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qualityMeasuresJacobian.cpp
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Amaury Johnen authoredAmaury Johnen authored
qualityMeasuresJacobian.cpp 65.26 KiB
// Gmsh - Copyright (C) 1997-2015 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.
#include <limits>
#include "qualityMeasuresJacobian.h"
#include "MElement.h"
#include "BasisFactory.h"
#include "bezierBasis.h"
#include "JacobianBasis.h"
// For debugging
#include <sstream>
#include <iomanip>
#include "pointsGenerators.h"
#include "OS.h"
#define TMBEG(n, what) static int I##n = 0, IND##n = _CoeffDataAnisotropy::mytimes.size(); \
if (++I##n == 1) { \
Msg::Info("Time%d = "#what, IND##n); \
_CoeffDataAnisotropy::mytimes.push_back(0); \
_CoeffDataAnisotropy::mynumbers.push_back(0); \
} \
_CoeffDataAnisotropy::mynumbers[IND##n] += 1; \
double TM##n = Cpu();
#define TMEND(n) _CoeffDataAnisotropy::mytimes[IND##n] += Cpu() - TM##n;
namespace jacobianBasedQuality {
bool _CoeffDataAnisotropy::hasError = false;
MElement *_CoeffDataAnisotropy::currentElement = NULL;
_CoeffDataAnisotropy *_CoeffDataAnisotropy::current = NULL;
std::fstream _CoeffDataAnisotropy::file;
std::vector<double> _CoeffDataAnisotropy::mytimes;
std::vector<int> _CoeffDataAnisotropy::mynumbers;
double _CoeffDataScaledJac::cTri = 2/std::sqrt(3);
double _CoeffDataScaledJac::cTet = std::sqrt(2);
double _CoeffDataScaledJac::cPyr = std::sqrt(2);
void minMaxJacobianDeterminant(MElement *el, double &min, double &max,
const fullMatrix<double> *normals)
{
_CoeffDataAnisotropy::currentElement = el;
const JacobianBasis *jfs = el->getJacobianFuncSpace();
if (!jfs) {
Msg::Error("Jacobian function space not implemented for type of element %d", el->getTypeForMSH());
min = 99;
max = -99;
return;
}
fullMatrix<double> nodesXYZ(el->getNumVertices(), 3);
el->getNodesCoord(nodesXYZ);
fullVector<double> coeffLag(jfs->getNumJacNodes());
fullVector<double> coeffBez(jfs->getNumJacNodes());
jfs->getSignedJacobian(nodesXYZ, coeffLag, normals);
jfs->lag2Bez(coeffLag, coeffBez);
std::vector<_CoeffData*> domains;
domains.push_back(new _CoeffDataJac(coeffBez, jfs->getBezier(), 0));
_subdivideDomains(domains);
min = domains[0]->minB();
max = domains[0]->maxB();
delete domains[0];
for (unsigned int i = 1; i < domains.size(); ++i) {
min = std::min(min, domains[i]->minB());
max = std::max(max, domains[i]->maxB()); delete domains[i];
}
}
double minScaledJacobian(MElement *el, bool knownValid, bool reversedOk)
{
bool isReversed = false;
if (!knownValid) {
double jmin, jmax;
minMaxJacobianDeterminant(el, jmin, jmax);
if (jmax < 0) {
if (!reversedOk) return 0;
isReversed = true;
}
else if (jmin <= 0) return 0;
}
// Computation of the minimum (or maximum) of the scaled Jacobian should never
// be performed to invalid elements (for which the measure is 0).
fullMatrix<double> nodesXYZ(el->getNumVertices(), 3);
el->getNodesCoord(nodesXYZ);
const JacobianBasis *jacBasis;
const GradientBasis *gradBasis;
const int type = el->getType();
const int order = el->getPolynomialOrder();
const int jacOrder = order * el->getDim();
const bool serendipFalse = false;
FuncSpaceData jacMatSpace, jacDetSpace;
switch(type) {
case TYPE_TRI:
jacMatSpace = FuncSpaceData(el, order-1, &serendipFalse);
jacDetSpace = FuncSpaceData(el, jacOrder-2, &serendipFalse);
break;
case TYPE_TET:
jacMatSpace = FuncSpaceData(el, order-1, &serendipFalse);
jacDetSpace = FuncSpaceData(el, jacOrder-3, &serendipFalse);
break;
case TYPE_QUA:
case TYPE_HEX:
case TYPE_PRI:
jacMatSpace = FuncSpaceData(el, order, &serendipFalse);
jacDetSpace = FuncSpaceData(el, jacOrder, &serendipFalse);
break;
case TYPE_PYR:
jacMatSpace = FuncSpaceData(el, false, order, order-1, &serendipFalse);
jacDetSpace = FuncSpaceData(el, false, jacOrder, jacOrder-3, &serendipFalse);
break;
default:
Msg::Error("Scaled Jacobian not implemented for type of element %d", el->getType());
return -1;
}
gradBasis = BasisFactory::getGradientBasis(jacMatSpace);
jacBasis = BasisFactory::getJacobianBasis(jacDetSpace);
fullVector<double> coeffDetBez;
{
fullVector<double> coeffDetLag(jacBasis->getNumJacNodes());
jacBasis->getSignedJacobian(nodesXYZ, coeffDetLag);
coeffDetBez.resize(jacBasis->getNumJacNodes());
jacBasis->lag2Bez(coeffDetLag, coeffDetBez);
if (isReversed) coeffDetBez.scale(-1);
}
fullMatrix<double> coeffMatBez; {
fullMatrix<double> coeffMatLag(gradBasis->getNumSamplingPoints(), 9);
gradBasis->getAllGradientsFromNodes(nodesXYZ, coeffMatLag);
coeffMatBez.resize(gradBasis->getNumSamplingPoints(), 9);
gradBasis->lag2Bez(coeffMatLag, coeffMatBez);
if (el->getDim() == 2) coeffMatBez.resize(coeffMatBez.size1(), 6, false);
}
std::vector<_CoeffData*> domains;
domains.push_back(
new _CoeffDataScaledJac(coeffDetBez, coeffMatBez, jacBasis->getBezier(),
gradBasis->getBezier(), 0, el->getType())
);
_subdivideDomains(domains);
// Msg::Info("element %d, type %d, numSub %d", el->getNum(), el->getType(),
// domains.size()/7);
if (domains.size()/7 > 500) {//fordebug
Msg::Info("S too much subdivision: %d (el %d, type %d, tag %d)",
domains.size()/7, el->getNum(), el->getType(), el->getTypeForMSH());
}
double min = domains[0]->minB();
delete domains[0];
for (unsigned int i = 1; i < domains.size(); ++i) {
min = std::min(min, domains[i]->minB());
delete domains[i];
}
return min;
}
double minAnisotropyMeasure(MElement *el,
bool knownValid,
bool reversedOk,
int n)
{
if (!knownValid) {
double jmin, jmax;
minMaxJacobianDeterminant(el, jmin, jmax);
if (jmin <= 0 && jmax >= 0) return 0;
if (!reversedOk && jmax < 0) return 0;
}
// Computation of the minimum of the anisotropy measure should never
// be performed to invalid elements (for which the measure is 0).
if (_CoeffDataAnisotropy::noMoreComputationPlease()) {
Msg::Info("Sorry, no more computation");
return -9; //fordebug
}
// double minSampled = minSampledAnisotropyMeasure(el, n); //fordebug
fullMatrix<double> nodesXYZ(el->getNumVertices(), 3);
el->getNodesCoord(nodesXYZ);
const GradientBasis *gradBasis;
const JacobianBasis *jacBasis = NULL;
const int type = el->getType();
const bool serendipFalse = false;
const int metricOrder = _CoeffDataAnisotropy::metricOrder(el);
const int jacDetOrder = 3*metricOrder/2;
if (metricOrder == -1) {
Msg::Error("Anisotropy measure not implemented for type of element %d", el->getType());
return -1;
}
FuncSpaceData metricSpace, jacDetSpace;
switch(type) {
case TYPE_TET:
case TYPE_HEX:
case TYPE_PRI:
jacDetSpace = FuncSpaceData(el, jacDetOrder, &serendipFalse);
jacBasis = BasisFactory::getJacobianBasis(jacDetSpace);
//no break
case TYPE_TRI:
case TYPE_QUA:
metricSpace = FuncSpaceData(el, metricOrder, &serendipFalse);
break;
case TYPE_PYR:
metricSpace = FuncSpaceData(el, false, metricOrder+2, metricOrder, &serendipFalse);
jacDetSpace = FuncSpaceData(el, false, jacDetOrder+3, jacDetOrder, &serendipFalse);
jacBasis = BasisFactory::getJacobianBasis(jacDetSpace);
break;
}
gradBasis = BasisFactory::getGradientBasis(metricSpace);
// Metric Coefficients
fullMatrix<double> coeffMetricBez;
{
fullMatrix<double> coeffMetricLag;
_CoeffDataAnisotropy::fillMetricCoeff(gradBasis, nodesXYZ, coeffMetricLag,
el->getDim(), true);
coeffMetricBez.resize(coeffMetricLag.size1(), coeffMetricLag.size2());
gradBasis->lag2Bez(coeffMetricLag, coeffMetricBez);
}
// Jacobian determinant coefficients
fullVector<double> coeffJacDetBez;
if (jacBasis) {
fullVector<double> coeffDetLag(jacBasis->getNumJacNodes());
jacBasis->getSignedIdealJacobian(nodesXYZ, coeffDetLag);
coeffJacDetBez.resize(jacBasis->getNumJacNodes());
jacBasis->lag2Bez(coeffDetLag, coeffJacDetBez);
}
std::vector<_CoeffData*> domains;
domains.push_back(
new _CoeffDataAnisotropy(coeffJacDetBez, coeffMetricBez,
jacBasis ? jacBasis->getBezier() : NULL,
gradBasis->getBezier(), 0, el)
);
_subdivideDomains(domains);
if (domains.size()/7 > 500) {//fordebug
Msg::Info("A too much subdivision: %d (el %d, type %d)", domains.size()/7, el->getNum(), el->getType());
}
double min = domains[0]->minB();
delete domains[0];
for (unsigned int i = 1; i < domains.size(); ++i) {
min = std::min(min, domains[i]->minB());
delete domains[i];
}
// if (min - minSampled > 1e-13) {//fordebug
// Msg::Error("no, works no el %d (%g vs %g, diff %g)", el->getNum(), min, minSampled, min-minSampled);
// }
return min;
}
double minIsotropyMeasure(MElement *el,
bool knownValid,
bool reversedOk){
bool isReversed = false;
if (!knownValid) {
double jmin, jmax;
minMaxJacobianDeterminant(el, jmin, jmax);
if (jmax < 0) {
if (!reversedOk) return 0;
isReversed = true;
}
else if (jmin <= 0) return 0;
}
// Computation of the minimum (or maximum) of the scaled Jacobian should never
// be performed to invalid elements (for which the measure is 0).
