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.inference package
ConstraintSetInferenceResultInferenceResult.best()InferenceResult.credible_interval()InferenceResult.effective_sample_size()InferenceResult.from_directory()InferenceResult.log_evidenceInferenceResult.log_evidence_errInferenceResult.log_posteriorInferenceResult.metricsInferenceResult.n_paramsInferenceResult.n_samplesInferenceResult.parameter_importance()InferenceResult.posterior_mean()InferenceResult.save()InferenceResult.to_anesthetic()InferenceResult.to_sweep_results()InferenceResult.weightsInferenceResult.samplesInferenceResult.log_likelihoodInferenceResult.log_priorInferenceResult.param_namesInferenceResult.methodInferenceResult.metadata
ParameterImportanceResultParameterImportanceResult.param_namesParameterImportanceResult.d_klParameterImportanceResult.d_kl_errParameterImportanceResult.d_gParameterImportanceResult.d_g_errParameterImportanceResult.marginal_d_klParameterImportanceResult.log_evidenceParameterImportanceResult.log_evidence_errParameterImportanceResult.consistency
Priorparse_constraint()
- 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
CoefficientEvaluatorCoefficientEvaluator.all_constant()CoefficientEvaluator.all_time_independent()CoefficientEvaluator.begin_timestep()CoefficientEvaluator.bsm_separable_factors()CoefficientEvaluator.check_periodic_coefficient_continuity()CoefficientEvaluator.classify_bsm_separability()CoefficientEvaluator.parametersCoefficientEvaluator.resolve()
FieldSetFieldSet.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()
GridInfoKineticEvaluationErrorPerturbativeResultPerturbativeSolverRHSEvaluatorSimulationDivergedErrorSolverResultStabilityResultStateLayoutStateLayout.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.implicit_dynamical_fieldsStateLayout.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()find_independent_blocks()operator_min_dim()solve_modal()solve_modal_pass1()validate_field_references()validate_operator_dimensions()- Submodules
- tidal.solver.analytical_jacobian module
- tidal.solver.coefficients module
CoefficientEvaluatorCoefficientEvaluator.parametersCoefficientEvaluator.resolve()CoefficientEvaluator.classify_bsm_separability()CoefficientEvaluator.bsm_separable_factors()CoefficientEvaluator.begin_timestep()CoefficientEvaluator.all_constant()CoefficientEvaluator.all_time_independent()CoefficientEvaluator.check_periodic_coefficient_continuity()
- 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.modal_jax 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.perturbative_driver module
- 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.implicit_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.kinetic_coefficient_symbolicComponentEquation.kinetic_position_dependentComponentEquation.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.base_spec()EquationSystem.canonicalEquationSystem.canonicalize_kinetic_for_perturbation()EquationSystem.coordinatesEquationSystem.coupling_matrix_symbolicEquationSystem.dependency_closure()EquationSystem.effective_coordinatesEquationSystem.equation_mapEquationSystem.filter_by_order()EquationSystem.from_dict()EquationSystem.has_constraint_velocity_termsEquationSystem.has_corrections()EquationSystem.has_position_dependent_kinetic()EquationSystem.implicit_dynamical_sectorEquationSystem.mass_matrix_symbolicEquationSystem.max_order()EquationSystem.signatureEquationSystem.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.order_in_epsOperatorTerm.coefficient_symbolicOperatorTerm.coordinate_dependentOperatorTerm.from_dict()OperatorTerm.order_in_epsOperatorTerm.position_dependentOperatorTerm.time_dependentOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.field
load_equation_system()normalize_kinetic_coefficients()- Submodules
- tidal.symbolic.json_loader module
AXIS_LETTERSis_known_operator()operator_time_order()LHSStructureOperatorTermOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.fieldOperatorTerm.coefficient_symbolicOperatorTerm.time_dependentOperatorTerm.coordinate_dependentOperatorTerm.order_in_epsOperatorTerm.coefficientOperatorTerm.operatorOperatorTerm.fieldOperatorTerm.coefficient_symbolicOperatorTerm.time_dependentOperatorTerm.coordinate_dependentOperatorTerm.order_in_epsOperatorTerm.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.order_in_epsHamiltonianTerm.coefficientHamiltonianTerm.factor_aHamiltonianTerm.factor_bHamiltonianTerm.coefficient_symbolicHamiltonianTerm.coordinate_dependentHamiltonianTerm.term_classHamiltonianTerm.order_in_epsHamiltonianTerm.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.kinetic_coefficient_symbolicComponentEquation.kinetic_position_dependentComponentEquation.from_dict()
ImplicitDynamicalSectorEquationSystemEquationSystem.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.signatureEquationSystem.mass_matrix_symbolicEquationSystem.coupling_matrix_symbolicEquationSystem.canonicalEquationSystem.time_ordersEquationSystem.state_sizeEquationSystem.state_layoutEquationSystem.effective_coordinatesEquationSystem.spatial_coordinatesEquationSystem.has_constraint_velocity_termsEquationSystem.equation_mapEquationSystem.implicit_dynamical_sectorEquationSystem.dependency_closure()EquationSystem.filter_by_order()EquationSystem.max_order()EquationSystem.has_corrections()EquationSystem.has_position_dependent_kinetic()EquationSystem.canonicalize_kinetic_for_perturbation()EquationSystem.base_spec()EquationSystem.from_dict()
validate_json_schema()SpecRestrictionrestrict_spec_dict()load_equation_system()normalize_kinetic_coefficients()
- tidal.symbolic.kinetic_matrix module
KineticMatrixCellKineticMatrixKineticMatrix.row_fieldsKineticMatrix.column_fieldsKineticMatrix.cellsKineticMatrix.row_fieldsKineticMatrix.column_fieldsKineticMatrix.cellsKineticMatrix.row_index()KineticMatrix.column_index()KineticMatrix.get()KineticMatrix.n_rowsKineticMatrix.n_colsKineticMatrix.is_squareKineticMatrix.fieldsKineticMatrix.field_index()KineticMatrix.n
build_kinetic_matrix()
- tidal.symbolic.latex module
- tidal.symbolic.reduction module
- tidal.symbolic.sign_algebra module
- tidal.symbolic.spec_query module
- Why this layer is Python and not Wolfram
CoefficientProvenanceCoefficientProvenance.effectiveCoefficientProvenance.order_spreadCoefficientProvenance.matrix_entryCoefficientProvenance.hamiltonian_termsCoefficientProvenance.checksCoefficientProvenance.effectiveCoefficientProvenance.order_spreadCoefficientProvenance.matrix_entryCoefficientProvenance.hamiltonian_termsCoefficientProvenance.checks
ConsistencyCheckEffectiveCoefficientEffectiveCoefficient.equation_fieldEffectiveCoefficient.fieldEffectiveCoefficient.operatorEffectiveCoefficient.termsEffectiveCoefficient.numeratorEffectiveCoefficient.kineticEffectiveCoefficient.equation_fieldEffectiveCoefficient.fieldEffectiveCoefficient.operatorEffectiveCoefficient.termsEffectiveCoefficient.numeratorEffectiveCoefficient.kineticEffectiveCoefficient.existsEffectiveCoefficient.expressionEffectiveCoefficient.term_countEffectiveCoefficient.sign()EffectiveCoefficient.value()
EquationComparisonFieldFamilySystemDiffcoefficient_provenance()compare_equations()diff_systems()effective_coefficient()field_families()self_terms()terms_for()
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