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subroutine fprf2(iflag,ntot,nv,io,zero,s2,eps,al,imp,u,eta,mm1,jc,
& ic,r,a,e,rr,xpr,y,w1,w2)
c Copyright INRIA
implicit double precision (a-h,o-z)
common /fprf2c/ u1,nc
C the dimension is mm1*mm1 for r
dimension al(ntot), jc(mm1), ic(mm1), a(mm1), e(mm1), r(*),
& rr(mm1), xpr(mm1), y(mm1), w1(mm1), w2(mm1)
dimension i5(1), d3(1), d4(1)
C
C ***** on entry *****
C
C iflag=0-1 initialize on one subgradient (mu in)
C
C iflag=2 " " " " " " "
C and strive to enter by priority the
C points of the previous corral at the
C beginning of the iterations.
C
C iflag=3 initialize on the previous projection
C (with its corresponding corral)
C
C
C ***** on exit *****
C
C iflag=0 normal end
C
C 1 old solution is already optimal
C
C 2 constraints non feasible
C
C 3 trying to enter a variable
C that is already in the corral
C
C 4 starting to loop
C
C
C
C
C imp > 5 one prints final information
C
C
C imp > 6 one prints information at each iteration
C
C
C imp > 7 one prints also
C
C - at each iteration the choleski matrix
C - and the initial information such as (pi,pj) ...
C
C
C
C
C
C **** begin ****
C
C prepare various data
C
C
iterpr = 0
nt1 = ntot + 1
itmax = 10 * ntot
deps = eps
incr = 0
k00 = 1
w1s = 0.d0
w2s = 0.d0
w12s = 0.d0
gama = .99d0
dzero = 10.d0 * zero
C initial printouts
if (imp .gt. 7) call n1fc1o(io,21,nt1,mm1,i3,i4,i5,deps,d2,a,r)
C
C initial point
C
100 if (iflag .ne. 3) goto 110
if (imp .gt. 6) call n1fc1o(io,22,nv,i2,i3,i4,jc,d1,d2,d3,d4)
j0 = nt1
ps = u1 * (a(nt1)-deps)
ment = (nt1-1) * mm1
do 103 k = 1,nv
jk = ment + jc(k)
103 ps = ps + xpr(k)*r(jk)
if (ps .lt. s2) goto 107
if (imp .gt. 0) call n1fc1o(io,23,i1,i2,i3,i4,i5,d1,d2,d3,d4)
iflag = 1
return
107 nv = nv + 1
nc = nc + 1
jc(nv) = j0
iterpr = 1
goto 300
110 if (iflag .le. 1) goto 140
C save the corral of previous call
do 120 i = 1,nt1
120 ic(i) = 0
do 130 k = 1,nv
jk = jc(k)
130 ic(jk) = 1
ic(nt1) = 1
C initialize with one feasible gradient
140 jc(1) = 1
nv = 2
nc = 1
jc(2) = 0
do 150 j = 2,nt1
if (a(j) .gt. deps) goto 150
jc(2) = j
150 continue
if (jc(2) .gt. 0) goto 160
if (imp .gt. 0) call n1fc1o(io,24,i1,i2,i3,i4,i5,d1,d2,d3,d4)
iflag = 2
return
160 j = jc(2)
rr(1) = 1.d0
jj = (j-1)*mm1 + j
ps = 1.d0 + r(jj)
if (ps .gt. 0.d0) goto 170
iflag = 3
return
170 rr(2) = dsqrt(ps)
r(2) = a(j)
do 180 i = 1,nt1
180 xpr(i) = 0.d0
xpr(1) = deps - a(j)
xpr(2) = 1.d0
u1 = 0.d0
u2 = -r(jj)
if (imp .gt. 6) call n1fc1o(io,25,j,i2,i3,i4,i5,d1,d2,d3,d4)
C
C stopping criterion
C
200 iterpr = iterpr + 1
