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Functions | |
| template<class T > | |
| Tps< T > | pow (const Tps< T > &x, int y) |
| Integer power. More... | |
| template<class T > | |
| Tps< T > | sqrt (const Tps< T > &x) |
| Square root. More... | |
| template<class T > | |
| Tps< T > | sin (const Tps< T > &x) |
| Sine. More... | |
| template<class T > | |
| Tps< T > | cos (const Tps< T > &x) |
| Cosine. More... | |
| template<class T > | |
| Tps< T > | tan (const Tps< T > &x) |
| Tangent. More... | |
| template<class T > | |
| Tps< T > | cot (const Tps< T > &x) |
| Cotangent. More... | |
| template<class T > | |
| Tps< T > | sec (const Tps< T > &x) |
| Secant. More... | |
| template<class T > | |
| Tps< T > | csc (const Tps< T > &x) |
| Cosecant. More... | |
| template<class T > | |
| Tps< T > | exp (const Tps< T > &x) |
| Exponential. More... | |
| template<class T > | |
| Tps< T > | log (const Tps< T > &x) |
| Natural logarithm. More... | |
| template<class T > | |
| Tps< T > | sinh (const Tps< T > &x) |
| Hyperbolic sine. More... | |
| template<class T > | |
| Tps< T > | cosh (const Tps< T > &x) |
| Hyperbolic cosine. More... | |
| template<class T > | |
| Tps< T > | tanh (const Tps< T > &x) |
| Hyperbolic tangent. More... | |
Function Documentation
Cosine.
Definition at line 129 of file TpsMath.h.
References Tps< T >::getTruncOrder(), sin(), T, and Tps< T >::Taylor().
Referenced by Harmonics< Value_type, Size_type >::__Mb6(), Harmonics< Value_type, Size_type >::__Mb6k(), TravelingWave::addKR(), RFCavity::addKR(), RFCavity::addKT(), Ring::appendElement(), mslang::Repeat::apply(), TravelingWave::apply(), VariableRFCavityFringeField::apply(), MultipoleT::apply(), RFCavity::apply(), Cyclotron::apply(), Distribution::applyEmissModelAstra(), Distribution::applyEmissModelNonEquil(), ThickMapper::applyEntranceFringe(), ThickMapper::applyExitFringe(), CollimatorPhysics::applyRandomRotation(), mslang::Rotation::applyRotation(), CollimatorPhysics::applyRotation(), TravelingWave::applyToReferenceParticle(), RFCavity::applyToReferenceParticle(), OscillatingField< Field >::Bfield(), ParallelCyclotronTracker::bunchDumpPhaseSpaceData(), MSplit::calcul(), Aperture::calcul(), Aperture::calcul_Apert(), Bend2D::calculateBendAngle(), Bend2D::calculateRefTrajectory(), Fieldmap::checkMap(), OpalBeamline::compute3DLattice(), mslang::Ellipse::computeBoundingBox(), CollimatorPhysics::computeCoulombScattering(), FM1DElectroStatic_fast::computeFieldDerivatives(), FM1DMagnetoStatic_fast::computeFieldDerivatives(), Astra1D_fast::computeFieldDerivatives(), FM1DDynamic_fast::computeFieldDerivatives(), FM1DElectroStatic::computeFieldOnAxis(), FM1DMagnetoStatic::computeFieldOnAxis(), FM1DDynamic::computeFieldOnAxis(), Harmonics< Value_type, Size_type >::computeMap(), OrbitThreader::computeMaximalImplicitDrift(), ClosedOrbitFinder< Value_type, Size_type, Stepper >::computeTune(), SectorField::convertToCartesian(), SectorField::convertToPolar(), cos(), cot(), MapAnalyser::createRotMatrix_m(), EnvelopeBunch::derivs(), RingSection::doesOverlap(), ParallelCyclotronTracker::dumpAzimuthAngles_m(), ParallelCyclotronTracker::dumpThetaEachTurn_m(), OscillatingField< Field >::Efield(), DragtFinnMap< N >::factorBerzForestIrwin(), OpalOffset::OpalLocalCartesianOffset::fillRegisteredAttributes(), Distribution::generateBinomial(), TravelingWave::getAutoPhaseEstimate(), RFCavity::getAutoPhaseEstimate(), MeshGenerator::getCylinder(), TravelingWave::getdA(), RFCavity::getdA(), TravelingWave::getdB(), RFCavity::getdB(), TravelingWave::getdE(), RFCavity::getdE(), Astra1DDynamic::getFieldDerivative(), FM1DDynamic::getFieldDerivative(), FM1DElectroStatic::getFieldDerivative(), FM1DMagnetoStatic::getFieldDerivative(), Astra1DDynamic::getFieldstrength(), Astra1DElectroStatic::getFieldstrength(), Astra1DMagnetoStatic::getFieldstrength(), SectorMagneticFieldMap::getFieldstrength(), ScalingFFAMagnet::getFieldValue(), RFCavity::getMomentaKick(), Ring::getNextNormal(), Ring::getNextPosition