Index

_

__init__() (gme.core.equations.Equations method) (gme.core.equations.EquationsBase method) (gme.core.equations.EquationsMixedIn method) (gme.core.equations_extended.EquationsGeodesic method) (gme.core.equations_extended.EquationsIbc method) (gme.core.equations_extended.EquationsIdtx method) (gme.core.equations_extended.EquationsIdtxIbc method) (gme.core.equations_extended.EquationsSetupOnly method) (gme.core.equations_subset.EquationSubset method) (gme.knickpoints.base.CompositeSolution method) (gme.knickpoints.base.InitialCornerSolution method) (gme.knickpoints.base.InitialProfileSolution method) (gme.ode.base.BaseSolution method) (gme.ode.extended.ExtendedSolution method) (gme.plot.indicatrix_new.IndicatrixNew method) (gme.plot.ray_geodesics.RayGeodesics method) (gme.plot.slicing.SlicingMath method) (gme.plot.slicing.SlicingPlots method)

_eventAttr() (in module gme.ode.solve)

A

alpha_anisotropy() (gme.plot.alphabeta.AlphaBeta method) alpha_beta() (gme.plot.alphabeta.AlphaBeta method) (gme.plot.ray_angles.RayAngles method) alpha_image() (gme.plot.alphabeta.AlphaBeta method) alpha_tfn (in module gme.core.symbols)

AlphaBeta (class in gme.plot.alphabeta) AnglesMixin (class in gme.core.angles) angular_disparity() (gme.plot.ray_angles.RayAngles method) annotations() (gme.plot.indicatrix_old.IndicatrixOld method) arrow_annotate_ray_custom() (gme.plot.base.Graphing method) arrows() (gme.plot.indicatrix_old.IndicatrixOld method)

B

BaseSolution (class in gme.ode.base) beta_anisotropy() (gme.plot.alphabeta.AlphaBeta method)

beta_tfn (in module gme.core.symbols) boundary_eqns (gme.core.ibc.IbcMixin attribute)

C

christoffel_ij_k_lambda (gme.core.geodesic.GeodesicMixin attribute) christoffel_ij_k_rx_rdot_lambda (gme.core.geodesic.GeodesicMixin attribute) comparison_logpolar() (gme.plot.indicatrix_old.IndicatrixOld method) CompositeSolution (class in gme.knickpoints.base) convex_concave_annotations() (gme.plot.indicatrix_new.IndicatrixNew method)

correct_quadrant() (gme.plot.base.Graphing method) cosbeta_pxpz_eqn (gme.core.rp.RpMixin attribute) cosbeta_pz_varphi_solns (gme.core.idtx.IdtxMixin attribute) covector_isochrones() (gme.plot.manuscript.Manuscript method) create_solutions() (gme.knickpoints.base.CompositeSolution method) CuspVelocity (class in gme.plot.cusp_velocity)

D

d_varphi_rx (in module gme.core.symbols) define_Ci_lambda() (gme.plot.slicing.SlicingMath method) define_d2Hdpzhat2_lambda() (gme.plot.slicing.SlicingMath method) define_detHessianSqrd_lambda() (gme.plot.slicing.SlicingMath method) define_Fstar_eqns() (gme.core.fundamental.FundamentalMixin method) define_g_eqns() (gme.core.metrictensor.MetricTensorMixin method) define_geodesic_eqns() (gme.core.geodesic.GeodesicMixin method) define_gstarhat_lambda() (gme.plot.slicing.SlicingMath method) define_H_eqns() (gme.core.fundamental.FundamentalMixin method) define_H_lambda() (gme.plot.slicing.SlicingMath method) define_Hamiltons_eqns() (gme.core.hamiltons.HamiltonsMixin method) define_Hessian_eigenvals() (gme.plot.slicing.SlicingMath method) define_ibc_eqns() (gme.core.ibc.IbcMixin method) define_idtx_fgtx_eqns() (gme.core.idtx.IdtxMixin method) define_modv_pxpzhat_lambda() (gme.plot.slicing.SlicingMath method) define_nodimensionalized_Hamiltons_eqns() (gme.core.ndim.NdimMixin method)

