Index

A

abs_error (fio_bridge.ValidationReport attribute), [1] action (geometry.PeriodicOrbitBase attribute) action_angle_transform() (in module symplectic) action_integral() (in module symplectic) AdaptiveCriticalPointSolver (class in caustics) AIRY_1D (asymptotic.SingularityType attribute) AIRY_2D (asymptotic.SingularityType attribute) airy_Ai() (caustics.CausticFunctions static method) airy_Ai_prime() (caustics.CausticFunctions static method) airy_Bi() (caustics.CausticFunctions static method) amp_sym (fio_bridge.FIOKernel attribute), [1] amplitude_expr (asymptotic.Analyzer attribute) amplitude_value (asymptotic.CriticalPoint attribute), [1] analyze_hamiltonian() (in module hamiltonian_catalog) analyze_integrability() (geometry.SpectralAnalysis static method)

analyze_point() (asymptotic.Analyzer method) Analyzer (class in asymptotic) animate() (solver.PDESolver method) animate_singularity() (psiop.PseudoDifferentialOperator method) apply() (psiop.PseudoDifferentialOperator method) apply_asymptotic() (fio_bridge.FourierIntegralOperator method) arc_length() (riemannian.Metric method) arnold_type (caustics.CausticEvent attribute), [1] as_callable() (fio_bridge.WKBState method) asymptotic module asymptotic_expansion() (psiop.PseudoDifferentialOperator method) AsymptoticContribution (class in asymptotic) AsymptoticEvaluator (class in asymptotic) AsymptoticVisualizer (class in asymptotic) AUTO (asymptotic.IntegralMethod attribute)

B

batch_export_hamiltonians() (in module hamiltonian_catalog) berry_tabor_formula() (geometry.SpectralAnalysis static method) bicharacteristic_flow() (in module microlocal)

bohr_sommerfeld_condition (geometry.PeriodicOrbit2D property) bohr_sommerfeld_quantization() (in module microlocal) build_kernel() (fio_bridge.PsiOpFIOBridge method)

C

canonical_coefficients (asymptotic.CriticalPoint attribute), [1] canonical_symplectic_form_construction() (in module cotangent_bundle) canonical_transformations_preserve_omega() (in module cotangent_bundle) caustic_indices (geometry.Geodesic2D attribute) caustic_points (geometry.Geodesic2D property) CausticEvent (class in caustics) CausticFunctions (class in caustics) caustics module caustics (geometry.Geodesic1D property) CausticStructure (class in geometry) characteristic_variety() (in module microlocal) christoffel() (in module riemannian) christoffel_func (riemannian.Metric attribute) christoffel_sym (riemannian.Metric attribute) circle_function() (in module misc) classify_arnold_1d() (in module caustics) classify_arnold_2d() (in module caustics) clear_cache() (psiop.PseudoDifferentialOperator method) color (geometry.GeodesicBase attribute) commutator_symbolic() (psiop.PseudoDifferentialOperator method) compare_orders() (in module wkb) complete_symplectic_example_unified() (in module cotangent_bundle) compose_asymptotic() (psiop.PseudoDifferentialOperator method)

CompositionBridge (class in fio_bridge) compute_caustics_2d() (in module microlocal) compute_geodesic() (geometry.SymbolGeometry method) (geometry.SymbolGeometry2D method) compute_maslov_index() (in module microlocal) compute_phase_space_volume() (geometry.SymbolGeometry2D method) compute_rotation_numbers() (geometry.Utilities2D static method) compute_winding_number() (geometry.Utilities2D static method) conceptual_architecture() (in module cotangent_bundle) contributions (fio_bridge.EvalResult attribute), [1] coords (riemannian.Metric attribute) correct() (fio_bridge.SemiclassicalCorrector method) correction_magnitude() (fio_bridge.SemiclassicalCorrector method) correction_term (asymptotic.AsymptoticContribution attribute), [1] cotangent_bundle module create_initial_data_circle() (in module wkb) create_initial_data_line() (in module wkb) create_initial_data_point_source() (in module wkb) CriticalPoint (class in asymptotic) cross_function() (in module misc) CrossValidator (class in fio_bridge) cubic_threshold (asymptotic.Analyzer attribute) cusp_uniform() (caustics.CausticFunctions static method)

