void L2Sphere::DiffRetraction(Variable *x, Vector *etax, Variable *y, Vector *xix, Vector *result, bool IsEtaXiSameDir) const
{
if (IsEtaXiSameDir)
{
VectorTransport(x, etax, y, xix, result);
if (IsEtaXiSameDir && (HasHHR || UpdBetaAlone))
{
const double *etaxTV = etax->ObtainReadData();
const double *xixTV = xix->ObtainReadData();
double EtatoXi = sqrt(Metric(x, etax, etax) / Metric(x, xix, xix));
SharedSpace *beta = new SharedSpace(1, 3);
double *betav = beta->ObtainWriteEntireData();
betav[0] = sqrt(Metric(x, etax, etax) / Metric(x, result, result)) / EtatoXi;
betav[1] = Metric(x, etax, etax);
betav[2] = Metric(x, result, result) * EtatoXi * EtatoXi;
etax->AddToTempData("beta", beta);
if (HasHHR)
{
Vector *TReta = result->ConstructEmpty();
result->CopyTo(TReta);
ScaleTimesVector(x, betav[0] * EtatoXi, TReta, TReta);
SharedSpace *SharedTReta = new SharedSpace(TReta);
etax->AddToTempData("betaTReta", SharedTReta);
}
}
return;
}
std::cout << "Warning: The differentiated retraction has not been implemented!" << std::endl;
xix->CopyTo(result);
};
void L2Sphere::Retraction(Variable *x, Vector *etax, Variable *result) const
{// exponential mapping
double norm = sqrt(Metric(x, etax, etax));
if (norm < std::numeric_limits<double>::epsilon())
ScaleTimesVector(x, cos(norm), x, result);
else
VectorLinearCombination(x, cos(norm), x, sin(norm) / norm, etax, result);
};
void L2Sphere::ObtainEtaxFlat(Variable *x, Vector *etax, Vector *etaxflat) const
{
etax->CopyTo(etaxflat);
double *etaxflatTV = etaxflat->ObtainWritePartialData();
double intv = 1.0 / (n - 1);
ScaleTimesVector(x, intv, etaxflat, etaxflat);
etaxflatTV[0] /= 2;
etaxflatTV[n - 1] /= 2;
};
void ProductManifold::DiffRetraction(Variable *x, Vector *etax, Variable *y, Vector *xix, Vector *result, bool IsEtaXiSameDir) const
{
ProdVariable *prodx = dynamic_cast<ProdVariable *> (x);
ProdVector *prodetax = dynamic_cast<ProdVector *> (etax);
ProdVariable *prody = dynamic_cast<ProdVariable *> (y);
ProdVector *prodxix = dynamic_cast<ProdVector *> (xix);
ProdVector *prodresult = dynamic_cast<ProdVector *> (result);
if (xix == result)
{
ProdVector *prodresultTemp = prodresult->ConstructEmpty();
prodresultTemp->NewMemoryOnWrite();
for (integer i = 0; i < numofmani; i++)
{
for (integer j = powsinterval[i]; j < powsinterval[i + 1]; j++)
{
manifolds[i]->DiffRetraction(prodx->GetElement(j), prodetax->GetElement(j), prody->GetElement(j), prodxix->GetElement(j), prodresultTemp->GetElement(j), IsEtaXiSameDir);
}
}
prodresultTemp->CopyTo(prodresult);
delete prodresultTemp;
}
else
{
prodresult->NewMemoryOnWrite();
for (integer i = 0; i < numofmani; i++)
{
for (integer j = powsinterval[i]; j < powsinterval[i + 1]; j++)
{
manifolds[i]->DiffRetraction(prodx->GetElement(j), prodetax->GetElement(j), prody->GetElement(j), prodxix->GetElement(j), prodresult->GetElement(j), IsEtaXiSameDir);
}
}
}
#ifdef CHECKMEMORY
prodresult->CheckMemory();
#endif
if (IsEtaXiSameDir)
{
const double *etaxTV = etax->ObtainReadData();
const double *xixTV = xix->ObtainReadData();
double EtatoXi = sqrt(Metric(x, etax, etax) / Metric(x, xix, xix));
SharedSpace *beta = new SharedSpace(1, 1);
double *betav = beta->ObtainWriteEntireData();
betav[0] = sqrt(Metric(x, etax, etax) / Metric(x, result, result)) / EtatoXi;
etax->AddToTempData("beta", beta);
Vector *TReta = result->ConstructEmpty();
result->CopyTo(TReta);
ScaleTimesVector(x, betav[0] * EtatoXi, TReta, TReta);
SharedSpace *SharedTReta = new SharedSpace(TReta);
etax->AddToTempData("betaTReta", SharedTReta);
}
};
void L2Sphere::InverseVectorTransport(Variable *x, Vector *etax, Variable *y, Vector *xiy, Vector *result) const
{
if (!etax->TempDataExist("xdydn2"))
{
Vector *xdy = x->ConstructEmpty();
SharedSpace *Sharedxdy = new SharedSpace(xdy);
VectorAddVector(x, x, y, xdy);
ScaleTimesVector(x, 1.0 / Metric(x, xdy, xdy), xdy, xdy);
etax->AddToTempData("xdydn2", Sharedxdy);
}
const SharedSpace *Sharedxdydn2 = etax->ObtainReadTempData("xdydn2");
