STATIC MYBOOL scaleCR(lprec *lp, REAL *scaledelta)
{
REAL *scalechange = NULL;
int Result;
if(!lp->scaling_used) {
allocREAL(lp, &lp->scalars, lp->sum_alloc + 1, FALSE);
for(Result = 0; Result <= lp->sum; Result++)
lp->scalars[Result] = 1;
lp->scaling_used = TRUE;
}
if(scaledelta == NULL)
allocREAL(lp, &scalechange, lp->sum + 1, FALSE);
else
scalechange = scaledelta;
Result=CurtisReidScales(lp, FALSE, scalechange, &scalechange[lp->rows]);
if(Result>0) {
/* Do the scaling*/
if(scale_updaterows(lp, scalechange, TRUE) ||
scale_updatecolumns(lp, &scalechange[lp->rows], TRUE))
lp->scalemode |= SCALE_CURTISREID;
set_action(&lp->spx_action, ACTION_REBASE | ACTION_REINVERT | ACTION_RECOMPUTE);
}
if(scaledelta == NULL)
FREE(scalechange);
return((MYBOOL) (Result > 0));
}
STATIC void formWeights(lprec *lp, int colnr, REAL *pcol, REAL **w)
/* This computes Bw = a, where B is the basis and a is a column of A */
{
allocREAL(lp, w, lp->rows+1, FALSE);
if(pcol == NULL)
fsolve(lp, colnr, *w, NULL, 0.0, 0.0, FALSE);
else {
MEMCOPY(*w, pcol, lp->rows+1);
/* *w[0] = 0; */ /* Test */
}
/*
if(pcol != NULL) {
REAL cEdge, hold;
int i;
cEdge = 0;
for(i = 1; i <= m; i++) {
hold = *w[i]-pcol[i];
cEdge += hold*hold;
}
cEdge /= m;
cEdge = sqrt(cEdge);
if(cEdge > lp->epspivot)
report(lp, SEVERE, "updatePricer: MRS error is %g\n", cEdge);
}
*/
}
STATIC int make_SOSchain(lprec *lp, MYBOOL forceresort)
{
int i, j, k, n;
MYBOOL *hold = NULL;
REAL *order, sum, weight;
SOSgroup *group = lp->SOS;
/* PART A: Resort individual SOS member lists, if specified */
if(forceresort)
SOS_member_sortlist(group, 0);
/* PART B: Tally SOS variables and create master SOS variable list */
n = 0;
for(i = 0; i < group->sos_count; i++)
n += group->sos_list[i]->size;
lp->sos_vars = n;
if(lp->sos_vars > 0) /* Prevent memory loss in case of multiple solves */
FREE(lp->sos_priority);
allocINT(lp, &lp->sos_priority, n, FALSE);
allocREAL(lp, &order, n, FALSE);
/* Move variable data to the master SOS list and sort by ascending weight */
n = 0;
sum = 0;
for(i = 0; i < group->sos_count; i++) {
for(j = 1; j <= group->sos_list[i]->size; j++) {
lp->sos_priority[n] = group->sos_list[i]->members[j];
weight = group->sos_list[i]->weights[j];
sum += weight;
order[n] = sum;
n++;
}
}
hpsortex(order, n, 0, sizeof(*order), FALSE, compareREAL, lp->sos_priority);
FREE(order);
/* Remove duplicate SOS variables */
allocMYBOOL(lp, &hold, lp->columns+1, TRUE);
k = 0;
for(i = 0; i < n; i++) {
j = lp->sos_priority[i];
if(!hold[j]) {
hold[j] = TRUE;
if(k < i)
lp->sos_priority[k] = j;
k++;
}
}
FREE(hold);
/* Adjust the size of the master variable list, if necessary */
if(k < lp->sos_vars) {
allocINT(lp, &lp->sos_priority, k, AUTOMATIC);
lp->sos_vars = k;
}
return( k );
}
STATIC MYBOOL resizePricer(lprec *lp)
{
if(!applyPricer(lp))
return( TRUE );
/* Reallocate vector for new size */
if(!allocREAL(lp, &(lp->edgeVector), lp->sum_alloc+1, AUTOMATIC))
return( FALSE );
/* Signal that we have not yet initialized the price vector */
MEMCLEAR(lp->edgeVector, lp->sum_alloc+1);
lp->edgeVector[0] = -1;
return( TRUE );
}
STATIC REAL auto_scale(lprec *lp)
{
int n = 1;
REAL scalingmetric = 0, *scalenew = NULL;
if(lp->scaling_used &&
((((lp->scalemode & SCALE_DYNUPDATE) == 0)) || (lp->bb_level > 0)))
return( scalingmetric);
if(lp->scalemode != SCALE_NONE) {
/* Allocate array for incremental scaling if appropriate */
if((lp->solvecount > 1) && (lp->bb_level < 1) &&
((lp->scalemode & SCALE_DYNUPDATE) != 0))
allocREAL(lp, &scalenew, lp->sum + 1, FALSE);
if(is_scaletype(lp, SCALE_CURTISREID)) {
scalingmetric = scaleCR(lp, scalenew);
}
else {
REAL scalinglimit, scalingdelta;
int count;
/* Integer value of scalelimit holds the maximum number of iterations; default to 1 */
count = (int) floor(lp->scalelimit);
scalinglimit = lp->scalelimit;
if((count == 0) || (scalinglimit == 0)) {
if(scalinglimit > 0)
count = DEF_SCALINGLIMIT; /* A non-zero convergence has been given, default to max 5 iterations */
else
count = 1;
}
else
scalinglimit -= count;
/* Scale to desired relative convergence or iteration limit */
n = 0;
scalingdelta = 1.0;
scalingmetric = 1.0;
while((n < count) && (fabs(scalingdelta) > scalinglimit)) {
n++;
scalingdelta = scale(lp, scalenew);
scalingmetric = scalingmetric*(1+scalingdelta);
}
scalingmetric -= 1;
}
}
/* Update the inf norm of the elements of the matrix (excluding the OF) */
mat_computemax(lp->matA);
/* Check if we really have to do scaling */
if(lp->scaling_used && (fabs(scalingmetric) >= lp->epsprimal))
/* Ok, do it */
finalize_scaling(lp, scalenew);
else {
/* Otherwise reset scaling variables */
if(lp->scalars != NULL) {
FREE(lp->scalars);
}
lp->scaling_used = FALSE;
lp->columns_scaled = FALSE;
}
if(scalenew != NULL)
FREE(scalenew);
return(scalingmetric);
}
STATIC int append_SOSrec(SOSrec *SOS, int size, int *variables, REAL *weights)
{
int i, oldsize, newsize, nn;
lprec *lp = SOS->parent->lp;
oldsize = SOS->size;
newsize = oldsize + size;
nn = abs(SOS->type);
/* Shift existing active data right (normally zero) */
if(SOS->members == NULL)
allocINT(lp, &SOS->members, 1+newsize+1+nn, TRUE);
else {
allocINT(lp, &SOS->members, 1+newsize+1+nn, AUTOMATIC);
for(i = newsize+1+nn; i > newsize+1; i--)
SOS->members[i] = SOS->members[i-size];
}
SOS->members[0] = newsize;
SOS->members[newsize+1] = nn;
/* Copy the new data into the arrays */
if(SOS->weights == NULL)
allocREAL(lp, &SOS->weights, 1+newsize, TRUE);
else
allocREAL(lp, &SOS->weights, 1+newsize, AUTOMATIC);
for(i = oldsize+1; i <= newsize; i++) {
SOS->members[i] = variables[i-oldsize-1];
if((SOS->members[i] < 1) || (SOS->members[i] > lp->columns))
report(lp, IMPORTANT, "append_SOS_rec: Invalid SOS variable definition for index %d\n", SOS->members[i]);
else {
if(SOS->isGUB)
lp->var_type[SOS->members[i]] |= ISGUB;
else
lp->var_type[SOS->members[i]] |= ISSOS;
}
if(weights == NULL)
SOS->weights[i] = i; /* Follow standard, which is sorted ascending */
else
SOS->weights[i] = weights[i-oldsize-1];
SOS->weights[0] += SOS->weights[i];
}
/* Sort the new paired lists ascending by weight (simple bubble sort) */
i = sortByREAL(SOS->members, SOS->weights, newsize, 1, TRUE);
if(i > 0)
report(lp, DETAILED, "append_SOS_rec: Non-unique SOS variable weight for index %d\n", i);
/* Define mapping arrays to search large SOS's faster */
allocINT(lp, &SOS->membersSorted, newsize, AUTOMATIC);
allocINT(lp, &SOS->membersMapped, newsize, AUTOMATIC);
for(i = oldsize+1; i <= newsize; i++) {
SOS->membersSorted[i - 1] = SOS->members[i];
SOS->membersMapped[i - 1] = i;
}
sortByINT(SOS->membersMapped, SOS->membersSorted, newsize, 0, TRUE);
/* Confirm the new size */
SOS->size = newsize;
return(newsize);
}
MYBOOL __WINAPI guess_basis(lprec *lp, REAL *guessvector, int *basisvector)
{
MYBOOL *isnz = NULL, status = FALSE;
REAL *values = NULL, *violation = NULL,
eps = lp->epsprimal,
*value, error, upB, loB, sortorder = -1.0;
int i, j, jj, n, *rownr, *colnr, *slkpos = NULL,
nrows = lp->rows, ncols = lp->columns, nsum = lp->sum;
int *basisnr;
MATrec *mat = lp->matA;
if(!mat_validate(mat))
return( status );
/* Create helper arrays, providing for multiple use of the violation array */
if(!allocREAL(lp, &values, nsum+1, TRUE) ||
!allocREAL(lp, &violation, nsum+1, TRUE))
goto Finish;
/* Compute the values of the constraints for the given guess vector */
i = 0;
n = get_nonzeros(lp);
rownr = &COL_MAT_ROWNR(i);
colnr = &COL_MAT_COLNR(i);
value = &COL_MAT_VALUE(i);
for(; i < n; i++, rownr += matRowColStep, colnr += matRowColStep, value += matValueStep)
values[*rownr] += unscaled_mat(lp, my_chsign(is_chsign(lp, *rownr), *value), *rownr, *colnr) *
guessvector[*colnr];
MEMMOVE(values+nrows+1, guessvector+1, ncols);
/* Initialize bound "violation" or primal non-degeneracy measures, expressed
as the absolute value of the differences from the closest bound. */
for(i = 1; i <= nsum; i++) {
if(i <= nrows) {
loB = get_rh_lower(lp, i);
upB = get_rh_upper(lp, i);
}
else {
loB = get_lowbo(lp, i-nrows);
upB = get_upbo(lp, i-nrows);
}
/* Free constraints/variables */
if(my_infinite(lp, loB) && my_infinite(lp, upB))
error = 0;
/* Violated constraints/variable bounds */
else if(values[i]+eps < loB)
error = loB-values[i];
else if(values[i]-eps > upB)
error = values[i]-upB;
/* Non-violated constraints/variables bounds */
else if(my_infinite(lp, upB))
error = MAX(0, values[i]-loB);
else if(my_infinite(lp, loB))
error = MAX(0, upB-values[i]);
else
error = MIN(upB-values[i], values[i]-loB); /* MAX(upB-values[i], values[i]-loB); */
if(error != 0)
violation[i] = sortorder*error;
basisvector[i] = i;
}
/* Sort decending , meaning that variables with the largest
"violations" will be designated basic. Effectively, we are performing a
greedy type algorithm, but start at the "least interesting" end. */
sortByREAL(basisvector, violation, nsum, 1, FALSE);
error = violation[1]; /* Used for setting the return value */
/* Let us check for obvious row singularities and try to fix these.
Note that we reuse the memory allocated to the violation array.
