void GetXrow(sdpdat *pd,double *sinve,double *xrowi,double *ei)
/* This routine finds one row of the primal matrix X */
{ int i,j,n=pd->nrow;
double rtmp,lambda,eSpSinve=0.0,*spSinve,*dySinvei,
*sDys,eTxrowi=0.0;
spSinve = pd->rw; /* inv(C-D(dy)) * e */
dySinvei = spSinve+n;
sDys = dySinvei+n; /* Sinv*D(dy)*Sinv*ei */
lambda =pd->lamda;
ChlSolve(pd->sf, ei, xrowi); /* Solve (C-D(dy))*xrowi=ei */
if (pd->ptyp==EquCut||pd->ptyp==UquCut) { /* Rank one update */
rtmp=0.0;
eSpSinve =0.0;
for (i=0; i<n; i++) {
rtmp+=xrowi[i];
eSpSinve +=spSinve[i];
}
eSpSinve=1.0-lambda*eSpSinve;
rtmp=lambda*rtmp/eSpSinve;
for (i=0; i<n; i++)
xrowi[i]=xrowi[i]+rtmp*spSinve[i];
} /* Now S*xrowi = ei */
for (j=0;j<pd->nrow; j++)
eTxrowi += xrowi[j];
for (j=0;j<pd->nrow; j++)
dySinvei[j] = xrowi[j]*pd->dy[j];
ChlSolve(pd->sf, dySinvei, sDys);
if (pd->ptyp==EquCut||pd->ptyp==UquCut) {
rtmp=0.0;
for (i=0; i<n; i++)
{
rtmp+=sDys[i];
}
rtmp=lambda*rtmp/eSpSinve;
for (i=0; i<n; i++)
sDys[i]=sDys[i]+rtmp*spSinve[i];
}
rtmp=pd->lamda * eTxrowi;
for (j=0;j<pd->nrow; j++)
xrowi[j] += sDys[j] + rtmp*sinve[j];
} /* GetXrow */
int MatSolve4(chfac*sf, double *b, double *x,int n){
memcpy(x,b,n*sizeof(double));
ChlSolve(sf, b, x);
return 0;
}
void GetSinve(sdpdat *pd,double *sinve)
/* Solve the system of equations S*sinve = e where e is vec of
all ones. Also save the solution to (C-D(dy))*spSinve = e */
{
int i,n;
double eSpSinve,rtmp,*spSinve,*e,lambda;
n=pd->nrow;
spSinve=pd->rw;
e=spSinve+n;
lambda=pd->lamda;
for (i=0; i<n; i++)
e[i]=1.0;
ChlSolve(pd->sf,e,spSinve);
if (pd->ptyp>=0) {
eSpSinve =0.0;
for (i=0; i<n; i++)
eSpSinve +=spSinve[i];
rtmp=1.0-lambda*eSpSinve;
rtmp=lambda*eSpSinve/rtmp;
for (i=0; i<n; i++)
sinve[i]=(1.0+rtmp)*spSinve[i];
}
else {
for (i=0; i<n; i++)
sinve[i]=spSinve[i];
}
} /* GetSinve */
static int DSDPLinearSolve2(void* ctx, double dd[], double xx[], int n){
int i,info;
double *bb;
MCholSolverALL *AMA = (MCholSolverALL *)ctx;
DSDPFunctionBegin;
info=DSDPVecGetArray(AMA->D1, &bb);DSDPCHKERR(info);
for (i=0;i<n;i++){ bb[i]=dd[i];}
ChlSolve(AMA->M, bb, xx);
info=DSDPVecRestoreArray(AMA->D1, &bb);
DSDPFunctionReturn(0);
}
void GetVhat(double *u,
double *q,
sdpdat *sdt)
{
int i,n;
double ese,lamda,dl,rtmp,*r,*y,*dy,*uv;
chfac *cf,*mf;
symat *cy;
syoff *st;
n =sdt->nrow;
lamda=sdt->lamda;
dl =sdt->dl;
cf =sdt->sf;
mf =sdt->mf;
y =sdt->y;
dy =sdt->dy;
r =sdt->rw+n;
uv =sdt->rw+5*n;
cy =sdt->cy;
st =sdt->st;
/*
* r=L*u;
*/
GetUhat(mf,u,r);
/*
* r=S^-1*u
*/
ChlSolve(cf,u,r);
dCopy(n,r,u);
if (sdt->ptyp==EquCut||sdt->ptyp==UquCut)
{
rtmp=0.0;
ese =0.0;
for (i=0; i<n; i++)
{
rtmp+=r[i];
ese +=q[i];
}
ese=1.0-lamda*ese;
rtmp=lamda*rtmp/ese;
for (i=0; i<n; i++)
u[i]=r[i]+rtmp*q[i];
}
} /* GetVhat */
void RankReduce(sdpdat *pd)
/* This routine generates a specific cut or solution to the original,
unrelaxed problem. */
{
int i,j,dim=pd->nrow, type = pd->ptyp;
double bestObj=0.0,thisObj=0.0,bestRObj=0.0,
