void Fdm2dBlackScholesOp::setTime(Time t1, Time t2) {
opX_.setTime(t1, t2);
opY_.setTime(t1, t2);
if (localVol1_) {
const boost::shared_ptr<FdmLinearOpLayout> layout=mesher_->layout();
const FdmLinearOpIterator endIter = layout->end();
Array vol1(layout->size()), vol2(layout->size());
for (FdmLinearOpIterator iter = layout->begin();
iter!=endIter; ++iter) {
const Size i = iter.index();
if (illegalLocalVolOverwrite_ < 0.0) {
vol1[i] = localVol1_->localVol(0.5*(t1+t2), x_[i], true);
vol2[i] = localVol2_->localVol(0.5*(t1+t2), y_[i], true);
}
else {
try {
vol1[i] = localVol1_->localVol(0.5*(t1+t2), x_[i],true);
} catch (Error&) {
vol1[i] = illegalLocalVolOverwrite_;
}
try {
vol2[i] = localVol2_->localVol(0.5*(t1+t2), y_[i],true);
} catch (Error&) {
vol2[i] = illegalLocalVolOverwrite_;
}
}
}
corrMapT_ = corrMapTemplate_.mult(vol1*vol2);
}
else {
const Real vol1 = p1_
->blackVolatility()->blackForwardVol(t1, t2, p1_->x0());
const Real vol2 = p2_
->blackVolatility()->blackForwardVol(t1, t2, p2_->x0());
corrMapT_ = corrMapTemplate_
.mult(Array(mesher_->layout()->size(), vol1*vol2));
}
currentForwardRate_ = p1_->riskFreeRate()
->forwardRate(t1, t2, Continuous).rate();
}
ASMmxBase::VolumeVec ASMmxBase::establishBases(Go::SplineVolume* svol,
MixedType type)
{
VolumeVec result(2);
// With mixed methods we need two separate spline spaces
if (type == FULL_CONT_RAISE_BASIS1 || type == FULL_CONT_RAISE_BASIS2)
{
// basis1 should be one degree higher than basis2 and C^p-1 continuous
int ndim = svol->dimension();
Go::BsplineBasis b1 = svol->basis(0).extendedBasis(svol->order(0)+1);
Go::BsplineBasis b2 = svol->basis(1).extendedBasis(svol->order(1)+1);
Go::BsplineBasis b3 = svol->basis(2).extendedBasis(svol->order(2)+1);
/* To lower order and regularity this can be used instead
std::vector<double>::const_iterator first = ++surf->basis(0).begin();
std::vector<double>::const_iterator last = --surf->basis(0).end();
Go::BsplineBasis b1 = Go::BsplineBasis(surf->order_u()-1,first,last);
first = ++surf->basis(1).begin();
last = --surf->basis(1).end();
Go::BsplineBasis b2 = Go::BsplineBasis(surf->order_v()-1,first,last);
*/
// Compute parameter values of the Greville points
size_t i;
RealArray ug(b1.numCoefs()), vg(b2.numCoefs()), wg(b3.numCoefs());
for (i = 0; i < ug.size(); i++)
ug[i] = b1.grevilleParameter(i);
for (i = 0; i < vg.size(); i++)
vg[i] = b2.grevilleParameter(i);
for (i = 0; i < wg.size(); i++)
wg[i] = b3.grevilleParameter(i);
if (svol->rational()) {
std::vector<double> rCoefs(svol->rcoefs_begin(), svol->rcoefs_end());
// we normally would set coefs as (x*w, y*w, w)
// however, gotools use this representation internally already.
