analytic-continuation

User Guide

  • API Reference
    • Main Package
      • SpaceAdapter
        • SpaceAdapter.__init__()
        • SpaceAdapter.offset
        • SpaceAdapter.scale
        • SpaceAdapter.screen_to_logical()
        • SpaceAdapter.logical_to_screen()
        • SpaceAdapter.screen_to_complex()
        • SpaceAdapter.complex_to_screen()
        • SpaceAdapter.transform_point_to_logical()
        • SpaceAdapter.transform_point_to_screen()
        • SpaceAdapter.transform_points_to_logical()
        • SpaceAdapter.transform_points_to_screen()
        • SpaceAdapter.transform_spline_to_logical()
        • SpaceAdapter.transform_spline_to_screen()
        • SpaceAdapter.transform_spline_export_to_logical()
        • SpaceAdapter.screen_distance_to_logical()
        • SpaceAdapter.logical_distance_to_screen()
        • SpaceAdapter.with_params()
        • SpaceAdapter.zoom()
        • SpaceAdapter.pan()
        • SpaceAdapter.to_dict()
        • SpaceAdapter.from_dict()
      • TransformParams
        • TransformParams.offset_x
        • TransformParams.offset_y
        • TransformParams.scale_x
        • TransformParams.scale_y
        • TransformParams.scale_y_effective
        • TransformParams.is_uniform
        • TransformParams.to_dict()
        • TransformParams.from_dict()
        • TransformParams.from_view_bounds()
        • TransformParams.__init__()
      • Point
        • Point.x
        • Point.y
        • Point.index
        • Point.to_complex()
        • Point.from_complex()
        • Point.to_dict()
        • Point.from_dict()
        • Point.__init__()
      • Spline
        • Spline.points
        • Spline.closed
        • Spline.to_dict()
        • Spline.from_dict()
        • Spline.__init__()
      • SplineExport
        • SplineExport.version
        • SplineExport.timestamp
        • SplineExport.closed
        • SplineExport.parameters
        • SplineExport.controlPoints
        • SplineExport.spline
        • SplineExport.adaptivePolyline
        • SplineExport.stats
        • SplineExport.get_polyline()
        • SplineExport.to_dict()
        • SplineExport.from_dict()
        • SplineExport.from_json()
        • SplineExport.to_json()
        • SplineExport.__init__()
      • LaurentMap
        • LaurentMap.N
        • LaurentMap.a0
        • LaurentMap.a
        • LaurentMap.b
        • LaurentMap.to_dict()
        • LaurentMap.from_dict()
        • LaurentMap.__init__()
      • Complex
        • Complex.re
        • Complex.im
        • Complex.to_complex()
        • Complex.from_complex()
        • Complex.to_dict()
        • Complex.from_dict()
        • Complex.__init__()
      • Singularity
        • Singularity.x
        • Singularity.y
        • Singularity.multiplicity
        • Singularity.z
        • Singularity.to_dict()
        • Singularity.from_dict()
        • Singularity.from_point()
        • Singularity.__init__()
      • MeromorphicBuilder
        • MeromorphicBuilder.__init__()
        • MeromorphicBuilder.zeros
        • MeromorphicBuilder.poles
        • MeromorphicBuilder.add_zero()
        • MeromorphicBuilder.add_pole()
        • MeromorphicBuilder.add_zero_from_screen()
        • MeromorphicBuilder.add_pole_from_screen()
        • MeromorphicBuilder.clear()
        • MeromorphicBuilder.remove_zero()
        • MeromorphicBuilder.remove_pole()
        • MeromorphicBuilder.build_expression()
        • MeromorphicBuilder.to_dict()
        • MeromorphicBuilder.from_dict()
      • build_meromorphic_expression()
      • meromorphic_from_points()
      • LaurentFitConfig
        • LaurentFitConfig.N_min
        • LaurentFitConfig.N_max
        • LaurentFitConfig.m_samples
        • LaurentFitConfig.lambda_init
        • LaurentFitConfig.lambda_increase_factor
        • LaurentFitConfig.max_lambda_tries
        • LaurentFitConfig.reparam_iters
        • LaurentFitConfig.theta_search_grid
        • LaurentFitConfig.theta_refine_iters