Vector *xdydn2 = Sharedxdydn2->GetSharedElement();
scalarVectorAddVector(x, -2.0 * Metric(x, xiy, x), xdydn2, xiy, result);
};
void L2Sphere::TranH(Variable *x, Vector *etax, Variable *y, LinearOPE *Hx, integer start, integer end, LinearOPE *result) const
{
if (!etax->TempDataExist("xdydn2"))
{
Vector *xdy = x->ConstructEmpty();
SharedSpace *Sharedxdy = new SharedSpace(xdy);
VectorAddVector(x, x, y, xdy);
ScaleTimesVector(x, 1.0 / Metric(x, xdy, xdy), xdy, xdy);
etax->AddToTempData("xdydn2", Sharedxdy);
}
integer ell = Hx->Getsize()[0];
integer length = etax->Getlength();
const double *M = Hx->ObtainReadData();
double *Hty = new double[ell];
Variable *yflat = y->ConstructEmpty();
y->CopyTo(yflat);
double *yflatptr = yflat->ObtainWritePartialData();
yflatptr[0] /= (2 * (n - 1));
yflatptr[n - 1] /= (2 * (n - 1));
for (integer i = 1; i < n - 1; i++)
{
yflatptr[i] /= (n - 1);
}
char *transt = const_cast<char *> ("t");
double one = 1, zero = 0;
integer inc = 1, N = ell;
dgemv_(transt, &length, &N, &one, const_cast<double *> (M + start), &N, yflatptr, &inc, &zero, Hty, &inc);
double scalar = -2.0;
Hx->CopyTo(result);
const SharedSpace *Sharedxdydn2 = etax->ObtainReadTempData("xdydn2");
Vector *xdydn2 = Sharedxdydn2->GetSharedElement();
const double *xdydn2TV = xdydn2->ObtainReadData();
double *resultL = result->ObtainWritePartialData();
dger_(&length, &N, &scalar, const_cast<double *> (xdydn2TV), &inc, Hty, &inc, resultL + start, &N);
delete[] Hty;
delete yflat;
};
void Stiefel::DiffqfRetraction(Variable *x, Vector *etax, Variable *y, Vector *xix, Vector *result, bool IsEtaXiSameDir) const
{
Vector *extempx = EMPTYEXTR->ConstructEmpty();
const double *extempxTV;
if (IsIntrApproach)
{
ObtainExtr(x, xix, extempx);
extempxTV = extempx->ObtainReadData();
}
else
{
xix->CopyTo(extempx);
extempxTV = extempx->ObtainWritePartialData();
}
const double *yM = y->ObtainReadData();
double *resultTV = result->ObtainWriteEntireData();
const SharedSpace *HHR = y->ObtainReadTempData("HHR");
const double *ptrHHR = HHR->ObtainReadData();
double *YtVRinv = new double[p * p];
integer inc = 1, N = n, P = p;
char *left = const_cast<char *> ("r"), *up = const_cast<char *> ("u"),
*transn = const_cast<char *> ("n"), *transt = const_cast<char *> ("t"), *nonunit = const_cast<char *> ("n");
double one = 1, zero = 0;
dtrsm_(left, up, transn, nonunit, &N, &P, &one, const_cast<double *> (ptrHHR), &N, const_cast<double *> (extempxTV), &N);
double sign;
for (integer i = 0; i < P; i++)
{
sign = (ptrHHR[i + i * N] >= 0) ? 1 : -1;
dscal_(&N, &sign, const_cast<double *> (extempxTV + i * N), &inc);
}
dgemm_(transt, transn, &P, &P, &N, &one, const_cast<double *> (yM), &N, const_cast<double *> (extempxTV), &N, &zero, YtVRinv, &P);
for (integer i = 0; i < p; i++)
{
YtVRinv[i + p * i] = -YtVRinv[i + p * i];
for (integer j = i + 1; j < p; j++)
{
YtVRinv[i + p * j] = -YtVRinv[j + p * i] - YtVRinv[i + p * j];
YtVRinv[j + p * i] = 0;
}
}
dgemm_(transn, transn, &N, &P, &P, &one, const_cast<double *> (yM), &N, YtVRinv, &P, &one, const_cast<double *> (extempxTV), &N);
if (IsIntrApproach)
{
ObtainIntr(y, extempx, result);
}
else
{
extempx->CopyTo(result);
}
delete[] YtVRinv;
delete extempx;
if (IsEtaXiSameDir && (HasHHR || UpdBetaAlone))
{
const double *etaxTV = etax->ObtainReadData();
const double *xixTV = xix->ObtainReadData();
double EtatoXi = sqrt(Metric(x, etax, etax) / Metric(x, xix, xix));
SharedSpace *beta = new SharedSpace(1, 3);
double *betav = beta->ObtainWriteEntireData();
betav[0] = sqrt(Metric(x, etax, etax) / Metric(x, result, result)) / EtatoXi;
betav[1] = Metric(x, etax, etax);
betav[2] = Metric(x, result, result) * EtatoXi * EtatoXi;
etax->AddToTempData("beta", beta);
if (HasHHR)
{
Vector *TReta = result->ConstructEmpty();
result->CopyTo(TReta);
ScaleTimesVector(x, betav[0] * EtatoXi, TReta, TReta);
SharedSpace *SharedTReta = new SharedSpace(TReta);
etax->AddToTempData("betaTReta", SharedTReta);
}
}
};