| 1 |
************************************************************************ |
| 2 |
* |
| 3 |
* File mi20amat fortran. |
| 4 |
* |
| 5 |
* m2core m2amat m2aprd m2apr1 m2apr5 |
| 6 |
* m2crsh m2scal m2scla m2unpk matcol |
| 7 |
* |
| 8 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 9 |
|
| 10 |
subroutine m2core( mode, mincor ) |
| 11 |
|
| 12 |
implicit double precision (a-h,o-z) |
| 13 |
|
| 14 |
* ------------------------------------------------------------------ |
| 15 |
* m2core allocates all array storage for MINOS, |
| 16 |
* using various dimensions stored in common blocks as follows: |
| 17 |
* (m2len ) mrows, mcols, melms |
| 18 |
* (m3len ) nscl |
| 19 |
* (m5len ) maxr, maxs, nn |
| 20 |
* (m7len ) nnobj |
| 21 |
* (m8len ) njac, nncon, nnjac |
| 22 |
* |
| 23 |
* if mode = 1, the call is from minos1 to estimate the storage |
| 24 |
* needed for all stages of the problem. |
| 25 |
* if mode = 2, the call is from m3inpt to find the minimum storage |
| 26 |
* needed for mps input. |
| 27 |
* if mode = 3, all dimensions should be known exactly. |
| 28 |
* The call is from m3inpt to find the minimum |
| 29 |
* storage to solve the problem and output the solution. |
| 30 |
* The basis factorization routines will say later |
| 31 |
* if they have sufficient storage. |
| 32 |
* if mode = 4, the call is from minoss and all dimensions are known |
| 33 |
* exactly. a, ha, ka etc need not be allocated. |
| 34 |
* ------------------------------------------------------------------ |
| 35 |
|
| 36 |
common /m1word/ nwordr,nwordi,nwordh |
| 37 |
common /m2len / mrows,mcols,melms |
| 38 |
common /m2mapa/ ne ,nka ,la ,lha ,lka |
| 39 |
common /m2mapz/ maxw ,maxz |
| 40 |
common /m3len / m ,n ,nb ,nscl |
| 41 |
common /m3loc / lascal,lbl ,lbu ,lbbl ,lbbu , |
| 42 |
$ lhrtyp,lhs ,lkb |
| 43 |
common /m3mps1/ lname1,lname2,lkeynm,nname |
| 44 |
common /m3scal/ sclobj,scltol,lscale |
| 45 |
common /m5len / maxr ,maxs ,mbs ,nn ,nn0 ,nr ,nx |
| 46 |
common /m5loc / lpi ,lpi2 ,lw ,lw2 , |
| 47 |
$ lx ,lx2 ,ly ,ly2 , |
| 48 |
$ lgsub ,lgsub2,lgrd ,lgrd2 , |
| 49 |
$ lr ,lrg ,lrg2 ,lxn |
| 50 |
common /m7len / fobj ,fobj2 ,nnobj ,nnobj0 |
| 51 |
common /m7loc / lgobj ,lgobj2 |
| 52 |
common /m7cg2 / lcg1,lcg2,lcg3,lcg4,modtcg,nitncg,nsubsp |
| 53 |
common /m8len / njac ,nncon ,nncon0,nnjac |
| 54 |
common /m8loc / lfcon ,lfcon2,lfdif ,lfdif2,lfold , |
| 55 |
$ lblslk,lbuslk,lxlam ,lrhs , |
| 56 |
$ lgcon ,lgcon2,lxdif ,lxold |
| 57 |
common /m8al1 / penpar,rowtol,ncom,nden,nlag,nmajor,nminor |
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* ------------------------------------------------------------------ |
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|
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m = mrows |
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n = mcols |
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ne = melms |
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mbs = m + maxs |
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nka = n + 1 |
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nb = n + m |
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nscl = nb |
| 67 |
if (lscale .eq. 0) nscl = 1 |
| 68 |
nname = nb |
| 69 |
if (mode .eq. 4) nname = 1 |
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|
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ncoli = n/nwordi + 1 |
| 72 |
nrowi = m/nwordi + 1 |
| 73 |
lenh = max( 3*nrowi, 100 ) |
| 74 |
|
| 75 |
nn0 = max( nn , 1 ) |
| 76 |
nncon0 = max( nncon, 1 ) |
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nnobj0 = max( nnobj, 1 ) |
| 78 |
maxr = max( maxr , 1 ) |
| 79 |
nr = maxr*(maxr + 1)/2 + (maxs - maxr) |
| 80 |
nx = max( mbs, nn ) |
| 81 |
nx2 = 0 |
| 82 |
if (lscale .ge. 2) nx2 = nn |
| 83 |
|
| 84 |
if (mode .le. 3) then |
| 85 |
|
| 86 |
* MINOS is getting its data from an MPS file. |
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* Allocate arrays that are arguments of minoss and misolv. |
| 88 |
* These are for the data, |
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* A, ha, ka, bl, bu, name1, name2, |
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* and for the solution |
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* hs, xn, pi, rc. |
| 92 |
|
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la = maxw + 1 |
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lha = la + ne |
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lka = lha + 1 + (ne /nwordh) |
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lbl = lka + 1 + (nka/nwordi) |
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lbu = lbl + nb |
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lname1 = lbu + nb |
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lname2 = lname1 + 1 + (nname/nwordi) |
| 100 |
lhs = lname2 + 1 + (nname/nwordi) |
| 101 |
lxn = lhs + 1 + (nb /nwordh) |
| 102 |
lpi = lxn + nb |
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lrc = lpi + m |
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minsub = lrc + nb |
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else |
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|
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* The subroutine version can use all of z except up to maxw. |
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|
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minsub = maxw + 1 |
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end if |
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|
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* Allocate arrays needed during and after MPS input. |
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|
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lhrtyp = minsub |
| 115 |
lkb = lhrtyp + 1 + (mbs/nwordh) |
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minz = lkb + 1 + (mbs/nwordi) |
| 117 |
|
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if (mode .le. 2) then |
| 119 |
|
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* Allocate additional arrays needed for MPS input. |
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* Currently just keynam -- the hash table. |
| 122 |
|
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lkeynm = minz |
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minmps = lkeynm + lenh |
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end if |
| 126 |
|
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* LP and reduced-gradient algorithm. |
| 128 |
***** Beware -- length 0000 is used below for arrays that are |
| 129 |
***** not needed in this version of MINOS. |
| 130 |
|
| 131 |
lascal = minz |
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lpi2 = lascal + nscl |
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lw = lpi2 + 0000 |
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lw2 = lw + nx |
| 135 |
lx = lw2 + 0000 |
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lx2 = lx + nx |
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ly = lx2 + nx2 |
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ly2 = ly + nx |
| 139 |
lgsub = ly2 + nx |
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lgsub2 = lgsub + nn |
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lgrd = lgsub2 + 0000 |
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lr = lgrd + mbs |
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lrg = lr + nr |
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lrg2 = lrg + maxs |
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minz = lrg2 + maxs |
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|
