficient vectors
c referencing original variables
c
c
c evaluate linear model from compressed coefficients and
c uncompressed predictor vectors:
c
c call lmodval(nt,x,nc,nx,a0,ca,ia,nin,ans);
c
c input:
c
c nt = number of observations
c x(nt,ni) = full (uncompressed) predictor vectors
c nc, nx = same as above
c a0(nc) = intercepts
c ca(nx,nc) = compressed coefficient values (for each class)
c ia(nx) = pointers to compressed coefficients
c nin = number of compressed coefficients
c
c output:
c
c ans(nc,nt) = model predictions
c
c
c evaluate linear model from compressed coefficients and
c compressed predictor matrix:
c
c call lcmodval(nc,nx,a0,ca,ia,nin,x,ix,jx,n,f);
c
c input:
c
c nc, nx = same as above
c a0(nc) = intercept
c ca(nx,nc) = compressed coefficient values for a solution
c ia(nx) = pointers to compressed coefficients
c nin = number of compressed coefficients for solution
c x, ix, jx = predictor matrix in compressed sparse row format
c n = number of predictor vectors (observations)
c
c output:
c
c f(nc,n) = model predictions
c
c
c
c
subroutine elnet (ka,parm,no,ni,x,y,w,jd,vp,ne,nx,nlam,flmin,ulam 352
*,thr,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
real x(no,ni),y(no),w(no),vp(ni),ca(nx,nlam) 353
real ulam(nlam),a0(nlam),rsq(nlam),alm(nlam) 354
integer jd(*),ia(nx),nin(nlam) 355
real, dimension (:), allocatable :: vq;
if(maxval(vp) .gt. 0.0)goto 10021 358
jerr=10000 358
return 358
10021 continue 359
allocate(vq(1:ni),stat=jerr) 359
if(jerr.ne.0) return 360
vq=max(0.0,vp) 360
vq=vq*ni/sum(vq) 361
if(ka .ne. 1)goto 10041 362
call elnetu (parm,no,ni,x,y,w,jd,vq,ne,nx,nlam,flmin,ulam,thr,isd 365
*, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
goto 10051 366
10041 continue 367
call elnetn (parm,no,ni,x,y,w,jd,vq,ne,nx,nlam,flmin,ulam,thr,isd, 370
* lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
10051 continue 371
10031 continue 371
deallocate(vq) 372
return 373
end 374
subroutine elnetu (parm,no,ni,x,y,w,jd,vp,ne,nx,nlam,flmin,ulam,t 377
*hr,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
real x(no,ni),y(no),w(no),vp(ni),ulam(nlam) 378
real ca(nx,nlam),a0(nlam),rsq(nlam),alm(nlam) 379
integer jd(*),ia(nx),nin(nlam) 380
real, dimension (:), allocatable :: xm,xs,g,xv,vlam
integer, dimension (:), allocatable :: ju
allocate(g(1:ni),stat=jerr) 385
allocate(xm(1:ni),stat=ierr) 385
jerr=jerr+ierr 386
allocate(xs(1:ni),stat=ierr) 386
jerr=jerr+ierr 387
allocate(ju(1:ni),stat=ierr) 387
jerr=jerr+ierr 388
allocate(xv(1:ni),stat=ierr) 388