(), Bend2D::getOutline(), getQuaternion(), ParallelCyclotronTracker::getQuaternionTwoVectors(), Aperture::getShape(), Bend2D::getSurfaceMesh(), Util::getTaitBryantAngles(), coordinatetransform::CoordinateTransform::getUnitTangentVector(), coordinatetransform::getUnitTangentVectorY(), Offset::globalCylindricalOffset(), ParallelCyclotronTracker::globalToLocal(), RFCavity::initialise(), Offset::localCylindricalOffset(), ParallelCyclotronTracker::localToGlobal(), IdealMapper::makeFocus(), OrbitTracker::makeFocus(), LinearMapper::makeFocus(), SecondaryEmissionPhysics::nSec(), GreenWakeFunction::Wake::operator()(), GlobalFunctions::_cos::operator()(), Line::parse(), LOMB_class::period(), H5PartWrapperForPT::readStepHeader(), Offset::rotate(), ParallelCyclotronTracker::rotateAroundX(), ParallelCyclotronTracker::rotateAroundZ(), MultipoleTBase::rotateFrame(), MultipoleT::rotateFrame(), MultipoleTBase::rotateFrameInverse(), MultipoleT::rotateFrameInverse(), Rotation3D::Rotation3D(), sec(), ParallelCyclotronTracker::seoMode_m(), FM1DProfile2::setEdgeConstants(), Bend2D::setFieldBoundaries(), Bend2D::setFieldCalcParam(), sin(), tan(), TpsWerrf(), TravelingWave::trackOnAxisParticle(), RBend3D::trackRefParticleThrough(), RDM< Value_type, Size_type >::transform(), MultipoleTCurvedConstRadius::transformBField(), MultipoleTCurvedVarRadius::transformBField(), matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_(), OpalElement::update(), RingSection::updateComponentOrientation(), Offset::updateGeometry(), ParallelCyclotronTracker::visitCyclotron(), LieMapper::visitRFCavity(), ParallelCyclotronTracker::visitRing(), ThinMapper::visitSolenoid(), OrbitTracker::visitSolenoid(), ThinTracker::visitSolenoid(), ThickMapper::visitSolenoid(), LinearMapper::visitSolenoid(), TransportMapper::visitSolenoid(), DumpEMFields::writeFieldLine(), mslang::Ellipse::writeGnuplot(), Rotation3D::XRotation(), Rotation3D::YRotation(), and Rotation3D::ZRotation().
Hyperbolic cosine.
Definition at line 222 of file TpsMath.h.
References Tps< T >::getTruncOrder(), sinh(), T, and Tps< T >::Taylor().
Referenced by Harmonics< Value_type, Size_type >::__Mb6k(), MultipoleT::apply(), MSplit::calcul(), Aperture::calcul(), Harmonics< Value_type, Size_type >::computeMap(), cosh(), coth(), DragtFinnMap< N >::factorBerzForestIrwin(), coordinatetransform::CoordinateTransform::getUnitTangentVector(), coordinatetransform::getUnitTangentVectorX(), coordinatetransform::getUnitTangentVectorY(), IdealMapper::makeFocus(), OrbitTracker::makeFocus(), LinearMapper::makeFocus(), sech(), sinh(), tanh(), RDM< Value_type, Size_type >::transform(), MultipoleTCurvedVarRadius::transformBField(), and matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_().
Cotangent.
Referenced by Harmonics< Value_type, Size_type >::computeMap().
Exponential.
Definition at line 165 of file TpsMath.h.
References Tps< T >::getTruncOrder(), T, and Tps< T >::Taylor().
Referenced by Distribution::applyEmissModelNonEquil(), SecondaryEmissionPhysics::betai(), SecondaryEmissionPhysics::betaiapprox(), SecondaryEmissionPhysics::calcDeltae(), SecondaryEmissionPhysics::calcDeltar(), SecondaryEmissionPhysics::calcEmiNum(), Bend2D::calcEngeFunction(), FM1DProfile1::computeFringe(), Distribution::createPriPart(), BeamStrippingPhysics::csChebyshevFitting(), erf(), Util::erfinv(), errfc(), exp(), SecondaryEmissionPhysics::gammpapprox(), BeamStrippingPhysics::gasStripping(), SecondaryEmissionPhysics::gcf(), FM1DProfile2::getFieldstrength(), VerticalFFAMagnet::getFieldValue(), endfieldmodel::Enge::GN(), SecondaryEmissionPhysics::gser(), SecondaryEmissionPhysics::invbetai(), SecondaryEmissionPhysics::invgammp(), BeamStrippingPhysics::lorentzStripping(), SecondaryEmissionPhysics::nSec(), ApplyField< T >::operator()(), GlobalFunctions::_pow::operator()(), GlobalFunctions::_exp::operator()(), LOMB_class::period(), LOMB_class::signi(), TpsWerrf(), matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_(), ThinTracker::visitBeamBeam(), and Werrf().