fullMatrix<double> nodesXYZ(el->getNumVertices(), 3);
el->getNodesCoord(nodesXYZ);
const JacobianBasis *jacBasis;
const GradientBasis *gradBasis;
const int type = el->getType();
const int order = el->getPolynomialOrder();
const int jacOrder = order * el->getDim();
const bool serendipFalse = false;
FuncSpaceData jacMatSpace, jacDetSpace;
switch(type) {
case TYPE_TRI:
jacMatSpace = FuncSpaceData(el, order-1, &serendipFalse);
jacDetSpace = FuncSpaceData(el, jacOrder-2, &serendipFalse);
break;
case TYPE_TET:
jacMatSpace = FuncSpaceData(el, order-1, &serendipFalse);
jacDetSpace = FuncSpaceData(el, jacOrder-3, &serendipFalse);
break;
case TYPE_QUA:
case TYPE_HEX:
case TYPE_PRI:
jacMatSpace = FuncSpaceData(el, order, &serendipFalse);
jacDetSpace = FuncSpaceData(el, jacOrder, &serendipFalse);
break;
case TYPE_PYR:
jacMatSpace = FuncSpaceData(el, false, order, order-1, &serendipFalse);
jacDetSpace = FuncSpaceData(el, false, jacOrder, jacOrder-3, &serendipFalse);
break;
default:
Msg::Error("Isotropy not implemented for type of element %d", el->getType());
return -1;
}
gradBasis = BasisFactory::getGradientBasis(jacMatSpace);
jacBasis = BasisFactory::getJacobianBasis(jacDetSpace);
fullVector<double> coeffDetBez;
{
fullVector<double> coeffDetLag(jacBasis->getNumJacNodes());
jacBasis->getSignedIdealJacobian(nodesXYZ, coeffDetLag);
coeffDetBez.resize(jacBasis->getNumJacNodes());
jacBasis->lag2Bez(coeffDetLag, coeffDetBez);
if (isReversed) coeffDetBez.scale(-1);
}
fullMatrix<double> coeffMatBez;
{
fullMatrix<double> coeffMatLag(gradBasis->getNumSamplingPoints(), 9);
gradBasis->getAllIdealGradientsFromNodes(nodesXYZ, coeffMatLag);
coeffMatBez.resize(gradBasis->getNumSamplingPoints(), 9); gradBasis->lag2Bez(coeffMatLag, coeffMatBez);
if (el->getDim() == 2) coeffMatBez.resize(coeffMatBez.size1(), 6, false);
}
std::vector<_CoeffData*> domains;
domains.push_back(
new _CoeffDataIsotropy(coeffDetBez, coeffMatBez, jacBasis->getBezier(),
gradBasis->getBezier(), 0)
);
_subdivideDomains(domains);
if (domains.size()/7 > 500) {//fordebug
Msg::Info("I too much subdivision: %d (el %d, type %d, tag %d)",
domains.size()/7, el->getNum(), el->getType(), el->getTypeForMSH());
}
double min = domains[0]->minB();
delete domains[0];
for (unsigned int i = 1; i < domains.size(); ++i) {
min = std::min(min, domains[i]->minB());
delete domains[i];
}
return min;
}
//double minSampledAnisotropyMeasure(MElement *el, int deg, bool writeInFile)//fordebug
//{
// fullMatrix<double> samplingPoints;
// bool serendip = false;
// gmshGeneratePoints(FuncSpaceData(el, deg, &serendip), samplingPoints);
//
// double values[3];
// double min = std::numeric_limits<double>::infinity();
// for (int i = 0; i < samplingPoints.size1(); ++i) {
// min = std::min(min, el->getEigenvaluesMetric(samplingPoints(i, 0),
// samplingPoints(i, 1),
// samplingPoints(i, 2),
// values));
// }
//
// return min;
//}
double minSampledIsotropyMeasure(MElement *el, int deg, bool writeInFile)//fordebug
{
fullMatrix<double> nodesXYZ(el->getNumVertices(), 3);
el->getNodesCoord(nodesXYZ);
const JacobianBasis *jacBasis;
const GradientBasis *gradBasis;
const int type = el->getType();
// const int order = el->getPolynomialOrder();
// const int jacOrder = order * el->getDim();
const bool serendipFalse = false;
FuncSpaceData jacMatSpace, jacDetSpace;
switch(type) {
case TYPE_TRI:
case TYPE_TET:
case TYPE_QUA:
case TYPE_HEX:
case TYPE_PRI:
jacMatSpace = FuncSpaceData(el, deg, &serendipFalse);
jacDetSpace = FuncSpaceData(el, deg, &serendipFalse);
break;
case TYPE_PYR:
// jacMatSpace = FuncSpaceData(el, false, order, order-1, &serendipFalse);// jacDetSpace = FuncSpaceData(el, false, jacOrder, jacOrder-3, &serendipFalse);
break;
default:
Msg::Error("Isotropy not implemented for type of element %d", el->getType());
return -1;
}
gradBasis = BasisFactory::getGradientBasis(jacMatSpace);
jacBasis = BasisFactory::getJacobianBasis(jacDetSpace);
fullVector<double> coeffDetLag(jacBasis->getNumJacNodes());
jacBasis->getSignedIdealJacobian(nodesXYZ, coeffDetLag);
fullMatrix<double> coeffMatLag(gradBasis->getNumSamplingPoints(), 9);
gradBasis->getAllIdealGradientsFromNodes(nodesXYZ, coeffMatLag);
double min = std::numeric_limits<double>::infinity();
for (int i = 0; i < coeffDetLag.size(); ++i) {
double frobNorm = 0;
if (el->getDim() == 2) {
for (int k = 0; k < 6; ++k)
frobNorm += coeffMatLag(i, k) * coeffMatLag(i, k);
min = std::min(min, 2*coeffDetLag(i)/frobNorm);
}
else if (el->getDim() == 3) {
for (int k = 0; k < 9; ++k)
frobNorm += coeffMatLag(i, k) * coeffMatLag(i, k);
min = std::min(min, 3*std::pow(coeffDetLag(i), 2/3.)/frobNorm);
}
}
return min;
}
double minSampledScaledJacobian(MElement *el, int deg, bool writeInFile)//fordebug
{
fullMatrix<double> nodesXYZ(el->getNumVertices(), 3);
el->getNodesCoord(nodesXYZ);
const JacobianBasis *jacBasis;
const GradientBasis *gradBasis;
const int type = el->getType();
// const int order = el->getPolynomialOrder();
// const int jacOrder = order * el->getDim();
const bool serendipFalse = false;
FuncSpaceData jacMatSpace, jacDetSpace;
switch(type) {
case TYPE_TRI:
case TYPE_TET:
case TYPE_QUA:
case TYPE_HEX:
case TYPE_PRI:
jacMatSpace = FuncSpaceData(el, deg, &serendipFalse);
jacDetSpace = FuncSpaceData(el, deg, &serendipFalse);
break;
case TYPE_PYR:
// jacMatSpace = FuncSpaceData(el, false, order, order-1, &serendipFalse);
// jacDetSpace = FuncSpaceData(el, false, jacOrder, jacOrder-3, &serendipFalse);
break;
default:
Msg::Error("Isotropy not implemented for type of element %d", el->getType());
return -1;
}
gradBasis = BasisFactory::getGradientBasis(jacMatSpace);
jacBasis = BasisFactory::getJacobianBasis(jacDetSpace);
fullVector<double> coeffDetLag(jacBasis->getNumJacNodes());
jacBasis->getSignedIdealJacobian(nodesXYZ, coeffDetLag);
fullMatrix<double> coeffMatLag(gradBasis->getNumSamplingPoints(), 9);
gradBasis->getAllIdealGradientsFromNodes(nodesXYZ, coeffMatLag);
double min = std::numeric_limits<double>::infinity();
for (int i = 0; i < coeffDetLag.size(); ++i) {
if (el->getDim() == 2) {
double v[2] = {0, 0};
for (int k = 0; k < 2; ++k) {
for (int l = k*3; l < k*3+3; ++l)
v[k] += coeffMatLag(i, l) * coeffMatLag(i, l);
}
min = std::min(min, coeffDetLag(i)/v[0]/v[1]);
}
else if (el->getDim() == 3) {
double v[3] = {0, 0, 0};
for (int k = 0; k < 3; ++k) {
for (int l = k*3; l < k*3+3; ++l)
v[k] += coeffMatLag(i, l) * coeffMatLag(i, l);
}
min = std::min(min, coeffDetLag(i)/std::sqrt(v[0]*v[1]*v[2]));
}
}
return min;
}
// Virtual class _CoeffData
bool _lessMinB::operator()(_CoeffData *cd1, _CoeffData *cd2) const
{
return cd1->minB() > cd2->minB();
}
bool _lessMaxB::operator()(_CoeffData *cd1, _CoeffData *cd2) const
{
return cd1->maxB() < cd2->maxB();
}
// Jacobian determinant (for validity of all elements)
_CoeffDataJac::_CoeffDataJac(fullVector<double> &v,
const bezierBasis *bfs,
int depth)
: _CoeffData(depth), _coeffs(v.getDataPtr(), v.size()), _bfs(bfs)
{
if (!v.getOwnData()) {
Msg::Fatal("Cannot create an instance of _CoeffDataJac from a "
"fullVector that does not own its data.");
}
// _coeffs reuses the data of v, this avoid to allocate a new array and to
// copy data that are not used outside of this object.