jerr=jerr+ierr 389
allocate(vlam(1:nlam),stat=ierr) 389
jerr=jerr+ierr 390
if(jerr.ne.0) return 391
call chkvars(no,ni,x,ju) 392
if(jd(1).gt.0) ju(jd(2:(jd(1)+1)))=0 393
if(maxval(ju) .gt. 0)goto 10071 393
jerr=7777 393
return 393
10071 continue 394
call standard(no,ni,x,y,w,isd,ju,g,xm,xs,ym,ys,xv,jerr) 395
if(jerr.ne.0) return 396
if(flmin.ge.1.0) vlam=ulam/ys 397
call elnet1(parm,ni,ju,vp,g,no,ne,nx,x,nlam,flmin,vlam,thr,xv, lm 399
*u,ca,ia,nin,rsq,alm,nlp,jerr)
if(jerr.ne.0) return 400
10080 do 10081 k=1,lmu 400
alm(k)=ys*alm(k) 400
nk=nin(k) 401
10090 do 10091 l=1,nk 401
ca(l,k)=ys*ca(l,k)/xs(ia(l)) 401
10091 continue 402
10092 continue 402
a0(k)=ym-dot_product(ca(1:nk,k),xm(ia(1:nk))) 403
10081 continue 404
10082 continue 404
deallocate(xm,xs,g,ju,xv,vlam) 405
return 406
end 407
subroutine standard (no,ni,x,y,w,isd,ju,g,xm,xs,ym,ys,xv,jerr) 408
real x(no,ni),y(no),w(no),g(ni),xm(ni),xs(ni),xv(ni) 408
integer ju(ni) 409
real, dimension (:), allocatable :: v
allocate(v(1:no),stat=jerr) 412
if(jerr.ne.0) return 413
w=w/sum(w) 413
v=sqrt(w) 414
10100 do 10101 j=1,ni 414
if(ju(j).eq.0)goto 10101 415
xm(j)=dot_product(w,x(:,j)) 415
x(:,j)=v*(x(:,j)-xm(j)) 416
xv(j)=dot_product(x(:,j),x(:,j)) 417
10101 continue 418
10102 continue 418
if(isd .ne. 0)goto 10121 418
xs=1.0 418
goto 10131 419
10121 continue 420
10140 do 10141 j=1,ni 420
if(ju(j).eq.0)goto 10141 420
xs(j)=sqrt(xv(j)) 420
x(:,j)=x(:,j)/xs(j) 420
10141 continue 421
10142 continue 421
xv=1.0 422
10131 continue 423
10111 continue 423
ym=dot_product(w,y) 423
y=v*(y-ym) 423
ys=sqrt(dot_product(y,y)) 423
y=y/ys 423
g=0.0 424
10150 do 10151 j=1,ni 424
if(ju(j).ne.0) g(j)=dot_product(y,x(:,j)) 424
10151 continue 425
10152 continue 425
deallocate(v) 426
return 427
end 428
subroutine elnet1 (beta,ni,ju,vp,g,no,ne,nx,x,nlam,flmin,ulam,thr, 430
*xv, lmu,ao,ia,kin,rsqo,almo,nlp,jerr)
parameter(sml=1.0e-5, eps=1.0e-6, big=9.9e30, mnlam=5, rsqmax=0.99 431
*9)
real vp(ni),g(ni),x(no,ni),ulam(nlam),ao(nx,nlam),rsqo(nlam),almo( 432
*nlam),xv(ni)
integer ju(ni),ia(nx),kin(nlam) 433
real, dimension (:), allocatable :: a,da
integer, dimension (:), allocatable :: mm
real, dimension (:,:), allocatable :: c
allocate(c(1:ni,1:nx),stat=jerr)
allocate(a(1:ni),stat=ierr) 439
jerr=jerr+ierr 440
allocate(mm(1:ni),stat=ierr) 440
jerr=jerr+ierr 441
allocate(da(1:ni),stat=ierr) 441
jerr=jerr+ierr 442
if(jerr.ne.0) return 443
bta=max(beta,1.0e-3) 443
omb=1.0-bta 444
if(flmin .ge. 1.0)goto 10171 444
eqs=max(eps,flmin) 444
alf=eqs**(1.0/(nlam-1)) 444
