tidal package#
TIDAL: Tensor Integration and Derivation for Any Lagrangian.
A symbolic physics pipeline for deriving PDEs from Lagrangians using xAct/Mathematica and simulating them with native solvers (SUNDIALS IDA/CVODE, leapfrog, scipy) and numpy spatial operators.
This package provides: - symbolic: Lagrangian-to-PDE pipeline (symbolic computation layer) - cli: Command-line interface for derivation, simulation, and measurement - measurement: Post-hoc analysis (energy, conversion, dispersion, mixing)
- tidal.has_tex_support()[source]#
Check if TeX support is available for high-quality plotting.
- Return type:
Subpackages#
- tidal.cli package
- tidal.measurement package
AsymptoticConversionResultAsymptoticConversionResult.P_finalAsymptoticConversionResult.P_reflectedAsymptoticConversionResult.P_transmittedAsymptoticConversionResult.E_source_initialAsymptoticConversionResult.E_target_finalAsymptoticConversionResult.source_fieldAsymptoticConversionResult.target_fieldAsymptoticConversionResult.source_wavevectorAsymptoticConversionResult.P_finalAsymptoticConversionResult.P_reflectedAsymptoticConversionResult.P_transmittedAsymptoticConversionResult.E_source_initialAsymptoticConversionResult.E_target_finalAsymptoticConversionResult.source_fieldAsymptoticConversionResult.target_fieldAsymptoticConversionResult.source_wavevector
ConversionResultConversionResult.timesConversionResult.probabilityConversionResult.source_energyConversionResult.target_energyConversionResult.total_energyConversionResult.relative_energy_errorConversionResult.source_fieldConversionResult.target_fieldConversionResult.timesConversionResult.probabilityConversionResult.source_energyConversionResult.target_energyConversionResult.total_energyConversionResult.relative_energy_errorConversionResult.source_fieldConversionResult.target_field
CriticalFieldResultDispersionResultDispersionResult.wavenumbersDispersionResult.frequenciesDispersionResult.powerDispersionResult.peak_frequenciesDispersionResult.peak_powersDispersionResult.field_nameDispersionResult.rayleigh_resolutionDispersionResult.wavenumbersDispersionResult.frequenciesDispersionResult.powerDispersionResult.peak_frequenciesDispersionResult.peak_powersDispersionResult.field_nameDispersionResult.rayleigh_resolution
EffectiveMassResultEffectiveMassResult.m2_effEffectiveMassResult.m2_eff_stdEffectiveMassResult.m2_eff_valuesEffectiveMassResult.wavenumbersEffectiveMassResult.frequenciesEffectiveMassResult.n_active_modesEffectiveMassResult.field_nameEffectiveMassResult.m2_effEffectiveMassResult.m2_eff_stdEffectiveMassResult.m2_eff_valuesEffectiveMassResult.wavenumbersEffectiveMassResult.frequenciesEffectiveMassResult.n_active_modesEffectiveMassResult.field_name
EnergyDiagnosticsEnergyDiagnostics.timesEnergyDiagnostics.total_energyEnergyDiagnostics.relative_errorEnergyDiagnostics.max_relative_errorEnergyDiagnostics.is_conservedEnergyDiagnostics.timesEnergyDiagnostics.total_energyEnergyDiagnostics.relative_errorEnergyDiagnostics.max_relative_errorEnergyDiagnostics.is_conserved
FieldEnergyMixingResultMixingResult.mixing_lengthMixingResult.mixing_length_uncertaintyMixingResult.dominant_frequencyMixingResult.frequency_fwhmMixingResult.max_conversionMixingResult.peaksMixingResult.mixing_lengthMixingResult.mixing_length_uncertaintyMixingResult.dominant_frequencyMixingResult.frequency_fwhmMixingResult.max_conversionMixingResult.peaks
MixingSpectrumMixingSpectrum.frequenciesMixingSpectrum.powerMixingSpectrum.dominant_frequencyMixingSpectrum.dominant_mixing_lengthMixingSpectrum.rayleigh_resolutionMixingSpectrum.frequenciesMixingSpectrum.powerMixingSpectrum.dominant_frequencyMixingSpectrum.dominant_mixing_lengthMixingSpectrum.rayleigh_resolution