define_p_eqns() (gme.core.rp.RpMixin method) define_pdot_eqns() (gme.core.hamiltons.HamiltonsMixin method) define_psi_eqns() (gme.core.angles.AnglesMixin method) define_px_poly_eqn() (gme.core.pxpoly.PxpolyMixin method) define_r_eqns() (gme.core.rp.RpMixin method) define_rdot_eqns() (gme.core.hamiltons.HamiltonsMixin method) define_tanalpha_eqns() (gme.core.angles.AnglesMixin method) define_tanbeta_eqns() (gme.core.angles.AnglesMixin method) define_v_pxpzhat_lambda() (gme.plot.slicing.SlicingMath method) define_varphi_model_eqns() (gme.core.varphi.VarphiMixin method) define_varphi_related_eqns() (gme.core.varphi.VarphiMixin method) define_xi_eqns() (gme.core.xi.XiMixin method) define_xi_model_eqn() (gme.core.xi.XiMixin method) define_xi_related_eqns() (gme.core.xi.XiMixin method) det_gstar_varphi_pxpz_eqn (gme.core.metrictensor.MetricTensorMixin attribute) dg_rk_ij_mat (gme.core.geodesic.GeodesicMixin attribute) draw_rays_with_arrows_simple() (gme.plot.base.Graphing method)

E

Equations (class in gme.core.equations) EquationsBase (class in gme.core.equations) EquationsGeodesic (class in gme.core.equations_extended) EquationsIbc (class in gme.core.equations_extended) EquationsIdtx (class in gme.core.equations_extended)

EquationsIdtxIbc (class in gme.core.equations_extended) EquationsMixedIn (class in gme.core.equations) EquationsSetupOnly (class in gme.core.equations_extended) EquationSubset (class in gme.core.equations_subset) eta_dbldenom (gme.core.xi.XiMixin attribute) ExtendedSolution (class in gme.ode.extended)

F

fgtx_cosbeta_pz_varphi_eqn (gme.core.idtx.IdtxMixin attribute) fgtx_px_pz_varphi_eqn (gme.core.idtx.IdtxMixin attribute) fgtx_tanbeta_pz_varphi_eqn (gme.core.idtx.IdtxMixin attribute) figuratrix() (gme.plot.indicatrix_old.IndicatrixOld method) find_dzdx_poly_root() (in module gme.core.utils)

FlowModel (class in gme.plot.flow_model) Fstar_eqn (gme.core.fundamental.FundamentalMixin attribute) Fstar_F_polar() (gme.plot.indicatrix_new.IndicatrixNew method) Fstar_F_rectlinear() (gme.plot.indicatrix_new.IndicatrixNew method) FundamentalMixin (class in gme.core.fundamental)

G

g_ij_mat (gme.core.geodesic.GeodesicMixin attribute) g_ij_mat_lambdified (gme.core.geodesic.GeodesicMixin attribute) g_ij_tanalpha_mat (gme.core.geodesic.GeodesicMixin attribute) g_ij_tanbeta_mat (gme.core.geodesic.GeodesicMixin attribute) g_varphi_pxpz_eqn (gme.core.metrictensor.MetricTensorMixin attribute) geodesic_eqns (gme.core.geodesic.GeodesicMixin attribute) GeodesicMixin (class in gme.core.geodesic) get_rxhat_pzhat() (gme.plot.slicing.SlicingMath method) gme.core.angles module gme.core.equations module gme.core.equations_extended module gme.core.equations_subset module gme.core.fundamental module gme.core.geodesic module gme.core.hamiltons module gme.core.ibc module gme.core.idtx module gme.core.metrictensor module gme.core.ndim module gme.core.pxpoly module gme.core.rp module gme.core.symbols module gme.core.utils module gme.core.varphi module gme.core.xi module gme.knickpoints.base module gme.ode.base module gme.ode.extended module