10171 continue 445
rsq=0.0 445
a=0.0 445
mm=0 445
nlp=0 445
nin=nlp 445
iz=0 445
mnl=min(mnlam,nlam) 446
10180 do 10181 m=1,nlam 447
if(flmin .lt. 1.0)goto 10201 447
alm=ulam(m) 447
goto 10191 448
10201 if(m .le. 2)goto 10211 448
alm=alm*alf 448
goto 10191 449
10211 if(m .ne. 1)goto 10221 449
alm=big 449
goto 10231 450
10221 continue 450
alm=0.0 451
10240 do 10241 j=1,ni 451
if(ju(j).eq.0)goto 10241 451
if(vp(j).le.0.0)goto 10241 452
alm=max(alm,abs(g(j))/vp(j)) 453
10241 continue 454
10242 continue 454
alm=alf*alm/bta 455
10231 continue 456
10191 continue 456
dem=alm*omb 456
ab=alm*bta 456
rsq0=rsq 456
jz=1 457
10250 continue 457
10251 continue 457
if(iz*jz.ne.0) go to 10260 457
nlp=nlp+1 457
dlx=0.0 458
10270 do 10271 k=1,ni 458
if(ju(k).eq.0)goto 10271 459
ak=a(k) 459
u=g(k)+ak*xv(k) 459
v=abs(u)-vp(k)*ab 459
a(k)=0.0 460
if(v.gt.0.0) a(k)=sign(v,u)/(xv(k)+vp(k)*dem) 461
if(a(k).eq.ak)goto 10271 462
if(mm(k) .ne. 0)goto 10291 462
nin=nin+1 462
if(nin.gt.nx)goto 10272 463
10300 do 10301 j=1,ni 463
if(ju(j).eq.0)goto 10301 464
if(mm(j) .eq. 0)goto 10321 464
c(j,nin)=c(k,mm(j)) 464
goto 10301 464
10321 continue 465
if(j .ne. k)goto 10341 465
c(j,nin)=xv(j) 465
goto 10301 465
10341 continue 466
c(j,nin)=dot_product(x(:,j),x(:,k)) 467
10301 continue 468
10302 continue 468
mm(k)=nin 468
ia(nin)=k 469
10291 continue 470
del=a(k)-ak 470
rsq=rsq+del*(2.0*g(k)-del*xv(k)) 471
dlx=max(abs(del)/sqrt(xv(k)),dlx) 472
10350 do 10351 j=1,ni 472
if(ju(j).ne.0) g(j)=g(j)-c(j,mm(k))*del 472
10351 continue 473
10352 continue 473
10271 continue 474
10272 continue 474
if(dlx.lt.thr)goto 10252 474
if(nin.gt.nx)goto 10252 475
10260 continue 475
iz=1 475
da(1:nin)=a(ia(1:nin)) 476
10360 continue 476
10361 continue 476
nlp=nlp+1 476
dlx=0.0 477
10370 do 10371 l=1,nin 477
k=ia(l) 477
ak=a(k) 477
u=g(k)+ak*xv(k) 477
v=abs(u)-vp(k)*ab 478
a(k)=0.0 479
if(v.gt.0.0) a(k)=sign(v,u)/(xv(k)+vp(k)*dem) 480
if(a(k).eq.ak)goto 10371 481
del=a(k)-ak 481
rsq=rsq+del*(2.0*g(k)-del*xv(k)) 482
dlx=max(abs(del)/sqrt(xv(k)),dlx) 483
10380 do 10381 j=1,nin 483
g(ia(j))=g(ia(j))-c(ia(j),mm(k))*del 483
10381 continue 484
10382 continue 484
10371 continue 485
10372 continue 485
if(dlx.lt.thr)goto 10362 485
goto 10361 486
10362 continue 486
da(1:nin)=a(ia(1:nin))-da(1:nin) 487
10390 do 10391 j=1,ni 487
if(mm(j).ne.0)goto 10391 488
if(ju(j).ne.0) g(j)=g(j)-dot_product(da(1:nin),c(j,1:nin)) 489
10391 continue 490
10392 continue 490
jz=0 491
goto 10251 492
10252 continue 492
if(nin.gt.nx)goto 10182 493