ResonanceResultResonanceResult.wavenumbersResonanceResult.omega_sourceResonanceResult.omega_targetResonanceResult.resonance_mismatchResonanceResult.resonant_modesResonanceResult.n_resonant_modesResonanceResult.conversion_bandwidthResonanceResult.peak_conversion_kResonanceResult.source_fieldResonanceResult.target_fieldResonanceResult.wavenumbersResonanceResult.omega_sourceResonanceResult.omega_targetResonanceResult.resonance_mismatchResonanceResult.resonant_modesResonanceResult.n_resonant_modesResonanceResult.conversion_bandwidthResonanceResult.peak_conversion_kResonanceResult.source_fieldResonanceResult.target_field
SimulationDataSimulationData.timesSimulationData.fieldsSimulationData.velocitiesSimulationData.grid_spacingSimulationData.grid_boundsSimulationData.periodicSimulationData.specSimulationData.parametersSimulationData.bc_typesSimulationData.bc_typesSimulationData.dtSimulationData.dynamical_fieldsSimulationData.from_directory()SimulationData.from_result()SimulationData.load()SimulationData.n_snapshotsSimulationData.save()SimulationData.volume_elementSimulationData.timesSimulationData.fieldsSimulationData.velocitiesSimulationData.grid_spacingSimulationData.grid_boundsSimulationData.periodicSimulationData.specSimulationData.parameters
SnapshotWriterSpectralPeakSpectralSnapshotSystemEnergyVelocityMismatchResultVelocityMismatchResult.source_velocityVelocityMismatchResult.target_velocityVelocityMismatchResult.mismatchVelocityMismatchResult.shared_wavenumbersVelocityMismatchResult.max_mismatchVelocityMismatchResult.mean_mismatchVelocityMismatchResult.source_velocityVelocityMismatchResult.target_velocityVelocityMismatchResult.mismatchVelocityMismatchResult.shared_wavenumbersVelocityMismatchResult.max_mismatchVelocityMismatchResult.mean_mismatch
VelocityResultVelocityResult.wavenumbersVelocityResult.group_velocityVelocityResult.phase_velocityVelocityResult.group_velocity_meanVelocityResult.phase_velocity_meanVelocityResult.n_active_modesVelocityResult.field_nameVelocityResult.wavenumbersVelocityResult.group_velocityVelocityResult.phase_velocityVelocityResult.group_velocity_meanVelocityResult.phase_velocity_meanVelocityResult.n_active_modesVelocityResult.field_name
check_energy_conservation()compute_asymptotic_conversion()compute_conversion_probability()compute_critical_field()compute_dispersion()compute_effective_mass()compute_energy_timeseries()compute_group_conversion()compute_mixing_length()compute_mixing_spectrum()compute_mode_amplitudes()compute_reference_threshold()compute_resonance_analysis()compute_snapshot_count()compute_spectral_energy()compute_spectrum()compute_system_energy()compute_velocities()compute_velocity_mismatch()create_snapshot_callback()critical_field_to_sweep_results()summarize()
- tidal.solver package
CoefficientEvaluatorFieldSetFieldSet.as_dict()FieldSet.check_finite()FieldSet.copy()FieldSet.field_namesFieldSet.fields_dict()FieldSet.flatFieldSet.from_dict()FieldSet.from_flat()FieldSet.grid_shapeFieldSet.layoutFieldSet.max_norm()FieldSet.momenta_dict()FieldSet.momentum_namesFieldSet.rebind()FieldSet.set_aux()FieldSet.slot_namesFieldSet.velocities_dict()FieldSet.velocity_namesFieldSet.zeros()
GridInfoRHSEvaluatorSimulationDivergedErrorSolverResultStabilityResultStateLayoutStateLayout.slotsStateLayout.num_pointsStateLayout.field_slot_mapStateLayout.velocity_slot_mapStateLayout.dynamical_fieldsStateLayout.algebraic_indicesStateLayout.constraint_slot_groupsStateLayout.drift_slot_pairsStateLayout.dynamical_field_slot_groupsStateLayout.first_order_slot_groupsStateLayout.from_spec()StateLayout.momentum_slot_mapStateLayout.num_slotsStateLayout.slot_name_to_idxStateLayout.slot_slice()StateLayout.total_sizeStateLayout.velocity_slot_groupsStateLayout.slotsStateLayout.num_pointsStateLayout.field_slot_mapStateLayout.velocity_slot_mapStateLayout.dynamical_fields