// instance a Bspline surface in ndim+1
Go::SplineVolume vol2(svol->basis(0), svol->basis(1), svol->basis(2), rCoefs.begin(), ndim+1, false);
// interpolate the Bspline surface onto new basis
RealArray XYZ((ndim+1)*ug.size()*vg.size()*wg.size());
vol2.gridEvaluator(XYZ,ug,vg,wg);
std::unique_ptr<Go::SplineVolume> svol3(Go::VolumeInterpolator::regularInterpolation(b1,b2,b3,ug,vg,wg,XYZ,ndim+1,false,XYZ));
// new rational coefs are (x/w', y/w', w')
// apparently gotools will rescale coeffs on surface creation.
result[0].reset(new Go::SplineVolume(svol3->basis(0), svol3->basis(1), svol3->basis(2), svol3->coefs_begin(), ndim, true));
} else {
RealArray XYZ(ndim*ug.size()*vg.size()*wg.size());
// Evaluate the spline surface at all points
svol->gridEvaluator(ug,vg,wg,XYZ);
// Project the coordinates onto the new basis (the 2nd XYZ is dummy here)
result[0].reset(Go::VolumeInterpolator::regularInterpolation(b1,b2,b3,
ug,vg,wg,XYZ,ndim,
false,XYZ));
}
result[1].reset(new Go::SplineVolume(*svol));
}
else if (type == REDUCED_CONT_RAISE_BASIS1 || type == REDUCED_CONT_RAISE_BASIS2)
{
// Order-elevate basis1 such that it is of one degree higher than basis2
// but only C^p-2 continuous
result[0].reset(new Go::SplineVolume(*svol));
result[0]->raiseOrder(1,1,1);
result[1].reset(new Go::SplineVolume(*svol));
}
else if (ASMmxBase::Type == ASMmxBase::DIV_COMPATIBLE)
{
result.resize(4);
// basis1 should be one degree higher than basis2 and C^p-1 continuous
int ndim = svol->dimension();
Go::BsplineBasis a1 = svol->basis(0);
Go::BsplineBasis a2 = svol->basis(1);
Go::BsplineBasis a3 = svol->basis(2);
Go::BsplineBasis b1 = svol->basis(0).extendedBasis(svol->order(0)+1);
Go::BsplineBasis b2 = svol->basis(1).extendedBasis(svol->order(1)+1);
Go::BsplineBasis b3 = svol->basis(2).extendedBasis(svol->order(2)+1);
// Compute parameter values of the Greville points
size_t i;
RealArray u0(a1.numCoefs()), v0(a2.numCoefs()), w0(a3.numCoefs());
for (i = 0; i < u0.size(); i++)
u0[i] = a1.grevilleParameter(i);
for (i = 0; i < v0.size(); i++)
v0[i] = a2.grevilleParameter(i);
for (i = 0; i < w0.size(); i++)
w0[i] = a3.grevilleParameter(i);
RealArray ug(b1.numCoefs()), vg(b2.numCoefs()), wg(b3.numCoefs());
for (i = 0; i < ug.size(); i++)
ug[i] = b1.grevilleParameter(i);
for (i = 0; i < vg.size(); i++)
vg[i] = b2.grevilleParameter(i);
for (i = 0; i < wg.size(); i++)
wg[i] = b3.grevilleParameter(i);
// Evaluate the spline surface at all points
// Project the coordinates onto the new basis (the 2nd XYZ is dummy here)
RealArray XYZ0(ndim*ug.size()*v0.size()*w0.size()), XYZ1(ndim*u0.size()*vg.size()*w0.size()), XYZ2(ndim*u0.size()*v0.size()*wg.size());
svol->gridEvaluator(ug,v0,w0,XYZ0);
svol->gridEvaluator(u0,vg,w0,XYZ1);
svol->gridEvaluator(u0,v0,wg,XYZ2);
result[0].reset(Go::VolumeInterpolator::regularInterpolation(b1,a2,a3,
ug,v0,w0,XYZ0,ndim,
false,XYZ0));
result[1].reset(Go::VolumeInterpolator::regularInterpolation(a1,b2,a3,
u0,vg,w0,XYZ1,ndim,
false,XYZ1));
result[2].reset(Go::VolumeInterpolator::regularInterpolation(a1,a2,b3,
u0,v0,wg,XYZ2,ndim,
false,XYZ2));
result[3].reset(new Go::SplineVolume(*svol));
geoBasis = 4;
}
if (type == FULL_CONT_RAISE_BASIS2 || type == REDUCED_CONT_RAISE_BASIS2)
std::swap(result[0], result[1]);
return result;
}