if(nin.gt.0) ao(1:nin,m)=a(ia(1:nin)) 493
kin(m)=nin 494
rsqo(m)=rsq 494
almo(m)=alm 494
lmu=m 495
if(m.lt.mnl)goto 10181 495
if(flmin.ge.1.0)goto 10181 496
me=0 496
10400 do 10401 j=1,nin 496
if(ao(j,m).ne.0.0) me=me+1 496
10401 continue 496
10402 continue 496
if(me.gt.ne)goto 10182 497
if(rsq-rsq0.lt.sml*rsq)goto 10182 497
if(rsq.gt.rsqmax)goto 10182 498
10181 continue 499
10182 continue 499
deallocate(a,mm,c,da) 500
return 501
end 502
subroutine elnetn (parm,no,ni,x,y,w,jd,vp,ne,nx,nlam,flmin,ulam,th 504
*r,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
real vp(ni),x(no,ni),y(no),w(no),ulam(nlam) 505
real ca(nx,nlam),a0(nlam),rsq(nlam),alm(nlam) 506
integer jd(*),ia(nx),nin(nlam) 507
real, dimension (:), allocatable :: xm,xs,xv,vlam
integer, dimension (:), allocatable :: ju
allocate(xm(1:ni),stat=jerr) 512
allocate(xs(1:ni),stat=ierr) 512
jerr=jerr+ierr 513
allocate(ju(1:ni),stat=ierr) 513
jerr=jerr+ierr 514
allocate(xv(1:ni),stat=ierr) 514
jerr=jerr+ierr 515
allocate(vlam(1:nlam),stat=ierr) 515
jerr=jerr+ierr 516
if(jerr.ne.0) return 517
call chkvars(no,ni,x,ju) 518
if(jd(1).gt.0) ju(jd(2:(jd(1)+1)))=0 519
if(maxval(ju) .gt. 0)goto 10421 519
jerr=7777 519
return 519
10421 continue 520
call standard1(no,ni,x,y,w,isd,ju,xm,xs,ym,ys,xv,jerr) 521
if(jerr.ne.0) return 522
if(flmin.ge.1.0) vlam=ulam/ys 523
call elnet2(parm,ni,ju,vp,y,no,ne,nx,x,nlam,flmin,vlam,thr,xv, lm 525
*u,ca,ia,nin,rsq,alm,nlp,jerr)
if(jerr.ne.0) return 526
10430 do 10431 k=1,lmu 526
alm(k)=ys*alm(k) 526
nk=nin(k) 527
10440 do 10441 l=1,nk 527
ca(l,k)=ys*ca(l,k)/xs(ia(l)) 527
10441 continue 528
10442 continue 528
a0(k)=ym-dot_product(ca(1:nk,k),xm(ia(1:nk))) 529
10431 continue 530
10432 continue 530
deallocate(xm,xs,ju,xv,vlam) 531
return 532
end 533
subroutine standard1 (no,ni,x,y,w,isd,ju,xm,xs,ym,ys,xv,jerr) 534
real x(no,ni),y(no),w(no),xm(ni),xs(ni),xv(ni) 534
integer ju(ni) 535
real, dimension (:), allocatable :: v
allocate(v(1:no),stat=jerr) 538
if(jerr.ne.0) return 539
w=w/sum(w) 539
v=sqrt(w) 540
10450 do 10451 j=1,ni 540
if(ju(j).eq.0)goto 10451 541
xm(j)=dot_product(w,x(:,j)) 541
x(:,j)=v*(x(:,j)-xm(j)) 542
xv(j)=dot_product(x(:,j),x(:,j)) 543
10451 continue 544
10452 continue 544
if(isd .ne. 0)goto 10471 544
xs=1.0 544
goto 10481 545
10471 continue 545
10490 do 10491 j=1,ni 545
if(ju(j).eq.0)goto 10491 545
xs(j)=sqrt(xv(j)) 545
x(:,j)=x(:,j)/xs(j) 545
10491 continue 546
10492 continue 546
xv=1.0 547
10481 continue 548
10461 continue 548
ym=dot_product(w,y) 548
y=v*(y-ym) 548
ys=sqrt(dot_product(y,y)) 548