bestHObj=0.0,*thisCut,*bestCut,*randVec,
*dblPtr,*sinve,*ei,hth=0.0,beta=0.0,*u,rtmp,ese;
orderCut *vhat;
thisCut = dAlloc(dim,"Insufficient memory to store cut");
bestCut = dAlloc(dim,"Insufficient memory to store cut");
randVec = dAlloc(dim,"Insufficient memory to store cut");
sinve = dAlloc(dim,"Insufficient memory to store cut");
vhat = OrdAlloc(dim,"Insufficient memory to store cut");
ei = dAlloc(dim,"Insufficient memory to store cut");
u = pd->rw+dim;
srand(clock()); /* Used to generate random vectors */
if (type == -3) /* For Box QP, use sqrt of the diagonal */
for (i=0;i<dim;i++)
thisCut[i]=bestCut[i]=sqrt(1-pd->rho*(pd->dy[i]-pd->y[i])/(pd->y[i]*pd->y[i]));
GetSinve(pd,sinve);
if (pd->par.findvec <= 0)
{
for (i=0; i<dim; i++)
{
memset(ei,0,sizeof(double)*dim);
ei[i]=1.0;
GetXrow(pd, sinve, randVec, ei);
for (j=0; j<dim; j++)
vhat[j].val=randVec[j];
DefineCut(thisCut,pd->ptyp,vhat,pd->nrow,pd->is,pd->it);
thisObj = EvalObjective(*(pd->cy),thisCut,dim,type);
if (i==0 || thisObj > bestHObj)
{
bestHObj=thisObj;
dblPtr=bestCut; bestCut=thisCut; thisCut=dblPtr;
}
}
}
/* We need to factor ( S + A(dy) ) when we want to
do ecut rank reduction */
if (pd->par.findvec >=0)
{
/* In case of ecut, we have to save L^-1 * e to sinve */
if(pd->ptyp == EquCut)
{
for(i=0;i<dim;i++) { randVec[i]=2.0; u[i]=0.0; }
FSubst( pd->mf,randVec,u , pd->mf->NegDiag);
for(i=0;i<dim;i++){ hth += u[i]*u[i]; }
beta = hth*( pd->dl - pd->lamda );
beta +=1.0;
if( beta < 0 )
{
printf("\n { 1 + h'h*(dl-l) } is less than zero. Error in rank reduction.");
ShutDown();
}
beta = sqrt(beta)-1.0;
beta /= hth;
}
bestRObj = -dim*dim;
for (i=0; i<dim; i++)
{
GetRandVec(randVec,dim);
if(pd->ptyp == EquCut)
{
if(pd->mf->NegDiag < 0) Uhat1(pd,u,randVec,ei,beta);
else Uhat2(pd,u,randVec,ei,beta,pd->mf->NegDiag,hth);
/* ChlSolve(cf,b,x); */
ChlSolve( pd->sf,randVec,ei);
rtmp = 0.0;
ese = 0.0;
for(j=0;j<dim;j++)
{
rtmp += ei[j];
ese += sinve[j];
}
ese = 1.0- pd->lamda*ese;
rtmp = pd->lamda*rtmp/ese;
for(j=0;j<dim;j++) randVec[j] = ei[j] + rtmp*sinve[j];
}
else
GetVhat(randVec,sinve,pd);
for (j=0; j<dim; j++) vhat[j].val=randVec[j];
DefineCut(thisCut,pd->ptyp,vhat,pd->nrow,pd->is,pd->it);
thisObj = EvalObjective(*(pd->cy),thisCut,dim,type);
if (i==dim || thisObj > bestRObj)
{
bestRObj=thisObj;
dblPtr=bestCut; bestCut=thisCut; thisCut=dblPtr;
}
}
}
else bestRObj = bestHObj;
bestObj = max(bestHObj, bestRObj);
if (pd->par.prtlev) SaveIt(bestCut,pd->ptyp,dim,pd->ss);
dFree(&thisCut);
dFree(&bestCut);
dFree(&randVec);
OrdFree(&vhat);
dFree(&sinve);
dFree(&ei);
if (pd->par.findvec == 0)
printf("\n The best solution found is : %8.6e \n",bestObj);
if (pd->par.findvec <= 0)
printf(" The best solution (heuristic) found is : %8.6e \n",bestHObj);
if (pd->par.findvec >= 0)
printf(" The best solution (randomized) found is : %8.6e \n",bestRObj);
printf("\n");
fprintf(fout," The best solution found is : %8.6e \n\n",bestObj);
}