apply_operator()check_cfl_stability()check_mass_sign()check_pointwise_mass_stability()operator_min_dim()validate_field_references()validate_operator_dimensions()- Submodules
- tidal.solver.analytical_jacobian module
- tidal.solver.coefficients module
- tidal.solver.constraint_solve module
- tidal.solver.cvode module
- tidal.solver.fields module
FieldSetFieldSet.set_aux()FieldSet.flatFieldSet.layoutFieldSet.grid_shapeFieldSet.field_namesFieldSet.velocity_namesFieldSet.momentum_namesFieldSet.slot_namesFieldSet.fields_dict()FieldSet.velocities_dict()FieldSet.momenta_dict()FieldSet.as_dict()FieldSet.copy()FieldSet.zeros()FieldSet.from_flat()FieldSet.rebind()FieldSet.from_dict()FieldSet.max_norm()FieldSet.check_finite()
- tidal.solver.grid module
- tidal.solver.ida module
- tidal.solver.leapfrog module
- tidal.solver.modal module
- tidal.solver.operators module
- Operator modes
- Finite-difference accuracy orders
- Boundary condition types
set_fd_order()get_fd_order()get_n_ghost()set_spectral()get_spectral()get_wavenumbers()SideBCSpecAxisBCSpecis_periodic_bc()BCSpecgradient()directional_laplacian()laplacian()cross_derivative()biharmonic()identity()operator_min_dim()apply_operator()
- tidal.solver.progress module
- tidal.solver.rhs module
- tidal.solver.scipy_solver module
- tidal.solver.sparsity module
- tidal.solver.state module
SlotInfoStateLayoutStateLayout.slotsStateLayout.num_pointsStateLayout.field_slot_mapStateLayout.velocity_slot_mapStateLayout.dynamical_fieldsStateLayout.slotsStateLayout.num_pointsStateLayout.field_slot_mapStateLayout.velocity_slot_mapStateLayout.dynamical_fieldsStateLayout.momentum_slot_mapStateLayout.from_spec()StateLayout.slot_name_to_idxStateLayout.total_sizeStateLayout.num_slotsStateLayout.slot_slice()StateLayout.velocity_slot_groupsStateLayout.dynamical_field_slot_groupsStateLayout.drift_slot_pairsStateLayout.first_order_slot_groupsStateLayout.constraint_slot_groupsStateLayout.algebraic_indices
state_to_flat()flat_to_fields()
- tidal.solver.validation module
- tidal.symbolic package
BoundaryConditionComponentEquationComponentEquation.field_nameComponentEquation.field_indexComponentEquation.time_derivative_orderComponentEquation.rhs_termsComponentEquation.constraint_solverComponentEquation.from_dict()ComponentEquation.field_nameComponentEquation.field_indexComponentEquation.time_derivative_orderComponentEquation.rhs_termsComponentEquation.constraint_solver
ConstraintSolverConfigConstraintSolverConfig.enabledConstraintSolverConfig.methodConstraintSolverConfig.boundary_conditionsConstraintSolverConfig.max_iterationsConstraintSolverConfig.toleranceConstraintSolverConfig.enabledConstraintSolverConfig.from_dict()ConstraintSolverConfig.max_iterationsConstraintSolverConfig.methodConstraintSolverConfig.toleranceConstraintSolverConfig.boundary_conditions
EquationSystemEquationSystem.n_componentsEquationSystem.dimensionEquationSystem.spatial_dimensionEquationSystem.component_namesEquationSystem.equationsEquationSystem.mass_matrixEquationSystem.coupling_matrixEquationSystem.metadataEquationSystem.coordinatesEquationSystem.canonicalEquationSystem.canonicalEquationSystem.coordinatesEquationSystem.coupling_matrix_symbolicEquationSystem.effective_coordinatesEquationSystem.equation_mapEquationSystem.from_dict()EquationSystem.has_constraint_velocity_termsEquationSystem.mass_matrix_symbolicEquationSystem.spatial_coordinatesEquationSystem.state_layoutEquationSystem.state_sizeEquationSystem.time_ordersEquationSystem.n_componentsEquationSystem.dimensionEquationSystem.spatial_dimensionEquationSystem.component_namesEquationSystem.equationsEquationSystem.mass_matrixEquationSystem.coupling_matrixEquationSystem.metadata
OperatorTermOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.fieldOperatorTerm.coefficient_symbolicOperatorTerm.time_dependentOperatorTerm.coordinate_dependentOperatorTerm.coefficient_symbolicOperatorTerm.coordinate_dependentOperatorTerm.from_dict()OperatorTerm.position_dependentOperatorTerm.time_dependentOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.field
load_equation_system()- Submodules
- tidal.symbolic.json_loader module
AXIS_LETTERSis_known_operator()LHSStructureOperatorTermOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.fieldOperatorTerm.coefficient_symbolicOperatorTerm.time_dependentOperatorTerm.coordinate_dependentOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.fieldOperatorTerm.coefficient_symbolicOperatorTerm.time_dependentOperatorTerm.coordinate_dependentOperatorTerm.position_dependentOperatorTerm.from_dict()
BoundaryConditionConstraintSolverConfigConstraintSolverConfig.enabledConstraintSolverConfig.methodConstraintSolverConfig.boundary_conditionsConstraintSolverConfig.max_iterationsConstraintSolverConfig.toleranceConstraintSolverConfig.enabledConstraintSolverConfig.methodConstraintSolverConfig.boundary_conditionsConstraintSolverConfig.max_iterationsConstraintSolverConfig.toleranceConstraintSolverConfig.from_dict()
HamiltonianFactorHamiltonianTermHamiltonianTerm.coefficientHamiltonianTerm.factor_aHamiltonianTerm.factor_bHamiltonianTerm.coefficient_symbolicHamiltonianTerm.coordinate_dependentHamiltonianTerm.term_classHamiltonianTerm.coefficientHamiltonianTerm.factor_aHamiltonianTerm.factor_bHamiltonianTerm.coefficient_symbolicHamiltonianTerm.coordinate_dependentHamiltonianTerm.term_classHamiltonianTerm.position_dependentHamiltonianTerm.is_self_energyHamiltonianTerm.base_field_aHamiltonianTerm.base_field_bHamiltonianTerm.from_dict()
CanonicalStructureComponentEquationComponentEquation.field_nameComponentEquation.field_indexComponentEquation.time_derivative_orderComponentEquation.rhs_termsComponentEquation.constraint_solverComponentEquation.field_nameComponentEquation.field_indexComponentEquation.time_derivative_orderComponentEquation.rhs_termsComponentEquation.constraint_solverComponentEquation.from_dict()
EquationSystemEquationSystem.n_componentsEquationSystem.dimensionEquationSystem.spatial_dimensionEquationSystem.component_namesEquationSystem.equationsEquationSystem.mass_matrixEquationSystem.coupling_matrixEquationSystem.metadataEquationSystem.coordinatesEquationSystem.canonicalEquationSystem.n_componentsEquationSystem.dimensionEquationSystem.spatial_dimensionEquationSystem.component_namesEquationSystem.equationsEquationSystem.mass_matrixEquationSystem.coupling_matrixEquationSystem.metadataEquationSystem.coordinatesEquationSystem.mass_matrix_symbolicEquationSystem.coupling_matrix_symbolicEquationSystem.canonicalEquationSystem.time_ordersEquationSystem.state_sizeEquationSystem.state_layoutEquationSystem.effective_coordinatesEquationSystem.spatial_coordinatesEquationSystem.has_constraint_velocity_termsEquationSystem.equation_mapEquationSystem.from_dict()
validate_json_schema()load_equation_system()
- tidal.symbolic.latex module
- tidal.symbolic.ostrogradsky module
- tidal.symbolic.reduction module
Submodules#
tidal.plot_pgf module#
- tidal.plot_pgf.check_tex_available()[source]#
Check if LaTeX executables are available on the system.
- Return type:
- tidal.plot_pgf.enable_pgf(texsystem='pdflatex', *, serif=True, base_size=10, fallback_on_error=True)[source]#
Enable PGF backend for matplotlib with LaTeX rendering.
If LaTeX or PGF backend is not available, falls back to standard matplotlib settings with similar font configuration.
- Args:
texsystem: LaTeX system to use (pdflatex, xelatex, or lualatex) serif: Whether to use serif fonts base_size: Base font size fallback_on_error: Whether to fall back to standard matplotlib on error
- Raises:
RuntimeError – If PGF backend, LaTeX system, or PDF converter is not available and fallback_on_error is False.
- Parameters:
- Return type:
None