Natural logarithm.
Definition at line 182 of file TpsMath.h.
References Tps< T >::getTruncOrder(), T, and Tps< T >::Taylor().
Referenced by MultipoleT::apply(), SecondaryEmissionPhysics::betai(), SecondaryEmissionPhysics::betaiapprox(), CSRIGFWakeFunction::calculateGreenFunction(), CollimatorPhysics::computeCoulombScattering(), CollimatorPhysics::computeEnergyLoss(), Distribution::createOpalE(), BeamStrippingPhysics::csChebyshevFitting(), TrimCoilMirrored::doApplyField(), Util::erfinv(), Dynamic::execute(), Static::execute(), FNormalForm< N >::FNormalForm(), SecondaryEmissionPhysics::gammln(), SecondaryEmissionPhysics::gammpapprox(), Random::gauss(), SecondaryEmissionPhysics::gaussRand(), SecondaryEmissionPhysics::gcf(), Distribution::generateLongFlattopT(), Distribution::GaussianLikeBehavior::get(), ScalingFFAMagnet::getFieldValueCylindrical(), Distribution::getTEmission(), coordinatetransform::CoordinateTransform::getUnitTangentVector(), coordinatetransform::getUnitTangentVectorX(), coordinatetransform::getUnitTangentVectorY(), SecondaryEmissionPhysics::gser(), FFTBoxPoissonSolver::integratedGreensFunction(), FFTPoissonSolver::integratedGreensFunction(), SecondaryEmissionPhysics::invbetai(), InverseGauss(), SecondaryEmissionPhysics::invgammp(), MapAnalyser::linTAnalyze(), log(), NormalForm::NormalForm(), GlobalFunctions::_log::operator()(), IndexMap::print(), FM1DProfile2::readMap(), Distribution::setDistParametersFlattop(), Distribution::setDistParametersGauss(), Distribution::setEmissionTime(), Distribution::setupEmissionModelNonEquil(), sgSmooth(), FFTBoxPoissonSolver::shiftedIntGreensFunction(), FFTPoissonSolver::shiftedIntGreensFunction(), Util::toStringWithThousandSep(), MultipoleTCurvedVarRadius::transformBField(), and matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_().
Integer power.
Definition at line 76 of file TpsMath.h.
References Tps< T >::inverse(), and T.
Referenced by RBend::addKR(), Distribution::adjustPhaseSpace(), Distribution::applyEmissModelNonEquil(), polynomial::RecursionRelation::applyOperator(), polynomial::RecursionRelationTwo::applyOperator(), matheval::detail::grammar< real_t, Iterator >::bfunc_::bfunc_(), PartBunchBase< T, Dim >::calcBeamParameters(), MultiBunchHandler::calcBunchBeamParameters(), SecondaryEmissionPhysics::calcDeltae(), SecondaryEmissionPhysics::calcDeltar(), SecondaryEmissionPhysics::calcDeltats(), SecondaryEmissionPhysics::calcEmiNum(), EnvelopeBunch::calcEnergyChirp(), Bend2D::calcEngeFunction(), Bend2D::calcEntranceFringeField(), Bend2D::calcExitFringeField(), SecondaryEmissionPhysics::calcProb(), CSRWakeFunction::calcPsi(), CSRIGFWakeFunction::calcPsi(), MSplit::calcul(), Aperture::calcul(), Bend2D::calculateBendAngle(), CSRIGFWakeFunction::calculateContributionAfter(), CSRWakeFunction::calculateContributionAfter(), CSRWakeFunction::calculateContributionInside(), CSRIGFWakeFunction::calculateGreenFunction(), Fieldmap::checkMap(), SocialNetworkGraph< TopoDiscoveryStrategy_t >::chooseRandomNeighbor(), CollimatorPhysics::computeCoulombScattering(), RootFinderForCSR::computeDerivative(), CollimatorPhysics::computeEnergyLoss(), FM1DElectroStatic_fast::computeFieldDerivatives(), FM1DMagnetoStatic_fast::computeFieldDerivatives(), FM1DDynamic_fast::computeFieldDerivatives(), FM1DElectroStatic::computeFieldOffAxis(), FM1DMagnetoStatic::computeFieldOffAxis(), FM1DDynamic::computeFieldOffAxis(), FM1DElectroStatic_fast::computeFieldOffAxis(), FM1DDynamic_fast::computeFieldOffAxis(), FM1DMagnetoStatic_fast::computeFieldOffAxis(), FM1DElectroStatic::computeFieldOnAxis(), FM1DMagnetoStatic::computeFieldOnAxis(), FM1DDynamic::computeFieldOnAxis(), FM1DProfile1::computeFringe(), LossDataSink::computeSetStatistics(), RootFinderForCSR::computeValue(), RootFinderForCSR::computeValueGSL(), Distribution::converteVToBetaGamma(), FM1DDynamic::convertHeaderData(), FM1DDynamic_fast::convertHeaderData(), Distribution::createOpalE(), SimulatedBinaryCrossover< T >::crossover(), BeamStrippingPhysics::csAnalyticFunctionNakai(), BeamStrippingPhysics::csAnalyticFunctionTabata(), EnvelopeBunch::derivs(), TrimCoilMirrored::doApplyField(), Distribution::doRestartOpalCycl(), DragtFinnNormalForm< N >::DragtFinnNormalForm(), Distribution::emitParticles(), Bend2D::estimateFieldAdjustmentStep(), DragtFinnMap< N >::factorBerzForestIrwin(), ParallelCyclotronTracker::finalizeTracking_m(), RBend::findChordLength(), Bend2D::findIdealBendParameters(), ParallelSliceTracker::findStartPosition(), ParallelTTracker::findStartPosition(), FNormalForm< N >::FNormalForm(), Distribution::generateBinomial(), Distribution::generateFlattopT(), Distribution::generateFlattopZ(), Distribution::generateGaussZ(), Distribution::generateTransverseGauss(), Distribution::MDependentBehavior::get(), PartBunchBase< T, Dim >::get_pmean_Distribution(), interpolation::PPSolveFactory::getDerivPoints(), ScalingFFAMagnet::getFieldValueCylindrical(), RFCavity::getMomentaKick(), CavityAutophaser::getMomentum(), Bend2D::getOutline(), Util::getP(), Bend2D::getSurfaceMesh(), Corrector::goOnline(), matheval::detail::grammar< real_t, Iterator >::grammar(), Cyclotron::gutdf5d(), RootFinderForCSR::hasPositiveRealRoots(), RBend3D::initialise(), SecondaryEmissionPhysics::invbetai(), SecondaryEmissionPhysics::invgammp(), Multipole::isFocusing(), mslang::Ellipse::isInside(), ElementBase::isInsideTransverse(), Profile::Leff2(), LOMB_class::moment(), NormalForm::NormalForm(), SecondaryEmissionPhysics::nSec(), GlobalFunctions::_pow::operator()(), LOMB_class::period(), pow(), H5PartWrapperForPC::readStepHeader(), PartBunchBase< T, Dim >::resetPartBinID2(), ParallelCyclotronTracker::RFkick(), RootFinderForCSR::RootFinderForCSR(), savgol(), Bend2D::setBendStrength(), Corrector::setDesignEnergy(), Bend2D::setFieldCalcParam(), Distribution::setupEmissionModelNonEquil(), Distribution::setupParticleBins(), sgSmooth(), LOMB_class::signi(), FM3DMagnetoStaticExtended::smoothData(), Migrad::symmetricEigen(), EnvelopeBunch::timeStep(), Util::toStringWithThousandSep(), TpsWerrf(), RBend3D::trackRefParticleThrough(), Bend2D::treatAsDrift(), Werrf(), and mslang::Ellipse::writeGnuplot().
Sine.
Definition at line 111 of file TpsMath.h.
References cos(), Tps< T >::getTruncOrder(), T, and Tps< T >::Taylor().