First assemble necessary basis statistics... */
slkpos = (int *) violation;
n = nrows+1;
MEMCLEAR(slkpos, n);
isnz = (MYBOOL *) (slkpos+n+1);
MEMCLEAR(isnz, n);
for(i = 1; i <= nrows; i++) {
j = abs(basisvector[i]);
if(j <= nrows) {
isnz[j] = TRUE;
slkpos[j] = i;
}
else {
j-= nrows;
jj = mat->col_end[j-1];
jj = COL_MAT_ROWNR(jj);
isnz[jj] = TRUE;
}
}
for(; i <= nsum; i++) {
j = abs(basisvector[i]);
if(j <= nrows)
slkpos[j] = i;
}
/* ...then set the corresponding slacks basic for row rank deficient positions */
for(j = 1; j <= nrows; j++) {
if(slkpos[j] == 0)
report(lp, SEVERE, "guess_basis: Internal error");
if(!isnz[j]) {
isnz[j] = TRUE;
i = slkpos[j];
swapINT(&basisvector[i], &basisvector[j]);
basisvector[j] = abs(basisvector[j]);
}
}
/* Adjust the non-basic indeces for the (proximal) bound state */
for(i = nrows+1, basisnr = basisvector+i; i <= nsum; i++, basisnr++) {
n = *basisnr;
if(n <= nrows) {
values[n] -= get_rh_lower(lp, n);
if(values[n] <= eps)
*basisnr = -(*basisnr);
}
else
if(values[n]-eps <= get_lowbo(lp, n-nrows))
*basisnr = -(*basisnr);
}
/* Lastly normalize all basic variables to be coded as lower-bounded,
or effectively zero-based in the case of free variables. */
for(i = 1; i <= nrows; i++)
basisvector[i] = -abs(basisvector[i]);
/* Clean up and return status */
status = (MYBOOL) (error <= eps);
Finish:
FREE(values);
FREE(violation);
return( status );
}
MYBOOL __WINAPI guess_basis(lprec *lp, REAL *guessvector, int *basisvector)
{
MYBOOL *isnz, status = FALSE;
REAL *values = NULL, *violation = NULL,
eps = lp->epsprimal,
*value, error, upB, loB, sortorder = 1.0;
int i, j, jj, n, *rownr, *colnr, *slkpos,
nrows = lp->rows, ncols = lp->columns;
MATrec *mat = lp->matA;
if(!mat_validate(mat))
return( status );
/* Create helper arrays */
if(!allocREAL(lp, &values, lp->sum+1, TRUE) ||
!allocREAL(lp, &violation, lp->sum+1, TRUE))
goto Finish;
/* Compute values of slack variables for given guess vector */
i = 0;
n = get_nonzeros(lp);
rownr = &COL_MAT_ROWNR(i);
colnr = &COL_MAT_COLNR(i);
value = &COL_MAT_VALUE(i);
for(; i < n; i++, rownr += matRowColStep, colnr += matRowColStep, value += matValueStep)
values[*rownr] += unscaled_mat(lp, my_chsign(is_chsign(lp, *rownr), *value), *rownr, *colnr) *
guessvector[*colnr];
MEMMOVE(values+nrows+1, guessvector+1, ncols);
/* Initialize constraint bound violation measures (expressed as positive values) */
for(i = 1; i <= nrows; i++) {
upB = get_rh_upper(lp, i);
loB = get_rh_lower(lp, i);
error = values[i] - upB;
if(error > -eps)
violation[i] = sortorder*MAX(0,error);
else {
error = loB - values[i];
if(error > -eps)
violation[i] = sortorder*MAX(0,error);
else if(my_infinite(lp, loB) && my_infinite(lp, upB))
;
else if(my_infinite(lp, upB))
violation[i] = sortorder*(loB - values[i]);
else if(my_infinite(lp, loB))
violation[i] = sortorder*(values[i] - upB);
else
violation[i] = -sortorder*MAX(upB - values[i], values[i] - loB);
}
basisvector[i] = i;
}
/* Initialize user variable bound violation measures (expressed as positive values) */
for(i = 1; i <= ncols; i++) {
n = nrows+i;
upB = get_upbo(lp, i);
loB = get_lowbo(lp, i);
error = guessvector[i] - upB;
if(error > -eps)
violation[n] = sortorder*MAX(0,error);
else {
error = loB - values[n];
if(error > -eps)
violation[n] = sortorder*MAX(0,error);
else if(my_infinite(lp, loB) && my_infinite(lp, upB))
;
else if(my_infinite(lp, upB))
violation[n] = sortorder*(loB - values[n]);
else if(my_infinite(lp, loB))
violation[n] = sortorder*(values[n] - upB);
else
violation[n] = -sortorder*MAX(upB - values[n], values[n] - loB);
}
basisvector[n] = n;
}
/* Sort decending by violation; this means that variables with
the largest violations will be designated as basic */
sortByREAL(basisvector, violation, lp->sum, 1, FALSE);
error = violation[1];
/* Adjust the non-basic indeces for the (proximal) bound state */
for(i = nrows+1, rownr = basisvector+i; i <= lp->sum; i++, rownr++) {
if(*rownr <= nrows) {
values[*rownr] -= lp->orig_rhs[*rownr];
if(values[*rownr] <= eps)
*rownr = -(*rownr);
}
else
if(values[i] <= get_lowbo(lp, (*rownr)-nrows)+eps)
*rownr = -(*rownr);
}
/* Let us check for obvious row singularities and try to fix these;
First assemble necessary basis statistics... */
isnz = (MYBOOL *) values;
MEMCLEAR(isnz, nrows+1);
slkpos = (int *) violation;
MEMCLEAR(slkpos, nrows+1);
for(i = 1; i <= nrows; i++) {
j = abs(basisvector[i]);
if(j <= nrows) {
isnz[j] = TRUE;
slkpos[j] = i;
}
else {
j-= nrows;
jj = mat->col_end[j-1];
isnz[COL_MAT_ROWNR(jj)] = TRUE;
/* if(++jj < mat->col_end[j])
isnz[COL_MAT_ROWNR(jj)] = TRUE; */
}
}
for(; i <= lp->sum; i++) {
j = abs(basisvector[i]);
if(j <= nrows)
slkpos[j] = i;
}
/* ...then set the corresponding slacks basic for row rank deficient positions */
for(j = 1; j <= nrows; j++) {
#ifdef Paranoia
if(slkpos[j] == 0)
report(lp, SEVERE, "guess_basis: Internal error");
#endif
if(!isnz[j]) {
isnz[j] = TRUE;
i = slkpos[j];
swapINT(&basisvector[i], &basisvector[j]);
basisvector[j] = abs(basisvector[j]);
}
}
/* Lastly normalize all basic variables to be coded as lower-bounded */
for(i = 1; i <= nrows; i++)
basisvector[i] = -abs(basisvector[i]);
/* Clean up and return status */
status = (MYBOOL) (error <= eps);
Finish:
FREE(values);
FREE(violation);
return( status );
}
MYBOOL __WINAPI guess_basis(lprec *lp, REAL *guessvector, int *basisvector)
{
MYBOOL status = FALSE;
REAL *values = NULL, *violation = NULL,
*value, error, upB, loB, sortorder = 1.0;
int i, n, *rownr, *colnr;
MATrec *mat = lp->matA;
if(!mat_validate(lp->matA))
return( status );
/* Create helper arrays */
if(!allocREAL(lp, &values, lp->sum+1, TRUE) ||
!allocREAL(lp, &violation, lp->sum+1, TRUE))
goto Finish;
/* Compute values of slack variables for given guess vector */
i = 0;
n = get_nonzeros(lp);
rownr = &COL_MAT_ROWNR(i);
colnr = &COL_MAT_COLNR(i);
value = &COL_MAT_VALUE(i);
for(; i < n; i++, rownr += matRowColStep, colnr += matRowColStep, value += matValueStep)
values[*rownr] += unscaled_mat(lp, my_chsign(is_chsign(lp, *rownr), *value), *rownr, *colnr) *
guessvector[*colnr];
MEMMOVE(values+lp->rows+1, guessvector+1, lp->columns);
/* Initialize constraint bound violation measures */
for(i = 1; i <= lp->rows; i++) {
upB = get_rh_upper(lp, i);
loB = get_rh_lower(lp, i);
error = values[i] - upB;
if(error > lp->epsprimal)
violation[i] = sortorder*error;
else {
error = loB - values[i];
if(error > lp->epsprimal)
violation[i] = sortorder*error;
else if(is_infinite(lp, loB) && is_infinite(lp, upB))
;
else if(is_infinite(lp, upB))
violation[i] = sortorder*(loB - values[i]);
else if(is_infinite(lp, loB))
violation[i] = sortorder*(values[i] - upB);
else
violation[i] = - sortorder*MAX(upB - values[i], values[i] - loB);
}
basisvector[i] = i;
}
/* Initialize user variable bound violation measures */
for(i = 1; i <= lp->columns; i++) {
n = lp->rows+i;
upB = get_upbo(lp, i);
loB = get_lowbo(lp, i);
error = guessvector[i] - upB;
if(error > lp->epsprimal)
violation[n] = sortorder*error;
else {
error = loB - values[n];
if(error > lp->epsprimal)
violation[n] = sortorder*error;
else if(is_infinite(lp, loB) && is_infinite(lp, upB))
;
else if(is_infinite(lp, upB))
violation[n] = sortorder*(loB - values[n]);
else if(is_infinite(lp, loB))
violation[n] = sortorder*(values[n] - upB);
else
violation[n] = - sortorder*MAX(upB - values[n], values[n] - loB);
}
basisvector[n] = n;
}
/* Sort decending by violation; this means that variables with
the largest violations will be designated as basic */
sortByREAL(basisvector, violation, lp->sum, 1, FALSE);
/* Adjust the non-basic indeces for the (proximal) bound state */
error = lp->epsprimal;
for(i = lp->rows+1, rownr = basisvector+i; i <= lp->sum; i++, rownr++) {
if(*rownr <= lp->rows) {
if(values[*rownr] <= get_rh_lower(lp, *rownr)+error)
*rownr = -(*rownr);
}
else
if(values[i] <= get_lowbo(lp, (*rownr)-lp->rows)+error)
*rownr = -(*rownr);
}
/* Clean up and return status */
status = (MYBOOL) (violation[1] == 0);
Finish:
FREE(values);
FREE(violation);
return( status );
}
MYBOOL crash_basis(lprec *lp)
{
int i;
MATrec *mat = lp->matA;
MYBOOL ok = TRUE;
/* Initialize basis indicators */
if(lp->basis_valid)
lp->var_basic[0] = FALSE;
else
default_basis(lp);
/* Set initial partial pricing blocks */
if(lp->rowblocks != NULL)
lp->rowblocks->blocknow = 1;
if(lp->colblocks != NULL)
lp->colblocks->blocknow = ((lp->crashmode == CRASH_NONE) || (lp->colblocks->blockcount == 1) ? 1 : 2);
/* Construct a basis that is in some measure the "most feasible" */
if((lp->crashmode == CRASH_MOSTFEASIBLE) && mat_validate(mat)) {
/* The logic here follows Maros */
LLrec *rowLL = NULL, *colLL = NULL;
int ii, rx, cx, ix, nz;
REAL wx, tx, *rowMAX = NULL, *colMAX = NULL;
int *rowNZ = NULL, *colNZ = NULL, *rowWT = NULL, *colWT = NULL;