// It remains to swap ownership:
v.setOwnData(false);
const_cast<fullVector<double>&>(_coeffs).setOwnData(true);
_minL = _maxL = v(0);
int i = 1;
for (; i < bfs->getNumLagCoeff(); i++) {
_minL = std::min(_minL, v(i));
_maxL = std::max(_maxL, v(i));
}
_minB = _minL;
_maxB = _maxL;
for (; i < v.size(); i++) {
_minB = std::min(_minB, v(i));
_maxB = std::max(_maxB, v(i));
}
}
bool _CoeffDataJac::boundsOk(double minL, double maxL) const
{ double tol = std::max(std::abs(minL), std::abs(maxL)) * 1e-3;
return (minL <= 0 || _minB > 0) &&
minL - _minB < tol &&
_maxB - maxL < tol;
}
void _CoeffDataJac::getSubCoeff(std::vector<_CoeffData*> &v) const
{
v.clear();
v.reserve(_bfs->getNumDivision());
fullVector<double> subCoeff;
_bfs->subdivideBezCoeff(_coeffs, subCoeff);
int sz = _coeffs.size();
for (int i = 0; i < _bfs->getNumDivision(); i++) {
fullVector<double> coeff(sz);
coeff.copy(subCoeff, i * sz, sz, 0);
_CoeffDataJac *newData = new _CoeffDataJac(coeff, _bfs, _depth+1);
v.push_back(newData);
}
}
// Scaled Jacobian (quality of quads and hexes)
_CoeffDataScaledJac::_CoeffDataScaledJac(fullVector<double> &det,
fullMatrix<double> &mat,
const bezierBasis *bfsDet,
const bezierBasis *bfsMat,
int depth, int type)
: _CoeffData(depth), _coeffsJacDet(det.getDataPtr(), det.size()),
_coeffsJacMat(mat.getDataPtr(), mat.size1(), mat.size2()),
_bfsDet(bfsDet), _bfsMat(bfsMat), _type(type)
{
if (!det.getOwnData() || !mat.getOwnData()) {
Msg::Fatal("Cannot create an instance of _CoeffDataScaledJac from a "
"fullVector or a fullMatrix that does not own its data.");
}
// _coeffsJacDet and _coeffsJacMat reuse data, this avoid to allocate new
// arrays and to copy data that are not used outside of this object.
// It remains to swap ownerships:
det.setOwnData(false);
mat.setOwnData(false);
const_cast<fullVector<double>&>(_coeffsJacDet).setOwnData(true);
const_cast<fullMatrix<double>&>(_coeffsJacMat).setOwnData(true);
_computeAtCorner(_minL, _maxL);
_minB = _computeLowerBound();
// Msg::Info("%g %g %g", _minB, _minL, _maxL);//fordebug
// _coeffsJacDet.print("_coeffsJacDet");
// _coeffsJacMat.print("_coeffsJacMat");
// computation of _maxB not implemented for now
}
bool _CoeffDataScaledJac::boundsOk(double minL, double maxL) const
{
static double tol = 1e-3;
return minL - _minB < tol;
}
void _CoeffDataScaledJac::getSubCoeff(std::vector<_CoeffData*> &v) const
{
v.clear();
v.reserve(_bfsDet->getNumDivision());
fullVector<double> subCoeffD;
fullMatrix<double> subCoeffM;
_bfsDet->subdivideBezCoeff(_coeffsJacDet, subCoeffD);
_bfsMat->subdivideBezCoeff(_coeffsJacMat, subCoeffM);
int szD = _coeffsJacDet.size();
int szM1 = _coeffsJacMat.size1();
int szM2 = _coeffsJacMat.size2(); for (int i = 0; i < _bfsDet->getNumDivision(); i++) {
fullVector<double> coeffD(szD);
fullMatrix<double> coeffM(szM1, szM2);
coeffD.copy(subCoeffD, i * szD, szD, 0);
coeffM.copy(subCoeffM, i * szM1, szM1, 0, szM2, 0, 0);
_CoeffDataScaledJac *newData;
newData = new _CoeffDataScaledJac(coeffD, coeffM, _bfsDet, _bfsMat,
_depth+1, _type);
v.push_back(newData);
}
}
void _CoeffDataScaledJac::_computeAtCorner(double &min, double &max) const
{
min = std::numeric_limits<double>::infinity();
max = -min;
fullMatrix<double> v;
_getCoeffLengthVectors(v, true);
for (int i = 0; i < _bfsDet->getNumLagCoeff(); i++) {
double sJ;
switch(_type) {
case TYPE_QUA:
sJ = _coeffsJacDet(i)/v(i, 0)/v(i,1);
break;
case TYPE_HEX:
sJ = _coeffsJacDet(i)/v(i,0)/v(i,1)/v(i,2);
break;
case TYPE_TRI:
sJ = cTri * _coeffsJacDet(i) * (1/v(i,0)/v(i,1) +
1/v(i,0)/v(i,2) +
1/v(i,1)/v(i,2)) / 3;
break;
case TYPE_TET:
sJ = cTet * _coeffsJacDet(i) * (1/v(i,0)/v(i,5)/v(i,1) +
1/v(i,0)/v(i,5)/v(i,2) +
1/v(i,0)/v(i,5)/v(i,3) +
1/v(i,0)/v(i,5)/v(i,4) +
1/v(i,1)/v(i,4)/v(i,0) +
1/v(i,1)/v(i,4)/v(i,2) +
1/v(i,1)/v(i,4)/v(i,3) +
1/v(i,1)/v(i,4)/v(i,5) +
1/v(i,2)/v(i,3)/v(i,0) +
1/v(i,2)/v(i,3)/v(i,1) +
1/v(i,2)/v(i,3)/v(i,4) +
1/v(i,2)/v(i,3)/v(i,5)) / 12;
break;
case TYPE_PRI:
sJ = cTri * _coeffsJacDet(i) * (1/v(i,0)/v(i,1)/v(i,2) +
1/v(i,0)/v(i,3)/v(i,2) +
1/v(i,1)/v(i,3)/v(i,2)) / 3;
break;
case TYPE_PYR:
sJ = cPyr * _coeffsJacDet(i) * (1/v(i,0)/v(i,1)/v(i,2) +
1/v(i,0)/v(i,1)/v(i,3) +
1/v(i,0)/v(i,1)/v(i,4) +
1/v(i,0)/v(i,1)/v(i,5) +
1/v(i,2)/v(i,3)/v(i,4) +
1/v(i,2)/v(i,3)/v(i,5) +
1/v(i,4)/v(i,5)/v(i,2) +
1/v(i,4)/v(i,5)/v(i,3) ) / 8;
break;
default:
Msg::Error("Unkown type for scaled jac computation");
return;
}
min = std::min(min, sJ);
max = std::max(max, sJ);
}}
double _CoeffDataScaledJac::_computeLowerBound() const
{
// Speedup: If one coeff _coeffsJacDet is negative, without bounding
// J^2/(a^2+b^2), we would get with certainty a negative lower bound.
// For now, returning 0.
