TpsMath.h File Reference

#include "Algebra/Tps.h"
#include "Utilities/DomainError.h"
#include <cmath>

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Functions
template<class T>
Tps< T >	pow (const Tps< T > &x, int y)
	Integer power.
template<class T>
Tps< T >	sqrt (const Tps< T > &x)
	Square root.
template<class T>
Tps< T >	sin (const Tps< T > &x)
	Sine.
template<class T>
Tps< T >	cos (const Tps< T > &x)
	Cosine.
template<class T>
Tps< T >	tan (const Tps< T > &x)
	Tangent.
template<class T>
Tps< T >	cot (const Tps< T > &x)
	Cotangent.
template<class T>
Tps< T >	sec (const Tps< T > &x)
	Secant.
template<class T>
Tps< T >	csc (const Tps< T > &x)
	Cosecant.
template<class T>
Tps< T >	exp (const Tps< T > &x)
	Exponential.
template<class T>
Tps< T >	log (const Tps< T > &x)
	Natural logarithm.
template<class T>
Tps< T >	sinh (const Tps< T > &x)
	Hyperbolic sine.
template<class T>
Tps< T >	cosh (const Tps< T > &x)
	Hyperbolic cosine.
template<class T>
Tps< T >	tanh (const Tps< T > &x)
	Hyperbolic tangent.

Function Documentation

cos()

template<class T>

Tps< T > cos

(

const Tps< T > &

x

)

Cosine.

Definition at line 129 of file TpsMath.h.

References cos(), Tps< T >::getTruncOrder(), sin(), and Tps< T >::Taylor().

Referenced by mslang::Repeat::apply(), mslang::Rotation::applyRotation(), OscillatingField< Field >::Bfield(), OpalBeamline::compute3DLattice(), mslang::Ellipse::computeBoundingBox(), ScatteringPhysics::computeCoulombScattering(), _Astra1D_fast::computeFieldDerivatives(), _FM1DDynamic_fast::computeFieldDerivatives(), _FM1DElectroStatic_fast::computeFieldDerivatives(), _FM1DMagnetoStatic_fast::computeFieldDerivatives(), _FM1DDynamic::computeFieldOnAxis(), _FM1DElectroStatic::computeFieldOnAxis(), _FM1DMagnetoStatic::computeFieldOnAxis(), ClosedOrbitFinder< Value_type, Size_type, Stepper >::computeTune(), cos(), cos(), OscillatingField< Field >::Efield(), MeshGenerator::getCylinder(), _Astra1DDynamic::getFieldDerivative(), _FM1DDynamic::getFieldDerivative(), _FM1DElectroStatic::getFieldDerivative(), _FM1DMagnetoStatic::getFieldDerivative(), _Astra1DDynamic::getFieldstrength(), _Astra1DElectroStatic::getFieldstrength(), _Astra1DMagnetoStatic::getFieldstrength(), SectorMagneticFieldMap::getFieldstrength(), MultipoleTCurvedVarRadius::localCartesianToOpalCartesian(), GlobalFunctions::_cos::operator()(), Line::parse(), LOMB_class::period(), sec(), sin(), tan(), MultipoleTCurvedVarRadius::transformBField(), MultipoleTCurvedVarRadius::transformCoords(), and mslang::Ellipse::writeGnuplot().

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cosh()

template<class T>

Tps< T > cosh

(

const Tps< T > &

x

)

Hyperbolic cosine.

Definition at line 222 of file TpsMath.h.

References cosh(), Tps< T >::getTruncOrder(), sinh(), and Tps< T >::Taylor().

Referenced by cosh(), cosh(), sinh(), tanh(), and MultipoleTCurvedVarRadius::transformBField().

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cot()

template<class T>

Tps< T > cot

(

const Tps< T > &

x

)

Cotangent.

csc()

template<class T>

Tps< T > csc

(

const Tps< T > &

x

)

Cosecant.

Definition at line 159 of file TpsMath.h.

References Tps< T >::inverse(), and sin().

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exp()

template<class T>

Tps< T > exp

(

const Tps< T > &

x

)

Exponential.