        • LaurentFitConfig.fit_tol_max_factor
        • LaurentFitConfig.prefer_smallest_N
        • LaurentFitConfig.rho_in
        • LaurentFitConfig.rho_out
        • LaurentFitConfig.check_theta_grid
        • LaurentFitConfig.min_abs_deriv_factor
        • LaurentFitConfig.min_sep_factor
        • LaurentFitConfig.poly_eps_factor
        • LaurentFitConfig.from_pipeline_config()
        • LaurentFitConfig.__init__()
      • LaurentMapResult
        • LaurentMapResult.N
        • LaurentMapResult.a0
        • LaurentMapResult.a
        • LaurentMapResult.b
        • LaurentMapResult.eval()
        • LaurentMapResult.eval_array()
        • LaurentMapResult.deriv()
        • LaurentMapResult.deriv_array()
        • LaurentMapResult.to_laurent_map()
        • LaurentMapResult.from_laurent_map()
        • LaurentMapResult.__init__()
      • FitResult
        • FitResult.ok
        • FitResult.failure_reason
        • FitResult.curve_scale
        • FitResult.polyline_used
        • FitResult.laurent_map
        • FitResult.fit_max_err
        • FitResult.fit_rms_err
        • FitResult.simple_on_unit_circle
        • FitResult.min_abs_deriv_unit
        • FitResult.min_sep_unit
        • FitResult.min_sep_in
        • FitResult.min_sep_out
        • FitResult.__init__()
      • fit_laurent_map()
      • load_polyline_from_export()
      • estimate_diameter()
      • Pole
        • Pole.z
        • Pole.multiplicity
        • Pole.__init__()
      • HolomorphicCheckConfig
        • HolomorphicCheckConfig.theta_grid
        • HolomorphicCheckConfig.rho_samples
        • HolomorphicCheckConfig.pole_margin_factor
        • HolomorphicCheckConfig.shrink_steps
        • HolomorphicCheckConfig.from_pipeline_config()
        • HolomorphicCheckConfig.__init__()
      • InvertConfig
        • InvertConfig.theta_grid
        • InvertConfig.seed_radii
        • InvertConfig.max_iters
        • InvertConfig.tol_abs_factor
        • InvertConfig.tol_rel_factor
        • InvertConfig.damping
        • InvertConfig.max_backtracks
        • InvertConfig.from_pipeline_config()
        • InvertConfig.__init__()
      • HolomorphicCheckResult
        • HolomorphicCheckResult.ok
        • HolomorphicCheckResult.min_pole_distance
        • HolomorphicCheckResult.closest_pole
        • HolomorphicCheckResult.failure_reason
        • HolomorphicCheckResult.updated_rho_in
        • HolomorphicCheckResult.updated_rho_out
        • HolomorphicCheckResult.__init__()
      • InvertResult
        • InvertResult.converged
        • InvertResult.zeta
        • InvertResult.residual
        • InvertResult.iters
        • InvertResult.__init__()
      • CompositionResult
        • CompositionResult.ok
        • CompositionResult.value
        • CompositionResult.zeta
        • CompositionResult.residual
        • CompositionResult.N
        • CompositionResult.failure_reason
        • CompositionResult.__init__()
      • check_f_holomorphic_on_annulus()
      • invert_z()
      • compute_composition()
      • compute_continuation_grid()
      • PipelineLogger
        • PipelineLogger.__new__()
        • PipelineLogger.__init__()
        • PipelineLogger.register_progress_callback()
        • PipelineLogger.unregister_progress_callback()
        • PipelineLogger.compute_input_hash()
        • PipelineLogger.find_resumable_session()
        • PipelineLogger.start_session()
        • PipelineLogger.update_session_stage()
        • PipelineLogger.get_session()
        • PipelineLogger.list_sessions()
        • PipelineLogger.start_task()
        • PipelineLogger.update_task()
        • PipelineLogger.complete_task()
        • PipelineLogger.cache_computation()
        • PipelineLogger.get_cached_computation()
        • PipelineLogger.end_session()
        • PipelineLogger.get_current_progress()
        • PipelineLogger.debug()
        • PipelineLogger.info()
        • PipelineLogger.warning()
