/*************************************************************************
* This function checks if the balance achieved is better than the diff
* For now, it uses a 2-norm measure
**************************************************************************/
int Serial_BetterBalance(int ncon, float *npwgts, float *tpwgts, float *diff)
{
int i;
float ndiff[MAXNCON];
for (i=0; i<ncon; i++)
ndiff[i] = fabs(tpwgts[i]-npwgts[i]);
return snorm2(ncon, ndiff) < snorm2(ncon, diff);
}
/*************************************************************************
* This function checks if the balance achieved is better than the diff
* For now, it uses a 2-norm measure
**************************************************************************/
int BetterBalance(int ncon, floattype *npwgts, floattype *tpwgts, floattype *diff)
{
int i;
floattype ndiff[MAXNCON];
for (i=0; i<ncon; i++)
ndiff[i] = fabs(tpwgts[0]-npwgts[i]);
return snorm2(ncon, ndiff) < snorm2(ncon, diff);
}
/*************************************************************************
* This function implements the CG solver used during the directed diffusion
**************************************************************************/
void ConjGrad2(MatrixType *A, floattype *b, floattype *x, floattype tol, floattype *workspace)
{
int i, k, n;
floattype *p, *r, *q, *z, *M;
floattype alpha, beta, rho, rho_1 = -1.0, error, bnrm2, tmp;
idxtype *rowptr, *colind;
floattype *values;
n = A->nrows;
rowptr = A->rowptr;
colind = A->colind;
values = A->values;
/* Initial Setup */
p = workspace;
r = workspace + n;
q = workspace + 2*n;
z = workspace + 3*n;
M = workspace + 4*n;
for (i=0; i<n; i++) {
x[i] = 0.0;
if (values[rowptr[i]] != 0.0)
M[i] = 1.0/values[rowptr[i]];
else
M[i] = 0.0;
}
/* r = b - Ax */
mvMult2(A, x, r);
for (i=0; i<n; i++)
r[i] = b[i]-r[i];
bnrm2 = snorm2(n, b);
if (bnrm2 > 0.0) {
error = snorm2(n, r) / bnrm2;
if (error > tol) {
/* Begin Iterations */
for (k=0; k<n; k++) {
for (i=0; i<n; i++)
z[i] = r[i]*M[i];
rho = sdot(n, r, z);
if (k == 0)
scopy(n, z, p);
else {
if (rho_1 != 0.0)
beta = rho/rho_1;
else
beta = 0.0;
for (i=0; i<n; i++)
p[i] = z[i] + beta*p[i];
}
mvMult2(A, p, q); /* q = A*p */
tmp = sdot(n, p, q);
if (tmp != 0.0)
alpha = rho/tmp;
else
alpha = 0.0;
saxpy(n, alpha, p, x); /* x = x + alpha*p */
saxpy(n, -alpha, q, r); /* r = r - alpha*q */
error = snorm2(n, r) / bnrm2;
if (error < tol)
break;
rho_1 = rho;
}
}
}
}
void run( Vector<Real> &s, Real &snorm, Real &del, int &iflag, int &iter, const Vector<Real> &x,
const Vector<Real> &grad, const Real &gnorm, ProjectedObjective<Real> &pObj ) {
Real tol = std::sqrt(ROL_EPSILON<Real>()), zero(0), one(1), two(2), half(0.5);
const Real gtol = std::min(tol1_,tol2_*gnorm);
// Gradient Vector
g_->set(grad);
Real normg = gnorm;
if ( pObj.isConActivated() ) {
primalVector_->set(grad.dual());
pObj.pruneActive(*primalVector_,grad.dual(),x);
g_->set(primalVector_->dual());
normg = g_->norm();
}
// Old and New Step Vectors
s.zero(); s_->zero();
snorm = zero;
Real snorm2(0), s1norm2(0);
// Preconditioned Gradient Vector
//pObj.precond(*v,*g,x,tol);
pObj.reducedPrecond(*v_,*g_,x,grad.dual(),x,tol);
// Basis Vector
p_->set(*v_);
p_->scale(-one);
Real pnorm2 = v_->dot(g_->dual());
iter = 0; iflag = 0;
Real kappa(0), beta(0), sigma(0), alpha(0), tmp(0), sMp(0);
Real gv = v_->dot(g_->dual());
pRed_ = zero;
for (iter = 0; iter < maxit_; iter++) {
//pObj.hessVec(*Hp,*p,x,tol);
pObj.reducedHessVec(*Hp_,*p_,x,grad.dual(),x,tol);
kappa = p_->dot(Hp_->dual());
if (kappa <= zero) {
sigma = (-sMp+sqrt(sMp*sMp+pnorm2*(del*del-snorm2)))/pnorm2;
s.axpy(sigma,*p_);
iflag = 2;
break;
}
alpha = gv/kappa;
s_->set(s);
s_->axpy(alpha,*p_);
s1norm2 = snorm2 + two*alpha*sMp + alpha*alpha*pnorm2;
if (s1norm2 >= del*del) {
sigma = (-sMp+sqrt(sMp*sMp+pnorm2*(del*del-snorm2)))/pnorm2;
s.axpy(sigma,*p_);
iflag = 3;
break;
}
pRed_ += half*alpha*gv;
s.set(*s_);
snorm2 = s1norm2;
g_->axpy(alpha,*Hp_);
normg = g_->norm();
if (normg < gtol) {
break;
}
//pObj.precond(*v,*g,x,tol);
pObj.reducedPrecond(*v_,*g_,x,grad.dual(),x,tol);
tmp = gv;
gv = v_->dot(g_->dual());
beta = gv/tmp;
p_->scale(beta);
p_->axpy(-one,*v_);
sMp = beta*(sMp+alpha*pnorm2);
pnorm2 = gv + beta*beta*pnorm2;
}
if (iflag > 0) {
pRed_ += sigma*(gv-half*sigma*kappa);
}
if (iter == maxit_) {
iflag = 1;
}
if (iflag != 1) {
iter++;
}
snorm = s.norm();
TrustRegion<Real>::setPredictedReduction(pRed_);
}