y=y/ys 549
deallocate(v) 550
return 551
end 552
subroutine elnet2(beta,ni,ju,vp,y,no,ne,nx,x,nlam,flmin,ulam,thr,x 554
*v, lmu,ao,ia,kin,rsqo,almo,nlp,jerr)
parameter(sml=1.0e-5, eps=1.0e-6, big=9.9e30, mnlam=5, rsqmax=0.99 555
*9)
real vp(ni),y(no),x(no,ni),ulam(nlam),ao(nx,nlam),rsqo(nlam),almo( 556
*nlam),xv(ni)
integer ju(ni),ia(nx),kin(nlam) 557
real, dimension (:), allocatable :: a
integer, dimension (:), allocatable :: mm
allocate(a(1:ni),stat=jerr) 562
allocate(mm(1:ni),stat=ierr) 562
jerr=jerr+ierr 563
if(jerr.ne.0) return 564
bta=max(beta,1.0e-3) 564
omb=1.0-bta 565
if(flmin .ge. 1.0)goto 10511 565
eqs=max(eps,flmin) 565
alf=eqs**(1.0/(nlam-1)) 565
10511 continue 566
rsq=0.0 566
a=0.0 566
mm=0 566
nlp=0 566
nin=nlp 566
iz=0 566
mnl=min(mnlam,nlam) 567
10520 do 10521 m=1,nlam 568
if(flmin .lt. 1.0)goto 10541 568
alm=ulam(m) 568
goto 10531 569
10541 if(m .le. 2)goto 10551 569
alm=alm*alf 569
goto 10531 570
10551 if(m .ne. 1)goto 10561 570
alm=big 570
goto 10571 571
10561 continue 571
alm=0.0 572
10580 do 10581 j=1,ni 572
if(ju(j).eq.0)goto 10581 572
if(vp(j).le.0.0)goto 10581 573
alm=max(alm,abs(dot_product(y,x(:,j)))/vp(j)) 574
10581 continue 575
10582 continue 575
alm=alf*alm/bta 576
10571 continue 577
10531 continue 577
dem=alm*omb 577
ab=alm*bta 577
rsq0=rsq 577
jz=1 578
10590 continue 578
10591 continue 578
if(iz*jz.ne.0) go to 10260 578
nlp=nlp+1 578
dlx=0.0 579
10600 do 10601 k=1,ni 579
if(ju(k).eq.0)goto 10601 579
gk=dot_product(y,x(:,k)) 580
ak=a(k) 580
u=gk+ak*xv(k) 580
v=abs(u)-vp(k)*ab 580
a(k)=0.0 581
if(v.gt.0.0) a(k)=sign(v,u)/(xv(k)+vp(k)*dem) 582
if(a(k).eq.ak)goto 10601 583
if(mm(k) .ne. 0)goto 10621 583
nin=nin+1 583
if(nin.gt.nx)goto 10602 584
mm(k)=nin 584
ia(nin)=k 585
10621 continue 586
del=a(k)-ak 586
rsq=rsq+del*(2.0*gk-del*xv(k)) 587
y=y-del*x(:,k) 587
dlx=max(abs(del)/sqrt(xv(k)),dlx) 588
10601 continue 589
10602 continue 589
if(dlx.lt.thr)goto 10592 589
if(nin.gt.nx)goto 10592 590
10260 continue 590
iz=1 591
10630 continue 591
10631 continue 591
nlp=nlp+1 591
dlx=0.0 592
10640 do 10641 l=1,nin 592
k=ia(l) 592
gk=dot_product(y,x(:,k)) 593
ak=a(k) 593
u=gk+ak*xv(k) 593
v=abs(u)-vp(k)*ab 593
a(k)=0.0 594
if(v.gt.0.0) a(k)=sign(v,u)/(xv(k)+vp(k)*dem) 595
if(a(k).eq.ak)goto 10641 596
del=a(k)-ak 596
rsq=rsq+del*(2.0*gk-del*xv(k)) 597
y=y-del*x(:,k) 597
dlx=max(abs(del)/sqrt(xv(k)),dlx) 598
10641 continue 599
10642 continue 599
if(dlx.lt.thr)goto 10632 599
goto 10631 600
10632 continue 600
jz=0 601
goto 10591 602
10592 continue 602