Definition at line 165 of file TpsMath.h.

References exp(), Tps< T >::getTruncOrder(), and Tps< T >::Taylor().

Referenced by Distribution::applyEmissModelNonEquil(), _FM1DProfile1::computeFringe(), Distribution::createDistributionMultiGauss(), exp(), exp(), endfieldmodel::Enge::gN(), GlobalFunctions::_exp::operator()(), GlobalFunctions::_pow::operator()(), LOMB_class::period(), and LOMB_class::signi().

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log()

template<class T>

Tps< T > log

(

const Tps< T > &

x

)

Natural logarithm.

Definition at line 182 of file TpsMath.h.

References Tps< T >::getTruncOrder(), log(), and Tps< T >::Taylor().

Referenced by Random::gauss(), FFTBoxPoissonSolver::integratedGreensFunction(), FFTPoissonSolver::integratedGreensFunction(), log(), log(), GlobalFunctions::_log::operator()(), IndexMap::print(), _FM1DProfile2::readMap(), FFTBoxPoissonSolver::shiftedIntGreensFunction(), FFTPoissonSolver::shiftedIntGreensFunction(), and MultipoleTCurvedVarRadius::transformBField().

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pow()

template<class T>

Tps< T > pow	(	const Tps< T > &	x,
		int	y )

Integer power.

Definition at line 76 of file TpsMath.h.

References Tps< T >::inverse().

Referenced by polynomial::RecursionRelation::applyOperator(), polynomial::RecursionRelationTwo::applyOperator(), _FM1DDynamic_fast::computeFieldDerivatives(), _FM1DElectroStatic_fast::computeFieldDerivatives(), _FM1DMagnetoStatic_fast::computeFieldDerivatives(), _FM1DDynamic::computeFieldOffAxis(), _FM1DDynamic_fast::computeFieldOffAxis(), _FM1DElectroStatic::computeFieldOffAxis(), _FM1DElectroStatic_fast::computeFieldOffAxis(), _FM1DMagnetoStatic::computeFieldOffAxis(), _FM1DMagnetoStatic_fast::computeFieldOffAxis(), _FM1DDynamic::computeFieldOnAxis(), _FM1DElectroStatic::computeFieldOnAxis(), _FM1DMagnetoStatic::computeFieldOnAxis(), _FM1DDynamic::convertHeaderData(), _FM1DDynamic_fast::convertHeaderData(), SimulatedBinaryCrossover< T >::crossover(), TpsData::fillSubst(), interpolation::PPSolveFactory::getDerivPoints(), matheval::detail::grammar< real_t, Iterator >::grammar(), LOMB_class::moment(), GlobalFunctions::_pow::operator()(), FTpsData< N >::operator=(), TpsData::operator=(), LOMB_class::period(), PETE_apply(), savgol(), LOMB_class::signi(), and Werrf().

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sec()

template<class T>

Tps< T > sec

(

const Tps< T > &

x

)

Secant.

Definition at line 153 of file TpsMath.h.

References cos(), and Tps< T >::inverse().

Referenced by PyOpal::Field::getElementEndNormal(), PyOpal::Field::getElementEndPosition(), PyOpal::Field::getElementName(), PyOpal::Field::getElementStartNormal(), PyOpal::Field::getElementStartPosition(), and Ring::getSection().

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sin()

template<class T>

Tps< T > sin

(

const Tps< T > &

x

)

Sine.

Definition at line 111 of file TpsMath.h.

References cos(), Tps< T >::getTruncOrder(), sin(), and Tps< T >::Taylor().