D

de_rham_laplacian() (in module riemannian) decompose_hamiltonian() (physics.HamiltonianSymbolicConverter static method) default_assumptions (misc.Op attribute) (misc.psiOp attribute) det_caustic (geometry.Geodesic2D attribute) det_J (caustics.CausticEvent attribute), [1] detect() (caustics.RayCausticDetector method) detect_catastrophes() (in module caustics)

detect_caustic_structures() (geometry.SymbolGeometry2D method) detect_kam_tori() (geometry.Utilities2D static method) dim (asymptotic.Analyzer attribute) (psiop.PseudoDifferentialOperator attribute) (riemannian.Metric attribute) distance() (in module riemannian) domain (asymptotic.Analyzer attribute) (fio_bridge.FIOKernel attribute), [1] dominant_wavenumber() (fio_bridge.WKBState method)

E

eigenvalues (asymptotic.CriticalPoint attribute), [1] eigenvectors (asymptotic.CriticalPoint attribute), [1] ellipse_function() (in module misc) energies (geometry.Spectrum attribute) energy (geometry.CausticStructure attribute) (geometry.GeodesicBase property) (geometry.PeriodicOrbitBase attribute) energy_ratio() (fio_bridge.SpectralSplitter method) error_spectrum (fio_bridge.ValidationReport attribute), [1] eta (geometry.Geodesic2D attribute) eta0 (geometry.PeriodicOrbit2D attribute) eta_cycle (geometry.PeriodicOrbit2D attribute) eval() (riemannian.Metric method) (symplectic.SymplecticForm method)

EvalResult (class in fio_bridge) evaluate() (asymptotic.AsymptoticEvaluator method) (asymptotic.LaplaceEvaluator method) (asymptotic.SaddlePointEvaluator method) (asymptotic.StationaryPhaseEvaluator method) (psiop.PseudoDifferentialOperator method) evaluate_at() (fio_bridge.PsiOpFIOBridge method) evaluate_grid() (fio_bridge.CompositionBridge method) (fio_bridge.PsiOpFIOBridge method) explicit_derivation_hamilton_equations() (in module cotangent_bundle) exponential_map() (in module riemannian) exponential_symbol() (psiop.PseudoDifferentialOperator method) export_latex_table() (in module hamiltonian_catalog)

F

fft_reference() (in module fio_bridge) find_caustics_1d() (in module microlocal) find_critical_points() (asymptotic.Analyzer method) find_critical_points_numerical() (in module caustics) find_fixed_points() (in module symplectic) find_periodic_orbits() (geometry.SymbolGeometry method) find_periodic_orbits_2d() (geometry.SymbolGeometry2D method) find_saddle_points() (asymptotic.SaddlePointEvaluator method) find_similar_hamiltonians() (in module hamiltonian_catalog) fio_bridge module

FIOKernel (class in fio_bridge) first_return_map() (in module symplectic) fold_uniform() (caustics.CausticFunctions static method) formal_adjoint() (psiop.PseudoDifferentialOperator method) FourierIntegralOperator (class in fio_bridge) freq_window_2d() (in module psiop) frequency() (in module symplectic) from_hamiltonian() (riemannian.Metric class method) from_omega_to_flow() (in module cotangent_bundle) from_poisson_to_commutator() (in module cotangent_bundle)