if(nin.gt.nx)goto 10522 603
if(nin.gt.0) ao(1:nin,m)=a(ia(1:nin)) 603
kin(m)=nin 604
rsqo(m)=rsq 604
almo(m)=alm 604
lmu=m 605
if(m.lt.mnl)goto 10521 605
if(flmin.ge.1.0)goto 10521 606
me=0 606
10650 do 10651 j=1,nin 606
if(ao(j,m).ne.0.0) me=me+1 606
10651 continue 606
10652 continue 606
if(me.gt.ne)goto 10522 607
if(rsq-rsq0.lt.sml*rsq)goto 10522 607
if(rsq.gt.rsqmax)goto 10522 608
10521 continue 609
10522 continue 609
deallocate(a,mm) 610
return 611
end 612
subroutine chkvars(no,ni,x,ju) 613
real x(no,ni) 613
integer ju(ni) 614
10660 do 10661 j=1,ni 614
ju(j)=0 614
t=x(1,j) 615
10670 do 10671 i=2,no 615
if(x(i,j).eq.t)goto 10671 615
ju(j)=1 615
goto 10672 615
10671 continue 616
10672 continue 616
10661 continue 617
10662 continue 617
return 618
end 619
subroutine uncomp(ni,ca,ia,nin,a) 620
real ca(*),a(ni) 620
integer ia(*) 621
a=0.0 621
if(nin.gt.0) a(ia(1:nin))=ca(1:nin) 622
return 623
end 624
subroutine modval(a0,ca,ia,nin,n,x,f) 625
real ca(nin),x(n,*),f(n) 625
integer ia(nin) 626
f=a0 626
if(nin.le.0) return 627
10680 do 10681 i=1,n 627
f(i)=f(i)+dot_product(ca(1:nin),x(i,ia(1:nin))) 627
10681 continue 628
10682 continue 628
return 629
end 630
subroutine spelnet (ka,parm,no,ni,x,ix,jx,y,w,jd,vp,ne,nx,nlam,fl 633
*min,ulam,thr,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
real x(*),y(no),w(no),vp(ni),ulam(nlam) 634
real ca(nx,nlam),a0(nlam),rsq(nlam),alm(nlam) 635
integer ix(*),jx(*),jd(*),ia(nx),nin(nlam) 636
real, dimension (:), allocatable :: vq;
if(maxval(vp) .gt. 0.0)goto 10701 639
jerr=10000 639
return 639
10701 continue 640
allocate(vq(1:ni),stat=jerr) 640
if(jerr.ne.0) return 641
vq=max(0.0,vp) 641
vq=vq*ni/sum(vq) 642
if(ka .ne. 1)goto 10721 643
call spelnetu (parm,no,ni,x,ix,jx,y,w,jd,vq,ne,nx,nlam,flmin,ulam 646
*,thr,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
goto 10731 647
10721 continue 648
call spelnetn (parm,no,ni,x,ix,jx,y,w,jd,vq,ne,nx,nlam,flmin,ulam, 651
*thr,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
10731 continue 652
10711 continue 652
deallocate(vq) 653
return 654
end 655
subroutine spelnetu (parm,no,ni,x,ix,jx,y,w,jd,vp,ne,nx,nlam,flmi 658
*n,ulam,thr,isd, lmu,a0,ca,ia,nin,rsq,alm,nlp,jerr)
real x(*),y(no),w(no),vp(ni),ulam(nlam) 659
real ca(nx,nlam),a0(nlam),rsq(nlam),alm(nlam) 660
integer ix(*),jx(*),jd(*),ia(nx),nin(nlam) 661
real, dimension (:), allocatable :: xm,xs,g,xv,vlam
integer, dimension (:), allocatable :: ju
allocate(g(1:ni),stat=jerr) 666
allocate(xm(1:ni),stat=ierr) 666
jerr=jerr+ierr 667