REAL *value;
int *rownr, *colnr;
report(lp, NORMAL, "crash_basis: 'Most feasible' basis crashing selected\n");
/* Tally row and column non-zero counts */
ok = allocINT(lp, &rowNZ, lp->rows+1, TRUE) &&
allocINT(lp, &colNZ, lp->columns+1, TRUE) &&
allocREAL(lp, &rowMAX, lp->rows+1, FALSE) &&
allocREAL(lp, &colMAX, lp->columns+1, FALSE);
if(!ok)
goto Finish;
nz = mat_nonzeros(mat);
rownr = &COL_MAT_ROWNR(0);
colnr = &COL_MAT_COLNR(0);
value = &COL_MAT_VALUE(0);
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep, value += matValueStep) {
rx = *rownr;
cx = *colnr;
wx = fabs(*value);
rowNZ[rx]++;
colNZ[cx]++;
if(i == 0) {
rowMAX[rx] = wx;
colMAX[cx] = wx;
colMAX[0] = wx;
}
else {
SETMAX(rowMAX[rx], wx);
SETMAX(colMAX[cx], wx);
SETMAX(colMAX[0], wx);
}
}
/* Reduce counts for small magnitude to preserve stability */
rownr = &COL_MAT_ROWNR(0);
colnr = &COL_MAT_COLNR(0);
value = &COL_MAT_VALUE(0);
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep, value += matValueStep) {
rx = *rownr;
cx = *colnr;
wx = fabs(*value);
#ifdef CRASH_SIMPLESCALE
if(wx < CRASH_THRESHOLD * colMAX[0]) {
rowNZ[rx]--;
colNZ[cx]--;
}
#else
if(wx < CRASH_THRESHOLD * rowMAX[rx])
rowNZ[rx]--;
if(wx < CRASH_THRESHOLD * colMAX[cx])
colNZ[cx]--;
#endif
}
/* Set up priority tables */
ok = allocINT(lp, &rowWT, lp->rows+1, TRUE);
createLink(lp->rows, &rowLL, NULL);
ok &= (rowLL != NULL);
if(!ok)
goto Finish;
for(i = 1; i <= lp->rows; i++) {
if(get_constr_type(lp, i)==EQ)
ii = 3;
else if(lp->upbo[i] < lp->infinite)
ii = 2;
else if(fabs(lp->rhs[i]) < lp->infinite)
ii = 1;
else
ii = 0;
rowWT[i] = ii;
if(ii > 0)
appendLink(rowLL, i);
}
ok = allocINT(lp, &colWT, lp->columns+1, TRUE);
createLink(lp->columns, &colLL, NULL);
ok &= (colLL != NULL);
if(!ok)
goto Finish;
for(i = 1; i <= lp->columns; i++) {
ix = lp->rows+i;
if(is_unbounded(lp, i))
ii = 3;
else if(lp->upbo[ix] >= lp->infinite)
ii = 2;
else if(fabs(lp->upbo[ix]-lp->lowbo[ix]) > lp->epsmachine)
ii = 1;
else
ii = 0;
colWT[i] = ii;
if(ii > 0)
appendLink(colLL, i);
}
/* Loop over all basis variables */
for(i = 1; i <= lp->rows; i++) {
/* Select row */
rx = 0;
wx = -lp->infinite;
for(ii = firstActiveLink(rowLL); ii > 0; ii = nextActiveLink(rowLL, ii)) {
tx = rowWT[ii] - CRASH_SPACER*rowNZ[ii];
if(tx > wx) {
rx = ii;
wx = tx;
}
}
if(rx == 0)
break;
removeLink(rowLL, rx);
/* Select column */
cx = 0;
wx = -lp->infinite;
for(ii = mat->row_end[rx-1]; ii < mat->row_end[rx]; ii++) {
/* Update NZ column counts for row selected above */
tx = fabs(ROW_MAT_VALUE(ii));
ix = ROW_MAT_COLNR(ii);
#ifdef CRASH_SIMPLESCALE
if(tx >= CRASH_THRESHOLD * colMAX[0])
#else
if(tx >= CRASH_THRESHOLD * colMAX[ix])
#endif
colNZ[ix]--;
if(!isActiveLink(colLL, ix) || (tx < CRASH_THRESHOLD * rowMAX[rx]))
continue;
/* Now do the test for best pivot */
tx = my_sign(lp->orig_obj[ix]) - my_sign(ROW_MAT_VALUE(ii));
tx = colWT[ix] + CRASH_WEIGHT*tx - CRASH_SPACER*colNZ[ix];
if(tx > wx) {
cx = ix;
wx = tx;
}
}
if(cx == 0)
break;
removeLink(colLL, cx);
/* Update row NZ counts */
ii = mat->col_end[cx-1];
rownr = &COL_MAT_ROWNR(ii);
value = &COL_MAT_VALUE(ii);
for(; ii < mat->col_end[cx];
ii++, rownr += matRowColStep, value += matValueStep) {
wx = fabs(*value);
ix = *rownr;
#ifdef CRASH_SIMPLESCALE
if(wx >= CRASH_THRESHOLD * colMAX[0])
#else
if(wx >= CRASH_THRESHOLD * rowMAX[ix])
#endif
rowNZ[ix]--;
}
/* Set new basis variable */
set_basisvar(lp, rx, lp->rows+cx);
}
/* Clean up */
Finish:
FREE(rowNZ);
FREE(colNZ);
FREE(rowMAX);
FREE(colMAX);
FREE(rowWT);
FREE(colWT);
freeLink(&rowLL);
freeLink(&colLL);
}
/* Construct a basis that is in some measure the "least degenerate" */
else if((lp->crashmode == CRASH_LEASTDEGENERATE) && mat_validate(mat)) {
/* The logic here follows Maros */
LLrec *rowLL = NULL, *colLL = NULL;
int ii, rx, cx, ix, nz, *merit = NULL;
REAL *value, wx, hold, *rhs = NULL, *eta = NULL;
int *rownr, *colnr;
report(lp, NORMAL, "crash_basis: 'Least degenerate' basis crashing selected\n");
/* Create temporary arrays */
ok = allocINT(lp, &merit, lp->columns + 1, FALSE) &&
allocREAL(lp, &eta, lp->rows + 1, FALSE) &&
allocREAL(lp, &rhs, lp->rows + 1, FALSE);
createLink(lp->columns, &colLL, NULL);
createLink(lp->rows, &rowLL, NULL);
ok &= (colLL != NULL) && (rowLL != NULL);
if(!ok)
goto FinishLD;
MEMCOPY(rhs, lp->orig_rhs, lp->rows + 1);
for(i = 1; i <= lp->columns; i++)
appendLink(colLL, i);
for(i = 1; i <= lp->rows; i++)
appendLink(rowLL, i);
/* Loop until we have found enough new bases */
while(colLL->count > 0) {
/* Tally non-zeros matching in RHS and each active column */
nz = mat_nonzeros(mat);
rownr = &COL_MAT_ROWNR(0);
colnr = &COL_MAT_COLNR(0);
ii = 0;
MEMCLEAR(merit, lp->columns + 1);
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep) {
rx = *rownr;
cx = *colnr;
if(isActiveLink(colLL, cx) && (rhs[rx] != 0)) {
merit[cx]++;
ii++;
}
}
if(ii == 0)
break;
/* Find maximal match; break ties with column length */
i = firstActiveLink(colLL);
cx = i;
for(i = nextActiveLink(colLL, i); i != 0; i = nextActiveLink(colLL, i)) {
if(merit[i] >= merit[cx]) {
if((merit[i] > merit[cx]) || (mat_collength(mat, i) > mat_collength(mat, cx)))
cx = i;
}
}
/* Determine the best pivot row */
i = mat->col_end[cx-1];
nz = mat->col_end[cx];
rownr = &COL_MAT_ROWNR(i);
value = &COL_MAT_VALUE(i);
rx = 0;
wx = 0;
MEMCLEAR(eta, lp->rows + 1);
for(; i < nz;
i++, rownr += matRowColStep, value += matValueStep) {
ix = *rownr;
hold = *value;
eta[ix] = rhs[ix] / hold;
hold = fabs(hold);
if(isActiveLink(rowLL, ix) && (hold > wx)) {
wx = hold;
rx = ix;
}
}
/* Set new basis variable */
if(rx > 0) {
/* We have to update the rhs vector for the implied transformation
in order to be able to find the new RHS non-zero pattern */
for(i = 1; i <= lp->rows; i++)
rhs[i] -= wx * eta[i];
rhs[rx] = wx;
/* Do the exchange */
set_basisvar(lp, rx, lp->rows+cx);
removeLink(rowLL, rx);
}
removeLink(colLL, cx);
}
/* Clean up */
FinishLD:
FREE(merit);
FREE(rhs);
freeLink(&rowLL);
freeLink(&colLL);
}
return( ok );
}
STATIC void updatePricer(lprec *lp, int rownr, int colnr, REAL *pcol, REAL *prow, int *nzprow)
{
REAL *vEdge = NULL, cEdge, hold, *newEdge, *w = NULL;
int i, m, n, exitcol, errlevel = DETAILED;
MYBOOL forceRefresh = FALSE, isDual, isDEVEX;
if(!applyPricer(lp))
return;
/* Make sure we have something to update */
hold = lp->edgeVector[0];
if(hold < 0)
return;
isDual = (MYBOOL) (hold > 0);
/* Do common initializations and computations */
m = lp->rows;
n = lp->sum;
isDEVEX = is_piv_rule(lp, PRICER_DEVEX);
exitcol = lp->var_basic[rownr];
/* Solve/copy Bw = a */
/* formWeights(lp, colnr, NULL, &w); Experimental */
formWeights(lp, colnr, pcol, &w);
/* Price norms for the dual simplex - the basic columns */
if(isDual) {
REAL rw;
int targetcol;
/* Don't need to compute cross-products with DEVEX */
if(!isDEVEX) {
allocREAL(lp, &vEdge, m+1, FALSE);
/* Extract the row of the inverse containing the leaving variable
and then form the dot products against the other variables, i.e. "Tau" */
#if 0 /* Extract row explicitly */
bsolve(lp, rownr, vEdge, 0, 0.0);
#else /* Reuse previously extracted row data */
MEMCOPY(vEdge, prow, m+1);
vEdge[0] = 0;
#endif
lp->bfp_ftran_normal(lp, vEdge, NULL);
}
/* Deal with the variable entering the basis to become a new leaving candidate */
cEdge = lp->edgeVector[exitcol];
rw = w[rownr];
hold = 1 / rw;
lp->edgeVector[colnr] = (hold*hold) * cEdge;
/* Possibly adjust initial value in case of Devex */
if(isDEVEX && !DEVEX_ENHANCED && (lp->edgeVector[colnr] < DEVEX_MINVALUE))
lp->edgeVector[colnr] = DEVEX_MINVALUE;
#ifdef Paranoia
if(lp->edgeVector[colnr] <= lp->epsmachine)
report(lp, errlevel, "updatePricer: Invalid dual norm %g at entering index %d - iteration %d\n",
lp->edgeVector[colnr], rownr, lp->total_iter+lp->current_iter);
#endif
/* Then loop over all basic variables, but skip the leaving row */
for(i = 1; i <= m; i++) {
if(i == rownr)
continue;
targetcol = lp->var_basic[i];
hold = w[i];
if(hold == 0)
continue;
hold /= rw;
if(fabs(hold) < lp->epsmachine)
continue;
newEdge = &(lp->edgeVector[targetcol]);
*newEdge += (hold*hold) * cEdge;
if(isDEVEX) {
if((*newEdge) > DEVEX_RESTARTLIMIT) {
forceRefresh = TRUE;
break;
}
}
else {
*newEdge -= 2*hold*vEdge[i];
#ifdef xxApplySteepestEdgeMinimum
*newEdge = my_max(*newEdge, hold*hold+1); /* Kludge; use the primal lower bound */
#else
if(*newEdge <= 0) {
report(lp, errlevel, "updatePricer: Invalid dual norm %g at index %d - iteration %d\n",
*newEdge, i, lp->total_iter+lp->current_iter);
forceRefresh = TRUE;
break;
}
#endif
}
}
}
/* Price norms for the primal simplex - the non-basic columns */
else {
REAL *vTemp, *vAlpha, cAlpha;
int *coltarget;
allocREAL(lp, &vTemp, m+1, TRUE);
allocREAL(lp, &vAlpha, n+1, TRUE);
/* Check if we have strategy fallback for the primal */
if(!isDEVEX)