for (int i = 0; i < _coeffsJacDet.size(); ++i) {
if (_coeffsJacDet(i) < 0) {
return 0;
}
}
fullMatrix<double> v;
_getCoeffLengthVectors(v, false);
fullVector<double> prox[6];
for (int i = 0; i < v.size2(); ++i) {
prox[i].setAsProxy(v, i);
}
bezierBasisRaiser *raiser = _bfsMat->getRaiser();
fullVector<double> coeffDenominator;
double result = 0;
switch (_type) {
case TYPE_QUA:
raiser->computeCoeff(prox[0], prox[1], coeffDenominator);
return _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
case TYPE_TRI:
raiser->computeCoeff(prox[0], prox[1], coeffDenominator);
result += _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
raiser->computeCoeff(prox[0], prox[2], coeffDenominator);
result += _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
raiser->computeCoeff(prox[1], prox[2], coeffDenominator);
result += _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
return cTri*result/3;
case TYPE_HEX:
raiser->computeCoeff(prox[0], prox[1], prox[2], coeffDenominator);
return _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
case TYPE_PRI:
raiser->computeCoeff(prox[0], prox[1], prox[2], coeffDenominator);
result += _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
raiser->computeCoeff(prox[0], prox[3], prox[2], coeffDenominator);
result += _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
raiser->computeCoeff(prox[1], prox[3], prox[2], coeffDenominator);
result += _computeBoundRational(_coeffsJacDet, coeffDenominator, true);
return cTri*result/3;
case TYPE_TET:
{
fullVector<double> thirdTerm, coeffNum1, tmp;
thirdTerm = prox[1];
thirdTerm.axpy(prox[2]);
thirdTerm.axpy(prox[3]);
thirdTerm.axpy(prox[4]);
raiser->computeCoeff(prox[0], prox[5], thirdTerm, coeffNum1);
thirdTerm = prox[0];
thirdTerm.axpy(prox[2]);
thirdTerm.axpy(prox[3]);
thirdTerm.axpy(prox[5]);
raiser->computeCoeff(prox[1], prox[4], thirdTerm, tmp);
coeffNum1.axpy(tmp);
thirdTerm = prox[0];
thirdTerm.axpy(prox[1]);
thirdTerm.axpy(prox[4]);
thirdTerm.axpy(prox[5]); raiser->computeCoeff(prox[2], prox[3], thirdTerm, tmp);
coeffNum1.axpy(tmp);
fullVector<double> coeffDen1, coeffDen2;
raiser->computeCoeff(prox[0], prox[1], prox[2], coeffDen1);
raiser->computeCoeff(prox[3], prox[4], prox[5], coeffDen2);
fullVector<double> &coeffNumerator = tmp;
bezierBasisRaiser *raiserBis;
raiserBis = raiser->getRaisedBezierBasis(3)->getRaiser();
raiserBis->computeCoeff(coeffNum1, _coeffsJacDet, coeffNumerator);
raiserBis->computeCoeff(coeffDen1, coeffDen2, coeffDenominator);
result = _computeBoundRational(coeffNumerator, coeffDenominator, true);
return cTet*result/12;
}
case TYPE_PYR:
{
fullVector<double> thirdTerm, coeffNum1, tmp;
thirdTerm = prox[2];
thirdTerm.axpy(prox[3]);
thirdTerm.axpy(prox[4]);
thirdTerm.axpy(prox[5]);
raiser->computeCoeff(prox[0], prox[1], thirdTerm, coeffNum1);
thirdTerm = prox[4];
thirdTerm.axpy(prox[5]);
raiser->computeCoeff(prox[2], prox[3], thirdTerm, tmp);
coeffNum1.axpy(tmp);
thirdTerm = prox[2];
thirdTerm.axpy(prox[3]);
raiser->computeCoeff(prox[4], prox[5], thirdTerm, tmp);
coeffNum1.axpy(tmp);
fullVector<double> coeffDen1, coeffDen2;
raiser->computeCoeff(prox[0], prox[1], prox[2], coeffDen1);
raiser->computeCoeff(prox[3], prox[4], prox[5], coeffDen2);
fullVector<double> &coeffNumerator = tmp;
bezierBasisRaiser *raiserBis;
raiserBis = raiser->getRaisedBezierBasis(3)->getRaiser();
raiserBis->computeCoeff(coeffNum1, _coeffsJacDet, coeffNumerator);
raiserBis->computeCoeff(coeffDen1, coeffDen2, coeffDenominator);
result = _computeBoundRational(coeffNumerator, coeffDenominator, true);
return cPyr*result/8;
}
default:
Msg::Info("Unknown type for scaled Jacobian (%d)", _type);
return -1;
}
}
void _CoeffDataScaledJac::_getCoeffLengthVectors(fullMatrix<double> &coeff,
bool corners) const
{
int sz1 = corners ? _bfsDet->getNumLagCoeff() : _coeffsJacMat.size1();
switch (_type) {
case TYPE_QUA: coeff.resize(sz1, 2); break;
case TYPE_TRI: coeff.resize(sz1, 3); break;
case TYPE_HEX: coeff.resize(sz1, 3); break;
case TYPE_PRI: coeff.resize(sz1, 4); break;
case TYPE_TET: coeff.resize(sz1, 6); break;
case TYPE_PYR: coeff.resize(sz1, 6); break;
default:
Msg::Error("Unkown type for scaled jac computation");
coeff.resize(0, 0);
return; }
const fullMatrix<double> &mat = _coeffsJacMat;
if (_type != TYPE_PYR) {
for (int i = 0; i < sz1; i++) {
coeff(i, 0) = std::sqrt(pow_int(mat(i, 0), 2) +
pow_int(mat(i, 1), 2) +
pow_int(mat(i, 2), 2) );
coeff(i, 1) = std::sqrt(pow_int(mat(i, 3), 2) +
pow_int(mat(i, 4), 2) +
pow_int(mat(i, 5), 2) );
}
if (mat.size2() > 6) {
for (int i = 0; i < sz1; i++) {
coeff(i, 2) = std::sqrt(pow_int(mat(i, 6), 2) +
pow_int(mat(i, 7), 2) +
pow_int(mat(i, 8), 2) );
}
}
else if (_type == TYPE_TRI) {
for (int i = 0; i < sz1; i++) {
coeff(i, 2) = std::sqrt(pow_int(mat(i, 3) - mat(i, 0), 2) +
pow_int(mat(i, 4) - mat(i, 1), 2) +
pow_int(mat(i, 5) - mat(i, 2), 2) );
}
}
switch (_type) {
case TYPE_TET:
case TYPE_PRI:
for (int i = 0; i < sz1; i++) {
coeff(i, 3) = std::sqrt(pow_int(mat(i, 3) - mat(i, 0), 2) +
pow_int(mat(i, 4) - mat(i, 1), 2) +
pow_int(mat(i, 5) - mat(i, 2), 2) );
}
}
if (_type == TYPE_TET) {
for (int i = 0; i < sz1; i++) {
coeff(i, 4) = std::sqrt(pow_int(mat(i, 6) - mat(i, 0), 2) +
pow_int(mat(i, 7) - mat(i, 1), 2) +
pow_int(mat(i, 8) - mat(i, 2), 2) );
coeff(i, 5) = std::sqrt(pow_int(mat(i, 6) - mat(i, 3), 2) +
pow_int(mat(i, 7) - mat(i, 4), 2) +
pow_int(mat(i, 8) - mat(i, 5), 2) );
}
}
}
else {
for (int i = 0; i < sz1; i++) {
coeff(i, 0) = std::sqrt(pow_int(2*mat(i, 0), 2) +
pow_int(2*mat(i, 1), 2) +
pow_int(2*mat(i, 2), 2) );
coeff(i, 1) = std::sqrt(pow_int(2*mat(i, 3), 2) +
pow_int(2*mat(i, 4), 2) +
pow_int(2*mat(i, 5), 2) );
coeff(i, 2) = std::sqrt(pow_int(mat(i, 6) + mat(i, 0) + mat(i, 3), 2) +
pow_int(mat(i, 7) + mat(i, 1) + mat(i, 4), 2) +
pow_int(mat(i, 8) + mat(i, 2) + mat(i, 5), 2) );
coeff(i, 3) = std::sqrt(pow_int(mat(i, 6) - mat(i, 0) + mat(i, 3), 2) +
pow_int(mat(i, 7) - mat(i, 1) + mat(i, 4), 2) +
pow_int(mat(i, 8) - mat(i, 2) + mat(i, 5), 2) );
coeff(i, 4) = std::sqrt(pow_int(mat(i, 6) - mat(i, 0) - mat(i, 3), 2) +
pow_int(mat(i, 7) - mat(i, 1) - mat(i, 4), 2) +
pow_int(mat(i, 8) - mat(i, 2) - mat(i, 5), 2) );
coeff(i, 5) = std::sqrt(pow_int(mat(i, 6) + mat(i, 0) - mat(i, 3), 2) +
pow_int(mat(i, 7) + mat(i, 1) - mat(i, 4), 2) +
pow_int(mat(i, 8) + mat(i, 2) - mat(i, 5), 2) );
}
}
}
// Isotropy measure
_CoeffDataIsotropy::_CoeffDataIsotropy(fullVector<double> &det,
fullMatrix<double> &mat,
const bezierBasis *bfsDet,
const bezierBasis *bfsMat,
int depth)
: _CoeffData(depth), _coeffsJacDet(det.getDataPtr(), det.size()),
_coeffsJacMat(mat.getDataPtr(), mat.size1(), mat.size2()),
_bfsDet(bfsDet), _bfsMat(bfsMat)
{
if (!det.getOwnData() || !mat.getOwnData()) {
Msg::Fatal("Cannot create an instance of _CoeffDataScaledJac from a "
"fullVector or a fullMatrix that does not own its data.");
}
// _coeffsJacDet and _coeffsMetric reuse data, this avoid to allocate new
// arrays and to copy data that are not used outside of this object.