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* Nonlinear objective. |
| 148 |
|
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lgobj = minz |
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lgobj2 = lgobj + nnobj |
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minz = lgobj2 + nnobj |
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|
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* Nonlinear constraints. |
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* If Jacobian = Dense we can set njac correctly. |
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* Otherwise we have to guess if the MPS file hasn't been |
| 156 |
* input yet (mode = 1 or 2). |
| 157 |
|
| 158 |
if (nden .eq. 1) then |
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njac = nncon * nnjac |
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else if (mode .le. 2) then |
| 161 |
njac = 5 * nnjac |
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end if |
| 163 |
njac = max( njac, 1 ) |
| 164 |
lfcon = minz |
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lfcon2 = lfcon + nncon |
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lfdif = lfcon2 + nncon |
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lfdif2 = lfdif + nncon |
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lfold = lfdif2 + 0000 |
| 169 |
lblslk = lfold + nncon |
| 170 |
lbuslk = lblslk + nncon |
| 171 |
lxlam = lbuslk + nncon |
| 172 |
lrhs = lxlam + nncon |
| 173 |
lgcon = lrhs + nncon |
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lgcon2 = lgcon + njac |
| 175 |
lxdif = lgcon2 + njac |
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lxold = lxdif + nn |
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minz = lxold + nn |
| 178 |
|
| 179 |
* Work arrays that can be overwritten by the names (see below) |
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* in between cycles. |
| 181 |
|
| 182 |
lbbl = minz |
| 183 |
lbbu = lbbl + mbs |
| 184 |
lgrd2 = lbbu + mbs |
| 185 |
minz = lgrd2 + mbs |
| 186 |
|
| 187 |
* Allocate arrays for the basis factorization routines. |
| 188 |
* minz points to the beginning of the LU factorization. |
| 189 |
* This is the beginning of free space between cycles |
| 190 |
* if the LU factors are allowed to be overwritten. |
| 191 |
|
| 192 |
call m2bmap( mode, m, n, ne, minz, maxz, nguess ) |
| 193 |
|
| 194 |
if (mode .eq. 1) mincor = max( minmps, nguess, minz ) |
| 195 |
if (mode .eq. 2) mincor = minmps |
| 196 |
if (mode .ge. 3) mincor = minz |
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|
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* end of m2core |
| 199 |
end |
| 200 |
|
| 201 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 202 |
|
| 203 |
subroutine m2amat( mode, m, n, nb, |
| 204 |
$ ne, nka, a, ha, ka, |
| 205 |
$ bl, bu, hrtype ) |
| 206 |
|
| 207 |
implicit double precision (a-h,o-z) |
| 208 |
integer*4 ha(ne), hrtype(m) |
| 209 |
integer ka(nka) |
| 210 |
double precision a(ne), bl(nb), bu(nb) |
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|
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* ------------------------------------------------------------------ |
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* If mode = 1 or 2, m2amat defines hrtype, the set of row types. |
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* If mode = 1, m2amat also prints the matrix statistics. |
| 215 |
* |
| 216 |
* The vector of row-types is as follows: |
| 217 |
* hrtype(i) = 0 for e rows (equalities), |
| 218 |
* hrtype(i) = 2 for n rows (objective or free rows), |
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* hrtype(i) = 1 otherwise. |
| 220 |
* They are used in m2scal and m2crsh. |
| 221 |
* ------------------------------------------------------------------ |
| 222 |
|
| 223 |
common /m1eps / eps,eps0,eps1,eps2,eps3,eps4,eps5,plinfy |
| 224 |
common /m1file/ iread,iprint,isumm |
| 225 |
common /m5lobj/ sinf,wtobj,minimz,ninf,iobj,jobj,kobj |
| 226 |
common /m8len / njac ,nncon ,nncon0,nnjac |
| 227 |
|
| 228 |
intrinsic abs, max, min |
| 229 |
parameter ( zero = 0.0d+0 ) |
| 230 |
|
| 231 |
bplus = 0.9*plinfy |
| 232 |
bminus = - bplus |
| 233 |
|
| 234 |
* Construct the vector of row-types. |
| 235 |
|
| 236 |
nfixed = 0 |
| 237 |
nfree = 0 |
| 238 |
nnorml = 0 |
| 239 |
do 100 i = 1, m |
| 240 |
j = n + i |
| 241 |
b1 = bl(j) |
| 242 |
b2 = bu(j) |
| 243 |
itype = 1 |
| 244 |
if (b1 .eq. b2 ) itype = 0 |
| 245 |
if (b1 .le. bminus .and. b2 .ge. bplus) itype = 2 |
| 246 |
hrtype(i) = itype |
| 247 |
if (itype .eq. 0) nfixed = nfixed + 1 |
| 248 |
if (itype .eq. 2) nfree = nfree + 1 |
| 249 |
if (itype .ne. 1) go to 100 |
| 250 |
if (b1 .le. bminus .or. b2 .ge. bplus) nnorml = nnorml + 1 |
| 251 |
100 continue |
| 252 |
|
| 253 |
if (mode .eq. 2) return |
| 254 |
if (iprint .le. 0) return |
| 255 |
|
| 256 |
nbnded = m - nfixed - nfree - nnorml |
| 257 |
write(iprint, 2200) |
| 258 |
write(iprint, 2300) ' Rows ', m, nnorml, nfree, nfixed, nbnded |
| 259 |
|
| 260 |
nfixed = 0 |
| 261 |
nfree = 0 |
| 262 |
nnorml = 0 |
| 263 |
|
| 264 |
do 200 j = 1, n |
| 265 |
b1 = bl(j) |
| 266 |
b2 = bu(j) |
| 267 |
if (b1 .eq. b2) then |
| 268 |
nfixed = nfixed + 1 |
| 269 |
else |
| 270 |
if (b1 .eq. zero ) then |
| 271 |
if (b2 .ge. bplus) then |
| 272 |
nnorml = nnorml + 1 |
| 273 |
end if |
| 274 |
else if (b1 .le. bminus) then |
| 275 |
if (b2 .eq. zero ) then |
| 276 |
nnorml = nnorml + 1 |
| 277 |
else if (b2 .ge. bplus) then |
| 278 |
nfree = nfree + 1 |
| 279 |
end if |
| 280 |
end if |
| 281 |
end if |
| 282 |
200 continue |
| 283 |
|
| 284 |
nbnded = n - nfixed - nfree - nnorml |
| 285 |
write(iprint, 2300) ' Columns', n, nnorml, nfree, nfixed, nbnded |
| 286 |
|
| 287 |
* Find the biggest and smallest elements in a, excluding free rows |
| 288 |
* and fixed columns. |
| 289 |
* Also find the largest objective coefficients in non-fixed columns. |
| 290 |
|
| 291 |
aijmax = zero |
| 292 |
aijmin = bplus |
| 293 |
cmax = zero |
| 294 |
cmin = bplus |
| 295 |
ncost = 0 |
| 296 |
|
| 297 |
do 300 j = 1, n |
| 298 |
if (bl(j) .lt. bu(j)) then |
| 299 |
do 250 k = ka(j), ka(j+1) - 1 |
| 300 |
i = ha(k) |
| 301 |
if (hrtype(i) .eq. 2) then |
| 302 |
if (i .eq. iobj) then |
| 303 |
aij = abs( a(k) ) |
| 304 |
if (aij .gt. zero) then |
| 305 |
ncost = ncost + 1 |
| 306 |
cmax = max( cmax, aij ) |
| 307 |
cmin = min( cmin, aij ) |
| 308 |
end if |
| 309 |
end if |
| 310 |
else |
| 311 |
aij = abs( a(k) ) |
| 312 |
aijmax = max( aijmax, aij ) |
| 313 |
aijmin = min( aijmin, aij ) |
| 314 |
end if |
| 315 |
250 continue |
| 316 |
end if |
| 317 |
300 continue |
| 318 |
|
| 319 |
if (aijmin .eq. bplus) aijmin = zero |
| 320 |
adnsty = 100.0*ne / (m*n) |
| 321 |
write(iprint, 2400) ne, adnsty, aijmax, aijmin, ncost |
| 322 |
if (ncost .gt. 0) write(iprint, 2410) cmax, cmin |
| 323 |
|
| 324 |
* Print a few things to be gathered as statistics |
| 325 |
* from a bunch of test runs. |
| 326 |
|
| 327 |
write(iprint, 2500) nncon, m-nncon, n |
| 328 |
return |
| 329 |
|
| 330 |
2200 format(/// |
| 331 |
$ ' Matrix Statistics' / |
| 332 |
$ ' -----------------' / |
| 333 |
$ 15x, 'Total', 6x, 'Normal', 8x, 'Free', 7x, 'Fixed', |
| 334 |
$ 5x, 'Bounded') |
| 335 |
2300 format(a, 5i12) |
| 336 |
2400 format(/ ' No. of matrix elements', i21, 5x, 'Density', f12.3 |
| 337 |
$ / ' Biggest ', 1p, e35.4, ' (excluding fixed columns,' |
| 338 |
$ / ' Smallest', e35.4, ' free rows, and RHS)' |
| 339 |
$ // ' No. of objective coefficients', i14) |
| 340 |
2410 format( ' Biggest ', 1p, e35.4, ' (excluding fixed columns)' |