isDEVEX = is_piv_mode(lp, PRICE_PRIMALFALLBACK);
/* Initialize column target array */
coltarget = (int *) mempool_obtainVector(lp->workarrays, lp->sum+1, sizeof(*coltarget));
if(!get_colIndexA(lp, SCAN_ALLVARS+USE_NONBASICVARS, coltarget, FALSE)) {
mempool_releaseVector(lp->workarrays, (char *) coltarget, FALSE);
return;
}
/* Don't need to compute cross-products with DEVEX */
if(!isDEVEX) {
vEdge = (REAL *) calloc((n + 1), sizeof(*vEdge));
/* Compute v and then N'v */
MEMCOPY(vTemp, w, m+1);
bsolve(lp, -1, vTemp, NULL, lp->epsmachine*DOUBLEROUND, 0.0);
vTemp[0] = 0;
prod_xA(lp, coltarget, vTemp, NULL, XRESULT_FREE, lp->epsmachine, 0.0,
vEdge, NULL);
}
/* Compute Sigma and then Alpha */
bsolve(lp, rownr, vTemp, NULL, 0*DOUBLEROUND, 0.0);
vTemp[0] = 0;
prod_xA(lp, coltarget, vTemp, NULL, XRESULT_FREE, lp->epsmachine, 0.0,
vAlpha, NULL);
mempool_releaseVector(lp->workarrays, (char *) coltarget, FALSE);
/* Update the squared steepest edge norms; first store some constants */
cEdge = lp->edgeVector[colnr];
cAlpha = vAlpha[colnr];
/* Deal with the variable leaving the basis to become a new entry candidate */
hold = 1 / cAlpha;
lp->edgeVector[exitcol] = (hold*hold) * cEdge;
/* Possibly adjust initial value in case of Devex */
if(isDEVEX && !DEVEX_ENHANCED && (lp->edgeVector[exitcol] < DEVEX_MINVALUE))
lp->edgeVector[exitcol] = DEVEX_MINVALUE;
#ifdef Paranoia
if(lp->edgeVector[exitcol] <= lp->epsmachine)
report(lp, errlevel, "updatePricer: Invalid primal norm %g at leaving index %d - iteration %d\n",
lp->edgeVector[exitcol], exitcol, lp->total_iter+lp->current_iter);
#endif
/* Then loop over all non-basic variables, but skip the entering column */
for(i = 1; i <= lp->sum; i++) {
if(lp->is_basic[i] || (i == colnr))
continue;
hold = vAlpha[i];
if(hold == 0)
continue;
hold /= cAlpha;
if(fabs(hold) < lp->epsmachine)
continue;
newEdge = &(lp->edgeVector[i]);
*newEdge += (hold*hold) * cEdge;
if(isDEVEX) {
if((*newEdge) > DEVEX_RESTARTLIMIT) {
forceRefresh = TRUE;
break;
}
}
else {
*newEdge -= 2*hold*vEdge[i];
#ifdef ApplySteepestEdgeMinimum
*newEdge = my_max(*newEdge, hold*hold+1);
#else
if(*newEdge < 0) {
report(lp, errlevel, "updatePricer: Invalid primal norm %g at index %d - iteration %d\n",
*newEdge, i, lp->total_iter+lp->current_iter);
if(lp->spx_trace)
report(lp, errlevel, "Error detail: (RelAlpha=%g, vEdge=%g, cEdge=%g)\n", hold, vEdge[i], cEdge);
forceRefresh = TRUE;
break;
}
#endif
}
}
FREE(vAlpha);
FREE(vTemp);
}
if(vEdge != NULL)
FREE(vEdge);
freeWeights(w);
if(forceRefresh)
restartPricer(lp, AUTOMATIC);
}
STATIC int dualloop(lprec *lp, MYBOOL feasible)
{
int i, ok = TRUE;
LREAL theta = 0.0;
REAL *drow = NULL, *prow = NULL, *pcol = NULL, prevobj, epsvalue;
MYBOOL primal = FALSE, forceoutEQ = FALSE;
MYBOOL minit, pivdynamic, bfpfinal = FALSE;
int oldpivrule, oldpivmode, pivrule, Blandswitches,
colnr, rownr, lastnr, minitcount = 0;
int Rcycle = 0, Ccycle = 0, Ncycle = 0, changedphase = TRUE;
#ifdef FixInaccurateDualMinit
int minitcolnr = 0;
#endif
int *nzprow = NULL, *workINT = NULL;
if(lp->spx_trace)
report(lp, DETAILED, "Entering dual simplex algorithm\n");
/* Set Extrad value to force dual feasibility; reset when
"local optimality" has been achieved or a dual non-feasibility
has been encountered (no candidate for a first leaving variable) */
if(feasible)
lp->Extrad = 0;
else
lp->Extrad = feasibilityOffset(lp, (MYBOOL)!primal);
if(lp->spx_trace)
report(lp, DETAILED, "Extrad = %g\n", (double)lp->Extrad);
/* Allocate work arrays */
allocREAL(lp, &drow, lp->sum + 1, TRUE);
#ifdef UseSparseReducedCost
allocINT(lp, &nzprow, lp->sum + 1, FALSE);
#endif
allocREAL(lp, &prow, lp->sum + 1, TRUE);
allocREAL(lp, &pcol, lp->rows + 1, TRUE);
/* Refactorize the basis and set status variables */
i = my_if(is_bb_action(lp, ACTION_REBASE), INITSOL_SHIFTZERO, INITSOL_USEZERO);
if(((lp->spx_status == SWITCH_TO_DUAL) && !lp->justInverted) ||
(lp->Extrad != 0) ||
is_bb_action(lp, ACTION_REINVERT)) {
simplexPricer(lp, (MYBOOL)!primal);
/* Do basis crashing before refactorization, if specified */
invert(lp, (MYBOOL) i, TRUE);
}
else {
if(is_bb_action(lp, ACTION_RECOMPUTE))
recompute_solution(lp, (MYBOOL) i);
restartPricer(lp, (MYBOOL)!primal);
}
lp->bb_action = ACTION_NONE;
lp->spx_status = RUNNING;
lp->doIterate = FALSE;
minit = ITERATE_MAJORMAJOR;
prevobj = lp->rhs[0];
oldpivmode = lp->piv_strategy;
oldpivrule = get_piv_rule(lp);
pivdynamic = ANTICYCLEBLAND && is_piv_mode(lp, PRICE_ADAPTIVE);
epsvalue = lp->epspivot;
Blandswitches = 0;
rownr = 0;
colnr = -1; /* Used to detect infeasibility at the beginning of the dual loop */
lastnr = 0;
lp->rejectpivot[0] = 0;
if(feasible)
lp->simplex_mode = SIMPLEX_Phase2_DUAL;
else
lp->simplex_mode = SIMPLEX_Phase1_DUAL;
/* Check if we have equality slacks in the basis and we should try to
drive them out in order to reduce chance of degeneracy in Phase 1 */
if(!feasible && (lp->fixedvars > 0) && is_anti_degen(lp, ANTIDEGEN_FIXEDVARS)) {
forceoutEQ = AUTOMATIC;
}
while(lp->spx_status == RUNNING) {
if(lp->spx_trace)
if(lastnr > 0)
report(lp, NORMAL, "dualloop: Objective at iteration %8d is " RESULTVALUEMASK " (%4d: %4d %s- %4d)\n",
get_total_iter(lp), lp->rhs[0], rownr, lastnr,
my_if(minit == ITERATE_MAJORMAJOR, "<","|"), colnr);
pivrule = get_piv_rule(lp);
if(pivdynamic && ((pivrule != PRICER_FIRSTINDEX) ||
(pivrule != oldpivrule))
#if DualPivotStickiness==2
/* Stays with pricing rule as long as possible (also preserves accuracy) */
&& (lp->fixedvars == 0)
#elif DualPivotStickiness==1
/* Stays with pricing rule only if the model is infeasible */
&& feasible
#endif
) {
/* Check if we have a stationary solution */
if((minit == ITERATE_MAJORMAJOR) && !lp->justInverted &&
(fabs(my_reldiff(lp->rhs[0], prevobj)) < epsvalue)) {
Ncycle++;
/* Start to monitor for variable cycling if this is the initial stationarity */
if(Ncycle <= 1) {
Ccycle = colnr;
Rcycle = rownr;
}
/* Check if we should change pivoting strategy due to stationary variable cycling */
else if((pivrule == oldpivrule) && (((MAX_STALLCOUNT > 1) && (Ncycle > MAX_STALLCOUNT)) ||
(Ccycle == rownr) || (Rcycle == colnr))) {
/* First check if we should give up on Bland's rule and try perturbed bound
relaxation instead */
#ifdef EnableStallAntiDegen
if((MAX_BLANDSWITCH >= 0) && (Blandswitches >= MAX_BLANDSWITCH)) {
lp->spx_status = DEGENERATE;
break;
}
#endif
Blandswitches++;
lp->piv_strategy = PRICER_FIRSTINDEX; /* There is no advanced normalization for Bland's rule, restart at end */
Ccycle = 0;
Rcycle = 0;
Ncycle = 0;
if(lp->spx_trace)
report(lp, DETAILED, "dualloop: Detected cycling at iteration %d; changed to FIRST INDEX rule!\n",
get_total_iter(lp));
}
}
/* Handle cycling or stationary situations by switching to the primal simplex */
else if((pivrule == oldpivrule) && feasible && (lp->simplex_strategy & SIMPLEX_DYNAMIC)) {
lp->spx_status = SWITCH_TO_PRIMAL;
break;
}
/* Change back to original selection strategy as soon as possible */
else if((minit == ITERATE_MAJORMAJOR) && (pivrule != oldpivrule)) {
lp->piv_strategy = oldpivmode;
restartPricer(lp, AUTOMATIC); /* Pricer restart following Bland's rule */
Ccycle = 0;
Rcycle = 0;
Ncycle = 0;
if(lp->spx_trace)
report(lp, DETAILED, "...returned to original pivot selection rule at iteration %d.\n",
get_total_iter(lp));
}
}
/* Store current LP value for reference at next iteration */
changedphase = FALSE;
prevobj = lp->rhs[0];
lastnr = lp->var_basic[rownr];
lp->doInvert = FALSE;
/* Do minor iterations (non-basic variable bound switches) for as
long as possible since this is a cheap way of iterating */
#ifdef Phase1DualPriceEqualities
RetryRow:
#endif
if(minit != ITERATE_MINORRETRY) {
/* forceoutEQ
FALSE : Only eliminate assured "good" violated equality constraint slacks
AUTOMATIC: Seek more elimination of equality constraint slacks
(but not as aggressive as the rule used in lp_solve v4.0 and earlier)
TRUE: Force remaining equality slacks out of the basis */
i = 0;
do {
if(partial_countBlocks(lp, (MYBOOL) !primal) > 1)
partial_blockStep(lp, (MYBOOL) !primal);
rownr = rowdual(lp, forceoutEQ);
i++;
} while ((rownr == 0) && (i < partial_countBlocks(lp, (MYBOOL) !primal)));
lastnr = lp->var_basic[rownr];
}
if(rownr > 0) {
#ifdef UseRejectionList
RetryCol:
#endif
lp->doIterate = FALSE;
colnr = coldual(lp, rownr, (MYBOOL)(minit == ITERATE_MINORRETRY),
prow, nzprow, drow, NULL);
if(colnr > 0) {
lp->doIterate = TRUE;
fsolve(lp, colnr, pcol, workINT, lp->epsmachine, 1.0, TRUE);
#ifdef FixInaccurateDualMinit
/* Prevent bound flip-flops during minor iterations; used to detect
infeasibility after triggering of minor iteration accuracy management */
if(colnr != minitcolnr)
minitcolnr = 0;
#endif
/* Getting division by zero here; catch it and try to recover */
if(pcol[rownr] == 0) {
if(lp->spx_trace)