        • PipelineLogger.error()
      • TaskStatus
        • TaskStatus.PENDING
        • TaskStatus.IN_PROGRESS
        • TaskStatus.COMPLETED
        • TaskStatus.FAILED
        • TaskStatus.SKIPPED
        • TaskStatus.__new__()
      • TaskProgress
        • TaskProgress.task_id
        • TaskProgress.name
        • TaskProgress.status
        • TaskProgress.progress
        • TaskProgress.message
        • TaskProgress.started_at
        • TaskProgress.completed_at
        • TaskProgress.error
        • TaskProgress.metadata
        • TaskProgress.to_dict()
        • TaskProgress.__init__()
      • PipelineSession
        • PipelineSession.session_id
        • PipelineSession.created_at
        • PipelineSession.expression
        • PipelineSession.curve_data
        • PipelineSession.zeros
        • PipelineSession.poles
        • PipelineSession.tasks
        • PipelineSession.result
        • PipelineSession.status
        • PipelineSession.to_dict()
        • PipelineSession.__init__()
      • get_logger()
      • ProgressTracker
        • ProgressTracker.__init__()
        • ProgressTracker.subscribe()
        • ProgressTracker.get_state()
        • ProgressTracker.start_stage()
        • ProgressTracker.update_stage()
        • ProgressTracker.complete_stage()
        • ProgressTracker.skip_stage()
        • ProgressTracker.sync_start_stage()
        • ProgressTracker.sync_update_stage()
        • ProgressTracker.sync_complete_stage()
      • StageInfo
        • StageInfo.id
        • StageInfo.name
        • StageInfo.description
        • StageInfo.status
        • StageInfo.progress
        • StageInfo.message
        • StageInfo.substeps_total
        • StageInfo.substeps_done
        • StageInfo.started_at
        • StageInfo.completed_at
        • StageInfo.error
        • StageInfo.to_dict()
        • StageInfo.__init__()
      • format_cli_progress()
      • CesaroRepresentation
        • CesaroRepresentation.arc_lengths
        • CesaroRepresentation.curvatures
        • CesaroRepresentation.total_arc_length
        • CesaroRepresentation.samples
        • CesaroRepresentation.arc_lengths
        • CesaroRepresentation.curvatures
        • CesaroRepresentation.total_arc_length
        • CesaroRepresentation.samples
        • CesaroRepresentation.kappa_at()
        • CesaroRepresentation.to_dict()
        • CesaroRepresentation.from_dict()
        • CesaroRepresentation.__init__()
      • WhewellRepresentation
        • WhewellRepresentation.arc_lengths
        • WhewellRepresentation.tangent_angles
        • WhewellRepresentation.total_arc_length
        • WhewellRepresentation.winding_number
        • WhewellRepresentation.samples
        • WhewellRepresentation.arc_lengths
        • WhewellRepresentation.tangent_angles
        • WhewellRepresentation.total_arc_length
        • WhewellRepresentation.winding_number
        • WhewellRepresentation.samples
        • WhewellRepresentation.phi_at()
        • WhewellRepresentation.to_dict()
        • WhewellRepresentation.from_dict()
        • WhewellRepresentation.__init__()
      • LogBijectionData
        • LogBijectionData.laurent_N
        • LogBijectionData.laurent_a0
        • LogBijectionData.laurent_a
        • LogBijectionData.laurent_b
        • LogBijectionData.curve_scale
        • LogBijectionData.theta_samples
        • LogBijectionData.log_z_samples
        • LogBijectionData.z_samples
        • LogBijectionData.log_derivative_samples
        • LogBijectionData.to_dict()
        • LogBijectionData.from_dict()
        • LogBijectionData.__init__()
      • ComplexityEstimates
        • ComplexityEstimates.total_curvature
        • ComplexityEstimates.curvature_variation
        • ComplexityEstimates.max_curvature
        • ComplexityEstimates.mean_curvature
        • ComplexityEstimates.curvature_std
        • ComplexityEstimates.winding_number
        • ComplexityEstimates.total_arc_length
