void Foam::FitData<FitDataType, ExtendedStencil, Polynomial>::calcFit
(
scalarList& coeffsi,
const List<point>& C,
const scalar wLin,
const label facei
)
{
vector idir(1,0,0);
vector jdir(0,1,0);
vector kdir(0,0,1);
findFaceDirs(idir, jdir, kdir, facei);
// Setup the point weights
scalarList wts(C.size(), scalar(1));
wts[0] = centralWeight_;
if (linearCorrection_)
{
wts[1] = centralWeight_;
}
// Reference point
point p0 = this->mesh().faceCentres()[facei];
// Info << "Face " << facei << " at " << p0 << " stencil points at:\n"
// << C - p0 << endl;
// p0 -> p vector in the face-local coordinate system
vector d;
// Local coordinate scaling
scalar scale = 1;
// Matrix of the polynomial components
scalarRectangularMatrix B(C.size(), minSize_, scalar(0));
for(label ip = 0; ip < C.size(); ip++)
{
const point& p = C[ip];
d.x() = (p - p0)&idir;
d.y() = (p - p0)&jdir;
# ifndef SPHERICAL_GEOMETRY
d.z() = (p - p0)&kdir;
# else
d.z() = mag(p) - mag(p0);
# endif
if (ip == 0)
{
scale = cmptMax(cmptMag((d)));
}
// Scale the radius vector
d /= scale;
Polynomial::addCoeffs
(
B[ip],
d,
wts[ip],
dim_
);
}
// Additional weighting for constant and linear terms
for(label i = 0; i < B.n(); i++)
{
B[i][0] *= wts[0];
B[i][1] *= wts[0];
}
// Set the fit
label stencilSize = C.size();
coeffsi.setSize(stencilSize);
bool goodFit = false;
for(int iIt = 0; iIt < 8 && !goodFit; iIt++)
{
SVD svd(B, SMALL);
scalar maxCoeff = 0;
label maxCoeffi = 0;
for(label i=0; i<stencilSize; i++)
{
coeffsi[i] = wts[0]*wts[i]*svd.VSinvUt()[0][i];
if (mag(coeffsi[i]) > maxCoeff)
{
maxCoeff = mag(coeffsi[i]);
maxCoeffi = i;
}
}
if (linearCorrection_)
{
goodFit =
(mag(coeffsi[0] - wLin) < linearLimitFactor_*wLin)
&& (mag(coeffsi[1] - (1 - wLin)) < linearLimitFactor_*(1 - wLin))
&& maxCoeffi <= 1;
}
else
{
// Upwind: weight on face is 1.
goodFit =
(mag(coeffsi[0] - 1.0) < linearLimitFactor_*1.0)
&& maxCoeffi <= 1;
}
// if (goodFit && iIt > 0)
// {
// Info << "FitData<Polynomial>::calcFit"
// << "(const List<point>& C, const label facei" << nl
// << "Can now fit face " << facei << " iteration " << iIt
// << " with sum of weights " << sum(coeffsi) << nl
// << " Weights " << coeffsi << nl
// << " Linear weights " << wLin << " " << 1 - wLin << nl
// << " sing vals " << svd.S() << endl;
// }
if (!goodFit) // (not good fit so increase weight in the centre and weight
// for constant and linear terms)
{
// if (iIt == 7)
// {
// WarningIn
// (
// "FitData<Polynomial>::calcFit"
// "(const List<point>& C, const label facei"
// ) << "Cannot fit face " << facei << " iteration " << iIt
// << " with sum of weights " << sum(coeffsi) << nl
// << " Weights " << coeffsi << nl
// << " Linear weights " << wLin << " " << 1 - wLin << nl
// << " sing vals " << svd.S() << endl;
// }
wts[0] *= 10;
if (linearCorrection_)
{
wts[1] *= 10;
}
for(label j = 0; j < B.m(); j++)
{
B[0][j] *= 10;
B[1][j] *= 10;
}
for(label i = 0; i < B.n(); i++)
{
B[i][0] *= 10;
B[i][1] *= 10;
}
}
}
if (goodFit)
{
if (linearCorrection_)
{
// Remove the uncorrected linear coefficients
coeffsi[0] -= wLin;
coeffsi[1] -= 1 - wLin;
}
else
{
// Remove the uncorrected upwind coefficients
coeffsi[0] -= 1.0;
}
}
else
{
// if (debug)
// {
WarningIn
(
"FitData<Polynomial>::calcFit(..)"