gme.ode.single_ray module gme.ode.solve module gme.ode.time_invariant module gme.ode.utils module gme.ode.velocity_boundary module gme.plot.alphabeta module gme.plot.base module gme.plot.cusp_velocity module gme.plot.flow_model module gme.plot.indicatrix_new module gme.plot.indicatrix_old module gme.plot.manuscript module gme.plot.ray_angles module gme.plot.ray_geodesics module gme.plot.ray_profiles module gme.plot.ray_velocities module gme.plot.slicing module gme.plot.time_dependent module gme.plot.time_invariant module gradient_value() (in module gme.core.utils) Graphing (class in gme.plot.base) gray_color() (gme.plot.base.Graphing method) gstar_eigen_varphi_pxpz (gme.core.metrictensor.MetricTensorMixin attribute) gstar_eigenvalues (gme.core.metrictensor.MetricTensorMixin attribute) gstar_eigenvectors (gme.core.metrictensor.MetricTensorMixin attribute) gstar_ij_mat (gme.core.geodesic.GeodesicMixin attribute) gstar_ij_mat_lambdified (gme.core.geodesic.GeodesicMixin attribute) gstar_ij_tanalpha_mat (gme.core.geodesic.GeodesicMixin attribute) gstar_ij_tanbeta_mat (gme.core.geodesic.GeodesicMixin attribute) gstar_varphi_pxpz_eqn (gme.core.metrictensor.MetricTensorMixin attribute)

H

H_eqn (gme.core.fundamental.FundamentalMixin attribute) h_fn (in module gme.core.symbols) H_pxpz_contours() (gme.plot.slicing.SlicingPlots method) H_rxpx_contours() (gme.plot.slicing.SlicingPlots method)

H_varphi_rx_eqn (gme.core.fundamental.FundamentalMixin attribute) hamiltons_eqns (gme.core.hamiltons.HamiltonsMixin attribute) HamiltonsMixin (class in gme.core.hamiltons) huygens_wavelets() (gme.plot.manuscript.Manuscript method)

I

IbcMixin (class in gme.core.ibc) idtx_rdotx_pz_varphi_eqn (gme.core.idtx.IdtxMixin attribute) idtx_rdotz_pz_varphi_eqn (gme.core.idtx.IdtxMixin attribute) IdtxMixin (class in gme.core.idtx) indicatrix() (gme.plot.indicatrix_old.IndicatrixOld method) IndicatrixNew (class in gme.plot.indicatrix_new) IndicatrixOld (class in gme.plot.indicatrix_old)

initial_conditions() (gme.knickpoints.base.InitialCornerSolution method) (gme.knickpoints.base.InitialProfileSolution method) (gme.ode.base.BaseSolution method) (gme.ode.single_ray.SingleRaySolution method) (gme.ode.velocity_boundary.VelocityBoundarySolution method) InitialCornerSolution (class in gme.knickpoints.base) InitialProfileSolution (class in gme.knickpoints.base) integrate_h_profile() (gme.ode.time_invariant.TimeInvariantSolution method)

L

legend() (gme.plot.indicatrix_old.IndicatrixOld method)

lines_and_points() (gme.plot.indicatrix_old.IndicatrixOld method)