        • ComplexityEstimates.log_deriv_variation
        • ComplexityEstimates.arg_deriv_variation
        • ComplexityEstimates.min_jacobian
        • ComplexityEstimates.max_jacobian
        • ComplexityEstimates.jacobian_ratio
        • ComplexityEstimates.inversion_difficulty
        • ComplexityEstimates.sampling_density_factor
        • ComplexityEstimates.newton_convergence_factor
        • ComplexityEstimates.to_dict()
        • ComplexityEstimates.from_dict()
        • ComplexityEstimates.summary()
        • ComplexityEstimates.__init__()
      • IntrinsicCurveAnalysis
        • IntrinsicCurveAnalysis.log_data
        • IntrinsicCurveAnalysis.cesaro
        • IntrinsicCurveAnalysis.whewell
        • IntrinsicCurveAnalysis.complexity
        • IntrinsicCurveAnalysis.to_dict()
        • IntrinsicCurveAnalysis.from_dict()
        • IntrinsicCurveAnalysis.summary()
        • IntrinsicCurveAnalysis.__init__()
      • analyze_bijection()
      • compute_log_bijection()
      • compute_cesaro_form()
      • compute_whewell_form()
      • estimate_complexity()
      • suggest_inversion_config()
      • ContourPreCheckResult
        • ContourPreCheckResult.ok
        • ContourPreCheckResult.proceed
        • ContourPreCheckResult.is_closed
        • ContourPreCheckResult.is_simple
        • ContourPreCheckResult.has_sufficient_points
        • ContourPreCheckResult.has_reasonable_aspect
        • ContourPreCheckResult.has_reasonable_curvature
        • ContourPreCheckResult.num_points
        • ContourPreCheckResult.perimeter
        • ContourPreCheckResult.bounding_box
        • ContourPreCheckResult.aspect_ratio
        • ContourPreCheckResult.estimated_diameter
        • ContourPreCheckResult.min_segment_length
        • ContourPreCheckResult.max_segment_length
        • ContourPreCheckResult.max_turning_angle
        • ContourPreCheckResult.warnings
        • ContourPreCheckResult.errors
        • ContourPreCheckResult.estimated_difficulty
        • ContourPreCheckResult.estimated_fit_time_seconds
        • ContourPreCheckResult.to_dict()
        • ContourPreCheckResult.__init__()
      • precheck_contour()
      • precheck_contour_from_spline_export()
      • get_schema()
      • get_config()
      • get_example()
      • validate()
      • list_schemas()
      • list_configs()
      • list_examples()
      • SchemaNotFoundError
      • ValidationError
    • Types Module
      • Point
        • Point.x
        • Point.y
        • Point.index
        • Point.to_complex()
        • Point.from_complex()
        • Point.to_dict()
        • Point.from_dict()
        • Point.__init__()
      • Spline
        • Spline.points
        • Spline.closed
        • Spline.to_dict()
        • Spline.from_dict()
        • Spline.__init__()
      • SplineParameters
        • SplineParameters.tension
        • SplineParameters.adaptiveTolerance
        • SplineParameters.minDistance
        • SplineParameters.to_dict()
        • SplineParameters.from_dict()
        • SplineParameters.__init__()
      • SplineExport
        • SplineExport.version
        • SplineExport.timestamp
        • SplineExport.closed
        • SplineExport.parameters
        • SplineExport.controlPoints
        • SplineExport.spline
        • SplineExport.adaptivePolyline
        • SplineExport.stats
        • SplineExport.get_polyline()
        • SplineExport.to_dict()
        • SplineExport.from_dict()
        • SplineExport.from_json()
        • SplineExport.to_json()
        • SplineExport.__init__()
      • Complex
        • Complex.re
        • Complex.im
        • Complex.to_complex()
        • Complex.from_complex()
        • Complex.to_dict()
        • Complex.from_dict()
        • Complex.__init__()
      • LaurentMap
        • LaurentMap.N
        • LaurentMap.a0
        • LaurentMap.a
        • LaurentMap.b
        • LaurentMap.to_dict()
        • LaurentMap.from_dict()
        • LaurentMap.__init__()
    • Space Adapter Module