report(lp, DETAILED, "dualloop: Attempt to divide by zero (pcol[%d])\n", rownr);
lp->doIterate = FALSE;
if(!lp->justInverted) {
report(lp, DETAILED, "...trying to recover by reinverting!\n");
lp->doInvert = TRUE;
bfpfinal = FALSE;
}
#ifdef UseRejectionList
else if(lp->rejectpivot[0] < DEF_MAXPIVOTRETRY) {
lp->rejectpivot[0]++;
lp->rejectpivot[lp->rejectpivot[0]] = colnr;
if(lp->bb_totalnodes == 0)
report(lp, DETAILED, "...trying to recover via another pivot column!\n");
goto RetryCol;
}
#endif
else {
if(lp->bb_totalnodes == 0)
report(lp, DETAILED, "...cannot recover by reinverting.\n");
lp->spx_status = NUMFAILURE;
ok = FALSE;
}
}
else {
lp->rejectpivot[0] = 0;
theta = lp->bfp_prepareupdate(lp, rownr, colnr, pcol);
/* Verify numeric accuracy of the inverse and change to
the "theoretically" correct version of the theta */
if((lp->improve & IMPROVE_INVERSE) &&
(my_reldiff(fabs(theta),fabs(prow[colnr])) >
lp->epspivot*10.0*log(2.0+50.0*lp->rows))) {
lp->doInvert = TRUE;
bfpfinal = TRUE;
#ifdef IncreasePivotOnReducedAccuracy
if(lp->bfp_pivotcount(lp) < 2*DEF_MAXPIVOTRETRY)
lp->epspivot *= 2.0;
#endif
report(lp, DETAILED, "dualloop: Refactorizing at iteration %d due to loss of accuracy.\n",
get_total_iter(lp));
}
theta = prow[colnr];
compute_theta(lp, rownr, &theta, !lp->is_lower[colnr], 0, primal);
}
}
#ifdef FixInaccurateDualMinit
/* Reinvert and try another row if we did not find a bound-violated leaving column */
else if((minit != ITERATE_MAJORMAJOR) && (colnr != minitcolnr)) {
minitcolnr = colnr;
lp->doInvert = TRUE;
i = invert(lp, INITSOL_USEZERO, TRUE);
if((lp->spx_status == USERABORT) || (lp->spx_status == TIMEOUT))
break;
else if(!i) {
lp->spx_status = SINGULAR_BASIS;
break;
}
minit = ITERATE_MAJORMAJOR;
continue;
}
#endif
else {
if(lp->justInverted && (lp->simplex_mode == SIMPLEX_Phase2_DUAL))
lp->spx_status = LOSTFEAS;
#if 1
else if(!lp->justInverted && (lp->bb_level <= 1)) {
#else
else if(!lp->justInverted) {
#endif
lp->doIterate = FALSE;
lp->doInvert = TRUE;
bfpfinal = TRUE;
}
else {
if((lp->spx_trace && (lp->bb_totalnodes == 0)) ||
(lp->bb_trace && (lp->bb_totalnodes > 0)))
report(lp, DETAILED, "Model lost dual feasibility.\n");
lp->spx_status = INFEASIBLE;
ok = FALSE;
break;
}
}
}
else {
/* New code to solve to optimality using the dual, but only if the user
has specified a preference for the dual simplex - KE added 20030731 */
lp->doIterate = FALSE;
bfpfinal = TRUE;
if((lp->Extrad != 0) && (colnr < 0) && !isPrimalFeasible(lp, lp->epsprimal)) {
if(feasible) {
if(lp->bb_totalnodes == 0)
report(lp, DETAILED, "Model is dual infeasible and primal feasible\n");
lp->spx_status = SWITCH_TO_PRIMAL;
lp->doInvert = (MYBOOL) (lp->Extrad != 0);
lp->Extrad = 0;
}
else {
if(lp->bb_totalnodes == 0)
report(lp, NORMAL, "Model is primal and dual infeasible\n");
lp->spx_status = INFEASIBLE;
ok = FALSE;
}
break;
}
else if(lp->Extrad == 0) {
/* We are feasible (and possibly also optimal) */
feasible = TRUE;
lp->simplex_mode = SIMPLEX_Phase2_DUAL;
/* Check if we still have equality slacks stuck in the basis; drive them out? */
if((lp->fixedvars > 0) && lp->bb_totalnodes == 0)
#ifdef Paranoia
report(lp, NORMAL,
#else
report(lp, DETAILED,
#endif
"Found dual solution with %d fixed slack variables left basic\n",
lp->fixedvars);
#ifdef Phase1DualPriceEqualities
if(forceoutEQ != TRUE) {
forceoutEQ = TRUE;
goto RetryRow;
}
colnr = 0;
#else
#if 1
/* Problem: Check if we are dual degenerate and need to switch to the
primal simplex (there is a flaw in the dual simplex code) */
colnr = colprim(lp, FALSE, drow, nzprow);
#else
colnr = 0;
#endif
#endif
if(colnr == 0)
lp->spx_status = OPTIMAL;
else {
lp->spx_status = SWITCH_TO_PRIMAL;
if(lp->total_iter == 0)
report(lp, NORMAL, "Use primal simplex for finalization at iteration %8d\n",
get_total_iter(lp));
}
if((lp->total_iter == 0) && (lp->spx_status == OPTIMAL))
report(lp, NORMAL, "Optimal solution with dual simplex at iteration %8d\n",
get_total_iter(lp));
break;
}
else {
/* Report the traditional tableau corresponding to the current basis */
MYBOOL REPORT_tableau(lprec *lp)
{
int j, row_nr, *coltarget;
LPSREAL *prow = NULL;
FILE *stream = lp->outstream;
if(lp->outstream == NULL)
return(FALSE);
if(!lp->model_is_valid || !has_BFP(lp) ||
(get_total_iter(lp) == 0) || (lp->spx_status == NOTRUN)) {
lp->spx_status = NOTRUN;
return(FALSE);
}
if(!allocREAL(lp, &prow,lp->sum + 1, TRUE)) {
lp->spx_status = NOMEMORY;
return(FALSE);
}
fprintf(stream, "\n");
fprintf(stream, "Tableau at iter %.0f:\n", (double) get_total_iter(lp));
for(j = 1; j <= lp->sum; j++)
if (!lp->is_basic[j])
fprintf(stream, "%15d", (j <= lp->rows ?
(j + lp->columns) * ((lp->orig_upbo[j] == 0) ||
(is_chsign(lp, j)) ? 1 : -1) : j - lp->rows) *
(lp->is_lower[j] ? 1 : -1));
fprintf(stream, "\n");
coltarget = (int *) mempool_obtainVector(lp->workarrays, lp->columns+1, sizeof(*coltarget));
if(!get_colIndexA(lp, SCAN_USERVARS+USE_NONBASICVARS, coltarget, FALSE)) {
mempool_releaseVector(lp->workarrays, (char *) coltarget, FALSE);
return(FALSE);
}
for(row_nr = 1; (row_nr <= lp->rows + 1); row_nr++) {
if (row_nr <= lp->rows)
fprintf(stream, "%3d", (lp->var_basic[row_nr] <= lp->rows ?
(lp->var_basic[row_nr] + lp->columns) * ((lp->orig_upbo[lp->var_basic [row_nr]] == 0) ||
(is_chsign(lp, lp->var_basic[row_nr])) ? 1 : -1) : lp->var_basic[row_nr] - lp->rows) *
(lp->is_lower[lp->var_basic [row_nr]] ? 1 : -1));
else
fprintf(stream, " ");
bsolve(lp, row_nr <= lp->rows ? row_nr : 0, prow, NULL, lp->epsmachine*DOUBLEROUND, 1.0);
prod_xA(lp, coltarget, prow, NULL, lp->epsmachine, 1.0,
prow, NULL, MAT_ROUNDDEFAULT);
for(j = 1; j <= lp->rows + lp->columns; j++)
if (!lp->is_basic[j])
fprintf(stream, "%15.7f", prow[j] * (lp->is_lower[j] ? 1 : -1) *
(row_nr <= lp->rows ? 1 : -1));
fprintf(stream, "%15.7f", lp->rhs[row_nr <= lp->rows ? row_nr : 0] *
(double) ((row_nr <= lp->rows) || (is_maxim(lp)) ? 1 : -1));
fprintf(stream, "\n");
}
fflush(stream);
mempool_releaseVector(lp->workarrays, (char *) coltarget, FALSE);
FREE(prow);
return(TRUE);
}
STATIC REAL scale(lprec *lp, REAL *scaledelta)
{
int i, j, nz, row_count, nzOF = 0;
REAL *row_max, *row_min, *scalechange = NULL, absval;
REAL col_max, col_min;
MYBOOL rowscaled, colscaled;
MATrec *mat = lp->matA;
REAL *value;
int *rownr;
if(is_scaletype(lp, SCALE_NONE))
return(0.0);
if(!lp->scaling_used) {
allocREAL(lp, &lp->scalars, lp->sum_alloc + 1, FALSE);
for(i = 0; i <= lp->sum; i++) {
lp->scalars[i] = 1;
}
lp->scaling_used = TRUE;
}
#ifdef Paranoia
else
for(i = 0; i <= lp->sum; i++) {
if(lp->scalars[i] == 0)
report(lp, SEVERE, "scale: Zero-valued scalar found at index %d\n", i);
}
#endif
if(scaledelta == NULL)
allocREAL(lp, &scalechange, lp->sum + 1, FALSE);
else
scalechange = scaledelta;
/* Must initialize due to computation of scaling statistic - KE */
for(i = 0; i <= lp->sum; i++)
scalechange[i] = 1;
row_count = lp->rows;
allocREAL(lp, &row_max, row_count + 1, TRUE);
allocREAL(lp, &row_min, row_count + 1, FALSE);
/* Initialise min and max values of rows */
for(i = 0; i <= row_count; i++) {
if(is_scaletype(lp, SCALE_MEAN))
row_min[i] = 0; /* Carries the count of elements */
else
row_min[i] = lp->infinite; /* Carries the minimum element */
}
/* Calculate row scaling data */
for(j = 1; j <= lp->columns; j++) {
absval = lp->orig_obj[j];
if(absval != 0) {
absval = scaled_mat(lp, absval, 0, j);
accumulate_for_scale(lp, &row_min[0], &row_max[0], absval);
nzOF++;
}
i = mat->col_end[j - 1];
value = &(COL_MAT_VALUE(i));
rownr = &(COL_MAT_ROWNR(i));
nz = mat->col_end[j];
for(; i < nz;
i++, value += matValueStep, rownr += matRowColStep) {
absval = scaled_mat(lp, *value, *rownr, j);
accumulate_for_scale(lp, &row_min[*rownr], &row_max[*rownr], absval);
}
}
/* Calculate scale factors for rows */
i = 0;
for(; i <= lp->rows; i++) {
if(i == 0)
nz = nzOF;
else
nz = mat_rowlength(lp->matA, i);
absval = minmax_to_scale(lp, row_min[i], row_max[i], nz); /* nz instead of nzOF KJEI 20/05/2010 */
if(absval == 0)
absval = 1;
scalechange[i] = absval;
}
FREE(row_max);
FREE(row_min);
/* Row-scale the matrix (including the objective function and Lagrangean constraints) */
rowscaled = scale_updaterows(lp, scalechange, TRUE);
/* Calculate column scales */
i = 1;
for(j = 1; j <= lp->columns; j++) {
if(is_int(lp,j) && !is_integerscaling(lp)) { /* do not scale integer columns */
scalechange[lp->rows + j] = 1;
}
else {
col_max = 0;
if(is_scaletype(lp, SCALE_MEAN))
col_min = 0;
else
col_min = lp->infinite;
absval = lp->orig_obj[j];
if(absval != 0) {
absval = scaled_mat(lp, absval, 0, j);
accumulate_for_scale(lp, &col_min, &col_max, absval);
}
i = mat->col_end[j - 1];
value = &(COL_MAT_VALUE(i));
rownr = &(COL_MAT_ROWNR(i));
nz = mat->col_end[j];
for(; i < nz;
i++, value += matValueStep, rownr += matRowColStep) {