G

gauss_curvature() (riemannian.Metric method) gaussian_function_1D() (in module misc) gaussian_function_2D() (in module misc) Geodesic (in module geometry) Geodesic1D (class in geometry) Geodesic2D (class in geometry) geodesic_hamiltonian_flow() (in module riemannian) geodesic_solver() (in module riemannian) GeodesicBase (class in geometry) geometry module

get_catalog_summary() (in module hamiltonian_catalog) get_dimensional_analysis() (in module hamiltonian_catalog) get_hamiltonian() (in module hamiltonian_catalog) get_hamiltonians_by_keywords() (in module hamiltonian_catalog) get_operator() (in module hamiltonian_catalog) get_parameters() (in module hamiltonian_catalog) get_tree() (in module hamiltonian_catalog) grad_amp (asymptotic.CriticalPoint attribute), [1] group_velocity_field() (psiop.PseudoDifferentialOperator method) gutzwiller_trace_formula() (geometry.SymbolGeometry method)

H

H (geometry.GeodesicBase attribute) H_to_L() (physics.LagrangianHamiltonianConverter static method) hamiltonian_catalog module hamiltonian_flow() (in module symplectic) hamiltonian_flow_4d() (in module symplectic) hamiltonian_to_symbolic_pde() (physics.HamiltonianSymbolicConverter class method)

hamiltonian_vector_field() (in module cotangent_bundle) HamiltonianSymbolicConverter (class in physics) hess_amp (asymptotic.CriticalPoint attribute), [1] hessian_det (asymptotic.CriticalPoint attribute), [1] hessian_inv (asymptotic.CriticalPoint attribute), [1] hessian_matrix (asymptotic.CriticalPoint attribute), [1] HIGHER_ORDER (asymptotic.SingularityType attribute) hodge_star() (in module riemannian)

I

image_to_sound() (in module misc) imports module IntegralMethod (class in asymptotic) intensity (geometry.Spectrum attribute) interactive_hamiltonian() (in module hamiltonian_catalog) interactive_symbol_analysis() (psiop.PseudoDifferentialOperator method)

interactive_symplectic_dynamics() (in module cotangent_bundle) invalidate_kn_cache() (in module psiop) is_elliptic_numerically() (psiop.PseudoDifferentialOperator method) is_homogeneous() (psiop.PseudoDifferentialOperator method) is_non_degenerate() (fio_bridge.FourierIntegralOperator method) is_self_adjoint() (psiop.PseudoDifferentialOperator method) is_stable (geometry.PeriodicOrbit2D property)

J

J (geometry.Geodesic1D attribute)

J_full (geometry.Geodesic2D attribute) jacobi_equation_solver() (in module riemannian)

K

K (geometry.Geodesic1D attribute) k_grid (fio_bridge.ValidationReport attribute), [1]

kohn_nirenberg_fft() (in module psiop) kohn_nirenberg_nonperiodic() (in module psiop)

L

L_to_H() (physics.LagrangianHamiltonianConverter static method) LagrangianHamiltonianConverter (class in physics) lam (fio_bridge.ValidationReport attribute), [1] lambda_sweep() (fio_bridge.CrossValidator method) LAPLACE (asymptotic.IntegralMethod attribute) laplace_beltrami() (in module riemannian) laplace_beltrami_symbol() (riemannian.Metric method)

laplace_evaluator (asymptotic.AsymptoticEvaluator attribute) LaplaceEvaluator (class in asymptotic) leading_term (asymptotic.AsymptoticContribution attribute), [1] left_inverse_asymptotic() (psiop.PseudoDifferentialOperator method) linearize_at_fixed_point() (in module symplectic) list_categories() (in module hamiltonian_catalog) list_hamiltonians() (in module hamiltonian_catalog) lyapunov_exponents() (in module symplectic)

M

make_symbol() (in module misc) make_video_with_sound() (in module misc) maslov_contribution (caustics.CausticEvent attribute), [1] maslov_index (geometry.CausticStructure attribute) (geometry.PeriodicOrbit2D attribute) maslov_index() (caustics.RayCausticDetector method) maslov_phase() (caustics.RayCausticDetector method) maslov_phase_shift() (caustics.CausticFunctions static method) max_abs_error (fio_bridge.ValidationReport attribute), [1] max_rel_error (fio_bridge.ValidationReport attribute), [1] merge() (fio_bridge.SpectralSplitter method) method (asymptotic.Analyzer attribute) (asymptotic.AsymptoticContribution attribute), [1] (asymptotic.CriticalPoint attribute) method_hint (fio_bridge.FIOKernel attribute), [1] Metric (class in riemannian) microlocal module misc module

module asymptotic caustics cotangent_bundle fio_bridge geometry hamiltonian_catalog imports microlocal misc physics psiop riemannian solver symplectic wkb momentum (caustics.CausticEvent attribute), [1] momentum_trajectory (geometry.Geodesic2D property) monodromy_matrix() (in module symplectic) MORSE (asymptotic.SingularityType attribute)