// It remains to swap ownerships:
det.setOwnData(false);
mat.setOwnData(false);
const_cast<fullVector<double>&>(_coeffsJacDet).setOwnData(true);
const_cast<fullMatrix<double>&>(_coeffsJacMat).setOwnData(true);
_computeAtCorner(_minL, _maxL);
_minB = 0;
if (boundsOk(_minL, _maxL)) return;
else _minB = _computeLowerBound();
// Msg::Info("%g %g %g ", _minB, _minL, _maxL);
// _coeffsJacDet.print("_coeffsJacDet");
// _coeffsJacMat.print("_coeffsJacMat");
// _maxB not used for now
}
bool _CoeffDataIsotropy::boundsOk(double minL, double maxL) const
{
static double tol = 1e-3;
return minL < tol*1e-3 || (_minB > minL-tol && _minB > minL*(1-100*tol));
}
void _CoeffDataIsotropy::getSubCoeff(std::vector<_CoeffData*> &v) const
{
v.clear();
v.reserve(_bfsMat->getNumDivision());
fullMatrix<double> subCoeffM;
fullVector<double> subCoeffD;
_bfsMat->subdivideBezCoeff(_coeffsJacMat, subCoeffM);
_bfsDet->subdivideBezCoeff(_coeffsJacDet, subCoeffD);
int szD = _coeffsJacDet.size();
int szM1 = _coeffsJacMat.size1();
int szM2 = _coeffsJacMat.size2();
for (int i = 0; i < _bfsMat->getNumDivision(); i++) {
fullVector<double> coeffD(szD);
fullMatrix<double> coeffM(szM1, szM2);
coeffD.copy(subCoeffD, i * szD, szD, 0);
coeffM.copy(subCoeffM, i * szM1, szM1, 0, szM2, 0, 0);
_CoeffDataIsotropy *newData
= new _CoeffDataIsotropy(coeffD, coeffM, _bfsDet, _bfsMat, _depth+1);
v.push_back(newData);
}
}
void _CoeffDataIsotropy::_computeAtCorner(double &min, double &max) const
{
min = std::numeric_limits<double>::infinity();
max = -min;
for (int i = 0; i < _bfsMat->getNumLagCoeff(); i++) { double p = 0;
for (int k = 0; k < _coeffsJacMat.size2(); ++k) {
p += pow_int(_coeffsJacMat(i, k), 2);
}
double qual;
if (_coeffsJacMat.size2() == 6)
qual = 2 * _coeffsJacDet(i) / p;
else
qual = 3 * std::pow(_coeffsJacDet(i), 2/3.) / p;
min = std::min(min, qual);
max = std::max(max, qual);
}
}
double _CoeffDataIsotropy::_computeLowerBound() const
{
// Speedup: If one coeff _coeffsJacDet is negative, we would get
// a negative lower bound. For now, returning 0.
for (int i = 0; i < _coeffsJacDet.size(); ++i) {
if (_coeffsJacDet(i) < 0) {
return 0;
}
}
// 2D element
if (_coeffsJacMat.size2() == 6) {
fullVector<double> coeffDenominator;
{
bezierBasisRaiser *raiser = _bfsMat->getRaiser();
fullVector<double> prox;
for (int k = 0; k < _coeffsJacMat.size2(); ++k) {
prox.setAsProxy(_coeffsJacMat, k);
fullVector<double> tmp;
raiser->computeCoeff(prox, prox, tmp);
if (k == 0) coeffDenominator.resize(tmp.size());
coeffDenominator.axpy(tmp, 1);
}
}
return 2*_computeBoundRational(_coeffsJacDet, coeffDenominator, true);
}
// 3D element NEW
fullVector<double> coeffDenominator;
{
// P: coefficients of function that bound from above the Frobenius norm of J
// element of P are automatically set to 0
fullVector<double> P(_coeffsJacMat.size1());
for (int i = 0; i < _coeffsJacMat.size1(); ++i) {
for (int k = 0; k < _coeffsJacMat.size2(); ++k) {
P(i) += _coeffsJacMat(i, k) * _coeffsJacMat(i, k);
}
P(i) = std::sqrt(P(i));
}
_bfsMat->getRaiser()->computeCoeff(P, P, P, coeffDenominator);
}
return 3*std::pow(_computeBoundRational(_coeffsJacDet,
coeffDenominator, true), 2/3.);
// // 3D element OLD
// fullVector<double> coeffNumerator;
// _bfsDet->getRaiser()->computeCoeff(_coeffsJacDet, _coeffsJacDet, coeffNumerator);
//
// fullVector<double> coeffDenominator;
// {
// fullVector<double> coeffDenCbrt;
// bezierBasisRaiser *raiser = _bfsMat->getRaiser();
//
// fullVector<double> prox;
// for (int k = 0; k < _coeffsJacMat.size2(); ++k) {// prox.setAsProxy(_coeffsJacMat, k);
// fullVector<double> tmp;
// raiser->computeCoeff(prox, prox, tmp);
// if (k == 0) coeffDenCbrt.resize(tmp.size());
// coeffDenCbrt.axpy(tmp, 1);
// }
//
// bezierBasisRaiser *raiser2 = raiser->getRaisedBezierBasis(2)->getRaiser();
// raiser2->computeCoeff(coeffDenCbrt, coeffDenCbrt, coeffDenCbrt, coeffDenominator);
// }
//
// return 3*std::pow(_computeBoundRational(coeffNumerator,
// coeffDenominator, true), 1/3.);
}
// Anisotropy measure
_CoeffDataAnisotropy::_CoeffDataAnisotropy(fullVector<double> &det,
fullMatrix<double> &metric,
const bezierBasis *bfsDet,
const bezierBasis *bfsMet,
int depth,
MElement *el,
int num)
: _CoeffData(depth), _coeffsJacDet(det.getDataPtr(), det.size()),
_coeffsMetric(metric.getDataPtr(), metric.size1(), metric.size2()),
_bfsDet(bfsDet), _bfsMet(bfsMet), _elForDebug(el), _numForDebug(num)
{
_CoeffDataAnisotropy::current = this;
if (!det.getOwnData() || !metric.getOwnData()) {
Msg::Fatal("Cannot create an instance of _CoeffDataScaledJac from a "
"fullVector or a fullMatrix that does not own its data.");
}
// _coeffsJacDet and _coeffsMetric reuse data, this avoid to allocate new
// arrays and to copy data that are not used outside of this object.
// It remains to swap ownerships:
det.setOwnData(false);
metric.setOwnData(false);
const_cast<fullVector<double>&>(_coeffsJacDet).setOwnData(true);
const_cast<fullMatrix<double>&>(_coeffsMetric).setOwnData(true);
_computeAtCorner(_minL, _maxL);
_minB = 0;
if (boundsOk(_minL, _maxL)) return;
else _minB = _computeLowerBound();
// computation of _maxB not implemented for now
//statsForMatlab(_elForDebug, _numForDebug);//fordebug
}
void _CoeffDataAnisotropy::_computeAtCorner(double &min, double &max) const
{
min = std::numeric_limits<double>::infinity();
max = -min;
for (int i = 0; i < _bfsMet->getNumLagCoeff(); i++) {
const double &q = _coeffsMetric(i, 0);
double p = 0;
for (int k = 1; k < _coeffsMetric.size2(); ++k) {
p += pow_int(_coeffsMetric(i, k), 2);
}
p = std::sqrt(p);
double qualSqrd;
if (_coeffsMetric.size2() == 3)
qualSqrd = _R2Dsafe(q, p);
else
qualSqrd = _R3Dsafe(q, p, _coeffsJacDet(i));
min = std::min(min, qualSqrd);
max = std::max(max, qualSqrd);
} min = std::sqrt(min);
max = std::sqrt(max);
}
double _CoeffDataAnisotropy::_computeLowerBound() const
{
// 2D element
if (_coeffsMetric.size2() == 3) {
double mina = _computeLowerBoundA();
return std::sqrt(_R2Dsafe(mina));
}
// 3D element
double mina = _computeLowerBoundA();
double minK = _computeLowerBoundK();
_moveInsideDomain(mina, minK, true);
double p_dRda, p_dRdK;
_computePseudoDerivatives(mina, minK, p_dRda, p_dRdK);
if (p_dRda < 0) {
// cases 1 & 2 => compute a lower bounding curve K = beta * a^3 + c * a
// with c such that the curve that passes through (minK, mina) has the
// slope equal to -dRda/dRdK
double slope = -p_dRda/p_dRdK;
double gamma = .5*(3*minK/mina - slope);
double beta;
_computeBoundingCurve(beta, gamma, true);
/*{//fordebug
double beta = (minK/mina-c)/mina/mina;
if (std::abs(p_dRda + p_dRdK * (3*beta*mina*mina+c)) > 1e-12) {
Msg::Error("Derivative along curve not zero %g", p_dRda + p_dRdK * (3*beta*mina*mina+c));
}
}*/
double a_int = mina, K_int = minK;
int where = _intersectionCurveLeftCorner(beta, gamma, a_int, K_int);
if (where == 1) {
// the minimum is on the curve, long to compute, we return this for now:
return std::sqrt(_R3Dsafe(mina, minK));
}
//Msg::Info("int (%g, %g) (beta %g, gamma %g)", a_int, K_int, beta, gamma);//fordebug
// Let a0 be the point at which R(a, minK) takes its minimum. If there is
// an intersection and if a_int < a0, the minimum is at (a_int, minK),
// otherwise it is at (a0, minK).
bool minIsAta0;
if (where == -1 || _moveInsideDomain(a_int, K_int, false)) {
minIsAta0 = true;
}
else {
double p_dRda, p_dRdK;
_computePseudoDerivatives(a_int, K_int, p_dRda, p_dRdK);
/*if (p_dRda + p_dRdK * (3*beta*a_int*a_int+c) < -1e-5) {//fordebug
Msg::Error("Derivative along curve not positive or zero %g", p_dRda + p_dRdK * (3*beta*a_int*a_int+c));
Msg::Info("(%g, %g) vs (%g, %g), diff (%g, %g)", mina, minK, a_int, K_int, a_int-mina, K_int-minK);
double beta2 = (minK/mina-c)/mina/mina;
Msg::Info("beta %g - %g = %g", beta, beta2, beta-beta2);
}*/
minIsAta0 = p_dRda > 0;
}
if (minIsAta0) {
double a0 = _computeAbscissaMinR(mina, minK);
return std::sqrt(_R3Dsafe(a0, minK));
}
else {
return std::sqrt(_R3Dsafe(a_int, minK));
} }
else if (p_dRdK < 0) {
// cases 4 & 5 => compute an upper bounding curve K = beta * a^3 + c * a
// with c such that the curve that passes through (minK, mina) has the
// slope equal to -dRda/dRdK
double slope = -p_dRda/p_dRdK;
double gamma = .5*(3*minK/mina - slope);
double beta;
_computeBoundingCurve(beta, gamma, false);
double a_int = mina, K_int = minK;
int where = _intersectionCurveLeftCorner(beta, gamma, a_int, K_int);
if (where == 0) {
// the minimum is on the curve, long to compute, we return this for now:
return std::sqrt(_R3Dsafe(mina, minK));
}
// Let K0 be the point at which R(mina, K) takes its minimum. If there is
// an intersection and if K_int < K0, the minimum is at (mina, K_int),
// otherwise it is at (mina, K0).