Referenced by Harmonics< Value_type, Size_type >::__Mb6(), Harmonics< Value_type, Size_type >::__Mb6k(), TravelingWave::addKR(), RFCavity::addKR(), Ring::appendElement(), mslang::Repeat::apply(), TravelingWave::apply(), VariableRFCavity::apply(), VariableRFCavityFringeField::apply(), MultipoleT::apply(), RFCavity::apply(), Cyclotron::apply(), Distribution::applyEmissModelAstra(), Distribution::applyEmissModelNonEquil(), ThickMapper::applyEntranceFringe(), ThickMapper::applyExitFringe(), CollimatorPhysics::applyRandomRotation(), mslang::Rotation::applyRotation(), CollimatorPhysics::applyRotation(), ParallelPlate::applyToReferenceParticle(), TravelingWave::applyToReferenceParticle(), RFCavity::applyToReferenceParticle(), ParallelCyclotronTracker::bunchDumpPhaseSpaceData(), MSplit::calcul(), Aperture::calcul(), Aperture::calcul_Apert(), Bend2D::calculateBendAngle(), Bend2D::calculateRefTrajectory(), Fieldmap::checkMap(), OpalBeamline::compute3DLattice(), mslang::Ellipse::computeBoundingBox(), CollimatorPhysics::computeCoulombScattering(), FM1DElectroStatic_fast::computeFieldDerivatives(), FM1DMagnetoStatic_fast::computeFieldDerivatives(), Astra1D_fast::computeFieldDerivatives(), FM1DDynamic_fast::computeFieldDerivatives(), FM1DElectroStatic::computeFieldOnAxis(), FM1DMagnetoStatic::computeFieldOnAxis(), FM1DDynamic::computeFieldOnAxis(), Harmonics< Value_type, Size_type >::computeMap(), OrbitThreader::computeMaximalImplicitDrift(), ClosedOrbitFinder< Value_type, Size_type, Stepper >::computeTune(), SectorField::convertToCartesian(), SectorField::convertToPolar(), cos(), cot(), MapAnalyser::createRotMatrix_m(), csc(), RingSection::doesOverlap(), ParallelCyclotronTracker::dumpAzimuthAngles_m(), ParallelCyclotronTracker::dumpThetaEachTurn_m(), DragtFinnMap< N >::factorBerzForestIrwin(), OpalOffset::OpalLocalCartesianOffset::fillRegisteredAttributes(), RBend::findChordLength(), Bend2D::findIdealBendParameters(), four1(), Distribution::generateBinomial(), Distribution::generateLongFlattopT(), RBendGeometry::getArcLength(), TravelingWave::getAutoPhaseEstimate(), RFCavity::getAutoPhaseEstimate(), MeshGenerator::getCylinder(), TravelingWave::getdA(), RFCavity::getdA(), TravelingWave::getdB(), RFCavity::getdB(), TravelingWave::getdE(), RFCavity::getdE(), Astra1DDynamic::getFieldDerivative(), FM1DDynamic::getFieldDerivative(), FM1DElectroStatic::getFieldDerivative(), FM1DMagnetoStatic::getFieldDerivative(), Astra1DDynamic::getFieldstrength(), Astra1DElectroStatic::getFieldstrength(), Astra1DMagnetoStatic::getFieldstrength(), SectorMagneticFieldMap::getFieldstrength(), ScalingFFAMagnet::getFieldValue(), RFCavity::getMomentaKick(), Ring::getNextNormal(), Ring::getNextPosition(), Bend2D::getOutline(), getQuaternion(), ParallelCyclotronTracker::getQuaternionTwoVectors(), Aperture::getShape(), Bend2D::getSurfaceMesh(), Util::getTaitBryantAngles(), coordinatetransform::CoordinateTransform::getUnitTangentVector(), coordinatetransform::getUnitTangentVectorX(), Offset::globalCylindricalOffset(), ParallelCyclotronTracker::globalToLocal(), TravelingWave::initialise(), RFCavity::initialise(), Offset::localCylindricalOffset(), ParallelCyclotronTracker::localToGlobal(), IdealMapper::makeFocus(), OrbitTracker::makeFocus(), LinearMapper::makeFocus(), SecondaryEmissionPhysics::nSec(), GlobalFunctions::_sin::operator()(), Line::parse(), LOMB_class::period(), H5PartWrapperForPT::readStepHeader(), Offset::rotate(), ParallelCyclotronTracker::rotateAroundX(), ParallelCyclotronTracker::rotateAroundZ(), MultipoleTBase::rotateFrame(), MultipoleT::rotateFrame(), MultipoleTBase::rotateFrameInverse(), MultipoleT::rotateFrameInverse(), Rotation3D::Rotation3D(), ParallelCyclotronTracker::seoMode_m(), FM1DProfile2::setEdgeConstants(), Bend2D::setFieldCalcParam(), ConcreteVar::setInternalValue(), sin(), sinti(), tan(), EnvelopeBunch::timeStep(), TpsWerrf(), RBend3D::trackRefParticleThrough(), RDM< Value_type, Size_type >::transform(), MultipoleTCurvedConstRadius::transformBField(), MultipoleTCurvedVarRadius::transformBField(), MultipoleTCurvedConstRadius::transformCoords(), MultipoleT::transformCoords(), matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_(), OpalSBend::update(), OpalRBend::update(), OpalRBend3D::update(), OpalElement::update(), RingSection::updateComponentOrientation(), Offset::updateGeometry(), ParallelCyclotronTracker::visitCyclotron(), MSplit::visitRBend(), Aperture::visitRBend(), ThinMapper::visitRFCavity(), OrbitTracker::visitRFCavity(), ThinTracker::visitRFCavity(), ThickMapper::visitRFCavity(), LinearMapper::visitRFCavity(), TransportMapper::visitRFCavity(), ParallelCyclotronTracker::visitRing(), ThinMapper::visitSolenoid(), OrbitTracker::visitSolenoid(), ThinTracker::visitSolenoid(), ThickMapper::visitSolenoid(), LinearMapper::visitSolenoid(), TransportMapper::visitSolenoid(), DumpEMFields::writeFieldLine(), Rotation3D::XRotation(), Rotation3D::YRotation(), and Rotation3D::ZRotation().