N

n_critical_points (fio_bridge.EvalResult attribute), [1]

nargs (misc.Op attribute) (misc.psiOp attribute)

O

Op (class in misc)

order_leading (asymptotic.AsymptoticContribution attribute), [1]

P

p_func (psiop.PseudoDifferentialOperator attribute) PDESolver (class in solver) PEARCEY (asymptotic.SingularityType attribute) pearcey() (caustics.CausticFunctions static method) pearcey_grid() (caustics.CausticFunctions static method) period (geometry.PeriodicOrbitBase attribute) PeriodicOrbit (in module geometry) PeriodicOrbit1D (class in geometry) PeriodicOrbit2D (class in geometry) PeriodicOrbitBase (class in geometry) phase_d3 (asymptotic.CriticalPoint attribute), [1] phase_d4 (asymptotic.CriticalPoint attribute), [1] phase_expr (asymptotic.Analyzer attribute) phase_portrait() (in module symplectic) phase_sym (fio_bridge.FIOKernel attribute), [1] phase_value (asymptotic.CriticalPoint attribute), [1] physics module plot_amplitude_decomposition() (in module wkb) plot_asymptotic_convergence() (asymptotic.AsymptoticVisualizer method) plot_bicharacteristics() (in module microlocal) plot_catastrophe() (in module caustics) plot_caustic_analysis() (in module wkb) plot_caustic_events() (in module caustics) plot_characteristic_set() (in module microlocal) plot_energy() (solver.PDESolver method) plot_hamiltonian_flow() (psiop.PseudoDifferentialOperator method)

plot_integrand() (asymptotic.AsymptoticVisualizer method) plot_lambda_sweep() (fio_bridge.CrossValidator static method) plot_phase_landscape() (asymptotic.AsymptoticVisualizer method) plot_phase_space() (in module wkb) plot_report() (fio_bridge.CrossValidator static method) plot_symplectic_vector_field() (psiop.PseudoDifferentialOperator method) plot_wavefront_set() (in module microlocal) plot_with_caustics() (in module wkb) poincare_section() (in module symplectic) point (asymptotic.AsymptoticContribution attribute), [1] poisson_bracket() (in module cotangent_bundle) (in module symplectic) position (asymptotic.CriticalPoint attribute), [1] (caustics.CausticEvent attribute), [1] principal_symbol() (psiop.PseudoDifferentialOperator method) print_hamiltonian_info() (in module hamiltonian_catalog) print_theory() (in module geometry) print_theory_summary() (in module geometry) project() (in module symplectic) propagate() (fio_bridge.PropagatorBridge method) propagate_singularity() (in module microlocal) PropagatorBridge (class in fio_bridge) PseudoDifferentialOperator (class in psiop) pseudospectrum_analysis() (psiop.PseudoDifferentialOperator method) psiop module psiOp (class in misc) PsiOpFIOBridge (class in fio_bridge)

Q

quantize_hamiltonian() (in module cotangent_bundle)

R

radial_gradient() (in module misc) ramp_function() (in module misc) ray_idx (caustics.CausticEvent attribute), [1] RayCausticDetector (class in caustics) rectangle_function() (in module misc) rel_error (fio_bridge.ValidationReport attribute), [1] ricci_scalar() (riemannian.Metric method) ricci_tensor() (riemannian.Metric method)

riemann_tensor() (riemannian.Metric method) riemannian module riemannian_volume() (riemannian.Metric method) right_inverse_asymptotic() (psiop.PseudoDifferentialOperator method) run() (fio_bridge.CrossValidator method) run_bridge_only() (fio_bridge.CrossValidator method) run_solver_only() (fio_bridge.CrossValidator method) run_test_suite() (in module fio_bridge)