      • TransformParams
        • TransformParams.offset_x
        • TransformParams.offset_y
        • TransformParams.scale_x
        • TransformParams.scale_y
        • TransformParams.scale_y_effective
        • TransformParams.is_uniform
        • TransformParams.to_dict()
        • TransformParams.from_dict()
        • TransformParams.from_view_bounds()
        • TransformParams.__init__()
      • SpaceAdapter
        • SpaceAdapter.__init__()
        • SpaceAdapter.offset
        • SpaceAdapter.scale
        • SpaceAdapter.screen_to_logical()
        • SpaceAdapter.logical_to_screen()
        • SpaceAdapter.screen_to_complex()
        • SpaceAdapter.complex_to_screen()
        • SpaceAdapter.transform_point_to_logical()
        • SpaceAdapter.transform_point_to_screen()
        • SpaceAdapter.transform_points_to_logical()
        • SpaceAdapter.transform_points_to_screen()
        • SpaceAdapter.transform_spline_to_logical()
        • SpaceAdapter.transform_spline_to_screen()
        • SpaceAdapter.transform_spline_export_to_logical()
        • SpaceAdapter.screen_distance_to_logical()
        • SpaceAdapter.logical_distance_to_screen()
        • SpaceAdapter.with_params()
        • SpaceAdapter.zoom()
        • SpaceAdapter.pan()
        • SpaceAdapter.to_dict()
        • SpaceAdapter.from_dict()
    • Laurent Module
      • LaurentFitConfig
        • LaurentFitConfig.N_min
        • LaurentFitConfig.N_max
        • LaurentFitConfig.m_samples
        • LaurentFitConfig.lambda_init
        • LaurentFitConfig.lambda_increase_factor
        • LaurentFitConfig.max_lambda_tries
        • LaurentFitConfig.reparam_iters
        • LaurentFitConfig.theta_search_grid
        • LaurentFitConfig.theta_refine_iters
        • LaurentFitConfig.fit_tol_max_factor
        • LaurentFitConfig.prefer_smallest_N
        • LaurentFitConfig.rho_in
        • LaurentFitConfig.rho_out
        • LaurentFitConfig.check_theta_grid
        • LaurentFitConfig.min_abs_deriv_factor
        • LaurentFitConfig.min_sep_factor
        • LaurentFitConfig.poly_eps_factor
        • LaurentFitConfig.from_pipeline_config()
        • LaurentFitConfig.__init__()
      • LaurentMapResult
        • LaurentMapResult.N
        • LaurentMapResult.a0
        • LaurentMapResult.a
        • LaurentMapResult.b
        • LaurentMapResult.eval()
        • LaurentMapResult.eval_array()
        • LaurentMapResult.deriv()
        • LaurentMapResult.deriv_array()
        • LaurentMapResult.to_laurent_map()
        • LaurentMapResult.from_laurent_map()
        • LaurentMapResult.__init__()
      • FitResult
        • FitResult.ok
        • FitResult.failure_reason
        • FitResult.curve_scale
        • FitResult.polyline_used
        • FitResult.laurent_map
        • FitResult.fit_max_err
        • FitResult.fit_rms_err
        • FitResult.simple_on_unit_circle
        • FitResult.min_abs_deriv_unit
        • FitResult.min_sep_unit
        • FitResult.min_sep_in
        • FitResult.min_sep_out
        • FitResult.__init__()
      • load_polyline_from_export()
      • estimate_diameter()
      • resample_closed_polyline()
      • build_laurent_matrix()
      • solve_tikhonov()
      • check_polyline_simple()
      • check_laurent_map()
      • reparam_closest_theta()
      • fit_laurent_map()
    • Meromorphic Module
      • Singularity
        • Singularity.x
        • Singularity.y
        • Singularity.multiplicity
        • Singularity.z
        • Singularity.to_dict()
        • Singularity.from_dict()
        • Singularity.from_point()
        • Singularity.__init__()
      • build_meromorphic_expression()
      • meromorphic_from_points()
      • MeromorphicBuilder
        • MeromorphicBuilder.__init__()
        • MeromorphicBuilder.zeros
        • MeromorphicBuilder.poles
        • MeromorphicBuilder.add_zero()
        • MeromorphicBuilder.add_pole()
        • MeromorphicBuilder.add_zero_from_screen()