absval = scaled_mat(lp, *value, *rownr, j);
accumulate_for_scale(lp, &col_min, &col_max, absval);
}
nz = mat_collength(lp->matA, j);
if(fabs(lp->orig_obj[j]) > 0)
nz++;
scalechange[lp->rows + j] = minmax_to_scale(lp, col_min, col_max, nz);
}
}
/* ... and then column-scale the already row-scaled matrix */
colscaled = scale_updatecolumns(lp, &scalechange[lp->rows], TRUE);
/* Create a geometric mean-type measure of the extent of scaling performed; */
/* ideally, upon successive calls to scale() the value should converge to 0 */
if(rowscaled || colscaled) {
col_max = 0;
for(j = 1; j <= lp->columns; j++)
col_max += log(scalechange[lp->rows + j]);
col_max = exp(col_max/lp->columns);
i = 0;
col_min = 0;
for(; i <= lp->rows; i++)
col_min += log(scalechange[i]);
col_min = exp(col_min/row_count);
}
else {
col_max = 1;
col_min = 1;
}
if(scaledelta == NULL)
FREE(scalechange);
return(1 - sqrt(col_max*col_min));
}
/* MUST MODIFY */
MYBOOL BFP_CALLMODEL bfp_resize(lprec *lp, int newsize)
{
INVrec *lu;
lu = lp->invB;
/* Increment dimensionality since we put the objective row at the top */
newsize = newsize + bfp_rowoffset(lp);
lu->dimalloc = newsize;
/* Allocate index tracker arrays, LU matrices and various work vectors */
if(!allocREAL(lp, &(lu->value), newsize+MATINDEXBASE, AUTOMATIC))
return( FALSE );
/* Data specific to the factorization engine */
if(lu->LUSOL != NULL) {
if(newsize > 0 || 1)
LUSOL_sizeto(lu->LUSOL, newsize, newsize, 0);
else {
LUSOL_free(lu->LUSOL);
lu->LUSOL = NULL;
}
}
else if(newsize > 0 || 1) {
int asize;
REAL bsize;
lu->LUSOL = LUSOL_create(NULL, 0, LUSOL_PIVMOD_TPP, bfp_pivotmax(lp)*0);
#if 1
lu->LUSOL->luparm[LUSOL_IP_ACCELERATION] = LUSOL_AUTOORDER;
lu->LUSOL->parmlu[LUSOL_RP_SMARTRATIO] = 0.50;
#endif
#if 0
lu->timed_refact = DEF_TIMEDREFACT;
#else
lu->timed_refact = FALSE;
#endif
/* The following adjustments seem necessary to make the really tough NETLIB
models perform reliably and still performant (e.g. cycle.mps) */
#if 0
lu->LUSOL->parmlu[LUSOL_RP_SMALLDIAG_U] =
lu->LUSOL->parmlu[LUSOL_RP_EPSDIAG_U] = lp->epsprimal;
#endif
#if 0
lu->LUSOL->parmlu[LUSOL_RP_ZEROTOLERANCE] = lp->epsvalue;
#endif
#if 1
LUSOL_setpivotmodel(lu->LUSOL, LUSOL_PIVMOD_NOCHANGE, LUSOL_PIVTOL_SLIM);
#else
LUSOL_setpivotmodel(lu->LUSOL, LUSOL_PIVMOD_NOCHANGE, LUSOL_PIVTOL_TIGHT);
#endif
#ifdef LUSOL_UseBLAS
/* if(fileSearchPath("PATH", "myBLAS.DLL", NULL) && load_BLAS("myBLAS")) */
if(is_nativeBLAS() && load_BLAS(libnameBLAS))
lp->report(lp, NORMAL, "Optimized BLAS was successfully loaded for bfp_LUSOL.\n");
#endif
/* Try to minimize memory allocation if we have a large number of unit columns */
bsize = (REAL) lp->get_nonzeros(lp);
if(newsize > lp->columns)
bsize += newsize;
else
bsize = bsize/lp->columns*newsize;
/* Add a "reasonable" delta to allow for B and associated factorizations
that are denser than average; this makes reallocations less frequent.
Values between 1.2 and 1.5 appear to be reasonable. */
asize = (int) (bsize*MAX_DELTAFILLIN*1.3333);
if(!LUSOL_sizeto(lu->LUSOL, newsize, newsize, asize))
return( FALSE );
}
lu->dimcount = newsize;
return( TRUE );
}
int CurtisReidScales(lprec *lp, MYBOOL _Advanced, REAL *FRowScale, REAL *FColScale)
{
int i, row, col, ent, nz;
REAL *RowScalem2, *ColScalem2,
*RowSum, *ColSum,
*residual_even, *residual_odd;
REAL sk, qk, ek,
skm1, qkm1, ekm1,
qkm2, qkqkm1, ekm2, ekekm1,
absvalue, logvalue,
StopTolerance;
int *RowCount, *ColCount, colMax;
int Result;
MATrec *mat = lp->matA;
REAL *value;
int *rownr, *colnr;
if(CurtisReidMeasure(lp, _Advanced, FRowScale, FColScale)<0.1*get_nonzeros(lp))
return(0);
/* Allocate temporary memory and find RowSum and ColSum measures */
nz = get_nonzeros(lp);
colMax = lp->columns;
allocREAL(lp, &RowSum, lp->rows+1, TRUE);
allocINT(lp, &RowCount, lp->rows+1, TRUE);
allocREAL(lp, &residual_odd, lp->rows+1, TRUE);
allocREAL(lp, &ColSum, colMax+1, TRUE);
allocINT(lp, &ColCount, colMax+1, TRUE);
allocREAL(lp, &residual_even, colMax+1, TRUE);
allocREAL(lp, &RowScalem2, lp->rows+1, FALSE);
allocREAL(lp, &ColScalem2, colMax+1, FALSE);
/* Set origin for row scaling */
for(i = 1; i <= colMax; i++) {
absvalue=fabs(lp->orig_obj[i]);
if(absvalue>0) {
logvalue = log(absvalue);
ColSum[i] += logvalue;
RowSum[0] += logvalue;
ColCount[i]++;
RowCount[0]++;
}
}
value = &(COL_MAT_VALUE(0));
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, value += matValueStep, rownr += matRowColStep, colnr += matRowColStep) {
absvalue=fabs(*value);
if(absvalue>0) {
logvalue = log(absvalue);
ColSum[*colnr] += logvalue;
RowSum[*rownr] += logvalue;
ColCount[*colnr]++;
RowCount[*rownr]++;
}
}
/* Make sure we dont't have division by zero errors */
for(row = 0; row <= lp->rows; row++)
if(RowCount[row] == 0)
RowCount[row] = 1;
for(col = 1; col <= colMax; col++)
if(ColCount[col] == 0)
ColCount[col] = 1;
/* Initialize to RowScale = RowCount-1 RowSum
ColScale = 0.0
residual = ColSum - ET RowCount-1 RowSum */
StopTolerance= MAX(lp->scalelimit-floor(lp->scalelimit), DEF_SCALINGEPS);
StopTolerance *= (REAL) nz;
for(row = 0; row <= lp->rows; row++) {
FRowScale[row] = RowSum[row] / (REAL) RowCount[row];
RowScalem2[row] = FRowScale[row];
}
/* Compute initial residual */
for(col = 1; col <= colMax; col++) {
FColScale[col] = 0;
ColScalem2[col] = 0;
residual_even[col] = ColSum[col];
if(lp->orig_obj[col] != 0)
residual_even[col] -= RowSum[0] / (REAL) RowCount[0];
i = mat->col_end[col-1];
rownr = &(COL_MAT_ROWNR(i));
ent = mat->col_end[col];
for(; i < ent;
i++, rownr += matRowColStep) {
residual_even[col] -= RowSum[*rownr] / (REAL) RowCount[*rownr];
}
}
/* Compute sk */
sk = 0;
skm1 = 0;
for(col = 1; col <= colMax; col++)
sk += (residual_even[col]*residual_even[col]) / (REAL) ColCount[col];
Result = 0;
qk=1; qkm1=0; qkm2=0;
ek=0; ekm1=0; ekm2=0;
while(sk>StopTolerance) {
/* Given the values of residual and sk, construct
ColScale (when pass is even)
RowScale (when pass is odd) */
qkqkm1 = qk * qkm1;
ekekm1 = ek * ekm1;
if((Result % 2) == 0) { /* pass is even; construct RowScale[pass+1] */
if(Result != 0) {
for(row = 0; row <= lp->rows; row++)
RowScalem2[row] = FRowScale[row];
if(qkqkm1 != 0) {
for(row = 0; row <= lp->rows; row++)
FRowScale[row]*=(1 + ekekm1 / qkqkm1);
for(row = 0; row<=lp->rows; row++)
FRowScale[row]+=(residual_odd[row] / (qkqkm1 * (REAL) RowCount[row]) -
RowScalem2[row] * ekekm1 / qkqkm1);
}
}
}
else { /* pass is odd; construct ColScale[pass+1] */
for(col = 1; col <= colMax; col++)
ColScalem2[col] = FColScale[col];
if(qkqkm1 != 0) {
for(col = 1; col <= colMax; col++)
FColScale[col] *= (1 + ekekm1 / qkqkm1);
for(col = 1; col <= colMax; col++)
FColScale[col] += (residual_even[col] / ((REAL) ColCount[col] * qkqkm1) -
ColScalem2[col] * ekekm1 / qkqkm1);
}
}
/* update residual and sk (pass + 1) */
if((Result % 2) == 0) { /* even */
/* residual */
for(row = 0; row <= lp->rows; row++)
residual_odd[row] *= ek;
for(i = 1; i <= colMax; i++)
if(lp->orig_obj[i] != 0)
residual_odd[0] += (residual_even[i] / (REAL) ColCount[i]);
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep) {
residual_odd[*rownr] += (residual_even[*colnr] / (REAL) ColCount[*colnr]);
}
for(row = 0; row <= lp->rows; row++)
residual_odd[row] *= (-1 / qk);
/* sk */
skm1 = sk;
sk = 0;
for(row = 0; row <= lp->rows; row++)
sk += (residual_odd[row]*residual_odd[row]) / (REAL) RowCount[row];
}
else { /* odd */
/* residual */
for(col = 1; col <= colMax; col++)
residual_even[col] *= ek;
for(i = 1; i <= colMax; i++)
if(lp->orig_obj[i] != 0)
residual_even[i] += (residual_odd[0] / (REAL) RowCount[0]);
rownr = &(COL_MAT_ROWNR(0));
colnr = &(COL_MAT_COLNR(0));
for(i = 0; i < nz;
i++, rownr += matRowColStep, colnr += matRowColStep) {
residual_even[*colnr] += (residual_odd[*rownr] / (REAL) RowCount[*rownr]);
}
for(col = 1; col <= colMax; col++)
residual_even[col] *= (-1 / qk);
/* sk */
skm1 = sk;
sk = 0;
for(col = 1; col <= colMax; col++)
sk += (residual_even[col]*residual_even[col]) / (REAL) ColCount[col];
}
/* Compute ek and qk */
ekm2=ekm1;
ekm1=ek;
ek=qk * sk / skm1;
qkm2=qkm1;
qkm1=qk;
qk=1-ek;
Result++;
}
/* Synchronize the RowScale and ColScale vectors */
ekekm1 = ek * ekm1;
if(qkm1 != 0) {
if((Result % 2) == 0) { /* pass is even, compute RowScale */
for(row = 0; row<=lp->rows; row++)
FRowScale[row]*=(1.0 + ekekm1 / qkm1);
for(row = 0; row<=lp->rows; row++)
FRowScale[row]+=(residual_odd[row] / (qkm1 * (REAL) RowCount[row]) -
RowScalem2[row] * ekekm1 / qkm1);
}
else { /* pass is odd, compute ColScale */
for(col=1; col<=colMax; col++)
FColScale[col]*=(1 + ekekm1 / qkm1);
for(col=1; col<=colMax; col++)
FColScale[col]+=(residual_even[col] / ((REAL) ColCount[col] * qkm1) -
ColScalem2[col] * ekekm1 / qkm1);
}
}
/* Do validation, if indicated */
if(FALSE && mat_validate(mat)){
double check, error;
/* CHECK: M RowScale + E ColScale = RowSum */