| 341 |
$ / ' Smallest', e35.4) |
| 342 |
2500 format(//' Number of Nonlinear constraints', i12 |
| 343 |
$ / ' Number of Linear constraints', i12 |
| 344 |
$ / ' Number of Variables ', i12) |
| 345 |
|
| 346 |
* end of m2amat |
| 347 |
end |
| 348 |
|
| 349 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 350 |
|
| 351 |
subroutine m2aprd( mode, x, lenx, y, leny, |
| 352 |
$ ne, nka, a, ha, ka, |
| 353 |
$ z, nwcore ) |
| 354 |
|
| 355 |
implicit double precision (a-h,o-z) |
| 356 |
integer*4 ha(ne) |
| 357 |
integer ka(nka) |
| 358 |
double precision a(ne) |
| 359 |
double precision x(lenx), y(leny), z(nwcore) |
| 360 |
|
| 361 |
* ------------------------------------------------------------------ |
| 362 |
* m2aprd computes various products involving the matrix A. |
| 363 |
* For mode 1 to 4, x is the basic and/or superbasic variables. |
| 364 |
* For mode 5 to 8, x is xn, the variables in natural order. |
| 365 |
* |
| 366 |
* mode function lenx leny called by |
| 367 |
* ---- -------- ---- ---- --------- |
| 368 |
* 1 y = y - B*x m m not used |
| 369 |
* 1 y = y - (B S)*x ms m not used |
| 370 |
* 2 y = y - S*x ns m m7rgit |
| 371 |
* 3 y = y - B(t)*x m m not used |
| 372 |
* 3 y = y - (B S)(t)*x m ms not used |
| 373 |
* 4 y = y - S(t)*x m ms m7chzq, m7rg |
| 374 |
* |
| 375 |
* 5 y = y - A*xn n m m5setx, m5solv |
| 376 |
* 6 not used |
| 377 |
* 7 y = y - (nonlinear A)*xn nnjac nncon m6fun1, m8setj |
| 378 |
* 8 y = y - (linear A)*xn n nncon m8viol |
| 379 |
* mode 7 and 8 deal with nonlinear rows only and ignore slacks. |
| 380 |
* |
| 381 |
* 14 Oct 1991: a, ha, ka added as parameters to help with minoss. |
| 382 |
* ------------------------------------------------------------------ |
| 383 |
|
| 384 |
common /m1eps / eps,eps0,eps1,eps2,eps3,eps4,eps5,plinfy |
| 385 |
common /m3len / m ,n ,nb ,nscl |
| 386 |
common /m3loc / lascal,lbl ,lbu ,lbbl ,lbbu , |
| 387 |
$ lhrtyp,lhs ,lkb |
| 388 |
common /m5len / maxr ,maxs ,mbs ,nn ,nn0 ,nr ,nx |
| 389 |
common /m8len / njac ,nncon ,nncon0,nnjac |
| 390 |
|
| 391 |
tolz = eps0 |
| 392 |
|
| 393 |
if (mode .lt. 5) then |
| 394 |
call m2apr1( mode, m, mbs, n, tolz, |
| 395 |
$ ne, nka, a, ha, ka, z(lkb), |
| 396 |
$ x, lenx, y, leny ) |
| 397 |
else |
| 398 |
call m2apr5( mode, m, n, nb, nncon, nnjac, tolz, |
| 399 |
$ ne, nka, a, ha, ka, |
| 400 |
$ x, lenx, y, leny ) |
| 401 |
end if |
| 402 |
|
| 403 |
* end of m2aprd |
| 404 |
end |
| 405 |
|
| 406 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 407 |
|
| 408 |
subroutine m2apr1( mode, m, mbs, n, tolz, |
| 409 |
$ ne, nka, a, ha, ka, kb, x, lenx, y, leny ) |
| 410 |
|
| 411 |
implicit double precision (a-h,o-z) |
| 412 |
integer*4 ha(ne) |
| 413 |
integer ka(nka), kb(mbs) |
| 414 |
double precision a(ne) |
| 415 |
double precision x(lenx), y(leny) |
| 416 |
|
| 417 |
* ------------------------------------------------------------------ |
| 418 |
* m2apr1 computes various matrix-vector products involving |
| 419 |
* B and S, the basic and superbasic columns of A. |
| 420 |
* |
| 421 |
* mode=1 y = y - B*x or y - (B S)*x (depending on lenx) |
| 422 |
* mode=2 y = y - S*x |
| 423 |
* mode=3 y = y - B(transpose)*x or y - (B S)(transpose)*x |
| 424 |
* (mode 3 is not used as yet) |
| 425 |
* mode=4 y = y - S(transpose)*x |
| 426 |
* ------------------------------------------------------------------ |
| 427 |
|
| 428 |
kbase = 0 |
| 429 |
if (mode .le. 2) then |
| 430 |
* ------------- |
| 431 |
* mode 1 and 2. |
| 432 |
* ------------- |
| 433 |
if (mode .eq. 2) kbase = m |
| 434 |
|
| 435 |
do 200 k = 1, lenx |
| 436 |
xj = x(k) |
| 437 |
if (abs(xj) .le. tolz) go to 200 |
| 438 |
j = kb(kbase + k) |
| 439 |
if (j .le. n) then |
| 440 |
do 150 i = ka(j), ka(j+1) - 1 |
| 441 |
ir = ha(i) |
| 442 |
y(ir) = y(ir) - a(i)*xj |
| 443 |
150 continue |
| 444 |
else |
| 445 |
ir = j - n |
| 446 |
y(ir) = y(ir) - xj |
| 447 |
end if |
| 448 |
200 continue |
| 449 |
else |
| 450 |
* ------------- |
| 451 |
* mode 3 and 4. |
| 452 |
* ------------- |
| 453 |
if (mode .eq. 4) kbase = m |
| 454 |
|
| 455 |
do 400 k = 1, leny |
| 456 |
t = y(k) |
| 457 |
j = kb(kbase + k) |
| 458 |
if (j .le. n) then |
| 459 |
do 350 i = ka(j), ka(j+1) - 1 |
| 460 |
ir = ha(i) |
| 461 |
t = t - x(ir)*a(i) |
| 462 |
350 continue |
| 463 |
y(k) = t |
| 464 |
else |
| 465 |
ir = j - n |
| 466 |
y(k) = t - x(ir) |
| 467 |
end if |
| 468 |
400 continue |
| 469 |
end if |
| 470 |
|
| 471 |
* end of m2apr1 |
| 472 |
end |
| 473 |
|
| 474 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 475 |
|
| 476 |
subroutine m2apr5( mode, m, n, nb, nncon, nnjac, tolz, |
| 477 |
$ ne, nka, a, ha, ka, xn, lenx, y, leny ) |
| 478 |
|
| 479 |
implicit double precision (a-h,o-z) |
| 480 |
integer*4 ha(ne) |
| 481 |
integer ka(nka) |
| 482 |
double precision a(ne) |
| 483 |
double precision xn(lenx), y(leny) |
| 484 |
|
| 485 |
* ------------------------------------------------------------------ |
| 486 |
* m2apr5 computes products involving parts of A and xn. |
| 487 |
* ------------------------------------------------------------------ |
| 488 |
|
| 489 |
intrinsic abs |
| 490 |
|
| 491 |
if (mode .eq. 5) then |
| 492 |
* ---------------------------------- |
| 493 |
* mode = 5. Set y = y - A*xn. |
| 494 |
* ---------------------------------- |
| 495 |
do 500 j = 1, n |
| 496 |
xj = xn(j) |
| 497 |
if (abs( xj ) .gt. tolz) then |
| 498 |
do 450 k = ka(j), ka(j+1) - 1 |
| 499 |
ir = ha(k) |
| 500 |
y(ir) = y(ir) - a(k)*xj |
| 501 |
450 continue |
| 502 |
end if |
| 503 |
500 continue |
| 504 |
|
| 505 |
else |
| 506 |
* ------------------------------------------------------------ |
| 507 |
* If mode = 7, set y = y - (Jacobian)*xn. |
| 508 |
* If mode = 8, set y = y - (linear A)*xn. |
| 509 |
* Only the first nncon rows are involved, and no slacks. |
| 510 |
* ------------------------------------------------------------ |
| 511 |
if (mode .eq. 7) then |
| 512 |
j1 = 1 |
| 513 |
j2 = nnjac |
| 514 |
else |
| 515 |
j1 = nnjac + 1 |
| 516 |
j2 = n |
| 517 |
end if |
| 518 |
|
| 519 |
do 800 j = j1, j2 |
| 520 |
xj = xn(j) |
| 521 |
if (abs( xj ) .gt. tolz) then |
| 522 |
do 750 k = ka(j), ka(j+1) - 1 |
| 523 |
ir = ha(k) |
| 524 |
if (ir .le. nncon) y(ir) = y(ir) - a(k)*xj |
| 525 |
750 continue |
| 526 |
end if |
| 527 |
800 continue |
| 528 |
end if |
| 529 |
|
| 530 |
* end of m2apr5 |
| 531 |
end |
| 532 |
|
| 533 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 534 |
|
| 535 |
subroutine m2crsh( lcrash, m , n , nb , nn , |
| 536 |
$ ne , nka , a , ha , ka , |
| 537 |
$ hpiv , hs , hrtype, bl , bu , |
| 538 |
$ xn , z , nwcore ) |
| 539 |
|
| 540 |
implicit double precision (a-h,o-z) |
| 541 |
integer*4 ha(ne), hpiv(m), hs(nb), hrtype(m) |
| 542 |
integer ka(nka) |
| 543 |
double precision a(ne), bl(nb), bu(nb), xn(nb), z(nwcore ) |
| 544 |
|
| 545 |
* ------------------------------------------------------------------ |
| 546 |
* m2crsh looks for a basis in the columns of ( A I ). |
| 547 |
* |
| 548 |
* ON ENTRY |
| 549 |
* |
| 550 |
* iparm(1) = Crash option (icrash) has been used by m4getb |
| 551 |
* to set lcrash. |
| 552 |
* dparm(5) = Crash tolerance (tcrash). Default = 0.1 |
| 553 |
* |
| 554 |
* lcrash specifies the action to be taken by Crash. |
| 555 |
* 0,1,2,3 The call is from m4getb. |
| 556 |
* 4 The call is from m5solv. |
| 557 |
* 5 The call is from m8setj. |
| 558 |
* |
| 559 |
* 0 The all-slack basis is set up. |
| 560 |
* |
| 561 |
* 1 A triangular crash is applied to the columns of A. |
| 562 |
* hs(1:n) is used to help select columns. |
| 563 |
* tcrash is used to ignore small entries in each column. |