double K0 = 2*std::cos(3*std::acos(-1/mina)-M_PI) + (mina*mina-3) * mina;
if (where == -1)
return std::sqrt(_R3Dsafe(mina, K0));
else
return std::sqrt(_R3Dsafe(mina, std::min(K0, K_int)));
}
else {
return std::sqrt(_R3Dsafe(mina, minK));
}
}
double _CoeffDataAnisotropy::_computeLowerBoundA() const
{
fullVector<double> coeffNumerator;
{
fullVector<double> coeffq;
coeffq.setAsProxy(_coeffsMetric, 0);
_bfsMet->getRaiser()->computeCoeff(coeffq, coeffq, coeffNumerator);
}
fullVector<double> coeffDenominator;
{
fullMatrix<double> prox, terms;
prox.setAsProxy(_coeffsMetric, 1, _coeffsMetric.size2()-1);
_bfsMet->getRaiser()->computeCoeff(prox, prox, terms);
coeffDenominator.resize(terms.size1(), true);
for (int i = 0; i < terms.size1(); ++i) {
for (int j = 0; j < terms.size2(); ++j) {
coeffDenominator(i) += terms(i, j);
}
}
}
double bound = _computeBoundRational(coeffNumerator, coeffDenominator, true);
return bound > 1 ? std::sqrt(bound) : 1;
}
double _CoeffDataAnisotropy::_computeLowerBoundK() const
{
fullVector<double> coeffNumerator;
_bfsDet->getRaiser()->computeCoeff(_coeffsJacDet,
_coeffsJacDet,
coeffNumerator);
fullVector<double> coeffDenominator;
{
fullVector<double> P(_coeffsMetric.size1());
// element of P are automatically set to 0
for (int i = 0; i < _coeffsMetric.size1(); ++i) {
for (int l = 1; l < 7; ++l) { P(i) += _coeffsMetric(i, l) * _coeffsMetric(i, l);
}
P(i) = std::sqrt(P(i));
}
_bfsMet->getRaiser()->computeCoeff(P, P, P, coeffDenominator);
}
return _computeBoundRational(coeffNumerator, coeffDenominator, true);
}
void _CoeffDataAnisotropy::_computeBoundingCurve(double &beta, double gamma,
bool compLowBound) const
{
// compute a lower/upper bounding curve K = beta * a^3 + gamma * a
// with gamma fixed.
fullVector<double> J2;
_bfsDet->getRaiser()->computeCoeff(_coeffsJacDet, _coeffsJacDet, J2);
fullVector<double> q(_coeffsMetric.size1());
for (int i = 0; i < q.size(); ++i) {
q(i) = _coeffsMetric(i, 0);
}
fullVector<double> qp2;
{
fullMatrix<double> terms_p, terms_qp2;
terms_p.setAsProxy(_coeffsMetric, 1, _coeffsMetric.size2()-1);
_bfsMet->getRaiser()->computeCoeff(q, terms_p, terms_p, terms_qp2);
qp2.resize(terms_qp2.size1(), true);
for (int i = 0; i < terms_qp2.size1(); ++i) {
for (int j = 0; j < terms_qp2.size2(); ++j) {
qp2(i) += terms_qp2(i, j);
}
}
}
fullVector<double> &coeffNumerator = J2;
coeffNumerator.axpy(qp2, -gamma);
fullVector<double> coeffDenominator;
_bfsMet->getRaiser()->computeCoeff(q, q, q, coeffDenominator);
beta = _computeBoundRational(coeffNumerator, coeffDenominator, compLowBound);
}
void _CoeffDataAnisotropy::fillMetricCoeff(const GradientBasis *gradients,
const fullMatrix<double> &nodes,
fullMatrix<double> &coeff,
int dim, bool ideal)
{
const int nSampPnts = gradients->getNumSamplingPoints();
switch (dim) {
case 0 :
return;
case 1 :
Msg::Fatal("Should not be here, metric for 1d not implemented");
break;
case 2 :
{
fullMatrix<double> dxydX(nSampPnts,3);
fullMatrix<double> dxydY(nSampPnts,3);
if (ideal)
gradients->getIdealGradientsFromNodes(nodes, &dxydX, &dxydY, NULL);
else
gradients->getGradientsFromNodes(nodes, &dxydX, &dxydY, NULL);
coeff.resize(nSampPnts, 3);
for (int i = 0; i < nSampPnts; i++) {
const double &dxdX = dxydX(i,0), &dydX = dxydX(i,1);
const double &dxdY = dxydY(i,0), &dydY = dxydY(i,1);
double dzdX = 0, dzdY = 0;
if (nodes.size2() > 2) {
dzdX = dxydX(i,2);
dzdY = dxydY(i,2);
}
const double dvxdX = dxdX*dxdX + dydX*dydX + dzdX*dzdX;
const double dvxdY = dxdY*dxdY + dydY*dydY + dzdY*dzdY;
coeff(i, 0) = (dvxdX + dvxdY) / 2;
coeff(i, 1) = dvxdX - coeff(i, 0);
coeff(i, 2) = (dxdX*dxdY + dydX*dydY + dzdX*dzdY);
}
}
break;
case 3 :
{
fullMatrix<double> dxyzdX(nSampPnts,3);
fullMatrix<double> dxyzdY(nSampPnts,3);
fullMatrix<double> dxyzdZ(nSampPnts,3);
if (ideal)
gradients->getIdealGradientsFromNodes(nodes, &dxyzdX, &dxyzdY, &dxyzdZ);
else
gradients->getGradientsFromNodes(nodes, &dxyzdX, &dxyzdY, &dxyzdZ);
coeff.resize(nSampPnts, 7);
for (int i = 0; i < nSampPnts; i++) {
const double &dxdX = dxyzdX(i,0), &dydX = dxyzdX(i,1), &dzdX = dxyzdX(i,2);
const double &dxdY = dxyzdY(i,0), &dydY = dxyzdY(i,1), &dzdY = dxyzdY(i,2);
const double &dxdZ = dxyzdZ(i,0), &dydZ = dxyzdZ(i,1), &dzdZ = dxyzdZ(i,2);
const double dvxdX = dxdX*dxdX + dydX*dydX + dzdX*dzdX;
const double dvxdY = dxdY*dxdY + dydY*dydY + dzdY*dzdY;
const double dvxdZ = dxdZ*dxdZ + dydZ*dydZ + dzdZ*dzdZ;
coeff(i, 0) = (dvxdX + dvxdY + dvxdZ) / 3;
static double fact1 = 1./std::sqrt(6.);
static double fact2 = 1./std::sqrt(3.);
coeff(i, 1) = fact1 * (dvxdX - coeff(i, 0));
coeff(i, 2) = fact1 * (dvxdY - coeff(i, 0));
coeff(i, 3) = fact1 * (dvxdZ - coeff(i, 0));
coeff(i, 4) = fact2 * (dxdX*dxdY + dydX*dydY + dzdX*dzdY);
coeff(i, 5) = fact2 * (dxdZ*dxdY + dydZ*dydY + dzdZ*dzdY);
coeff(i, 6) = fact2 * (dxdX*dxdZ + dydX*dydZ + dzdX*dzdZ);
}
}
break;
}
}
bool _CoeffDataAnisotropy::_moveInsideDomain(double &a,
double &K,
bool bottomleftCorner)
{
// - bottomleftCorner: if false, then it is a top left or a bottom right corner
// (it is the same treatment)
// - Return true if the point has been moved, false otherwise
// NB: When moving 'a', we use N-R to compute the root of
// f(a) = .5 * (K - a^3 + 3*a) - 'w' where 'w' is -1 or 1.
if (bottomleftCorner) {
K = std::max(K, .0);
a = std::max(a, 1.);
}
double w = _w(a, K);
if (std::abs(w) <= 1) return false;
const double tolerance = 1e-5;
if (w > 1) {
if (bottomleftCorner) {
// make sure to compute the right root (a>1) and
// avoid slopes that are too small:
a = std::max(a, 1.1);
// N-R approaches the root from the right, we can impose w > 1
while (w > 1 || w < 1-tolerance) {
double df = w - 1;
double slope = 1.5*(1-a*a);
a -= df/slope;
w = _w(a, K);
}
}
else {
K -= 2*w - 2;
}
}
else {
if (bottomleftCorner) {
K -= 2*w + 2;
}
else {
// make sure to compute the right root (a>2)
a = std::max(a, 2.);
while (std::abs(w+1) > tolerance) {
double df = w + 1;
double slope = 1.5*(1-a*a);
a -= df/slope;
w = _w(a, K);
}
}
}
return true;
}
bool _CoeffDataAnisotropy::_computePseudoDerivatives(double a, double K,
double &dRda, double &dRdK)
{
// Return derivative without the positive (but non-constant) coefficient
// Useful when only the sign of dRda and dRdK or the ratio dRda/dRdK
// are needed.