allocate(xs(1:ni),stat=ierr) 667
jerr=jerr+ierr 668
allocate(ju(1:ni),stat=ierr) 668
jerr=jerr+ierr 669
allocate(xv(1:ni),stat=ierr) 669
jerr=jerr+ierr 670
allocate(vlam(1:nlam),stat=ierr) 670
jerr=jerr+ierr 671
if(jerr.ne.0) return 672
call spchkvars(no,ni,x,ix,ju) 673
if(jd(1).gt.0) ju(jd(2:(jd(1)+1)))=0 674
if(maxval(ju) .gt. 0)goto 10751 674
jerr=7777 674
return 674
10751 continue 675
call spstandard(no,ni,x,ix,jx,y,w,ju,isd,g,xm,xs,ym,ys,xv,jerr) 676
if(jerr.ne.0) return 677
if(flmin.ge.1.0) vlam=ulam/ys 678
call spelnet1(parm,ni,g,no,w,ne,nx,x,ix,jx,ju,vp,nlam,flmin,vlam,t 680
*hr, xm,xs,xv,lmu,ca,ia,nin,rsq,alm,nlp,jerr)
if(jerr.ne.0) return 681
10760 do 10761 k=1,lmu 681
alm(k)=ys*alm(k) 681
nk=nin(k) 682
10770 do 10771 l=1,nk 682
ca(l,k)=ys*ca(l,k)/xs(ia(l)) 682
10771 continue 683
10772 continue 683
a0(k)=ym-dot_product(ca(1:nk,k),xm(ia(1:nk))) 684
10761 continue 685
10762 continue 685
deallocate(xm,xs,g,ju,xv,vlam) 686
return 687
end 688
subroutine spstandard (no,ni,x,ix,jx,y,w,ju,isd,g,xm,xs,ym,ys,xv,j 689
*err)
real x(*),y(no),w(no),g(ni),xm(ni),xs(ni),xv(ni) 689
integer ix(*),jx(*),ju(ni) 690
w=w/sum(w) 691
10780 do 10781 j=1,ni 691
if(ju(j).eq.0)goto 10781 692
jb=ix(j) 692
je=ix(j+1)-1 692
xm(j)=dot_product(w(jx(jb:je)),x(jb:je)) 693
xv(j)=dot_product(w(jx(jb:je)),x(jb:je)**2)-xm(j)**2 694
10781 continue 695
10782 continue 695
if(isd .ne. 0)goto 10801 695
xs=1.0 695
goto 10811 696
10801 continue 696
10820 do 10821 j=1,ni 696
if(ju(j).ne.0) xs(j)=sqrt(xv(j)) 696
10821 continue 696
10822 continue 696
xv=1.0 696
10811 continue 697
10791 continue 697
ym=dot_product(w,y) 697
y=y-ym 697
ys=sqrt(dot_product(w,y**2)) 697
y=y/ys 697
g=0.0 698
10830 do 10831 j=1,ni 698
if(ju(j).eq.0)goto 10831 698
jb=ix(j) 698
je=ix(j+1)-1 699
g(j)=dot_product(w(jx(jb:je))*y(jx(jb:je)),x(jb:je))/xs(j) 700
10831 continue 701
10832 continue 701
return 702
end 703
subroutine spelnet1(beta,ni,g,no,w,ne,nx,x,ix,jx,ju,vp,nlam,flmin, 705
*ulam, thr,xm,xs,xv,lmu,ao,ia,kin,rsqo,almo,nlp,jerr)
parameter(sml=1.0e-5, eps=1.0e-6, big=9.9e30, mnlam=5, rsqmax=0.99 706
*9)
real g(ni),vp(ni),x(*),ulam(nlam),w(no) 707
real ao(nx,nlam),rsqo(nlam),almo(nlam),xm(ni),xs(ni),xv(ni) 708
integer ix(*),jx(*),ju(ni),ia(nx),kin(nlam) 709
real, dimension (:), allocatable :: a,da
integer, dimension (:), allocatable :: mm
real, dimension (:,:), allocatable :: c
allocate(c(1:ni,1:nx),stat=jerr)
allocate(a(1:ni),stat=ierr) 715
jerr=jerr+ierr 716
allocate(mm(1:ni),stat=ierr) 716
jerr=jerr+ierr 717