| 564 |
* Depending on the size of tcrash, the resulting basis |
| 565 |
* will be nearly (but not strictly) lower triangular. |
| 566 |
* |
| 567 |
* 2 As for 1, but nonlinear rows are ignored. |
| 568 |
* |
| 569 |
* 3 As for 2, but linear LG rows are also ignored. |
| 570 |
* |
| 571 |
* 4 Linear LG rows are now included. |
| 572 |
* All hs(1:nb) and xn(n+i) are defined. |
| 573 |
* Slack values of xn(n+i) are used to select LG rows. |
| 574 |
* |
| 575 |
* 5 Nonlinear rows are now included. |
| 576 |
* |
| 577 |
* hrtype(*) should be defined as described in m2amat: |
| 578 |
* hrtype(i) = 0 for E rows (equalities) |
| 579 |
* hrtype(i) = 1 for L or G rows (inequalities) |
| 580 |
* hrtype(i) = 2 for N rows (objective or free rows) |
| 581 |
* |
| 582 |
* xn If lcrash <= 4, xn(1:n) is used to initialize |
| 583 |
* slacks as xn(n+1:nb) = - A*xn. |
| 584 |
* Used to select slacks from LG rows to be in B (basis). |
| 585 |
* If lcrash = 5, xn(n+1:n+nncon) contains slack values |
| 586 |
* evaluated from xn(1:n) and fcon(*). |
| 587 |
* Used to select slacks from nonlinear rows to be in B. |
| 588 |
* |
| 589 |
* hs If lcrash = 1, 2 or 3, hs(1:n) is used. |
| 590 |
* If lcrash = 4 or 5, hs(1:nb) is used. |
| 591 |
* If hs(j) = 0, 1 or 3, column j is eligible for B, |
| 592 |
* with 3 being "preferred". |
| 593 |
* If hs(j) = 2, 4 or 5, column j is ignored. |
| 594 |
* |
| 595 |
* |
| 596 |
* Crash has several stages. |
| 597 |
* |
| 598 |
* Stage 1: Insert any slacks (N, L or G rows, hrtype = 1 or 2). |
| 599 |
* |
| 600 |
* Stage 2: Do triangular crash on any free columns (wide bounds) |
| 601 |
* |
| 602 |
* Stage 3: Do triangular crash on "preferred" columns (hs(j) < 0). |
| 603 |
* For the linear crash, this includes variables set |
| 604 |
* between their bounds in the MPS file via FR INITIAL. |
| 605 |
* For the nonlinear crash, it includes nonbasics |
| 606 |
* between their bounds. |
| 607 |
* (That is, "pegged" variables in both cases.) |
| 608 |
* |
| 609 |
* Stage 4: Grab unit columns. |
| 610 |
* |
| 611 |
* Stage 5: Grab double columns. |
| 612 |
* |
| 613 |
* Stage 6: Do triangular crash on all columns. |
| 614 |
* |
| 615 |
* Slacks are then used to pad the basis. |
| 616 |
* |
| 617 |
* |
| 618 |
* ON EXIT |
| 619 |
* |
| 620 |
* hs is set to denote an initial (B S N) partition. |
| 621 |
* hs(j) = 3 denotes variables for the initial basis. |
| 622 |
* If hs(j) = 2 still, variable j will be superbasic. |
| 623 |
* If hs(j) = 4 or 5 still, it will be changed to 0 or 1 |
| 624 |
* by m4chek and variable j will be nonbasic. |
| 625 |
* |
| 626 |
* xn If lcrash <= 4, slacks xn(n+1:nb) are initialized. |
| 627 |
* |
| 628 |
* ------------------------------------------------------------------ |
| 629 |
* Nov 1986: Essentially the same as in 1976. |
| 630 |
* Crash tolerance added. |
| 631 |
* Attention paid to various hs values. |
| 632 |
* |
| 633 |
* 12 Nov 1988: After free rows and columns have been processed |
| 634 |
* (stage 1 and 2), slacks on L or G rows are inserted |
| 635 |
* if their rows have not yet been assigned. |
| 636 |
* |
| 637 |
* 28 Dec 1988: Refined as follows. |
| 638 |
* Stage 1 inserts free and preferred rows (slacks). |
| 639 |
* Stage 2 performs a triangular crash on free or |
| 640 |
* preferred columns, ignoring free rows. |
| 641 |
* Unpivoted L or G slacks are then inserted. |
| 642 |
* Stage 3 performs a triangular crash on the other |
| 643 |
* columns, ignoring rows whose slack is basic. |
| 644 |
* (Such rows form the top part of U. The |
| 645 |
* remaining rows form the beginning of L.) |
| 646 |
* |
| 647 |
* 30 Apr 1989: Stage 1 now also looks for singleton columns |
| 648 |
* (ignoring free and preferred rows). |
| 649 |
* 05 May 1989: Stage 2 doesn't insert slacks if crash option < 0. |
| 650 |
* |
| 651 |
* 06 Dec 1989: Stage 2, 3, 4 modified. Columns of length 2 are |
| 652 |
* now treated specially. |
| 653 |
* |
| 654 |
* 20 Dec 1989: Stage 2 thru 5 modified. Free columns done before |
| 655 |
* unit and double columns. |
| 656 |
* |
| 657 |
* 19 May 1992: xn now used to help initialize slacks. |
| 658 |
* Stage 1 thru 7 redefined as above. |
| 659 |
* |
| 660 |
* 01 Jun 1992: abs used to define closeness of slacks to bounds. |
| 661 |
* Unfortunately, xn(1:n) seldom has meaningful values. |
| 662 |
* |
| 663 |
* 02 Jun 1992: Poor performance on the larger problems. |
| 664 |
* Reverted to simple approach: all slacks grabbed. |
| 665 |
* |
| 666 |
* 04 Jun 1992: Compromise -- Crash 3 now has 3 phases: |
| 667 |
* (a) E rows. |
| 668 |
* (b) LG rows. |
| 669 |
* (c) Nonlinear rows. |
| 670 |
* xn(1:n) should then define the slack values better |
| 671 |
* for (b) and (c). |
| 672 |
* ------------------------------------------------------------------ |
| 673 |
|
| 674 |
common /m1eps / eps,eps0,eps1,eps2,eps3,eps4,eps5,plinfy |
| 675 |
common /m1file/ iread,iprint,isumm |
| 676 |
common /m2parm/ dparm(30),iparm(30) |
| 677 |
common /m5log1/ idebug,ierr,lprint |
| 678 |
common /m7len / fobj ,fobj2 ,nnobj ,nnobj0 |
| 679 |
common /m8len / njac ,nncon ,nncon0,nnjac |
| 680 |
|
| 681 |
equivalence ( iparm(1), icrash ) |
| 682 |
equivalence ( dparm(5), tcrash ) |
| 683 |
|
| 684 |
intrinsic abs, max |
| 685 |
double precision apiv(2) |
| 686 |
integer ipiv(2) |
| 687 |
parameter ( nstage = 6 ) |
| 688 |
integer num(nstage), stage |
| 689 |
logical free, prefer, gotslk, |
| 690 |
$ stage2, stage3, stage4, stage5 |
| 691 |
parameter ( zero = 0.0d+0, |
| 692 |
$ small = 1.0d-3, big = 1.0d+4 ) |
| 693 |
|
| 694 |
if (iprint .gt. 0) then |
| 695 |
if (lcrash .le. 3) write(iprint, 1000) icrash |
| 696 |
if (lcrash .eq. 3 .and. nncon .lt. m) write(iprint, 1030) |
| 697 |
if (lcrash .eq. 4) write(iprint, 1040) |
| 698 |
if (lcrash .eq. 5) write(iprint, 1050) |
| 699 |
end if |
| 700 |
|
| 701 |
if (lcrash .le. 4) then |
| 702 |
|
| 703 |
* Sets slacks xn(n+1:nb) = - A*xn. |
| 704 |
* This is where the slacks are initialized. |
| 705 |
* They may be altered later (see the end of Crash). |
| 706 |
|
| 707 |
call dload ( m, zero, xn(n+1), 1 ) |
| 708 |
call m2aprd( 5, xn, n, xn(n+1), m, |
| 709 |
$ ne, nka, a, ha, ka, |
| 710 |
$ z, nwcore ) |
| 711 |
end if |
| 712 |
|
| 713 |
* ------------------------------------------------------------------ |
| 714 |
* For Crash option 0, set hs(j) = 3 for all slacks and quit. |
| 715 |
* ------------------------------------------------------------------ |
| 716 |
if (lcrash .eq. 0) then |
| 717 |
call hload ( n, 0, hs , 1 ) |
| 718 |
call hload ( m, 3, hs(n+1), 1 ) |
| 719 |
go to 900 |
| 720 |
end if |
| 721 |
|
| 722 |
* ------------------------------------------------------------------ |
| 723 |
* Crash option 1, 2 or 3. lcrash = 1, 2, 3, 4, or 5. |
| 724 |
* tolslk measures closeness of slacks to bounds. |
| 725 |
* i1,i2 are the first and last rows of A involved in Stage 1. |
| 726 |
* ------------------------------------------------------------------ |
| 727 |
tolslk = 0.25 |
| 728 |
call iload ( nstage, 0, num, 1 ) |
| 729 |
|
| 730 |
if (lcrash .le. 3) then |
| 731 |
* --------------------------------------------------------------- |
| 732 |
* First call. lcrash = 1, 2 or 3. |
| 733 |
* Initialize hpiv(*) for all rows and hs(*) for all slacks. |
| 734 |
* --------------------------------------------------------------- |
| 735 |
i1 = 1 |
| 736 |
if (lcrash .ge. 2) i1 = nncon + 1 |
| 737 |
i2 = m |
| 738 |
nrows = i2 - i1 + 1 |
| 739 |
|
| 740 |
* Make sure there are no basic columns already (hs(j) = 3). |
| 741 |
* If there are, make them "preferred". |
| 742 |
|
| 743 |
do 20 j = 1, n |
| 744 |
if (hs(j) .eq. 3) hs(j) = -1 |