Hyperbolic sine.
Definition at line 204 of file TpsMath.h.
References cosh(), Tps< T >::getTruncOrder(), T, and Tps< T >::Taylor().
Referenced by Harmonics< Value_type, Size_type >::__Mb6k(), MSplit::calcul(), Aperture::calcul(), Harmonics< Value_type, Size_type >::computeMap(), cosh(), coth(), csch(), DragtFinnMap< N >::factorBerzForestIrwin(), IdealMapper::makeFocus(), OrbitTracker::makeFocus(), LinearMapper::makeFocus(), sinh(), tanh(), RDM< Value_type, Size_type >::transform(), and matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_().
Square root.
Definition at line 91 of file TpsMath.h.
References Tps< T >::getTruncOrder(), T, and Tps< T >::Taylor().
Referenced by Harmonics< Value_type, Size_type >::__Mb6k(), AmrOpenBoundary< Level >::abc1_m(), AmrOpenBoundary< Level >::abc2_m(), AmrOpenBoundary< Level >::abc3_m(), RBend::addKT(), FlexibleCollimator::apply(), GreenWakeFunction::apply(), Degrader::apply(), P3MPoissonSolver::applyConstantFocusing(), Mapper::applyDrift(), Tracker::applyDrift(), ThickMapper::applyDrift(), LieMapper::applyDrift(), TransportMapper::applyDrift(), Distribution::applyEmissModelAstra(), Distribution::applyEmissModelNonEquil(), ThickMapper::applyEntranceFringe(), ThickMapper::applyExitFringe(), IdealMapper::applyLinearMap(), OrbitTracker::applyLinearMap(), LinearMapper::applyLinearMap(), CollimatorPhysics::applyRandomRotation(), Mapper::applyTransform(), Tracker::applyTransform(), OrbitTracker::applyTransform(), LinearMapper::applyTransform(), TransportMapper::applyTransform(), TransportMapper::applyTransportMap(), Hamiltonian::bendFringe(), bessj(), SecondaryEmissionPhysics::betaiapprox(), ParallelCyclotronTracker::bunchDumpPhaseSpaceData(), ParallelCyclotronTracker::bunchDumpStatData(), EnvelopeBunch::calcBeamParameters(), PartBunchBase< T, Dim >::calcBeamParameters(), PartBunchBase< T, Dim >::calcBeamParametersInitial(), MultiBunchHandler::calcBunchBeamParameters(), PartBunchBase< T, Dim >::calcEMean(), EnvelopeBunch::calcEmittance(), EnvelopeBunch::calcEnergyChirp(), PartBunchBase< T, Dim >::calcGammas(), PartBunchBase< T, Dim >::calcGammas_cycl(), EnvelopeBunch::calcI(), MSplit::calcul(), Aperture::calcul(), Aperture::calcul_Apert(), SpecializedGreensFunction< 3 >::calculate(), Bend2D::calculateBendAngle(), CSRIGFWakeFunction::calculateGreenFunction(), Bend2D::calculateRefTrajectory(), PluginElement::changeWidth(), Fieldmap::checkMap(), BeamStripping::checkPoint(), BeamStripping::checkPressure(), CollimatorPhysics::computeCoulombScattering(), CollimatorPhysics::computeEnergyLoss(), EnvelopeSlice::computeGamma(), Harmonics< Value_type, Size_type >::computeMap(), ClosedOrbitFinder< Value_type, Size_type, Stepper >::computeOrbitProperties(), ParallelCyclotronTracker::computePathLengthUpdate(), LaserProfile::computeProfileStatistics(), ParallelCyclotronTracker::computeRadius(), PartBunch::computeSelfFields(), PartBunch::computeSelfFields_cycl(), AmrBoxLib::computeSelfFields_cycl(), LossDataSink::computeSetStatistics(), ParallelCyclotronTracker::computeSpaceChargeFields_m(), ConcreteVar::ConcreteVar(), Distribution::converteVToBetaGamma(), SectorField::convertToPolar(), PartBunchBase< T, Dim >::correctEnergy(), Distribution::createMatchedGaussDistribution(), Distribution::createOpalE(), Distribution::createPriPart(), EnvelopeBunch::cSpaceCharge(), ParallelCyclotronTracker::deleteParticle(), RK4< FieldFunction, Arguments >::derivate_m(), Migrad::derivatives(), EnvelopeBunch::derivs(), Stripper::doCheck(), Probe::doCheck(), BeamStrippingPhysics::doPhysics(), Distribution::doRestartOpalCycl(), Hamiltonian::drift(), ParallelCyclotronTracker::dumpThetaEachTurn_m(), SigmaGenerator< Value_type, Size_type >::eigsolve_m(), Distribution::emitParticles(), BoundaryGeometry::emitSecondaryFurmanPivi(), BoundaryGeometry::emitSecondaryVaughan(), EnvelopeSlice::EnvelopeSlice(), erf(), Util::erfinv(), Bend2D::estimateFieldAdjustmentStep(), euclidean_norm(), LMDif::execute(), ParallelSliceTracker::execute(), Insertion::fill(), ParallelCyclotronTracker::finalizeTracking_m(), RBend::findChordLength(), Bend2D::findIdealBendParameters(), ClosedOrbitFinder< Value_type, Size_type, Stepper >::findOrbit(), ClosedOrbitFinder< Value_type, Size_type, Stepper >::findOrbitOfEnergy_m(), ParallelSliceTracker::findStartPosition(), ParallelTTracker::findStartPosition(), SecondaryEmissionPhysics::gammpapprox(), ParallelCyclotronTracker::gapCrossKick_m(), Random::gauss(), SecondaryEmissionPhysics::gaussRand(), Distribution::generateAstraFlattopT(), Distribution::generateBinomial(), Distribution::generateLongFlattopT(), Distribution::MDependentBehavior::get(), Distribution::GaussianLikeBehavior::get(), PartBunchBase< T, Dim >::get_pmean_Distribution(), Euclid3DGeometry::getArcLength(), RFCavity::getAutoPhaseEstimate(), Rotation3D::getAxis(), MapAnalyser::getBlockDiagonal_m(), RbendMap::getBodyMap(), PartBunchBase< T, Dim >::getBoundingSphere(), TravelingWave::getdT(), RFCavity::getdT(), CavityAutophaser::getEnergyMeV(), FM2DMagnetoStatic::getFieldDerivative(), FM2DElectroStatic::getFieldstrength(), FM2DMagnetoStatic::getFieldstrength(), FM2DDynamic::getFieldstrength(), ScalingFFAMagnet::getFieldValue(), Util::getGamma(), RbendMap::getHamiltonian(), ConcreteVar::getInternalValue(), PartBunchBase< T, Dim >::getLocalBoundingSphere(), RFCavity::getMomentaKick(), CavityAutophaser::getMomentum(), Util::getP(), CavityAutophaser::getPhaseAtMaxEnergy(), Survey::getPhi(), getQuaternion(), ParallelCyclotronTracker::getQuaternionTwoVectors(), Ring::getRingMaxR(), Ring::getRingMinR(), Distribution::getTEmission(), RbendMap::getTransformMap(), RingSection::getVirtualBoundingBox(), Corrector::goOnline(), RootFinderForCSR::hasPositiveRealRoots(), Migrad::hessenberg(), ComplexEigen::hqr(), FComplexEigen< N >::hqr(), FDoubleEigen< N >::hqr(), DoubleEigen::hqr(), ComplexEigen::hqr2(), FComplexEigen< N >::hqr2(), FDoubleEigen< N >::hqr2(), DoubleEigen::hqr2(), ParallelCyclotronTracker::initDistInGlobalFrame(), RBend3D::initialise(), BoundaryGeometry::initialize(), SigmaGenerator< Value_type, Size_type >::initialize(), OrbitThreader::integrate(), FFTBoxPoissonSolver::integratedGreensFunction(), FFTPoissonSolver::integratedGreensFunction(), SecondaryEmissionPhysics::invbetai(), InverseGauss(), Migrad::invertSymmetric(), SecondaryEmissionPhysics::invgammp(), FM2DMagnetoStatic::isInside(), FM2DElectroStatic::isInside(), FM2DDynamic::isInside(), BorisPusher::kick(), SigmaGenerator< Value_type, Size_type >::L2ErrorNorm(), Quaternion::length(), linfit(), MapAnalyser::linTAnalyze(), CorrectionBase::listCorrectors(), CorrectionBase::listMonitors(), BeamStrippingPhysics::lorentzStripping(), IdealMapper::makeFocus(), OrbitTracker::makeFocus(), LinearMapper::makeFocus(), SocialNetworkGraph< TopoDiscoveryStrategy_t >::manhattenDistance(), LOMB_class::moment(), RingSection::normalise(), ParallelCyclotronTracker::normalizeQuaternion(), ParallelCyclotronTracker::normalizeVector(), SecondaryEmissionPhysics::nSec(), SumErrSqRadialPeak::operator()(), SumErrSq::operator()(), GlobalFunctions::_sqrt::operator()(), GreenWakeFunction::Wake::operator()(), ApplyField< T >::operator()(), NormalForm::orderModes(), DragtFinnNormalForm< N >::orderModes(), FNormalForm< N >::orderModes(), DragtFinnMap< N >::orderModes(), ComplexEigen::orthes(), FComplexEigen< N >::orthes(), BoundaryGeometry::partInside(), LOMB_class::period(), OpalElement::printMultipoleStrength(), BorisPusher::push(), ParallelCyclotronTracker::push(), LF2< FieldFunction, Arguments >::push_m(), Twiss::put(), QRSolver::QRSolver(), Hamiltonian::quadrupole(), Quaternion::Quaternion(), QRSolver::R_to_S(), Hamiltonian::rbend(), H5PartWrapperForPC::readStepHeader(), PartBunchBase< T, Dim >::resetPartBinID2(), ParallelCyclotronTracker::RFkick(), Expressions::Rmsa(), Rotation3D::Rotation3D(), EnvelopeBunch::runStats(), SampleGaussianSequence::SampleGaussianSequence(), Hamiltonian::sbend(), scaled_norm(), Bend2D::setBendStrength(), PartData::setBeta(), EnvelopeBunch::setBinnedLShape(), OrbitThreader::setDesignEnergy(), Corrector::setDesignEnergy(), PluginElement::setDimensions(), Distribution::setDistParametersFlattop(), Distribution::setDistParametersGauss(), PartData::setE(), Distribution::setEmissionTime(), EnvelopeBunch::setEnergy(), PartData::setGamma(), PluginElement::setGeom(), SocialNetworkGraph< TopoDiscoveryStrategy_t >::setNetworkNeighbors(), MapAnalyser::setNMatrix_m(), PartData::setP(), EnvelopeBunch::setP(), Distribution::setupEmissionModelNonEquil(), Distribution::setupParticleBins(), FFTBoxPoissonSolver::shiftedIntGreensFunction(), FFTPoissonSolver::shiftedIntGreensFunction(), SigmaGenerator< Value_type, Size_type >::SigmaGenerator(), Micado::solve(), QRDecomposition::solve(), QRSolver::solveS(), PartBins::sortArray(), sqrt(), Migrad::symmetricEigen(), EnvelopeBunch::timeStep(), TpsWerrf(), TravelingWave::trackOnAxisParticle(), RFCavity::trackOnAxisParticle(), RBend3D::trackRefParticleThrough(), Bend2D::treatAsDrift(), matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_(), ThickTracker::update_m(), Offset::updateGeometry(), ThickTracker::updateParticle_m(), ThinTracker::visitBeamBeam(), ParallelCyclotronTracker::visitCyclotron(), LieMapper::visitMultipole(), ThickMapper::visitMultipole(), ThickMapper::visitRBend(), LieMapper::visitRBend(), ThinMapper::visitRFCavity(), ThinTracker::visitRFCavity(), ThickMapper::visitRFCavity(), ParallelCyclotronTracker::visitRing(), ThickMapper::visitSBend(), LieMapper::visitSBend(), ThickTracker::visitSBend(), ThinMapper::visitSolenoid(), ThinTracker::visitSolenoid(), ThickMapper::visitSolenoid(), LieMapper::visitSolenoid(), TransportMapper::visitSolenoid(), Werrf(), and mslang::Ellipse::writeGnuplot().
Tangent.
Definition at line 147 of file TpsMath.h.
Referenced by OrbitTracker::applyEntranceFringe(), ThickMapper::applyEntranceFringe(), LinearMapper::applyEntranceFringe(), TransportMapper::applyEntranceFringe(), OrbitTracker::applyExitFringe(), ThickMapper::applyExitFringe(), LinearMapper::applyExitFringe(), TransportMapper::applyExitFringe(), mslang::Shear::applyShear(), MSplit::calcul(), Aperture::calcul(), Bend2D::calculateBendAngle(), Bend2D::calculateRefTrajectory(), Harmonics< Value_type, Size_type >::computeMap(), Hamiltonian::fringeField(), RbendMap::getEntranceFringeMap(), RBendGeometry::getEntrancePatch(), RbendMap::getExitFringeMap(), RBendGeometry::getExitPatch(), Aperture::getShape(), GlobalFunctions::_tan::operator()(), Bend2D::setExitAngle(), Bend2D::setFieldCalcParam(), RBend3D::trackRefParticleThrough(), matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_(), and mslang::Ellipse::writeGnuplot().
Hyperbolic tangent.
Definition at line 240 of file TpsMath.h.
References cosh(), and sinh().
Referenced by MultipoleT::apply(), OpalVariableRFCavityFringeField::fillRegisteredAttributes(), endfieldmodel::Tanh::getNegTanh(), endfieldmodel::Tanh::getTanh(), coordinatetransform::CoordinateTransform::getUnitTangentVector(), coordinatetransform::getUnitTangentVectorX(), coordinatetransform::getUnitTangentVectorY(), MultipoleTCurvedVarRadius::transformBField(), matheval::detail::grammar< real_t, Iterator >::ufunc_::ufunc_(), and OpalVariableRFCavityFringeField::update().