S

saddle_evaluator (asymptotic.AsymptoticEvaluator attribute) SADDLE_POINT (asymptotic.IntegralMethod attribute) SaddlePointEvaluator (class in asymptotic) search_hamiltonians() (in module hamiltonian_catalog) semiclassical_spectrum() (geometry.SymbolGeometry method) SemiclassicalCorrector (class in fio_bridge) separatrix_analysis() (in module symplectic) setup() (solver.PDESolver method) show_stationary_solution() (solver.PDESolver method) sigmoid_ramp() (in module misc) sign_change (caustics.CausticEvent attribute), [1] signature (asymptotic.CriticalPoint attribute), [1] singularity_type (asymptotic.CriticalPoint attribute), [1] SingularityType (class in asymptotic) solve() (caustics.AdaptiveCriticalPointSolver method) (solver.PDESolver method) solve_stationary_psiOp() (solver.PDESolver method) solver module sonify_solution() (in module misc) sp_evaluator (asymptotic.AsymptoticEvaluator attribute) spatial_trajectory (geometry.Geodesic2D property) SpectralAnalysis (class in geometry) SpectralSplitter (class in fio_bridge) Spectrum (class in geometry) split() (fio_bridge.SpectralSplitter method)

stability (geometry.PeriodicOrbit1D attribute) stability_1 (geometry.PeriodicOrbit2D attribute) stability_2 (geometry.PeriodicOrbit2D attribute) stability_matrix_ode_1d() (caustics.RayCausticDetector static method) stability_matrix_ode_2d() (caustics.RayCausticDetector static method) STATIONARY_PHASE (asymptotic.IntegralMethod attribute) StationaryPhaseEvaluator (class in asymptotic) StationaryPhaseVisualizer (in module asymptotic) strength (geometry.CausticStructure attribute) sturm_liouville_reduce() (in module riemannian) suggest_k_cut() (fio_bridge.SpectralSplitter method) summary() (caustics.RayCausticDetector method) swallowtail() (caustics.CausticFunctions static method) symbol_order() (psiop.PseudoDifferentialOperator method) SymbolGeometry (class in geometry) SymbolGeometry2D (class in geometry) SymbolGeometryBase (class in geometry) SymbolVisualizer (class in geometry) SymbolVisualizer2D (class in geometry) SymbolVisualizerBase (class in geometry) symplectic module symplectic_flow() (psiop.PseudoDifferentialOperator method) symplectic_structure_higher_dimensions() (in module cotangent_bundle) SymplecticForm (class in symplectic) SymplecticForm1D() (in module symplectic) SymplecticForm2D() (in module symplectic)

T

t (geometry.CausticStructure attribute) (geometry.GeodesicBase attribute) t_cycle (geometry.PeriodicOrbitBase attribute) tanh_ramp() (in module misc) test() (solver.PDESolver method) test_bicharacteristic_flow() (in module microlocal) test_bohr_sommerfeld() (in module microlocal) test_characteristic_variety() (in module microlocal) test_coupled_oscillators() (in module symplectic) test_distance_and_exp_map() (in module riemannian) test_error_handling_1d() (in module riemannian) test_euclidean_metric() (in module riemannian) test_fixed_points_1d() (in module symplectic) test_geodesic_integrators_2d() (in module riemannian) test_geodesic_integrators_accuracy() (in module riemannian) test_hamiltonian_construction() (in module riemannian) test_hamiltonian_flow_conservation() (in module riemannian) test_harmonic_oscillator() (in module symplectic) test_hodge_star_and_volume() (in module riemannian) test_integration_methods_consistency() (in module riemannian) test_jacobi_field_stability() (in module riemannian)