| 745 |
20 continue |
| 746 |
|
| 747 |
* Make relevant rows available: hpiv(i) = 1, hs(n+i) = 0. |
| 748 |
|
| 749 |
if (nrows .gt. 0) then |
| 750 |
call hload ( nrows, 1, hpiv(i1), 1 ) |
| 751 |
call hload ( nrows, 0, hs(n+i1), 1 ) |
| 752 |
end if |
| 753 |
|
| 754 |
if (lcrash .eq. 1) then |
| 755 |
nbasic = 0 |
| 756 |
else |
| 757 |
|
| 758 |
* lcrash = 2 or 3: Insert nonlinear slacks. |
| 759 |
|
| 760 |
nbasic = nncon |
| 761 |
if (nncon .gt. 0) then |
| 762 |
call hload ( nncon, 3, hpiv , 1 ) |
| 763 |
call hload ( nncon, 3, hs(n+1), 1 ) |
| 764 |
end if |
| 765 |
end if |
| 766 |
|
| 767 |
if (lcrash .eq. 3) then |
| 768 |
|
| 769 |
* Insert linear inequality slacks (including free rows). |
| 770 |
|
| 771 |
do 25 i = i1, m |
| 772 |
if (hrtype(i) .ge. 1) then |
| 773 |
nbasic = nbasic + 1 |
| 774 |
nrows = nrows - 1 |
| 775 |
hpiv(i) = 3 |
| 776 |
hs(n+i) = 3 |
| 777 |
end if |
| 778 |
25 continue |
| 779 |
end if |
| 780 |
|
| 781 |
* We're done if there are no relevant rows. |
| 782 |
|
| 783 |
if (nrows .eq. 0) go to 800 |
| 784 |
|
| 785 |
else |
| 786 |
* --------------------------------------------------------------- |
| 787 |
* Second or third call. lcrash = 4 or 5. |
| 788 |
* Initialize hpiv(*) for all rows. |
| 789 |
* hs(*) already defines a basis for the full problem, |
| 790 |
* but we want to do better by including only some of the slacks. |
| 791 |
* --------------------------------------------------------------- |
| 792 |
if (lcrash .eq. 4) then |
| 793 |
* ------------------------------------------------------------ |
| 794 |
* Crash on linear LG rows. |
| 795 |
* ------------------------------------------------------------ |
| 796 |
if (nncon .eq. m) go to 900 |
| 797 |
i1 = nncon + 1 |
| 798 |
i2 = m |
| 799 |
|
| 800 |
* Mark nonlinear rows as pivoted: hpiv(i) = 3. |
| 801 |
|
| 802 |
nbasic = nncon |
| 803 |
if (nbasic .gt. 0) then |
| 804 |
call hload ( nbasic, 3, hpiv, 1 ) |
| 805 |
end if |
| 806 |
|
| 807 |
* Mark linear E rows as pivoted: hpiv(i) = 3 |
| 808 |
* Make linear LG rows available: hpiv(i) = 1, hs(n+i) = 0. |
| 809 |
|
| 810 |
do 30 i = i1, m |
| 811 |
if (hrtype(i) .eq. 0) then |
| 812 |
nbasic = nbasic + 1 |
| 813 |
hpiv(i) = 3 |
| 814 |
else |
| 815 |
hpiv(i) = 1 |
| 816 |
hs(n+i) = 0 |
| 817 |
end if |
| 818 |
30 continue |
| 819 |
|
| 820 |
* Mark linear LG rows with hpiv(i) = 2 |
| 821 |
* if any basic columns contain a nonzero in row i. |
| 822 |
|
| 823 |
do 50 j = 1, n |
| 824 |
if (hs(j) .eq. 3) then |
| 825 |
do 40 k = ka(j), ka(j+1) - 1 |
| 826 |
i = ha(k) |
| 827 |
if (hrtype(i) .eq. 1) then |
| 828 |
if (i .gt. nncon) then |
| 829 |
if (a(k) .ne. zero) hpiv(i) = 2 |
| 830 |
end if |
| 831 |
end if |
| 832 |
40 continue |
| 833 |
end if |
| 834 |
50 continue |
| 835 |
|
| 836 |
else |
| 837 |
* ------------------------------------------------------------ |
| 838 |
* lcrash = 5. Crash on nonlinear rows. |
| 839 |
* ------------------------------------------------------------ |
| 840 |
i1 = 1 |
| 841 |
i2 = nncon |
| 842 |
|
| 843 |
* Mark all linear rows as pivoted: hpiv(i) = 3 |
| 844 |
|
| 845 |
nbasic = m - nncon |
| 846 |
if (nbasic .gt. 0) then |
| 847 |
call hload ( nbasic, 3, hpiv(nncon+1), 1 ) |
| 848 |
end if |
| 849 |
|
| 850 |
* Make nonlinear rows available: hpiv(i) = 1, hs(n+i) = 0. |
| 851 |
|
| 852 |
call hload ( nncon, 1, hpiv , 1 ) |
| 853 |
call hload ( nncon, 0, hs(n+1), 1 ) |
| 854 |
|
| 855 |
* Mark nonlinear rows with hpiv(i) = 2 |
| 856 |
* if any basic columns contain a nonzero in row i. |
| 857 |
|
| 858 |
do 70 j = 1, n |
| 859 |
if (hs(j) .eq. 3) then |
| 860 |
do 60 k = ka(j), ka(j+1) - 1 |
| 861 |
i = ha(k) |
| 862 |
if (i .le. nncon) then |
| 863 |
if (a(k) .ne. zero) hpiv(i) = 2 |
| 864 |
end if |
| 865 |
60 continue |
| 866 |
end if |
| 867 |
70 continue |
| 868 |
end if |
| 869 |
end if |
| 870 |
|
| 871 |
* ------------------------------------------------------------------ |
| 872 |
* Stage 1: Insert relevant slacks (N, L or G rows, hrtype = 1 or 2). |
| 873 |
* If lcrash = 4 or 5, grab them only if they are more than |
| 874 |
* tolslk from their bound. |
| 875 |
* ------------------------------------------------------------------ |
| 876 |
stage = 1 |
| 877 |
gotslk = lcrash .eq. 4 .or. lcrash .eq. 5 |
| 878 |
|
| 879 |
do 100 i = i1, i2 |
| 880 |
j = n + i |
| 881 |
if (hs(j) .le. 1 .and. hrtype(i) .gt. 0) then |
| 882 |
if (gotslk) then |
| 883 |
d1 = xn(j) - bl(j) |
| 884 |
d2 = bu(j) - xn(j) |
| 885 |
if (min( d1, d2 ) .le. tolslk) then |
| 886 |
|
| 887 |
* The slack is close to a bound or infeasible. |
| 888 |
* Move it exactly onto the bound. |
| 889 |
|
| 890 |
if (d1 .le. d2) then |
| 891 |
xn(j) = bl(j) |
| 892 |
hs(j) = 0 |
| 893 |
else |
| 894 |
xn(j) = bu(j) |
| 895 |
hs(j) = 1 |
| 896 |
end if |
| 897 |
go to 100 |
| 898 |
end if |
| 899 |
end if |
| 900 |
|
| 901 |
nbasic = nbasic + 1 |
| 902 |
num(stage) = num(stage) + 1 |
| 903 |
hpiv(i) = 3 |
| 904 |
hs(j) = 3 |
| 905 |
end if |
| 906 |
100 continue |
| 907 |
|
| 908 |
if (nbasic .eq. m) go to 700 |
| 909 |
|
| 910 |
* ------------------------------------------------------------------ |
| 911 |
* Apply a triangular crash to various subsets of the columns of A. |
| 912 |
* |
| 913 |
* hpiv(i) = 1 if row i is unmarked (initial state). |
| 914 |
* hpiv(i) = 3 if row i has been given a pivot |
| 915 |
* in one of a set of triangular columns. |
| 916 |
* hpiv(i) = 2 if one of the triangular columns contains |
| 917 |
* a nonzero in row i below the triangle. |
| 918 |
* ------------------------------------------------------------------ |
| 919 |
|
| 920 |
do 600 stage = 2, nstage |
| 921 |
stage2 = stage .eq. 2 |
| 922 |
stage3 = stage .eq. 3 |
| 923 |
stage4 = stage .eq. 4 |
| 924 |
stage5 = stage .eq. 5 |
| 925 |
|
| 926 |
* --------------------------------------------------------------- |
| 927 |
* Main loop for triangular crash. |
| 928 |
* --------------------------------------------------------------- |
| 929 |
do 200 j = 1, n |
| 930 |
js = hs(j) |
| 931 |
if (js .gt. 1 ) go to 200 |
| 932 |
if (bl(j) .eq. bu(j)) go to 200 |
| 933 |
|
| 934 |
if ( stage2 ) then |
| 935 |
free = bl(j) .le. - big .and. bu(j) .ge. big |
| 936 |
if ( .not. free ) go to 200 |
| 937 |
|
| 938 |
else if ( stage3 ) then |
| 939 |
prefer = js .lt. 0 |
| 940 |
if ( .not. prefer) go to 200 |
| 941 |
end if |
| 942 |
|
| 943 |
* Find the biggest aij, ignoring free rows. |
| 944 |
|
| 945 |
k1 = ka(j) |
| 946 |
k2 = ka(j+1) - 1 |
| 947 |
aimax = zero |
| 948 |
|
| 949 |
do 130 k = k1, k2 |
| 950 |
i = ha(k) |
| 951 |
if (hrtype(i) .ne. 2) then |
| 952 |
ai = a(k) |
| 953 |
aimax = max( aimax, abs( ai ) ) |
| 954 |
end if |
| 955 |
130 continue |
| 956 |
|
| 957 |
* Prevent small pivots if crash tol is too small. |
| 958 |
|
| 959 |
if (aimax .le. small) go to 200 |
| 960 |
|
| 961 |
* Find the biggest pivots in rows that are still |
| 962 |
* unpivoted and unmarked. Ignore smallish elements. |
| 963 |
* nz counts the number of relevant nonzeros. |
| 964 |
|
| 965 |
aitol = aimax * tcrash |
| 966 |
nz = 0 |
| 967 |
npiv = 0 |
| 968 |
ipiv(1) = 0 |
| 969 |
ipiv(2) = 0 |
| 970 |
apiv(1) = zero |
| 971 |
apiv(2) = zero |
| 972 |
|
| 973 |
do 150 k = k1, k2 |
| 974 |
i = ha(k) |
| 975 |
if (hs(n+i) .ne. 3) then |
| 976 |
ai = abs( a(k) ) |
| 977 |
if (ai .gt. aitol) then |
| 978 |
nz = nz + 1 |
| 979 |
ip = hpiv(i) |
| 980 |
if (ip .le. 2) then |
| 981 |
if (apiv(ip) .lt. ai) then |
| 982 |
apiv(ip) = ai |
| 983 |
ipiv(ip) = i |
| 984 |
end if |
| 985 |
else |
| 986 |
npiv = npiv + 1 |
| 987 |
end if |
| 988 |
end if |
| 989 |
end if |
| 990 |
150 continue |