double w = _wSafe(a, K);
if (std::abs(w) > 1) {
Msg::Error("Cannot compute pseudo derivatives of R "
"outside the domain (w=%g)", w);
return false;
}
const double phip = (std::acos(w) + M_PI) / 3;
const double C = 1 + a * std::cos(phip);
dRdK = C / 3;
dRda = 2 * std::sqrt(1-w*w) * std::sin(phip) + (1-a*a) * C;
return true;
}
bool _CoeffDataAnisotropy::_computeDerivatives(double a, double K,
double &dRda, double &dRdK,
double &dRdaa, double &dRdaK,
double &dRdKK)
{
const double w = _wSafe(a, K);
if (std::abs(w) > 1) {
Msg::Error("Cannot compute derivatives of R outside the domain (w=%g)", w);
return false; }
const double phi = (std::acos(w)) / 3;
const double phip = phi + M_PI / 3;
const double S = 1./std::sqrt(1-w*w);
const double A = (1-a*a)*S;
const double sin = std::sin(phi);
const double sinp = std::sin(phip);
const double cosp = std::cos(phip);
const double C = 1 + a*cosp;
const double D = 1./(a+2*std::cos(phi));
static const double sq3 = std::sqrt(3);
const double coeff = sq3*D*D/18;
dRdK = coeff*6 * (C*S);
dRda = coeff*18 * (2*sinp + A*C);
dRdKK = coeff*S*S * (a*sinp - 4*C*sin*D + 3*w*C*S);
dRdaK = coeff*S*3 * (a*A*sinp + 3*w*A*C*S + 2*cosp - 4*C*(1+A*sin)*D);
dRdaa = coeff*9 * (3*w*A*A*C*S - 4*a*C*S + a*A*A*sinp - 4*(1+A*sin)*D*(2*sinp + A*C));
return true;
}
int _CoeffDataAnisotropy::_intersectionCurveLeftCorner(double beta, double gamma,
double &a, double &K)
{
// curve K = beta * a^3 + gamma * a
// on input, a and K are the bottom left corner
// on output, a and K are the intersection
// return 0 if the intersection is on the horizontal
// 1 if the intersection is on the vertical
// -1 if there is no intersection
// if (beta < 0) {
// Msg::Warning("Negative curvature, there are 2 or 0 intersections... Is it "
// "normal? Anyway, I will compute the left one if it exists.");
//// Msg::Info("%g %g | %g %g", beta, gamma, a, K);
// }
const double minK = K;
K = (beta*a*a + gamma)*a;
if (K >= minK) return 1;
// Find the root by Newton-Raphson.
K = minK;
if (beta < 0) {
// When beta < 0, check if the intersection exists:
double aMaximum = std::sqrt(-gamma/3/beta);
double KMaximum = (beta * aMaximum*aMaximum + gamma) * aMaximum;
if (gamma < 0 || aMaximum < a || KMaximum < K) {
// Msg::Warning("Sorry but there is no intersection");
return -1;
}
}
else if (beta > 0) {
// When beta > 0 and aMin > 'a', we must move 'a' to the right of aMin,
// otherwise we would compute a wrong intersection:
double aMinimum = std::sqrt(-gamma/3/beta);
if (aMinimum > a) a += 2*(aMinimum - a);
}
// Which precision? We know that w is in [-1, 1] with w = .5 * (K + (3-a*a)*a)
// We thus seek a good precision on 'K' and '3*a - a^3'
double a3 = (3-a*a)*a;
double da3 = std::numeric_limits<double>::infinity();
double dK = std::numeric_limits<double>::infinity();
while (std::abs(da3) > 1e-5 || std::abs(dK) > 1e-4) {
const double slope = 3*beta*a*a + gamma;
dK = (beta*a*a + gamma)*a - minK;
a -= dK / slope;
da3 = a3; a3 = (3-a*a)*a;
da3 -= a3;
}
return 0;
}
double _CoeffDataAnisotropy::_computeAbscissaMinR(double aStart, double K)
{
// If K == 0, then R == 0. Note, there are less numerical problems when
// computing R(2, 0) than R(1, 0), so return 2:
if (K == 0) return 2;
double a = aStart;
double a3 = (3-a*a)*a;
double da3 = std::numeric_limits<double>::infinity();
double dRda = da3, dRdK, dRdaa, dRdaK, dRdKK;
while (std::abs(da3) > 1e-5 || std::abs(dRda) > 1e-5) {
_computeDerivatives(a, K, dRda, dRdK, dRdaa, dRdaK, dRdKK);
double da = - dRda / dRdaa;
da3 = a3;
double potentiala = a+da;
a3 = (3-potentiala*potentiala)*potentiala;
da3 -= a3;
// Make sure we are not going outside the domain:
while (std::abs(_w(a+da, K)) > 1) da /= 2;
a += da;
}
return a;
}
bool _CoeffDataAnisotropy::boundsOk(double minL, double maxL) const
{
static double tol = 1e-3;
return minL < tol*1e-3 || (_minB > minL-tol && _minB > minL*(1-100*tol));
}
void _CoeffDataAnisotropy::getSubCoeff(std::vector<_CoeffData*> &v) const
{
v.clear();
v.reserve(_bfsMet->getNumDivision());
fullMatrix<double> subCoeffM;
fullVector<double> subCoeffD;
_bfsMet->subdivideBezCoeff(_coeffsMetric, subCoeffM);
// in 2D, _bfsDet is NULL
if (_bfsDet) _bfsDet->subdivideBezCoeff(_coeffsJacDet, subCoeffD);
// in 2D, _coeffsJacDet is empty (szD == 0)
int szD = _coeffsJacDet.size();
int szM1 = _coeffsMetric.size1();
int szM2 = _coeffsMetric.size2();
for (int i = 0; i < _bfsMet->getNumDivision(); i++) {
fullVector<double> coeffD(szD);
fullMatrix<double> coeffM(szM1, szM2);
coeffD.copy(subCoeffD, i * szD, szD, 0);
coeffM.copy(subCoeffM, i * szM1, szM1, 0, szM2, 0, 0);
int newNum = _numForDebug + (i+1) * pow_int(10, _depth);
_CoeffDataAnisotropy *newData
= new _CoeffDataAnisotropy(coeffD, coeffM, _bfsDet, _bfsMet, _depth+1, _elForDebug, newNum);
v.push_back(newData);
}
}
double _CoeffDataAnisotropy::_R2Dsafe(double q, double p)
{
if (p <= q && p >= 0 && p < std::numeric_limits<double>::infinity()) {
if (q == 0) return 0;
if (q == std::numeric_limits<double>::infinity()) {
Msg::Warning("q had infinite value in computation of 2D Raniso");
return 1;
} return (q-p) / (q+p);
}
else {
Msg::Error("Wrong argument for 2d Raniso (%g, %g)", q, p);
return -1;
}
}
double _CoeffDataAnisotropy::_R2Dsafe(double a)
{
if (a >= 1) {
if (a == std::numeric_limits<double>::infinity())
return 1;
return (a - 1) / (a + 1);
}
else {
Msg::Error("Wrong argument for 2d metRanisoric (%g)", a);
return -1;
}
}
double _CoeffDataAnisotropy::_R3Dsafe(double q, double p, double J)
{
if (p < 0 || p == std::numeric_limits<double>::infinity() || J != J) {
Msg::Error("Wrong argument for 3d Raniso (%g, %g, %g)", q, p, J);
return -1;
}
if (q == 0) return 0;
if (q > 0 && p == 0) return 1;
if (q == std::numeric_limits<double>::infinity()) {
Msg::Warning("q had infinite value in computation of 3D Raniso");
return 1;
}
const double a = q/p;
const double K = J*J/p/p/p;
return _R3Dsafe(a, K);
}
double _CoeffDataAnisotropy::_R3Dsafe(double a, double K)
{
if (a < 1 || K < 0) {
if (K >= 0 && a > 1-1e-6 && K < 1e-12) {
return 0;
}
Msg::Error("Wrong argument for 3d Raniso (%g, %g)", a, K);
_CoeffDataAnisotropy::youReceivedAnError();
return -1;
}
if (a == std::numeric_limits<double>::infinity() ||
K == std::numeric_limits<double>::infinity()) {
Msg::Warning("a and/or K had infinite value in computation of 3D Raniso");
return 1;
}
const double w = _wSafe(a, K);
const double phi = std::acos(w) / 3;
const double R = (a + 2*std::cos(phi + 2*M_PI/3)) / (a + 2*std::cos(phi));
return std::max(.0, std::min(1., R));
}
double _CoeffDataAnisotropy::_wSafe(double a, double K) {
if (a >= 1 && K >= 0) {
if (a == std::numeric_limits<double>::infinity() ||
K == std::numeric_limits<double>::infinity()) {
Msg::Error("Cannot compute w with infinite numbers (%g, %g)", a, K);
return 0; }
const double w = _w(a, K);
if (w > 1) {
if (w < 1+1e-5 || w < 1+K*1e-14) return 1;
else {
Msg::Error("outside the domain w(%g, %g) = %g", a, K, w);
hasError = true;
}
}
else if (w < -1) {
if (w > -1-1e-5 || w > -1-K*1e-14) return -1;
else {
Msg::Error("outside the domain w(%g, %g) = %g", a, K, w);
hasError = true;
}
}
return w;
}
else {
youReceivedAnError();
Msg::Error("Wrong argument for w (%g, %g)", a, K);
return -1;
}
}
int _CoeffDataAnisotropy::metricOrder(MElement *el)
{
const int order = el->getPolynomialOrder();
switch (el->getType()) {
case TYPE_PNT : return 0;
case TYPE_LIN : return order;
case TYPE_TRI :
case TYPE_TET :
case TYPE_PYR : return 2*order-2;
case TYPE_QUA :
case TYPE_PRI :
case TYPE_HEX : return 2*order;
default :