) << "Could not fit face " << facei
<< " Weights = " << coeffsi
<< ", reverting to linear." << nl
<< " Linear weights " << wLin << " " << 1 - wLin << endl;
// }
coeffsi = 0;
}
}
Foam::label Foam::quadraticFitSnGradData::calcFit
(
const List<point>& C,
const label faci
)
{
vector idir(1,0,0);
vector jdir(0,1,0);
vector kdir(0,0,1);
findFaceDirs(idir, jdir, kdir, mesh(), faci);
scalarList wts(C.size(), scalar(1));
wts[0] = centralWeight_;
wts[1] = centralWeight_;
point p0 = mesh().faceCentres()[faci];
scalar scale = 0;
// calculate the matrix of the polynomial components
scalarRectangularMatrix B(C.size(), minSize_, scalar(0));
for(label ip = 0; ip < C.size(); ip++)
{
const point& p = C[ip];
scalar px = (p - p0)&idir;
scalar py = (p - p0)&jdir;
#ifdef SPHERICAL_GEOMETRY
scalar pz = mag(p) - mag(p0);
#else
scalar pz = (p - p0)&kdir;
#endif
if (ip == 0) scale = max(max(mag(px), mag(py)), mag(pz));
px /= scale;
py /= scale;
pz /= scale;
label is = 0;
B[ip][is++] = wts[0]*wts[ip];
B[ip][is++] = wts[0]*wts[ip]*px;
B[ip][is++] = wts[ip]*sqr(px);
if (dim_ >= 2)
{
B[ip][is++] = wts[ip]*py;
B[ip][is++] = wts[ip]*px*py;
B[ip][is++] = wts[ip]*sqr(py);
}
if (dim_ == 3)
{
B[ip][is++] = wts[ip]*pz;
B[ip][is++] = wts[ip]*px*pz;
//B[ip][is++] = wts[ip]*py*pz;
B[ip][is++] = wts[ip]*sqr(pz);
}
}
// Set the fit
label stencilSize = C.size();
fit_[faci].setSize(stencilSize);
scalarList singVals(minSize_);
label nSVDzeros = 0;
const scalar& deltaCoeff = mesh().deltaCoeffs()[faci];
bool goodFit = false;
for(int iIt = 0; iIt < 10 && !goodFit; iIt++)
{
SVD svd(B, SMALL);
scalar fit0 = wts[0]*wts[0]*svd.VSinvUt()[1][0]/scale;
scalar fit1 = wts[0]*wts[1]*svd.VSinvUt()[1][1]/scale;
goodFit =
fit0 < 0 && fit1 > 0
&& mag(fit0 + deltaCoeff) < 0.5*deltaCoeff
&& mag(fit1 - deltaCoeff) < 0.5*deltaCoeff;
if (goodFit)
{
fit_[faci][0] = fit0;
fit_[faci][1] = fit1;
for(label i = 2; i < stencilSize; i++)
{
fit_[faci][i] = wts[0]*wts[i]*svd.VSinvUt()[1][i]/scale;
}
singVals = svd.S();
nSVDzeros = svd.nZeros();
}
else // (not good fit so increase weight in the centre and for linear)
{
wts[0] *= 10;
wts[1] *= 10;
for(label i = 0; i < B.n(); i++)
{
B[i][0] *= 10;
B[i][1] *= 10;
}
for(label j = 0; j < B.m(); j++)
{
B[0][j] *= 10;
B[1][j] *= 10;
}
}
}
if (goodFit)
{
// remove the uncorrected snGradScheme coefficients
fit_[faci][0] += deltaCoeff;
fit_[faci][1] -= deltaCoeff;
}
else
{
Pout<< "quadratifFitSnGradData could not fit face " << faci
<< " fit_[faci][0] = " << fit_[faci][0]
<< " fit_[faci][1] = " << fit_[faci][1]
<< " deltaCoeff = " << deltaCoeff << endl;
fit_[faci] = 0;
}
return minSize_ - nSVDzeros;
}