| 991 |
|
| 992 |
* Grab unit or double columns. |
| 993 |
|
| 994 |
if ( stage4 ) then |
| 995 |
if (nz .ne. 1) go to 200 |
| 996 |
else if ( stage5 ) then |
| 997 |
if (nz .ne. 2) go to 200 |
| 998 |
end if |
| 999 |
|
| 1000 |
* See if the column contained a potential pivot. |
| 1001 |
* An unmarked row is favored over a marked row. |
| 1002 |
|
| 1003 |
ip = 1 |
| 1004 |
if (ipiv(1) .eq. 0 .and. npiv .eq. 0) ip = 2 |
| 1005 |
i = ipiv(ip) |
| 1006 |
|
| 1007 |
if (i .gt. 0) then |
| 1008 |
nbasic = nbasic + 1 |
| 1009 |
num(stage) = num(stage) + 1 |
| 1010 |
hpiv(i) = 3 |
| 1011 |
hs(j) = 3 |
| 1012 |
if (nbasic .ge. m) go to 700 |
| 1013 |
|
| 1014 |
* Mark off all relevant unmarked rows. |
| 1015 |
|
| 1016 |
do 180 k = k1, k2 |
| 1017 |
i = ha(k) |
| 1018 |
if (hs(n+i) .ne. 3) then |
| 1019 |
ai = abs( a(k) ) |
| 1020 |
if (ai .gt. aitol) then |
| 1021 |
if (hpiv(i) .eq. 1) hpiv(i) = 2 |
| 1022 |
end if |
| 1023 |
end if |
| 1024 |
180 continue |
| 1025 |
end if |
| 1026 |
200 continue |
| 1027 |
600 continue |
| 1028 |
|
| 1029 |
* ------------------------------------------------------------------ |
| 1030 |
* All stages finished. |
| 1031 |
* Fill remaining gaps with slacks. |
| 1032 |
* ------------------------------------------------------------------ |
| 1033 |
700 npad = m - nbasic |
| 1034 |
if (iprint .gt. 0) write(iprint, 1200) num, npad |
| 1035 |
|
| 1036 |
if (npad .gt. 0) then |
| 1037 |
do 720 i = 1, m |
| 1038 |
if (hpiv(i) .lt. 3) then |
| 1039 |
nbasic = nbasic + 1 |
| 1040 |
hs(n+i) = 3 |
| 1041 |
if (nbasic .ge. m) go to 800 |
| 1042 |
end if |
| 1043 |
720 continue |
| 1044 |
end if |
| 1045 |
|
| 1046 |
* ------------------------------------------------------------------ |
| 1047 |
* Make sure there aren't lots of nonbasic slacks floating off |
| 1048 |
* their bounds. They could take lots of iterations to move. |
| 1049 |
* ------------------------------------------------------------------ |
| 1050 |
800 do 850 i = i1, i2 |
| 1051 |
j = n + i |
| 1052 |
if (hs(j) .le. 1 .and. hrtype(i) .gt. 0) then |
| 1053 |
d1 = xn(j) - bl(j) |
| 1054 |
d2 = bu(j) - xn(j) |
| 1055 |
if (min( d1, d2 ) .le. tolslk) then |
| 1056 |
|
| 1057 |
* The slack is close to a bound or infeasible. |
| 1058 |
* Move it exactly onto the bound. |
| 1059 |
|
| 1060 |
if (d1 .le. d2) then |
| 1061 |
xn(j) = bl(j) |
| 1062 |
hs(j) = 0 |
| 1063 |
else |
| 1064 |
xn(j) = bu(j) |
| 1065 |
hs(j) = 1 |
| 1066 |
end if |
| 1067 |
end if |
| 1068 |
end if |
| 1069 |
850 continue |
| 1070 |
|
| 1071 |
900 return |
| 1072 |
|
| 1073 |
1000 format(// ' Crash option', i3) |
| 1074 |
1030 format( ' Crash on linear E rows:') |
| 1075 |
1040 format( ' Crash on linear LG rows:') |
| 1076 |
1050 format( ' Crash on nonlinear rows:') |
| 1077 |
1200 format( |
| 1078 |
$ ' Slacks', i6, ' Free cols', i6, ' Preferred', i6 |
| 1079 |
$ / ' Unit ', i6, ' Double ', i6, ' Triangle ', i6, |
| 1080 |
$ ' Pad', i6) |
| 1081 |
|
| 1082 |
* end of m2crsh |
| 1083 |
end |
| 1084 |
|
| 1085 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 1086 |
|
| 1087 |
subroutine m2scal( m, n, nb, ne, nka, nn, nncon, nnjac, |
| 1088 |
$ hrtype, ha, ka, a, ascale, bl, bu, rmin, rmax ) |
| 1089 |
|
| 1090 |
implicit double precision (a-h,o-z) |
| 1091 |
integer*4 hrtype(m), ha(ne) |
| 1092 |
integer ka(nka) |
| 1093 |
double precision a(ne), ascale(nb), bl(nb), bu(nb) |
| 1094 |
double precision rmin(m), rmax(m) |
| 1095 |
|
| 1096 |
* ------------------------------------------------------------------ |
| 1097 |
* m2scal computes scale factors ascale from A, bl, bu. |
| 1098 |
* |
| 1099 |
* In phase 1, an iterative procedure based on geometric means is |
| 1100 |
* used to compute scales from a alone. This procedure is derived |
| 1101 |
* from a routine written by Robert Fourer, 1979. The main steps |
| 1102 |
* are: |
| 1103 |
* |
| 1104 |
* (1) Compute aratio = max(i1,i2,j) a(i1,j) / a(i2,j). |
| 1105 |
* (2) Divide each row i by |
| 1106 |
* ( min(j) a(i,j) * max(j) a(i,j) ) ** 1/2. |
| 1107 |
* (3) Divide each column j by |
| 1108 |
* ( min(i) a(i,j) * max(i) a(i,j) ) ** 1/2. |
| 1109 |
* (4) Compute sratio as in (1). |
| 1110 |
* (5) If sratio .lt. scltol * aratio, repeat from step (1). |
| 1111 |
* |
| 1112 |
* Free rows (hrtype=2) and fixed columns (bl=bu) are not used |
| 1113 |
* at this stage. |
| 1114 |
* |
| 1115 |
* In phase 2, the scales for free rows are set to be their largest |
| 1116 |
* element. |
| 1117 |
* |
| 1118 |
* In phase 3, fixed columns are summed in order to compute |
| 1119 |
* a scale factor sigma that allows for the effective rhs of the |
| 1120 |
* constraints. All scales are then multiplied by sigma. |
| 1121 |
* |
| 1122 |
* |
| 1123 |
* If lscale = 1, the first nncon rows and the first nn columns will |
| 1124 |
* retain scales of 1.0 during phases 1-2, and phase 3 will not be |
| 1125 |
* performed. (This takes effect if the problem is nonlinear but |
| 1126 |
* the user has specified scale linear variables only.) |
| 1127 |
* However, all rows contribute to the linear column scales, |
| 1128 |
* and all columns contribute to the linear row scales. |
| 1129 |
* |
| 1130 |
* If lscale = 2, all rows and columns are scaled. To guard against |
| 1131 |
* misleadingly small Jacobians, if the maximum element in any of |
| 1132 |
* the first nncon rows or the first nnjac columns is less than |
| 1133 |
* smallj, the corresponding row or column retains a scale of 1.0. |
| 1134 |
* |
| 1135 |
* Initial version March 1981. |
| 1136 |
* Feb 1983. For convenience, everything is now double-precision. |
| 1137 |
* Aug 1983. Revised to damp the effect of very small elements. |
| 1138 |
* On each pass, a new row or column scale will not be |
| 1139 |
* smaller than sqrt(damp) times the largest (scaled) |
| 1140 |
* element in that row or column. |
| 1141 |
* Oct 1986. Scale option 2 and phase 3 implemented. |
| 1142 |
* Nov 1989. Large scales are now reduced to at most 0.1/tolx (say) |
| 1143 |
* to help prevent obvious infeasibilities when the |
| 1144 |
* problem is unscaled. |
| 1145 |
* ------------------------------------------------------------------ |
| 1146 |
|
| 1147 |
common /m1eps / eps,eps0,eps1,eps2,eps3,eps4,eps5,plinfy |
| 1148 |
common /m1file/ iread,iprint,isumm |
| 1149 |
common /m2parm/ dparm(30),iparm(30) |
| 1150 |
common /m3scal/ sclobj,scltol,lscale |
| 1151 |
common /m5log1/ idebug,ierr,lprint |
| 1152 |
common /m5tols/ toldj(3),tolx,tolpiv,tolrow,rowerr,xnorm |
| 1153 |
|
| 1154 |
intrinsic abs, min, max, sqrt |
| 1155 |
|
| 1156 |
double precision ac, ar, amin, amax, aratio, bnd, b1, b2, |
| 1157 |
$ cmin, cmax, cratio, damp, sigma, |
| 1158 |
$ small, smallj, sratio |
| 1159 |
|
| 1160 |
parameter ( zero = 0.0d+0, one = 1.0d+0, |
| 1161 |
$ damp = 1.0d-4, smallj = 1.0d-2 ) |
| 1162 |
|
| 1163 |
if (iprint .gt. 0 ) write(iprint, 1000) |
| 1164 |
if (scltol .ge. one) scltol = 0.99 |
| 1165 |
bplus = 0.1*plinfy |
| 1166 |
aratio = bplus |
| 1167 |
maxk = 11 |
| 1168 |
if (lscale .eq. 1) then |
| 1169 |
* Do linear rows and columns only. |
| 1170 |
istart = nncon + 1 |
| 1171 |
jstart = nn + 1 |
| 1172 |
else |
| 1173 |
* Do all rows and cols if lscale .ge. 2 |
| 1174 |
istart = 1 |
| 1175 |
jstart = 1 |
| 1176 |
end if |
| 1177 |
|
| 1178 |
do 50 j = 1, nb |
| 1179 |
ascale(j) = one |
| 1180 |
50 continue |
| 1181 |
|
| 1182 |
if (jstart .gt. n) go to 900 |
| 1183 |
|
| 1184 |
* ------------------------------------------------------------------ |
| 1185 |
* Main loop for phase 1. |
| 1186 |
* Only the following row-types are used: |
| 1187 |
* hrtype(i) = 2 for n rows (objective or free rows), |