error = 0;
for(row = 0; row <= lp->rows; row++) {
check = (REAL) RowCount[row] * FRowScale[row];
if(row == 0) {
for(i = 1; i <= colMax; i++) {
if(lp->orig_obj[i] != 0)
check += FColScale[i];
}
}
else {
i = mat->row_end[row-1];
ent = mat->row_end[row];
for(; i < ent; i++) {
col = ROW_MAT_COLNR(i);
check += FColScale[col];
}
}
check -= RowSum[row];
error += check*check;
}
/* CHECK: E^T RowScale + N ColScale = ColSum */
error = 0;
for(col = 1; col <= colMax; col++) {
check = (REAL) ColCount[col] * FColScale[col];
if(lp->orig_obj[col] != 0)
check += FRowScale[0];
i = mat->col_end[col-1];
ent = mat->col_end[col];
rownr = &(COL_MAT_ROWNR(i));
for(; i < ent;
i++, rownr += matRowColStep) {
check += FRowScale[*rownr];
}
check -= ColSum[col];
error += check*check;
}
}
/* Convert to scaling factors (rounding to nearest power
of 2 can optionally be done as a separate step later) */
for(col = 1; col <= colMax; col++) {
absvalue = exp(-FColScale[col]);
if(absvalue < MIN_SCALAR) absvalue = MIN_SCALAR;
if(absvalue > MAX_SCALAR) absvalue = MAX_SCALAR;
if(!is_int(lp,col) || is_integerscaling(lp))
FColScale[col] = absvalue;
else
FColScale[col] = 1;
}
for(row = 0; row <= lp->rows; row++) {
absvalue = exp(-FRowScale[row]);
if(absvalue < MIN_SCALAR) absvalue = MIN_SCALAR;
if(absvalue > MAX_SCALAR) absvalue = MAX_SCALAR;
FRowScale[row] = absvalue;
}
/* free temporary memory */
FREE(RowSum);
FREE(ColSum);
FREE(RowCount);
FREE(ColCount);
FREE(residual_even);
FREE(residual_odd);
FREE(RowScalem2);
FREE(ColScalem2);
return(Result);
}
STATIC MYBOOL restartPricer(lprec *lp, MYBOOL isdual)
{
REAL *sEdge = NULL, seNorm, hold;
int i, j, m;
MYBOOL isDEVEX, ok = applyPricer(lp);
/* Correction from V6, apparently, via Kjell Eikland and the
** lpSolve mailing list 2014-06-18 2:57 p.m. */
if (ok && (lp->edgeVector[0] < 0) && (isdual == AUTOMATIC))
ok = FALSE;
if(!ok)
return( ok );
/* Store the active/current pricing type */
if(isdual == AUTOMATIC)
isdual = (MYBOOL) lp->edgeVector[0];
else
lp->edgeVector[0] = isdual;
m = lp->rows;
/* Determine strategy and check if we have strategy fallback for the primal */
isDEVEX = is_piv_rule(lp, PRICER_DEVEX);
if(!isDEVEX && !isdual)
isDEVEX = is_piv_mode(lp, PRICE_PRIMALFALLBACK);
/* Check if we only need to do the simple DEVEX initialization */
if(!is_piv_mode(lp, PRICE_TRUENORMINIT)) {
if(isdual) {
for(i = 1; i <= m; i++)
lp->edgeVector[lp->var_basic[i]] = 1.0;
}
else {
for(i = 1; i <= lp->sum; i++)
if(!lp->is_basic[i])
lp->edgeVector[i] = 1.0;
}
return( ok );
}
/* Otherwise do the full Steepest Edge norm initialization */
ok = allocREAL(lp, &sEdge, m+1, FALSE);
if(!ok)
return( ok );
if(isdual) {
/* Extract the rows of the basis inverse and compute their squared norms */
for(i = 1; i <= m; i++) {
bsolve(lp, i, sEdge, NULL, 0, 0.0);
/* Compute the edge norm */
seNorm = 0;
for(j = 1; j <= m; j++) {
hold = sEdge[j];
seNorm += hold*hold;
}
j = lp->var_basic[i];
lp->edgeVector[j] = seNorm;
}
}
else {
/* Solve a=Bb for b over all non-basic variables and compute their squared norms */
for(i = 1; i <= lp->sum; i++) {
if(lp->is_basic[i])
continue;
fsolve(lp, i, sEdge, NULL, 0, 0.0, FALSE);
/* Compute the edge norm */
seNorm = 1;
for(j = 1; j <= m; j++) {
hold = sEdge[j];
seNorm += hold*hold;
}
lp->edgeVector[i] = seNorm;
}
}
FREE(sEdge);
return( ok );
}
/* Save a matrix column subset to a MatrixMarket formatted file,
say to export the basis matrix for further numerical analysis.
If colndx is NULL, then the full constraint matrix is assumed. */
MYBOOL REPORT_mat_mmsave(lprec *lp, char *filename, int *colndx, MYBOOL includeOF, char *infotext)
{
int n, m, nz, i, j, k, kk;
MATrec *mat = lp->matA;
MM_typecode matcode;
FILE *output = stdout;
MYBOOL ok;
LPSREAL *acol = NULL;
int *nzlist = NULL;
/* Open file */
ok = (MYBOOL) ((filename == NULL) || ((output = fopen(filename,"w")) != NULL));
if(!ok)
return(ok);
if((filename == NULL) && (lp->outstream != NULL))
output = lp->outstream;
/* Compute column and non-zero counts */
if(colndx == lp->var_basic) {
if(!lp->basis_valid)
return( FALSE );
m = lp->rows;
}
else if(colndx != NULL)
m = colndx[0];
else
m = lp->columns;
n = lp->rows;
nz = 0;
for(j = 1; j <= m; j++) {
k = (colndx == NULL ? n + j : colndx[j]);
if(k > n) {
k -= lp->rows;
nz += mat_collength(mat, k);
if(includeOF && is_OF_nz(lp, k))
nz++;
}
else
nz++;
}
kk = 0;
if(includeOF) {
n++; /* Row count */
kk++; /* Row index offset */
}
/* Initialize */
mm_initialize_typecode(&matcode);
mm_set_matrix(&matcode);
mm_set_coordinate(&matcode);
mm_set_real(&matcode);
mm_write_banner(output, matcode);
mm_write_mtx_crd_size(output, n+kk, m, nz+(colndx == lp->var_basic ? 1 : 0));
/* Allocate working arrays for sparse column storage */
allocREAL(lp, &acol, n+2, FALSE);
allocINT(lp, &nzlist, n+2, FALSE);
/* Write the matrix non-zero values column-by-column.
NOTE: matrixMarket files use 1-based indeces,
i.e. first row of a vector has index 1, not 0. */
if(infotext != NULL) {
fprintf(output, "%%\n");
fprintf(output, "%% %s\n", infotext);
fprintf(output, "%%\n");
}
if(includeOF && (colndx == lp->var_basic))
fprintf(output, "%d %d %g\n", 1, 1, 1.0);
for(j = 1; j <= m; j++) {
k = (colndx == NULL ? lp->rows + j : colndx[j]);
if(k == 0)
continue;
nz = obtain_column(lp, k, acol, nzlist, NULL);
for(i = 1; i <= nz; i++) {
if(!includeOF && (nzlist[i] == 0))
continue;
fprintf(output, "%d %d %g\n", nzlist[i]+kk, j+kk, acol[i]);
}
}
fprintf(output, "%% End of MatrixMarket file\n");
/* Finish */
FREE(acol);
FREE(nzlist);
fclose(output);
return(ok);
}
STATIC int primloop(lprec *lp, MYBOOL feasible)
{
int i, j, k, ok = TRUE;
LREAL theta = 0.0;
REAL *prow = NULL, *drow = NULL, *pcol = NULL, prevobj, epsvalue;
MYBOOL primal = TRUE, minit;
MYBOOL pivdynamic, bfpfinal = FALSE;
int oldpivrule, oldpivmode, pivrule, Blandswitches,
colnr, rownr, lastnr, minitcount = 0;
int Rcycle = 0, Ccycle = 0, Ncycle = 0, changedphase = FALSE;
int *nzdrow = NULL, *workINT = NULL;
/* Add sufficent number of artificial variables to make the problem feasible
through the first phase; delete when primal feasibility has been achieved */
lp->Extrap = 0;
#ifdef EnablePrimalPhase1
if(!feasible) {
#ifdef Paranoia
if(!verifyBasis(lp))
report(lp, SEVERE, "primloop: No valid basis for artificial variables\n");
#endif
#if 0
/* First check if we can get away with a single artificial variable */
if(lp->equalities == 0) {
i = (int) feasibilityOffset(lp, !primal);
add_artificial(lp, i);
}
else
#endif
/* Otherwise add as many as is necessary to force basic feasibility */
for(i = 1; i <= lp->rows; i++)
add_artificial(lp, i);
}
if(lp->spx_trace)
report(lp, DETAILED, "Extrap count = %d\n", lp->Extrap);
#endif
if(lp->spx_trace)
report(lp, DETAILED, "Entered primal simplex algorithm with feasibility %s\n",
my_boolstr(feasible));
/* Create work arrays */
#ifdef UseSparseReducedCost
allocINT(lp, &nzdrow, lp->sum + 1, FALSE);
#endif
allocREAL(lp, &prow, lp->sum + 1, TRUE);
allocREAL(lp, &drow, lp->sum + 1, TRUE);
allocREAL(lp, &pcol, lp->rows + 1, TRUE);
/* Refactorize the basis and set status variables */
i = my_if(is_bb_action(lp, ACTION_REBASE), INITSOL_SHIFTZERO, INITSOL_USEZERO);
if(((lp->spx_status == SWITCH_TO_PRIMAL) && !lp->justInverted) ||
(lp->Extrap != 0) ||
is_bb_action(lp, ACTION_REINVERT)) {
simplexPricer(lp, (MYBOOL)!primal);
/* Do basis crashing before refactorization, if specified */
invert(lp, (MYBOOL) i, TRUE);
}
else {
if(is_bb_action(lp, ACTION_RECOMPUTE))
recompute_solution(lp, (MYBOOL) i);
restartPricer(lp, (MYBOOL)!primal);
}
lp->bb_action = ACTION_NONE;
lp->spx_status = RUNNING;
lp->doIterate = FALSE;
minit = ITERATE_MAJORMAJOR;
prevobj = lp->rhs[0];
oldpivmode = lp->piv_strategy;
oldpivrule = get_piv_rule(lp);
pivdynamic = ANTICYCLEBLAND && is_piv_mode(lp, PRICE_ADAPTIVE);
epsvalue = lp->epspivot;
Blandswitches = 0;
rownr = 0;
colnr = 0;
lastnr = 0;
lp->rejectpivot[0] = 0;
if(feasible)
lp->simplex_mode = SIMPLEX_Phase2_PRIMAL;
else
lp->simplex_mode = SIMPLEX_Phase1_PRIMAL;
/* Iterate while we are successful; exit when the model is infeasible/unbounded,
or we must terminate due to numeric instability or user-determined reasons */
while(lp->spx_status == RUNNING) {
if(lp->spx_trace)
if(lastnr > 0)
report(lp, NORMAL, "primloop: Objective at iteration %8d is " RESULTVALUEMASK " (%4d: %4d %s- %4d)\n",
get_total_iter(lp), lp->rhs[0], rownr, lastnr,
my_if(minit == ITERATE_MAJORMAJOR, "<","|"), colnr);
pivrule = get_piv_rule(lp);
if(pivdynamic && ((pivrule != PRICER_FIRSTINDEX) ||
(pivrule != oldpivrule))
#if PrimalPivotStickiness==2
&& (lp->fixedvars == 0)
#elif PrimalPivotStickiness==1
&& feasible
#endif
) {
/* Check if we have a stationary solution */
if((minit == ITERATE_MAJORMAJOR) && !lp->justInverted &&
(fabs(my_reldiff(lp->rhs[0], prevobj)) < epsvalue)) {