if (imp .gt. 6) call n1fc1o(io,26,nv,i2,i3,i4,i5,d1,d2,d3,xpr)
if (iterpr .le. itmax) goto 205
if (imp .gt. 0) call n1fc1o(io,27,i1,i2,i3,i4,i5,d1,d2,d3,d4)
iflag = 4
return
205 s2 = (-deps)*u1 - u2
if (s2 .le. eta) goto 900
sp = gama * s2
C first compute all the tests,
C and test with the corral of previous call
j0 = 0
do 220 j = 2,nt1
ps = u1 * (a(j)-deps)
do 210 k = 1,nv
jj = jc(k)
if (jj .eq. 1) goto 210
j1 = max0(j,jj)
j2 = min0(j,jj)
jj = (j1-1)*mm1 + j2
ps = ps + xpr(k)*r(jj)
210 continue
y(j) = ps
if (iflag .ne. 2) goto 220
if (ic(j) .ne. 1) goto 220
if (ps .ge. sp) goto 220
j0 = j
sp = ps
220 continue
if (j0 .eq. 0) goto 240
if (sp .ge. gama*s2) goto 240
ps1 = dabs(u1*(deps-a(j0)))
do 230 k = 1,nv
j = jc(k)
if (j .eq. j0) goto 240
if (j .eq. 1) goto 230
j1 = max0(j0,j)
j2 = min0(j0,j)
jj = (j1-1)*mm1 + j2
ps1 = ps1 + xpr(k)*dabs(u1*(2.d0*deps-a(j))+2.d0*y(j)-r(jj))
230 continue
ps1 = ps1 * 1000.d0 * dzero
if (sp .gt. s2-ps1) goto 240
ic(j0) = 0
goto 280
C now the remaining ones
240 j0 = 0
sp = gama * s2
do 260 j = 2,nt1
if (iflag.eq.2 .and. ic(j).eq.1) goto 260
if (y(j) .ge. sp) goto 260
sp = y(j)
j0 = j
260 continue
if (j0 .eq. 0) goto 290
ps1 = dabs(u1*(deps-a(j0)))
do 270 k = 1,nv
j = jc(k)
if (j .eq. 1) goto 270
j1 = max0(j0,j)
j2 = min0(j0,j)
jj = (j1-1)*mm1 + j2
ps1 = ps1 + xpr(k)*dabs(u1*(2.d0*deps-a(j))+2.d0*y(j)-r(jj))
270 continue
ps1 = ps1 * 1000.d0 * dzero
if (sp .gt. s2-ps1) goto 290
280 nc = nc + 1
nv = nv + 1
jc(nv) = j0
if (imp .gt. 6) call n1fc1o(io,28,j0,i2,i3,i4,i5,s2,sp,d3,d4)
goto 300
C first set of optimality conditions satisfied
290 if (u1 .ge. (-dble(float(nv)))*dzero) goto 900
j0 = 1
nv = nv + 1
jc(nv) = 1
if (imp .gt. 6) call n1fc1o(io,29,i1,i2,i3,i4,i5,s2,u1,d3,d4)
C
C augmenting r
C
300 nv1 = nv - 1
do 305 k = 1,nv1
if (jc(k) .ne. j0) goto 305
if (imp .gt. 0) call n1fc1o(io,30,j0,i2,i3,i4,i5,d1,d2,d3,d4)
iflag = 3
return
305 continue
j = jc(1)
j1 = max0(j,j0)
j2 = min0(j,j0)
jj = (j1-1)*mm1 + j2
r(nv) = (a(j)*a(j0)+e(j)*e(j0)+r(jj)) / rr(1)
ps0 = r(nv) * r(nv)
if (nv1 .eq. 1) goto 330
do 320 k = 2,nv1
j = jc(k)
j1 = max0(j,j0)
j2 = min0(j,j0)
jj = (j1-1)*mm1 + j2
ps = a(j)*a(j0) + e(j)*e(j0) + r(jj)
k1 = k - 1
do 310 kk = 1,k1
j1 = (kk-1)*mm1 + k
j2 = (kk-1)*mm1 + nv
310 ps = ps - r(j1)*r(j2)
mek = k1*mm1 + nv
r(mek) = ps / rr(k)
320 ps0 = ps0 + r(mek)*r(mek)
jj = (j0-1)*mm1 + j0
ps0 = a(j0)*a(j0) + e(j0)*e(j0) + r(jj) - ps0
if (ps0 .gt. 0.d0) goto 330
iflag = 3
return
330 rr(nv) = dsqrt(ps0)
if (iterpr .le. 1) goto 400
incr = 1
k00 = nv
C
C solving the corral-system
C
400 k = k00
if (k .gt. nv) goto 430