| 1188 |
* hrtype(i) = 0 or 1 otherwise. |
| 1189 |
* ------------------------------------------------------------------ |
| 1190 |
|
| 1191 |
do 400 kk = 1, maxk |
| 1192 |
|
| 1193 |
* Find the largest column ratio. |
| 1194 |
* Also set new column scales (except on pass 0). |
| 1195 |
|
| 1196 |
npass = kk - 1 |
| 1197 |
amin = bplus |
| 1198 |
amax = zero |
| 1199 |
small = smallj |
| 1200 |
sratio = one |
| 1201 |
|
| 1202 |
do 250 j = jstart, n |
| 1203 |
if (bl(j) .lt. bu(j)) then |
| 1204 |
cmin = bplus |
| 1205 |
cmax = zero |
| 1206 |
|
| 1207 |
do 230 k = ka(j), ka(j+1) - 1 |
| 1208 |
i = ha(k) |
| 1209 |
if (hrtype(i) .eq. 2 ) go to 230 |
| 1210 |
ar = abs( a(k) ) |
| 1211 |
if (ar .eq. zero) go to 230 |
| 1212 |
ar = ar / ascale(n+i) |
| 1213 |
cmin = min( cmin, ar ) |
| 1214 |
cmax = max( cmax, ar ) |
| 1215 |
230 continue |
| 1216 |
|
| 1217 |
ac = max( cmin, damp*cmax ) |
| 1218 |
ac = sqrt( ac ) * sqrt( cmax ) |
| 1219 |
if (j .gt. nnjac) small = zero |
| 1220 |
if (cmax .le. small) ac = one |
| 1221 |
if (npass .gt. 0 ) ascale(j) = ac |
| 1222 |
amin = min( amin, cmin / ascale(j) ) |
| 1223 |
amax = max( amax, cmax / ascale(j) ) |
| 1224 |
cratio = cmax / cmin |
| 1225 |
sratio = max( sratio, cratio ) |
| 1226 |
end if |
| 1227 |
250 continue |
| 1228 |
|
| 1229 |
if (iprint .gt. 0) then |
| 1230 |
write(iprint, 1200) npass, amin, amax, sratio |
| 1231 |
end if |
| 1232 |
if (npass .ge. 3 .and. |
| 1233 |
$ sratio .ge. aratio*scltol) go to 420 |
| 1234 |
if (kk .eq. maxk ) go to 420 |
| 1235 |
aratio = sratio |
| 1236 |
|
| 1237 |
|
| 1238 |
* Set new row scales for the next pass. |
| 1239 |
|
| 1240 |
if (istart .le. m) then |
| 1241 |
do 300 i = istart, m |
| 1242 |
rmin(i) = bplus |
| 1243 |
rmax(i) = zero |
| 1244 |
300 continue |
| 1245 |
|
| 1246 |
do 350 j = 1, n |
| 1247 |
if (bl(j) .lt. bu(j)) then |
| 1248 |
ac = ascale(j) |
| 1249 |
|
| 1250 |
do 330 k = ka(j), ka(j+1) - 1 |
| 1251 |
i = ha(k) |
| 1252 |
if (i .lt. istart) go to 330 |
| 1253 |
ar = abs( a(k) ) |
| 1254 |
if (ar .eq. zero ) go to 330 |
| 1255 |
ar = ar / ac |
| 1256 |
rmin(i) = min( rmin(i), ar ) |
| 1257 |
rmax(i) = max( rmax(i), ar ) |
| 1258 |
330 continue |
| 1259 |
end if |
| 1260 |
350 continue |
| 1261 |
|
| 1262 |
do 360 i = istart, m |
| 1263 |
j = n + i |
| 1264 |
ar = rmax(i) |
| 1265 |
if (i .le. nncon .and. ar .le. smallj) then |
| 1266 |
ascale(j) = one |
| 1267 |
else |
| 1268 |
ac = max( rmin(i), damp*ar ) |
| 1269 |
ascale(j) = sqrt( ac ) * sqrt( ar ) |
| 1270 |
end if |
| 1271 |
360 continue |
| 1272 |
end if |
| 1273 |
400 continue |
| 1274 |
|
| 1275 |
* ------------------------------------------------------------------ |
| 1276 |
* End of main loop. |
| 1277 |
* ------------------------------------------------------------------ |
| 1278 |
|
| 1279 |
* Invert the column scales, so that structurals and logicals |
| 1280 |
* can be treated the same way during subsequent unscaling. |
| 1281 |
* Find the min and max column scales while we're at it. |
| 1282 |
* Nov 1989: nclose counts how many are "close" to 1. |
| 1283 |
* For problems that are already well-scaled, it seemed sensible to |
| 1284 |
* set the "close" ones exactly equal to 1. |
| 1285 |
* Tried "close" = (0.5,2.0) and (0.9,1.1), but they helped only |
| 1286 |
* occasionally. Have decided not to interfree. |
| 1287 |
|
| 1288 |
420 amin = bplus |
| 1289 |
amax = zero |
| 1290 |
close1 = 0.5 |
| 1291 |
close2 = 2.0 |
| 1292 |
nclose = 0 |
| 1293 |
|
| 1294 |
|
| 1295 |
do 430 j = 1, n |
| 1296 |
ac = one / ascale(j) |
| 1297 |
|
| 1298 |
if (amin .gt. ac) then |
| 1299 |
amin = ac |
| 1300 |
jmin = j |
| 1301 |
end if |
| 1302 |
if (amax .lt. ac) then |
| 1303 |
amax = ac |
| 1304 |
jmax = j |
| 1305 |
end if |
| 1306 |
|
| 1307 |
if (ac .gt. close1 .and. ac .lt. close2) then |
| 1308 |
nclose = nclose + 1 |
| 1309 |
*---- ac = one |
| 1310 |
end if |
| 1311 |
|
| 1312 |
ascale(j) = ac |
| 1313 |
430 continue |
| 1314 |
|
| 1315 |
* Remember, column scales are upside down. |
| 1316 |
|
| 1317 |
amax = one / amax |
| 1318 |
amin = one / amin |
| 1319 |
k = max( 1, n - jstart + 1 ) |
| 1320 |
percnt = nclose * 100.0 / k |
| 1321 |
if (iprint .gt. 0) then |
| 1322 |
write(iprint, 1300) |
| 1323 |
write(iprint, 1310) 'Col', jmax, amax, 'Col', jmin, amin, |
| 1324 |
$ nclose, percnt |
| 1325 |
end if |
| 1326 |
|
| 1327 |
* ------------------------------------------------------------------ |
| 1328 |
* Phase 2. Deal with empty rows and free rows. |
| 1329 |
* Find the min and max row scales while we're at it. |
| 1330 |
* ------------------------------------------------------------------ |
| 1331 |
amin = bplus |
| 1332 |
amax = zero |
| 1333 |
imin = 0 |
| 1334 |
imax = 0 |
| 1335 |
nclose = 0 |
| 1336 |
|
| 1337 |
do 440 i = istart, m |
| 1338 |
j = n + i |
| 1339 |
|
| 1340 |
if (hrtype(i) .eq. 2) then |
| 1341 |
ar = rmax(i) |
| 1342 |
if (ar .eq. zero) ar = one |
| 1343 |
else |
| 1344 |
ar = ascale(j) |
| 1345 |
if (ar .eq. zero) ar = one |
| 1346 |
|
| 1347 |
if (amin .gt. ar) then |
| 1348 |
amin = ar |
| 1349 |
imin = i |
| 1350 |
end if |
| 1351 |
if (amax .lt. ar) then |
| 1352 |
amax = ar |
| 1353 |
imax = i |
| 1354 |
end if |
| 1355 |
|
| 1356 |
if (ar .gt. close1 .and. ar .lt. close2) then |
| 1357 |
nclose = nclose + 1 |
| 1358 |
*---- ar = one |
| 1359 |
end if |
| 1360 |
end if |
| 1361 |
|
| 1362 |
ascale(j) = ar |
| 1363 |
440 continue |
| 1364 |
|
| 1365 |
if (imin .eq. 0) then |
| 1366 |
amin = zero |
| 1367 |
amax = zero |
| 1368 |
end if |
| 1369 |
k = max( 1, m - istart + 1 ) |
| 1370 |
percnt = nclose * 100.0 / k |
| 1371 |
if (iprint .gt. 0) then |
| 1372 |
write(iprint, 1310) 'Row', imin, amin, 'Row', imax, amax, |
| 1373 |
$ nclose, percnt |
| 1374 |
end if |
| 1375 |
|
| 1376 |
* ------------------------------------------------------------------ |
| 1377 |
* Phase 3. |
| 1378 |
* Compute what is effectively the rhs for the constraints. |
| 1379 |
* We set rmax = ( A I ) * x for fixed columns and slacks, |
| 1380 |
* including positive lower bounds and negative upper bounds. |
| 1381 |
* ------------------------------------------------------------------ |
| 1382 |
if (lscale .ge. 2) then |
| 1383 |
call dload ( m, zero, rmax, 1 ) |
| 1384 |
|
| 1385 |
do 500 j = 1, nb |
| 1386 |
bnd = zero |
| 1387 |
b1 = bl(j) |
| 1388 |
b2 = bu(j) |
| 1389 |
if (b1 .eq. b2 ) bnd = b1 |
| 1390 |
if (b1 .gt. zero) bnd = b1 |
| 1391 |
if (b2 .lt. zero) bnd = b2 |
| 1392 |
if (bnd .eq. zero) go to 500 |
| 1393 |
|
| 1394 |
if (j .le. n ) then |
| 1395 |
do 480 k = ka(j), ka(j+1) - 1 |
| 1396 |
i = ha(k) |
| 1397 |
rmax(i) = rmax(i) + a(k) * bnd |
| 1398 |
480 continue |
| 1399 |
else |
| 1400 |
* Free slacks never get here, |
| 1401 |
* so we don't have to skip them. |
| 1402 |
i = j - n |
| 1403 |
rmax(i) = rmax(i) + bnd |
| 1404 |
end if |
| 1405 |
500 continue |
| 1406 |
|
| 1407 |
* We don't want nonzeros in free rows to interfere. |
| 1408 |
|
| 1409 |
do 520 i = 1, m |
| 1410 |
if (hrtype(i) .eq. 2) rmax(i) = zero |
| 1411 |
520 continue |
| 1412 |
|
| 1413 |
* Scale rmax = rmax / (row scales), and use its norm sigma |
| 1414 |
* to adjust both row and column scales. |
| 1415 |
|
| 1416 |
ac = dnorm1( m, rmax, 1 ) |
| 1417 |
call dddiv ( m, ascale(n+1), 1, rmax, 1 ) |
| 1418 |
sigma = dnorm1( m, rmax, 1 ) |
| 1419 |
if (iprint .gt. 0) write(iprint, 1400) ac, sigma |
| 1420 |
sigma = max( sigma, one ) |
| 1421 |
call dscal ( nb, sigma, ascale, 1 ) |
| 1422 |
|
| 1423 |
* Big scales might lead to excessive infeasibility when the |
| 1424 |
* problem is unscaled. If any are too big, scale them down. |
| 1425 |
|
| 1426 |