M

make_dzdx_poly() (in module gme.core.utils) make_model() (gme.ode.base.BaseSolution method) Manuscript (class in gme.plot.manuscript) measure_cusp_propagation() (gme.ode.base.BaseSolution method) merge_rays() (gme.knickpoints.base.CompositeSolution method) MetricTensorMixin (class in gme.core.metrictensor) module gme.core.angles gme.core.equations gme.core.equations_extended gme.core.equations_subset gme.core.fundamental gme.core.geodesic gme.core.hamiltons gme.core.ibc gme.core.idtx gme.core.metrictensor gme.core.ndim gme.core.pxpoly gme.core.rp gme.core.symbols gme.core.utils gme.core.varphi gme.core.xi gme.knickpoints.base gme.ode.base gme.ode.extended gme.ode.single_ray gme.ode.solve gme.ode.time_invariant gme.ode.utils gme.ode.velocity_boundary gme.plot.alphabeta gme.plot.base gme.plot.cusp_velocity gme.plot.flow_model gme.plot.indicatrix_new gme.plot.indicatrix_old gme.plot.manuscript gme.plot.ray_angles gme.plot.ray_geodesics gme.plot.ray_profiles gme.plot.ray_velocities gme.plot.slicing gme.plot.time_dependent gme.plot.time_invariant

mycolors() (gme.plot.base.Graphing method)

N

NdimMixin (class in gme.core.ndim)

nondimensionalize() (gme.core.ndim.NdimMixin method)

O

Okubo_Fstar_eqn (gme.core.fundamental.FundamentalMixin attribute)

P

p_covec_eqn (gme.core.rp.RpMixin attribute) p_initial_eqn (gme.core.ibc.IbcMixin attribute) p_norm_pxpz_eqn (gme.core.rp.RpMixin attribute) p_pz_cosbeta_eqn (gme.core.rp.RpMixin attribute) p_rx_pxpz_eqn (gme.core.varphi.VarphiMixin attribute) p_rx_tanbeta_eqn (gme.core.varphi.VarphiMixin attribute) p_varphi_beta_eqn (gme.core.varphi.VarphiMixin attribute) p_varphi_pxpz_eqn (gme.core.varphi.VarphiMixin attribute) p_xi_eqn (gme.core.xi.XiMixin attribute) pdot_covec_eqn (gme.core.hamiltons.HamiltonsMixin attribute) pdotx_pxpz_eqn (gme.core.hamiltons.HamiltonsMixin attribute) pdotx_tfn (in module gme.core.symbols) pdotxhat_thatfn (in module gme.core.symbols) pdotz_pxpz_eqn (gme.core.hamiltons.HamiltonsMixin attribute) pdotz_tfn (in module gme.core.symbols) pdotzhat_thatfn (in module gme.core.symbols) plot_dHdp_slice() (gme.plot.slicing.SlicingPlots method) plot_figuratrix() (gme.plot.indicatrix_old.IndicatrixOld method) plot_Hetc_contours() (gme.plot.slicing.SlicingPlots method) plot_indicatrix() (gme.plot.indicatrix_old.IndicatrixOld method) plot_modv_slice() (gme.plot.slicing.SlicingPlots method) plot_unit_circle() (gme.plot.indicatrix_old.IndicatrixOld method) point_pairing() (gme.plot.manuscript.Manuscript method) poly_px_xiv_eqn (gme.core.pxpoly.PxpolyMixin attribute) poly_px_xiv_varphi_eqn (gme.core.pxpoly.PxpolyMixin attribute) postprocessing() (gme.ode.base.BaseSolution method) (gme.ode.single_ray.SingleRaySolution method) (gme.ode.time_invariant.TimeInvariantSolution method) prep_geodesic_eqns() (gme.core.geodesic.GeodesicMixin method) prep_ibc_eqns() (gme.core.ibc.IbcMixin method) profile_alpha() (gme.plot.ray_angles.RayAngles method) profile_angular_disparity() (gme.plot.ray_angles.RayAngles method) profile_aniso() (gme.plot.time_invariant.TimeInvariant method) profile_beta() (gme.plot.time_invariant.TimeInvariant method) profile_beta_error() (gme.plot.time_invariant.TimeInvariant method) profile_cusp_horizontal_speed() (gme.plot.cusp_velocity.CuspVelocity method) profile_ensemble() (gme.plot.time_invariant.TimeInvariant method) profile_flow_model() (gme.plot.flow_model.FlowModel method)