test_laplace_beltrami_properties() (in module riemannian) test_metric_geometry_and_sl() (in module riemannian) test_monodromy_simple() (in module symplectic) test_poincare_half_plane() (in module riemannian) test_poincare_section() (in module symplectic) test_polar_coordinates() (in module riemannian) test_sphere_metric() (in module riemannian) test_wkb() (in module microlocal) time (caustics.CausticEvent attribute), [1] time_idx (caustics.CausticEvent attribute), [1] to_array() (fio_bridge.WKBState method) to_dict_list() (caustics.AdaptiveCriticalPointSolver method) tolerance (asymptotic.Analyzer attribute) (asymptotic.StationaryPhaseEvaluator attribute) top_hat_band() (in module misc) total_value (asymptotic.AsymptoticContribution attribute), [1] trace (geometry.Spectrum attribute) trace_formula() (psiop.PseudoDifferentialOperator method) trace_hamiltonian() (in module hamiltonian_catalog) trace_t (geometry.Spectrum attribute) type (geometry.CausticStructure attribute)

U

u_bridge (fio_bridge.ValidationReport attribute), [1]

u_solver (fio_bridge.ValidationReport attribute), [1] Utilities2D (class in geometry)

V

validate_hamiltonians() (in module hamiltonian_catalog) ValidationReport (class in fio_bridge) value (fio_bridge.EvalResult attribute), [1] variables (asymptotic.Analyzer attribute) vars_int (fio_bridge.FIOKernel attribute), [1] verify_canonical_relations() (in module cotangent_bundle) verify_gauss_bonnet() (in module riemannian) verify_symplectic_preservation() (in module cotangent_bundle) verify_symplectic_structure() (in module cotangent_bundle) visualize_characteristic_gradient() (psiop.PseudoDifferentialOperator method) visualize_characteristic_set() (psiop.PseudoDifferentialOperator method) visualize_complete() (geometry.SymbolVisualizer method) (geometry.SymbolVisualizer2D method) (geometry.SymbolVisualizerBase method)

visualize_curvature() (in module riemannian) visualize_fiber() (psiop.PseudoDifferentialOperator method) visualize_geodesics() (in module riemannian) visualize_hamiltonian() (in module hamiltonian_catalog) visualize_micro_support() (psiop.PseudoDifferentialOperator method) visualize_phase() (psiop.PseudoDifferentialOperator method) visualize_phase_space_structure() (in module symplectic) visualize_poincare_section() (in module symplectic) visualize_symbol() (in module geometry) visualize_symbol_2d() (in module geometry) visualize_symbol_amplitude() (psiop.PseudoDifferentialOperator method) visualize_symplectic_geometry() (in module cotangent_bundle) visualize_wkb_rays() (in module wkb)

W

warnings_list (fio_bridge.EvalResult attribute), [1] weyl_law() (geometry.SpectralAnalysis static method) wkb module

wkb_approximation() (in module wkb) wkb_phase_gradient() (fio_bridge.WKBState method) wkb_threshold (fio_bridge.ValidationReport attribute), [1] wkb_valid (fio_bridge.ValidationReport attribute), [1] WKBState (class in fio_bridge)

X

x (geometry.CausticStructure attribute) (geometry.Geodesic1D attribute) (geometry.Geodesic2D attribute) x0 (geometry.PeriodicOrbit1D attribute) (geometry.PeriodicOrbit2D attribute) x_cycle (geometry.PeriodicOrbitBase attribute) x_grid (fio_bridge.ValidationReport attribute), [1]

x_val (fio_bridge.EvalResult attribute), [1] (fio_bridge.FIOKernel attribute), [1] xi (geometry.Geodesic1D attribute) (geometry.Geodesic2D attribute) xi0 (geometry.PeriodicOrbit1D attribute) (geometry.PeriodicOrbit2D attribute) xi_cycle (geometry.PeriodicOrbitBase attribute)

Y

y (geometry.CausticStructure attribute) (geometry.Geodesic2D attribute)

y0 (geometry.PeriodicOrbit2D attribute) y_cycle (geometry.PeriodicOrbit2D attribute)