allocate(da(1:ni),stat=ierr) 717
jerr=jerr+ierr 718
if(jerr.ne.0) return 719
bta=max(beta,1.0e-3) 719
omb=1.0-bta 720
if(flmin .ge. 1.0)goto 10851 720
eqs=max(eps,flmin) 720
alf=eqs**(1.0/(nlam-1)) 720
10851 continue 721
rsq=0.0 721
a=0.0 721
mm=0 721
nlp=0 721
nin=nlp 721
iz=0 721
mnl=min(mnlam,nlam) 722
10860 do 10861 m=1,nlam 723
if(flmin .lt. 1.0)goto 10881 723
alm=ulam(m) 723
goto 10871 724
10881 if(m .le. 2)goto 10891 724
alm=alm*alf 724
goto 10871 725
10891 if(m .ne. 1)goto 10901 725
alm=big 725
goto 10911 726
10901 continue 726
alm=0.0 727
10920 do 10921 j=1,ni 727
if(ju(j).eq.0)goto 10921 727
if(vp(j).le.0.0)goto 10921 728
alm=max(alm,abs(g(j))/vp(j)) 729
10921 continue 730
10922 continue 730
alm=alf*alm/bta 731
10911 continue 732
10871 continue 732
dem=alm*omb 732
ab=alm*bta 732
rsq0=rsq 732
jz=1 733
10930 continue 733
10931 continue 733
if(iz*jz.ne.0) go to 10260 733
nlp=nlp+1 733
dlx=0.0 734
10940 do 10941 k=1,ni 734
if(ju(k).eq.0)goto 10941 735
ak=a(k) 735
u=g(k)+ak*xv(k) 735
v=abs(u)-vp(k)*ab 735
a(k)=0.0 736
if(v.gt.0.0) a(k)=sign(v,u)/(xv(k)+vp(k)*dem) 737
if(a(k).eq.ak)goto 10941 738
if(mm(k) .ne. 0)goto 10961 738
nin=nin+1 738
if(nin.gt.nx)goto 10942 739
10970 do 10971 j=1,ni 739
if(ju(j).eq.0)goto 10971 740
if(mm(j) .eq. 0)goto 10991 740
c(j,nin)=c(k,mm(j)) 740
goto 10971 740
10991 continue 741
if(j .ne. k)goto 11011 741
c(j,nin)=xv(j) 741
goto 10971 741
11011 continue 742
c(j,nin)= (row_prod(j,k,ix,jx,x,w)-xm(j)*xm(k))/(xs(j)*xs(k)) 744
10971 continue 745
10972 continue 745
mm(k)=nin 745
ia(nin)=k 746
10961 continue 747
del=a(k)-ak 747
rsq=rsq+del*(2.0*g(k)-del*xv(k)) 748
dlx=max(abs(del)/sqrt(xv(k)),dlx) 749
11020 do 11021 j=1,ni 749
if(ju(j).ne.0) g(j)=g(j)-c(j,mm(k))*del 749
11021 continue 750
11022 continue 750
10941 continue 751
10942 continue 751
if(dlx.lt.thr)goto 10932 751
if(nin.gt.nx)goto 10932 752
10260 continue 752
iz=1 752
da(1:nin)=a(ia(1:nin)) 753
11030 continue 753
11031 continue 753
nlp=nlp+1 753
dlx=0.0 754
11040 do 11041 l=1,nin 754
k=ia(l) 755
ak=a(k) 755
u=g(k)+ak*xv(k) 755
v=abs(u)-vp(k)*ab 755
a(k)=0.0 756
if(v.gt.0.0) a(k)=sign(v,u)/(xv(k)+vp(k)*dem) 757
if(a(k).eq.ak)goto 11041 758
del=a(k)-ak 758
rsq=rsq+del*(2.0*g(k)-del*xv(k)) 759
dlx=max(abs(del)/sqrt(xv(k)),dlx) 760
11050 do 11051 j=1,nin 760
g(ia(j))=g(ia(j))-c(ia(j),mm(k))*del 760
11051 continue 761
11052 continue 761
11041 continue 762
11042 continue 762
if(dlx.lt.thr)goto 11032 762
goto 11031 763
11032 continue 763
da(1:nin)=a(ia(1:nin))-da(1:nin) 764
11060 do 11061 j=1,ni 764