profile_g_properties() (gme.plot.ray_geodesics.RayGeodesics method) profile_h() (gme.plot.ray_profiles.RayProfiles method) profile_h_rays() (gme.plot.ray_profiles.RayProfiles method) profile_isochrones() (gme.plot.time_dependent.TimeDependent method) profile_ray() (gme.plot.ray_profiles.RayProfiles method) profile_v() (gme.plot.ray_velocities.RayVelocities method) profile_vdot() (gme.plot.ray_velocities.RayVelocities method) profile_xi() (gme.plot.time_invariant.TimeInvariant method) profile_xihorizontal() (gme.plot.time_invariant.TimeInvariant method) profile_xivertical() (gme.plot.time_invariant.TimeInvariant method) psi_alpha_beta_eqn (gme.core.angles.AnglesMixin attribute) psi_eta_alpha() (gme.plot.ray_angles.RayAngles method) px_beta_eqn (gme.core.varphi.VarphiMixin attribute) px_initial_eqn (gme.core.ibc.IbcMixin attribute) px_p_beta_eqn (gme.core.rp.RpMixin attribute) px_pz_tanbeta_eqn (gme.core.rp.RpMixin attribute) px_tfn (in module gme.core.symbols) px_value() (in module gme.core.utils) px_value_search() (in module gme.core.utils) px_varphi_beta_eqn (gme.core.varphi.VarphiMixin attribute) px_varphi_rx_beta_eqn (gme.core.varphi.VarphiMixin attribute) px_xiv_varphi_eqn (gme.core.xi.XiMixin attribute) pxhat_Ci_soln() (gme.plot.slicing.SlicingMath method) pxhatsqrd_Ci_polylike_eqn() (gme.plot.slicing.SlicingMath method) PxpolyMixin (class in gme.core.pxpoly) pxpz0_from_xiv0() (in module gme.core.utils) pxpzhat0_values() (gme.plot.slicing.SlicingMath method) pz0_xiv0_eqn (gme.core.ibc.IbcMixin attribute) pz_beta_eqn (gme.core.varphi.VarphiMixin attribute) pz_cosbeta_varphi_eqn (gme.core.idtx.IdtxMixin attribute) pz_initial_eqn (gme.core.ibc.IbcMixin attribute) pz_p_beta_eqn (gme.core.rp.RpMixin attribute) pz_px_tanbeta_eqn (gme.core.rp.RpMixin attribute) pz_tfn (in module gme.core.symbols) pz_varphi_beta_eqn (gme.core.varphi.VarphiMixin attribute) pz_varphi_rx_beta_eqn (gme.core.varphi.VarphiMixin attribute) pz_xiv_eqn (gme.core.xi.XiMixin attribute) pzpx_unity_eqn (gme.core.ibc.IbcMixin attribute)

R

RayAngles (class in gme.plot.ray_angles) RayGeodesics (class in gme.plot.ray_geodesics) RayProfiles (class in gme.plot.ray_profiles) RayVelocities (class in gme.plot.ray_velocities) rdot_p_unity_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdot_vec_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdotx_pxpz_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdotx_rdot_alpha_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdotx_tfn (in module gme.core.symbols) rdotxhat_thatfn (in module gme.core.symbols) rdotz_on_rdotx_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdotz_on_rdotx_tanbeta_eqn (gme.core.hamiltons.HamiltonsMixin attribute)

rdotz_pxpz_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdotz_rdot_alpha_eqn (gme.core.hamiltons.HamiltonsMixin attribute) rdotz_tfn (in module gme.core.symbols) rdotzhat_thatfn (in module gme.core.symbols) relative_geometry() (gme.plot.indicatrix_old.IndicatrixOld method) report_progress() (in module gme.ode.utils) resolve_isochrones() (gme.ode.base.BaseSolution method) RpMixin (class in gme.core.rp) rx_r_alpha_eqn (gme.core.rp.RpMixin attribute) rx_tfn (in module gme.core.symbols) rz_initial_eqn (gme.core.ibc.IbcMixin attribute) rz_r_alpha_eqn (gme.core.rp.RpMixin attribute) rz_tfn (in module gme.core.symbols)