if (imp .gt. 7) call n1fc1o(io,31,nv,mm1,i3,i4,i5,d1,d2,rr,r)
410 j = jc(k)
ps1 = a(j)
ps2 = e(j)
if (k .eq. 1) goto 420
k1 = k - 1
do 415 kk = 1,k1
jj = (kk-1)*mm1 + k
ps0 = r(jj)
ps1 = ps1 - ps0*w1(kk)
415 ps2 = ps2 - ps0*w2(kk)
420 ps0 = rr(k)
w1(k) = ps1 / ps0
w2(k) = ps2 / ps0
k = k + 1
if (k .le. nv) goto 410
C two-two system
430 k = 1
if (incr .eq. 1) k = nv
440 w1s = w1s + w1(k)*w1(k)
w2s = w2s + w2(k)*w2(k)
w12s = w12s + w1(k)*w2(k)
k = k + 1
if (k .le. nv) goto 440
det = w1s*w2s - w12s*w12s
ps2 = w2s*deps - w12s
ps1 = w1s - w12s*deps
450 v1 = ps2 / det
v2 = ps1 / det
460 u1 = deps - v1
u2 = 1.d0 - v2
if (nv .eq. nc+1) u1 = 0.d0
C backward
y(nv) = (v1*w1(nv)+v2*w2(nv)) / rr(nv)
if (nv .eq. 1) goto 500
do 480 l = 2,nv
k = nv - l + 1
k1 = k + 1
ps = v1*w1(k) + v2*w2(k)
mek = (k-1) * mm1
do 470 kk = k1,nv
mej = mek + kk
470 ps = ps - r(mej)*y(kk)
480 y(k) = ps / rr(k)
C
C test for positivity
C
500 continue
do 530 k = 1,nv
if (y(k) .le. 0.d0) goto 550
530 continue
do 540 k = 1,nv
540 xpr(k) = y(k)
goto 200
C interpolating between x and y
550 teta = 0.d0
k0 = k
do 560 k = 1,nv
if (y(k) .ge. 0.d0) goto 560
ps = y(k) / (y(k)-xpr(k))
if (teta .ge. ps) goto 560
teta = ps
k0 = k
560 continue
do 570 k = 1,nv
ps = teta*xpr(k) + (1.d0-teta)*y(k)
if (ps .le. dzero) ps = 0.d0
570 xpr(k) = ps
if (imp .le. 6) goto 600
ps1 = 0.d0
ps2 = 0.d0
do 580 k = 1,nv
do 580 kk = 1,nv
j1 = max0(jc(k),jc(kk))
j2 = min0(jc(k),jc(kk))
jj = (j1-1)*mm1 + j2
ps1 = ps1 + xpr(k)*xpr(kk)*r(jj)
ps2 = ps2 + y(k)*y(kk)*r(jj)
580 continue
C
C compressing the corral
C
600 nv = nv - 1
incr = 0
k00 = k0
w1s = 0.d0
w2s = 0.d0
w12s = 0.d0
l = jc(k0)
if (l .ne. 1) nc = nc - 1
if (imp .gt. 6) call n1fc1o(io,32,k0,l,i3,i4,i5,y(k0),ps1,ps2,d4)
if (k0 .gt. nv) goto 400
k1 = k0 - 1
do 620 k = k0,nv
xpr(k) = xpr(k+1)
if (k0 .eq. 1) goto 620
do 610 kk = 1,k1
mek = (kk-1)*mm1 + k
610 r(mek) = r(mek+1)
620 jc(k) = jc(k+1)
xpr(nv+1) = 0.d0
630 mek = (k0-1)*mm1 + k0 + 1
ps = r(mek)
ps12 = rr(k0+1)
ps0 = dsqrt(ps*ps+ps12*ps12)
ps = ps / ps0
ps12 = ps12 / ps0
rr(k0) = ps0
if (k0 .eq. nv) goto 400
k1 = k0 + 1
mek01 = (k0-1) * mm1
mek = k0 * mm1
mekk = mek - mm1
do 640 k = k1,nv
j1 = mekk + k
j2 = mek + k
r(j1) = ps*r(j1+1) + ps12*r(j2+1)
if (k .gt. k1) r(j2) = ps2
640 ps2 = (-ps12)*r(j1+1) + ps*r(j2+1)
r(j2+1) = ps2
k0 = k0 + 1
goto 630
C
C *** finished ***
C
900 iflag = 0
do 930 j = 1,ntot
930 al(j) = 0.
do 940 k = 1,nv
j = jc(k) - 1
if (j .ne. 0) al(j) = xpr(k)
940 continue
u = u1
if (imp .le. 5) return
call n1fc1o(io,34,nc,nv,i3,i4,jc,s2,sp,u1,d4)
return
end
|