Msg::Error("Unknown element type %d, returning -1", el->getType());
return -1;
}
}
void _CoeffDataAnisotropy::interpolateForMatlab(const fullMatrix<double> &nodes) const
{
fullVector<double> jac;
fullMatrix<double> metric;
_bfsMet->interpolate(_coeffsMetric, nodes, metric);
switch (_coeffsMetric.size2()) {
case 1:
// nothing to do
break;
case 3:
_CoeffDataAnisotropy::file << "q p myR eigR" << std::endl;
_CoeffDataAnisotropy::file << _bfsMet->getNumLagCoeff();
_CoeffDataAnisotropy::file << " " << metric.size1() << std::endl;
for (int i = 0; i < metric.size1(); ++i) {
// Compute from q, p
double p = pow(metric(i, 1), 2);
p += pow(metric(i, 2), 2);
p = std::sqrt(p);
double myR = std::sqrt(_R2Dsafe(metric(i, 0), p));
// Comppute from tensor fullMatrix<double> metricTensor(2, 2);
metricTensor(0, 0) = metric(i, 0) + metric(i, 1);
metricTensor(1, 1) = metric(i, 0) - metric(i, 1);
metricTensor(0, 1) = metricTensor(1, 0) = metric(i, 2);
fullVector<double> valReal(2), valImag(2);
fullMatrix<double> vecLeft(2, 2), vecRight(2, 2);
metricTensor.eig(valReal, valImag, vecLeft, vecRight, true);
double eigR = std::sqrt(valReal(0) / valReal(1));
_CoeffDataAnisotropy::file << metric(i, 0) << " ";
_CoeffDataAnisotropy::file << p << " ";
_CoeffDataAnisotropy::file << myR << " ";
_CoeffDataAnisotropy::file << eigR << std::endl;
}
break;
case 7:
_CoeffDataAnisotropy::file << "a K myR eigR" << std::endl;
_CoeffDataAnisotropy::file << _bfsMet->getNumLagCoeff();
_CoeffDataAnisotropy::file << " " << metric.size1() << std::endl;
_bfsDet->interpolate(_coeffsJacDet, nodes, jac);
for (int i = 0; i < metric.size1(); ++i) {
// Compute from q, p, J
double p = 0;
for (int k = 1; k < 7; ++k) p += pow(metric(i, k), 2);
p = std::sqrt(p);
double myR = std::sqrt(_R3Dsafe(metric(i, 0), p, jac(i)));
// Compute from tensor
fullMatrix<double> metricTensor(3, 3);
for (int k = 0; k < 3; ++k) {
static double fact1 = std::sqrt(6.);
static double fact2 = std::sqrt(3.);
const int ki = k%2;
const int kj = std::min(k+1, 2);
metricTensor(k, k) = metric(i, k+1)*fact1 + metric(i, 0);
metricTensor(ki, kj) = metricTensor(kj, ki) = metric(i, k+4)*fact2;
}
fullVector<double> valReal(3), valImag(3);
fullMatrix<double> vecLeft(3, 3), vecRight(3, 3);
metricTensor.eig(valReal, valImag, vecLeft, vecRight, true);
double eigR = std::sqrt(valReal(0) / valReal(2));
_CoeffDataAnisotropy::file << metric(i, 0)/p << " ";
_CoeffDataAnisotropy::file << jac(i)*jac(i)/p/p/p << " ";
_CoeffDataAnisotropy::file << myR << " ";
_CoeffDataAnisotropy::file << eigR << std::endl;
}
break;
default:
Msg::Error("Wrong number of functions for metric: %d", _coeffsMetric.size2());
}
}
void _CoeffDataAnisotropy::statsForMatlab(MElement *el, int num) const
{
if (num > 1000000) return;
static unsigned int aa = 0;
if (++aa < 1000) {
std::stringstream name;
name << "metricStat_" << el->getNum() << "_";
name << (num % 10);
name << (num % 100)/10;
name << (num % 1000)/100;
name << (num % 10000)/1000;
name << (num % 100000)/10000;
name << ".txt";
_CoeffDataAnisotropy::file.open(name.str().c_str(), std::fstream::out);
{
_CoeffDataAnisotropy::file << "mina minKfast minKsharp cmin beta_m beta_M beta c_m a_int K_int pdRda pdRdK a0" << std::endl;
double mina, minKs, minKf, gamma, beta_m, beta_M, beta, c_m; double a_int, K_int, p_dRda, p_dRdK, a0;
mina = _computeLowerBoundA();
if (el->getDim() == 3) {
minKs = minKf = _computeLowerBoundK();
double minK = minKf;
_moveInsideDomain(mina, minK, true);
_computePseudoDerivatives(mina, minK, p_dRda, p_dRdK);
double slope = -p_dRda/p_dRdK;
gamma = .5*(3*minK/mina - slope);
_computeBoundingCurve(beta_m, gamma, true);
_computeBoundingCurve(beta_M, gamma, false);
beta = -p_dRda/(p_dRdK*3*mina*mina);
c_m = -1;
if (p_dRda < 0) {
a_int = mina, K_int = minK;
_intersectionCurveLeftCorner(beta_m, gamma, a_int, K_int);
}
else {
a_int = mina, K_int = minK;
_intersectionCurveLeftCorner(beta_M, gamma, a_int, K_int);
}
a0 = _computeAbscissaMinR(mina, minK);
}
else {
minKs = minKf = gamma = beta_m = beta_M = beta = c_m = -1;
a_int = K_int = p_dRda = p_dRdK = a0 = -1;
}
_CoeffDataAnisotropy::file << std::setprecision(15);
_CoeffDataAnisotropy::file << mina << " " << minKf << " " << minKs << " " << std::endl;
_CoeffDataAnisotropy::file << gamma << " " << beta_m << " " << beta_M << " " << std::endl;
_CoeffDataAnisotropy::file << beta << " " << c_m << std::endl;
_CoeffDataAnisotropy::file << a_int << " " << K_int << std::endl;
_CoeffDataAnisotropy::file << p_dRda << " " << p_dRdK << std::endl;
_CoeffDataAnisotropy::file << a0 << std::endl;
_CoeffDataAnisotropy::file << std::setprecision(8);
}
}
fullMatrix<double> samplingPoints;
bool serendip = false;
gmshGeneratePoints(FuncSpaceData(el, 20, &serendip), samplingPoints);
interpolateForMatlab(samplingPoints);
_CoeffDataAnisotropy::file.close();
}
// Miscellaneous
template<typename Comp>
void _subdivideDomainsMinOrMax(std::vector<_CoeffData*> &domains,
double &minL,
double &maxL)
{
std::vector<_CoeffData*> subs;
make_heap(domains.begin(), domains.end(), Comp());
int k = 0;
while (!domains[0]->boundsOk(minL, maxL) && k++ < 1000) {
_CoeffData *cd = domains[0];
pop_heap(domains.begin(), domains.end(), Comp());
domains.pop_back();
cd->getSubCoeff(subs);
delete cd;
for (unsigned int i = 0; i < subs.size(); i++) {
minL = std::min(minL, subs[i]->minL());
maxL = std::max(maxL, subs[i]->maxL());
domains.push_back(subs[i]);
push_heap(domains.begin(), domains.end(), Comp());
} }
if (k > 1000) {
if (domains[0]->getNumMeasure() == 3)
_CoeffDataAnisotropy::youReceivedAnError();
Msg::Error("Max subdivision (1000) (size %d)", domains.size());
}
}
void _subdivideDomains(std::vector<_CoeffData*> &domains)
{
if (domains.empty()) {
Msg::Warning("empty vector in Bezier subdivision, nothing to do");
return;
}
double minL = domains[0]->minL();
double maxL = domains[0]->maxL();
for (unsigned int i = 1; i < domains.size(); ++i) {
minL = std::min(minL, domains[i]->minL());
maxL = std::max(maxL, domains[i]->maxL());
}
_subdivideDomainsMinOrMax<_lessMinB>(domains, minL, maxL);
_subdivideDomainsMinOrMax<_lessMaxB>(domains, minL, maxL);
}
double _computeBoundRational(const fullVector<double> &numerator,
const fullVector<double> &denominator,
bool lower, bool positiveDenom)
{
if (numerator.size() != denominator.size()) {
Msg::Fatal("In order to compute a bound on a rational function, I need "
"vectors of the same size! (%d vs %d)", numerator.size(),
denominator.size());
_CoeffDataAnisotropy::youReceivedAnError();
return 0;
}
// upper and lower bound of the desired bound:
const double inf = std::numeric_limits<double>::infinity();
double upperBound = inf;
double lowerBound = -inf;
if (!positiveDenom) lower = !lower;
if (lower) {
// if lower is true, we seek: bound * den <= num
for (int i = 0; i < numerator.size(); ++i) {
if (denominator(i) == 0) {
if (numerator(i) < 0) return -inf;
}
else if (denominator(i) > 0) {
upperBound = std::min(upperBound, numerator(i)/denominator(i));
}
else {
lowerBound = std::max(lowerBound, numerator(i)/denominator(i));
}
}
if (lowerBound > upperBound)
return -inf;
else
return upperBound;
}
else {
// otherwise, we seek: bound * den >= num
for (int i = 0; i < numerator.size(); ++i) {
if (denominator(i) == 0) {
if (numerator(i) > 0) return inf;
}
else if (denominator(i) > 0) {
lowerBound = std::max(lowerBound, numerator(i)/denominator(i)); }
else {
upperBound = std::min(upperBound, numerator(i)/denominator(i));
}
}
if (lowerBound > upperBound)
return inf;
else
return lowerBound;
}
}
} // end namespace jacobianBasedQuality