Ncycle++;
/* Start to monitor for variable cycling if this is the initial stationarity */
if(Ncycle <= 1) {
Ccycle = colnr;
Rcycle = rownr;
}
/* Check if we should change pivoting strategy due to stationary variable cycling */
else if((pivrule == oldpivrule) && (((MAX_STALLCOUNT > 1) && (Ncycle > MAX_STALLCOUNT)) ||
(Ccycle == rownr) || (Rcycle == colnr))) {
/* First check if we should give up on Bland's rule and try perturbed bound
relaxation instead */
#ifdef EnableStallAntiDegen
if((MAX_BLANDSWITCH >= 0) && (Blandswitches >= MAX_BLANDSWITCH)) {
lp->spx_status = DEGENERATE;
break;
}
#endif
Blandswitches++;
lp->piv_strategy = PRICER_FIRSTINDEX; /* There is no advanced normalization for Bland's rule, restart at end */
Ccycle = 0;
Rcycle = 0;
Ncycle = 0;
if(lp->spx_trace)
report(lp, DETAILED, "primloop: Detected cycling at iteration %d; changed to FIRST INDEX rule!\n",
get_total_iter(lp));
}
}
#if 0
/* Handle cycling or stationary situations by switching to the dual simplex */
else if((pivrule == oldpivrule) && feasible && (lp->simplex_strategy & SIMPLEX_DYNAMIC)) {
lp->spx_status = SWITCH_TO_DUAL;
if(lp->total_iter == 0)
report(lp, NORMAL, "Start dual simplex for finalization at iteration %8d\n",
get_total_iter(lp));
break;
}
#endif
/* Change back to original selection strategy as soon as possible */
else if((minit == ITERATE_MAJORMAJOR) && (pivrule != oldpivrule)) {
lp->piv_strategy = oldpivmode;
restartPricer(lp, AUTOMATIC); /* Pricer restart following Bland's rule */
Ccycle = 0;
Rcycle = 0;
Ncycle = 0;
if(lp->spx_trace)
report(lp, DETAILED, "...returned to original pivot selection rule at iteration %d.\n",
get_total_iter(lp));
}
}
/* Store current LP value for reference at next iteration */
prevobj = lp->rhs[0];
lp->doIterate = FALSE;
lp->doInvert = FALSE;
/* Find best column to enter the basis */
RetryCol:
if(!changedphase) {
i = 0;
do {
if(partial_countBlocks(lp, (MYBOOL) !primal) > 1)
partial_blockStep(lp, (MYBOOL) !primal);
colnr = colprim(lp, (MYBOOL) (minit == ITERATE_MINORRETRY), drow, nzdrow);
i++;
} while ((colnr == 0) && (i < partial_countBlocks(lp, (MYBOOL) !primal)));
#ifdef FinalOptimalErrorLimitation
/* Do additional checking that we have a correct identification of optimality */
if((colnr == 0) && !lp->justInverted) {
lp->doInvert = TRUE;
i = invert(lp, INITSOL_USEZERO, TRUE);
colnr = colprim(lp, FALSE, drow, nzdrow);
}
#endif
}
if(colnr > 0) {
changedphase = FALSE;
fsolve(lp, colnr, pcol, workINT, lp->epsmachine, 1.0, TRUE); /* Solve entering column for Pi */
#ifdef UseRejectionList
if(is_anti_degen(lp, ANTIDEGEN_COLUMNCHECK) && !check_degeneracy(lp, pcol, NULL)) {
if(lp->rejectpivot[0] < DEF_MAXPIVOTRETRY/3) {
i = ++lp->rejectpivot[0];
lp->rejectpivot[i] = colnr;
report(lp, DETAILED, "Entering column %d found to be non-improving due to degeneracy!\n",
colnr);
goto RetryCol;
}
else {
lp->rejectpivot[0] = 0;
report(lp, DETAILED, "Gave up trying to find a strictly improving entering column!\n");
}
}
#endif
/* Find the leaving variable that gives the most stringent bound on the entering variable */
theta = drow[colnr];
rownr = rowprim(lp, colnr, &theta, pcol);
#if 0
report(lp, NORMAL, "Iteration %d: Enter %d, Leave %d\n", lp->current_iter, colnr, rownr);
#endif
/* See if we can do a straight artificial<->slack replacement (when "colnr" is a slack) */
if((lp->Extrap != 0) && (rownr == 0) && (colnr <= lp->rows))
rownr = findAnti_artificial(lp, colnr);
if(rownr > 0) {
lp->rejectpivot[0] = 0;
lp->bfp_prepareupdate(lp, rownr, colnr, pcol);
}
else if(lp->spx_status == UNBOUNDED) {
report(lp, DETAILED, "primloop: The model is primal unbounded.\n");
break;
}
#ifdef UseRejectionList
else if(lp->rejectpivot[0] < DEF_MAXPIVOTRETRY) {
lp->spx_status = RUNNING;
if(lp->justInverted) {
lp->rejectpivot[0]++;
lp->rejectpivot[lp->rejectpivot[0]] = colnr;
report(lp, DETAILED, "...trying to recover via another pivot column!\n");
}
else {
lp->doInvert = TRUE;
invert(lp, INITSOL_USEZERO, TRUE);
}
goto RetryCol;
}
#endif
else {
/* Assume failure if we are still unsuccessful and the model is not unbounded */
if((rownr == 0) && (lp->spx_status == RUNNING)) {
report(lp, IMPORTANT, "primloop: Could not find a leaving variable for entering %d (iteration %d)\n",
colnr, get_total_iter(lp));
lp->spx_status = NUMFAILURE;
}
}
}
#ifdef EnablePrimalPhase1
else if(!feasible || isPhase1(lp)) {
if(feasiblePhase1(lp, epsvalue)) {
lp->spx_status = RUNNING;
if(lp->bb_totalnodes == 0) {
report(lp, NORMAL, "Found feasibility by primal simplex at iteration %8d\n",
get_total_iter(lp));
if((lp->usermessage != NULL) && (lp->msgmask & MSG_LPFEASIBLE))
lp->usermessage(lp, lp->msghandle, MSG_LPFEASIBLE);
}
changedphase = FALSE;
feasible = TRUE;
lp->simplex_mode = SIMPLEX_Phase2_PRIMAL;
/* We can do two things now;
1) delete the rows belonging to those variables, since they are redundant, OR
2) drive out the existing artificial variables via pivoting. */
if(lp->Extrap > 0) {
#ifdef Phase1EliminateRedundant
/* If it is not a MIP model we can try to delete redundant rows */
if((lp->bb_totalnodes == 0) && (MIP_count(lp) == 0)) {
while(lp->Extrap > 0) {
i = lp->rows;
while((i > 0) && (lp->var_basic[i] <= lp->sum-lp->Extrap))
i--;
#ifdef Paranoia
if(i <= 0) {
report(lp, SEVERE, "primloop: Could not find redundant artificial.\n");
break;
}
#endif
/* Obtain column and row indeces */
j = lp->var_basic[i]-lp->rows;
k = get_artificialRow(lp, j);
/* Delete row before column due to basis "compensation logic" */
if(lp->is_basic[k]) {
lp->is_basic[lp->rows+j] = FALSE;
del_constraint(lp, k);
}
else
setBasisVar(lp, i, k);
del_column(lp, j);
lp->Extrap--;
}
lp->basis_valid = TRUE;
}
/* Otherwise we drive out the artificials by elimination pivoting */
else {
eliminate_artificials(lp, prow);
lp->doIterate = FALSE;
}
#else
lp->Extrap = my_flipsign(lp->Extrap);
#endif
}
lp->doInvert = TRUE;
prevobj = lp->infinite;
}
else {
lp->spx_status = INFEASIBLE;
minit = ITERATE_MAJORMAJOR;
if(lp->spx_trace)
report(lp, NORMAL, "Model infeasible by primal simplex at iteration %8d\n",
get_total_iter(lp));
}
}
#endif
/* Pivot row/col and update the inverse */
if(lp->doIterate) {
lastnr = lp->var_basic[rownr];
if(lp->justInverted)
minitcount = 0;
else if(minitcount > MAX_MINITUPDATES) {
recompute_solution(lp, INITSOL_USEZERO);
minitcount = 0;
}
minit = performiteration(lp, rownr, colnr, theta, primal, NULL, NULL,
pcol, NULL);
if(minit != ITERATE_MAJORMAJOR)
minitcount++;
if((lp->spx_status == USERABORT) || (lp->spx_status == TIMEOUT))
break;
else if(minit == ITERATE_MINORMAJOR)
continue;
#ifdef UsePrimalReducedCostUpdate
/* Do a fast update of the reduced costs in preparation for the next iteration */
if(minit == ITERATE_MAJORMAJOR)
update_reducedcosts(lp, primal, lastnr, colnr, pcol, drow);
#endif
#ifdef EnablePrimalPhase1
/* Detect if an auxiliary variable has left the basis and delete it; if
the non-basic variable only changed bound (a "minor iteration"), the
basic artificial variable did not leave and there is nothing to do */
if((minit == ITERATE_MAJORMAJOR) && (lastnr > lp->sum - abs(lp->Extrap))) {
#ifdef Paranoia
if(lp->is_basic[lastnr] || !lp->is_basic[colnr])
report(lp, SEVERE, "primloop: Invalid basis indicator for variable %d at iteration %d\n",
lastnr, get_total_iter(lp));
#endif
del_column(lp, lastnr-lp->rows);
if(lp->Extrap > 0)
lp->Extrap--;
else
lp->Extrap++;
if(lp->Extrap == 0) {
colnr = 0;
prevobj = lp->infinite;
changedphase = TRUE;
}
}
#endif
}
if(lp->spx_status == SWITCH_TO_DUAL)
;
else if(!changedphase && lp->bfp_mustrefactorize(lp)) {
i = invert(lp, INITSOL_USEZERO, FALSE);
#ifdef ResetMinitOnReinvert
minit = ITERATE_MAJORMAJOR;
#endif
if((lp->spx_status == USERABORT) || (lp->spx_status == TIMEOUT))
break;
else if(!i) {
lp->spx_status = SINGULAR_BASIS;
break;
}
/* Check whether we are still feasible or not... */
if(!isPrimalFeasible(lp, lp->epspivot)) {
lp->spx_status = LOSTFEAS;
}
}
userabort(lp, -1);
}
if (lp->piv_strategy != oldpivmode)
lp->piv_strategy = oldpivmode;
#ifdef EnablePrimalPhase1
/* Remove any remaining artificial variables (feasible or infeasible model) */
lp->Extrap = abs(lp->Extrap);
if(lp->Extrap > 0) {
clear_artificials(lp);
if(lp->spx_status != OPTIMAL)
restore_basis(lp);
i = invert(lp, INITSOL_USEZERO, TRUE);
}
#ifdef Paranoia
if(!verifyBasis(lp))
report(lp, SEVERE, "primloop: Invalid basis detected due to internal error\n");
#endif
/* Switch to dual phase 1 simplex for MIP models during B&B phases */
if((lp->bb_totalnodes == 0) && (MIP_count(lp) > 0) &&
((lp->simplex_strategy & SIMPLEX_Phase1_DUAL) == 0)) {
lp->simplex_strategy &= !SIMPLEX_Phase1_PRIMAL;
lp->simplex_strategy += SIMPLEX_Phase1_DUAL;
}
#endif
FREE(nzdrow);
FREE(drow);
FREE(prow);
FREE(pcol);
return(ok);
} /* primloop */