amax = zero |
| 1427 |
do 540 j = 1, n |
| 1428 |
amax = max( amax, ascale(j) ) |
| 1429 |
540 continue |
| 1430 |
|
| 1431 |
do 550 i = 1, m |
| 1432 |
if (hrtype(i) .ne. 2) then |
| 1433 |
amax = max( amax, ascale(n + i) ) |
| 1434 |
end if |
| 1435 |
550 continue |
| 1436 |
|
| 1437 |
big = 0.1 / tolx |
| 1438 |
sigma = big / amax |
| 1439 |
if (sigma .lt. one) then |
| 1440 |
call dscal ( nb, sigma, ascale, 1 ) |
| 1441 |
if (iprint .gt. 0) write(iprint, 1410) sigma |
| 1442 |
end if |
| 1443 |
end if |
| 1444 |
|
| 1445 |
if (iparm(4) .gt. 0 .and. iprint .gt. 0) then |
| 1446 |
if (istart .le. m) write(iprint,1500) (i,ascale(n+i),i=istart,m) |
| 1447 |
if (jstart .le. n) write(iprint,1600) (j,ascale(j ),j=jstart,n) |
| 1448 |
end if |
| 1449 |
|
| 1450 |
900 return |
| 1451 |
|
| 1452 |
1000 format(// ' Scaling' / ' -------' |
| 1453 |
$ / ' Min elem Max elem Max col ratio') |
| 1454 |
1200 format( ' After', i3, 1p, e12.2, e12.2, 0p, f20.2) |
| 1455 |
1300 format(/ 12x, 'Min scale', 23x, 'Max scale', 6x, |
| 1456 |
$ 'Between 0.5 and 2.0') |
| 1457 |
1310 format(1x, a, i7, 1p, e10.1, 12x, a, i7, e10.1, i17, 0p, f8.1) |
| 1458 |
1400 format(/ ' Norm of fixed columns and slacks', 1p, e20.1 |
| 1459 |
$ / ' (before and after row scaling) ', 1p, e20.1) |
| 1460 |
1410 format( ' Scales are large --- reduced by ', 1p, e20.1) |
| 1461 |
1500 format(// ' Row scales r(i)', |
| 1462 |
$ 8x, ' a(i,j) = r(i) * scaled a(i,j) / c(j)' |
| 1463 |
$ / ' ----------------' // 5(i6, g16.5)) |
| 1464 |
1600 format(// ' Column scales c(j)', |
| 1465 |
$ 5x, ' x(j) = c(j) * scaled x(j)' |
| 1466 |
$ / ' -------------------' // 5(i6, g16.5)) |
| 1467 |
|
| 1468 |
* end of m2scal |
| 1469 |
end |
| 1470 |
|
| 1471 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 1472 |
|
| 1473 |
subroutine m2scla( mode, m, n, nb, ne, nka, |
| 1474 |
$ ha, ka, a, ascale, bl, bu, pi, xn ) |
| 1475 |
|
| 1476 |
implicit double precision (a-h,o-z) |
| 1477 |
integer*4 ha(ne) |
| 1478 |
integer ka(nka) |
| 1479 |
double precision a(ne), ascale(nb), bl(nb), bu(nb) |
| 1480 |
double precision pi(m), xn(nb) |
| 1481 |
|
| 1482 |
* ------------------------------------------------------------------ |
| 1483 |
* m2scla scales or unscales a, bl, bu, pi, xn using ascale. |
| 1484 |
* ------------------------------------------------------------------ |
| 1485 |
|
| 1486 |
common /m1eps / eps,eps0,eps1,eps2,eps3,eps4,eps5,plinfy |
| 1487 |
common /m3scal/ sclobj,scltol,lscale |
| 1488 |
common /m5lobj/ sinf,wtobj,minimz,ninf,iobj,jobj,kobj |
| 1489 |
|
| 1490 |
parameter ( one = 1.0d+0 ) |
| 1491 |
|
| 1492 |
bplus = 0.1*plinfy |
| 1493 |
if (mode .eq. 1) then |
| 1494 |
* --------------------------------------------------------------- |
| 1495 |
* mode = 1 --- scale a, bl, bu, xn and pi. |
| 1496 |
* --------------------------------------------------------------- |
| 1497 |
do 150 j = 1, nb |
| 1498 |
scale = ascale(j) |
| 1499 |
if (j .le. n) then |
| 1500 |
do 110 k = ka(j), ka(j+1) - 1 |
| 1501 |
i = ha(k) |
| 1502 |
a(k) = a(k) * ( scale / ascale(n+i) ) |
| 1503 |
110 continue |
| 1504 |
end if |
| 1505 |
xn(j) = xn(j) / scale |
| 1506 |
if (bl(j) .gt. -bplus) bl(j) = bl(j) / scale |
| 1507 |
if (bu(j) .lt. bplus) bu(j) = bu(j) / scale |
| 1508 |
150 continue |
| 1509 |
|
| 1510 |
call ddscl ( m, ascale(n+1), 1, pi, 1 ) |
| 1511 |
if (jobj .gt. 0) sclobj = ascale(jobj) |
| 1512 |
else |
| 1513 |
* --------------------------------------------------------------- |
| 1514 |
* mode = 2 --- unscale everything. |
| 1515 |
* --------------------------------------------------------------- |
| 1516 |
do 250 j = 1, nb |
| 1517 |
scale = ascale(j) |
| 1518 |
if (j .le. n) then |
| 1519 |
do 210 k = ka(j), ka(j+1) - 1 |
| 1520 |
i = ha(k) |
| 1521 |
a(k) = a(k) * ( ascale(n+i) / scale ) |
| 1522 |
210 continue |
| 1523 |
end if |
| 1524 |
xn(j) = xn(j) * scale |
| 1525 |
if (bl(j) .gt. -bplus) bl(j) = bl(j) * scale |
| 1526 |
if (bu(j) .lt. bplus) bu(j) = bu(j) * scale |
| 1527 |
250 continue |
| 1528 |
|
| 1529 |
call dddiv ( m, ascale(n+1), 1, pi, 1 ) |
| 1530 |
sclobj = one |
| 1531 |
end if |
| 1532 |
|
| 1533 |
* end of m2scla |
| 1534 |
end |
| 1535 |
|
| 1536 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 1537 |
|
| 1538 |
subroutine m2unpk( jq, m, n, ne, nka, a, ha, ka, y ) |
| 1539 |
|
| 1540 |
implicit double precision (a-h,o-z) |
| 1541 |
integer*4 ha(ne) |
| 1542 |
integer ka(nka) |
| 1543 |
double precision a(ne) |
| 1544 |
double precision y(m) |
| 1545 |
|
| 1546 |
* ------------------------------------------------------------------ |
| 1547 |
* m2unpk expands the jq-th column of ( A I ) into y. |
| 1548 |
* ------------------------------------------------------------------ |
| 1549 |
|
| 1550 |
parameter ( zero = 0.0d+0, one = 1.0d+0 ) |
| 1551 |
|
| 1552 |
call dload ( m, zero, y, 1 ) |
| 1553 |
|
| 1554 |
if (jq .le. n) then |
| 1555 |
do 10 k = ka(jq), ka(jq+1) - 1 |
| 1556 |
i = ha(k) |
| 1557 |
y(i) = a(k) |
| 1558 |
10 continue |
| 1559 |
else |
| 1560 |
islack = jq - n |
| 1561 |
y(islack) = one |
| 1562 |
end if |
| 1563 |
|
| 1564 |
* end of m2unpk |
| 1565 |
end |
| 1566 |
|
| 1567 |
*+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| 1568 |
|
| 1569 |
subroutine matcol( m, n, nb, ne, nka, |
| 1570 |
$ a, ha, ka, bl, bu, col, ztol ) |
| 1571 |
|
| 1572 |
implicit double precision (a-h,o-z) |
| 1573 |
integer*4 ha(ne) |
| 1574 |
integer ka(nka) |
| 1575 |
double precision a(ne), bl(nb), bu(nb), col(m) |
| 1576 |
|
| 1577 |
* ------------------------------------------------------------------ |
| 1578 |
* matcol creates a new matrix column from the dense vector col. |
| 1579 |
* It becomes column number jnew, which is updated accordingly. |
| 1580 |
* Elements as small as the zero tolerance ztol are not retained. |
| 1581 |
* Default bounds are given to the new variable. |
| 1582 |
* ------------------------------------------------------------------ |
| 1583 |
|
| 1584 |
common /m1file/ iread,iprint,isumm |
| 1585 |
common /m3mps3/ aijtol,bstruc(2),mlst,mer, |
| 1586 |
$ aijmin,aijmax,na0,line,ier(20) |
| 1587 |
common /cyclcm/ cnvtol,jnew,materr,maxcy,nephnt,nphant,nprint |
| 1588 |
|
| 1589 |
intrinsic abs |
| 1590 |
|
| 1591 |
if (jnew .ge. n) go to 900 |
| 1592 |
jnew = jnew + 1 |
| 1593 |
ia = ka(jnew) |
| 1594 |
|
| 1595 |
do 100 i = 1, m |
| 1596 |
if (abs( col(i) ) .le. ztol) go to 100 |
| 1597 |
if (ia .gt. ne) go to 910 |
| 1598 |
a (ia) = col(i) |
| 1599 |
ha(ia) = i |
| 1600 |
ia = ia + 1 |
| 1601 |
100 continue |
| 1602 |
|
| 1603 |
if (ia .eq. ka(jnew)) go to 920 |
| 1604 |
bl(jnew) = bstruc(1) |
| 1605 |
bu(jnew) = bstruc(2) |
| 1606 |
ka(jnew + 1) = ia |
| 1607 |
return |
| 1608 |
|
| 1609 |
* Too many columns. |
| 1610 |
|
| 1611 |
900 if (iprint .gt. 0) write(iprint, 1000) |
| 1612 |
if (isumm .gt. 0) write(isumm , 1000) |
| 1613 |
go to 990 |
| 1614 |
|
| 1615 |
* Too many elements. |
| 1616 |
|
| 1617 |
910 if (iprint .gt. 0) write(iprint, 1100) |
| 1618 |
if (isumm .gt. 0) write(isumm , 1100) |
| 1619 |
go to 990 |
| 1620 |
|
| 1621 |
* Zero column. |
| 1622 |
|
| 1623 |
920 if (iprint .gt. 0) write(iprint, 1200) |
| 1624 |
if (isumm .gt. 0) write(isumm , 1200) |
| 1625 |
|
| 1626 |
* Error exit. |
| 1627 |
|
| 1628 |
990 materr = materr + 1 |
| 1629 |
return |
| 1630 |
|
| 1631 |
1000 format(/ ' XXX MATCOL error. Not enough Phantom columns.') |
| 1632 |
1100 format(/ ' XXX MATCOL error. Not enough Phantom elements.') |
| 1633 |
1200 format(/ ' XXX MATCOL error. New column of A was zero.') |
| 1634 |
|
| 1635 |
* end of matcol |
| 1636 |
end |
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