Referenced by mslang::Repeat::apply(), mslang::Rotation::applyRotation(), OpalBeamline::compute3DLattice(), mslang::Ellipse::computeBoundingBox(), ScatteringPhysics::computeCoulombScattering(), _Astra1D_fast::computeFieldDerivatives(), _FM1DDynamic_fast::computeFieldDerivatives(), _FM1DElectroStatic_fast::computeFieldDerivatives(), _FM1DMagnetoStatic_fast::computeFieldDerivatives(), _FM1DDynamic::computeFieldOnAxis(), _FM1DElectroStatic::computeFieldOnAxis(), _FM1DMagnetoStatic::computeFieldOnAxis(), cos(), csc(), RBendGeometry::getArcLength(), MeshGenerator::getCylinder(), _Astra1DDynamic::getFieldDerivative(), _FM1DDynamic::getFieldDerivative(), _FM1DElectroStatic::getFieldDerivative(), _FM1DMagnetoStatic::getFieldDerivative(), _Astra1DDynamic::getFieldstrength(), _Astra1DElectroStatic::getFieldstrength(), _Astra1DMagnetoStatic::getFieldstrength(), SectorMagneticFieldMap::getFieldstrength(), MultipoleTCurvedVarRadius::localCartesianToOpalCartesian(), GlobalFunctions::_sin::operator()(), Line::parse(), LOMB_class::period(), PETE_apply(), sin(), sinti(), tan(), MultipoleTCurvedVarRadius::transformBField(), MultipoleTCurvedVarRadius::transformCoords(), OpalRBend3D::update(), OpalRBend::update(), and OpalSBend::update().

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sinh()

template<class T>

Tps< T > sinh

(

const Tps< T > &

x

)

Hyperbolic sine.

Definition at line 204 of file TpsMath.h.

References cosh(), Tps< T >::getTruncOrder(), sinh(), and Tps< T >::Taylor().

Referenced by cosh(), PETE_apply(), sinh(), and tanh().

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sqrt()

template<class T>

Tps< T > sqrt

(

const Tps< T > &

x

)

Square root.

Definition at line 91 of file TpsMath.h.

References Tps< T >::getTruncOrder(), sqrt(), and Tps< T >::Taylor().

Referenced by GreenWakeFunction::apply(), Hamiltonian::bendFringe(), P3MGreensFunction< 3 >::calculate(), SpecializedGreensFunction< 3 >::calculate(), Hamiltonian::drift(), euclidean_norm(), ParallelTTracker::findStartPosition(), Random::gauss(), CavityAutophaser::getPhaseAtMaxEnergy(), getQuaternion(), RootFinderForCSR::hasPositiveRealRoots(), OrbitThreader::integrate(), FFTBoxPoissonSolver::integratedGreensFunction(), FFTPoissonSolver::integratedGreensFunction(), SocialNetworkGraph< TopoDiscoveryStrategy_t >::manhattenDistance(), LOMB_class::moment(), GlobalFunctions::_sqrt::operator()(), SumErrSq::operator()(), LOMB_class::period(), PETE_apply(), Hamiltonian::quadrupole(), Hamiltonian::rbend(), H5PartWrapperForPC::readStepHeader(), MultipoleTCurvedVarRadius::reverseTransformResidual(), Expressions::Rmsa(), SampleGaussianSequence::SampleGaussianSequence(), Hamiltonian::sbend(), scaled_norm(), OrbitThreader::setDesignEnergy(), SocialNetworkGraph< TopoDiscoveryStrategy_t >::setNetworkNeighbors(), FFTBoxPoissonSolver::shiftedIntGreensFunction(), FFTPoissonSolver::shiftedIntGreensFunction(), SigmaGenerator::SigmaGenerator(), sqrt(), Werrf(), and mslang::Ellipse::writeGnuplot().

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tan()

template<class T>

Tps< T > tan

(

const Tps< T > &

x

)

Tangent.

Definition at line 147 of file TpsMath.h.

References cos(), and sin().

Referenced by mslang::Shear::applyShear(), RBendGeometry::getEntrancePatch(), RBendGeometry::getExitPatch(), GlobalFunctions::_tan::operator()(), PETE_apply(), and mslang::Ellipse::writeGnuplot().

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tanh()

template<class T>

Tps< T > tanh

(

const Tps< T > &

x

)

Hyperbolic tangent.

Definition at line 240 of file TpsMath.h.

References cosh(), and sinh().

Referenced by PETE_apply(), MultipoleTCurvedVarRadius::transformBField(), and OpalVariableRFCavityFringeField::update().

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