S

save() (gme.ode.base.BaseSolution method) set_ibc_eqns() (gme.core.ibc.IbcMixin method) sinbeta_pxpz_eqn (gme.core.rp.RpMixin attribute) SingleRaySolution (class in gme.ode.single_ray) SlicingMath (class in gme.plot.slicing) SlicingPlots (class in gme.plot.slicing) solve() (gme.knickpoints.base.CompositeSolution method) (gme.knickpoints.base.InitialCornerSolution method) (gme.knickpoints.base.InitialProfileSolution method) (gme.ode.base.BaseSolution method) (gme.ode.single_ray.SingleRaySolution method) (gme.ode.velocity_boundary.VelocityBoundarySolution method)

solve_Hamiltons_equations() (in module gme.ode.solve) solve_ODE_system() (in module gme.ode.solve)

T

tanalpha_beta_eqn (gme.core.angles.AnglesMixin attribute) tanalpha_ext_eqn (gme.core.angles.AnglesMixin attribute) tanalpha_ext_eqns (gme.core.angles.AnglesMixin attribute) tanalpha_pxpz_eqn (gme.core.angles.AnglesMixin attribute) tanalpha_rdot_eqn (gme.core.angles.AnglesMixin attribute) tanbeta_alpha_eqn (gme.core.angles.AnglesMixin attribute) tanbeta_alpha_eqns (gme.core.angles.AnglesMixin attribute) tanbeta_crit_eqn (gme.core.angles.AnglesMixin attribute) tanbeta_crit_eqns (gme.core.angles.AnglesMixin attribute)

tanbeta_eqn (gme.core.geodesic.GeodesicMixin attribute) tanbeta_initial_eqn (gme.core.ibc.IbcMixin attribute) tanbeta_poly_eqn (gme.core.geodesic.GeodesicMixin attribute) tanbeta_pxpz_eqn (gme.core.rp.RpMixin attribute) tanbeta_rdotxz_pz_eqn (gme.core.angles.AnglesMixin attribute) tanbeta_rdotxz_xiv_eqn (gme.core.angles.AnglesMixin attribute) text_labels() (gme.plot.indicatrix_old.IndicatrixOld method) TimeDependent (class in gme.plot.time_dependent) TimeInvariant (class in gme.plot.time_invariant) TimeInvariantSolution (class in gme.ode.time_invariant)

V

varphi_model_ramp_eqn (gme.core.varphi.VarphiMixin attribute) varphi_model_sramp_eqn (gme.core.varphi.VarphiMixin attribute) varphi_r (in module gme.core.symbols) varphi_rhat (in module gme.core.symbols) varphi_rx (in module gme.core.symbols)

varphi_rx_eqn (gme.core.varphi.VarphiMixin attribute) varphi_rxhat_fn (in module gme.core.symbols) VarphiMixin (class in gme.core.varphi) vdotx_lambdified (gme.core.geodesic.GeodesicMixin attribute) vdotz_lambdified (gme.core.geodesic.GeodesicMixin attribute) VelocityBoundarySolution (class in gme.ode.velocity_boundary)

X

xi_p_eqn (gme.core.xi.XiMixin attribute) xi_varphi_beta_eqn (gme.core.xi.XiMixin attribute) XiMixin (class in gme.core.xi)

xiv_pxpz_eqn (gme.core.varphi.VarphiMixin attribute) xiv_pz_eqn (gme.core.xi.XiMixin attribute) xiv_varphi_pxpz_eqn (gme.core.xi.XiMixin attribute)