        • MeromorphicBuilder.add_pole_from_screen()
        • MeromorphicBuilder.clear()
        • MeromorphicBuilder.remove_zero()
        • MeromorphicBuilder.remove_pole()
        • MeromorphicBuilder.build_expression()
        • MeromorphicBuilder.to_dict()
        • MeromorphicBuilder.from_dict()
    • Continuation Module
      • Pole
        • Pole.z
        • Pole.multiplicity
        • Pole.__init__()
      • HolomorphicCheckConfig
        • HolomorphicCheckConfig.theta_grid
        • HolomorphicCheckConfig.rho_samples
        • HolomorphicCheckConfig.pole_margin_factor
        • HolomorphicCheckConfig.shrink_steps
        • HolomorphicCheckConfig.from_pipeline_config()
        • HolomorphicCheckConfig.__init__()
      • InvertConfig
        • InvertConfig.theta_grid
        • InvertConfig.seed_radii
        • InvertConfig.max_iters
        • InvertConfig.tol_abs_factor
        • InvertConfig.tol_rel_factor
        • InvertConfig.damping
        • InvertConfig.max_backtracks
        • InvertConfig.from_pipeline_config()
        • InvertConfig.__init__()
      • HolomorphicCheckResult
        • HolomorphicCheckResult.ok
        • HolomorphicCheckResult.min_pole_distance
        • HolomorphicCheckResult.closest_pole
        • HolomorphicCheckResult.failure_reason
        • HolomorphicCheckResult.updated_rho_in
        • HolomorphicCheckResult.updated_rho_out
        • HolomorphicCheckResult.__init__()
      • InvertResult
        • InvertResult.converged
        • InvertResult.zeta
        • InvertResult.residual
        • InvertResult.iters
        • InvertResult.__init__()
      • CompositionResult
        • CompositionResult.ok
        • CompositionResult.value
        • CompositionResult.zeta
        • CompositionResult.residual
        • CompositionResult.N
        • CompositionResult.failure_reason
        • CompositionResult.__init__()
      • check_f_holomorphic_on_annulus()
      • invert_z()
      • compute_composition()
      • compute_continuation_grid()
    • Intrinsic Curve Module
      • Theory
      • Complexity Indicators
      • CesaroRepresentation
        • CesaroRepresentation.arc_lengths
        • CesaroRepresentation.curvatures
        • CesaroRepresentation.total_arc_length
        • CesaroRepresentation.samples
        • CesaroRepresentation.arc_lengths
        • CesaroRepresentation.curvatures
        • CesaroRepresentation.total_arc_length
        • CesaroRepresentation.samples
        • CesaroRepresentation.kappa_at()
        • CesaroRepresentation.to_dict()
        • CesaroRepresentation.from_dict()
        • CesaroRepresentation.__init__()
      • WhewellRepresentation
        • WhewellRepresentation.arc_lengths
        • WhewellRepresentation.tangent_angles
        • WhewellRepresentation.total_arc_length
        • WhewellRepresentation.winding_number
        • WhewellRepresentation.samples
        • WhewellRepresentation.arc_lengths
        • WhewellRepresentation.tangent_angles
        • WhewellRepresentation.total_arc_length
        • WhewellRepresentation.winding_number
        • WhewellRepresentation.samples
        • WhewellRepresentation.phi_at()
        • WhewellRepresentation.to_dict()
        • WhewellRepresentation.from_dict()
        • WhewellRepresentation.__init__()
      • LogBijectionData
        • LogBijectionData.laurent_N
        • LogBijectionData.laurent_a0
        • LogBijectionData.laurent_a
        • LogBijectionData.laurent_b
        • LogBijectionData.curve_scale
        • LogBijectionData.theta_samples
        • LogBijectionData.log_z_samples
        • LogBijectionData.z_samples
        • LogBijectionData.log_derivative_samples
        • LogBijectionData.to_dict()
        • LogBijectionData.from_dict()
        • LogBijectionData.__init__()
      • ComplexityEstimates
        • ComplexityEstimates.total_curvature
        • ComplexityEstimates.curvature_variation
        • ComplexityEstimates.max_curvature
        • ComplexityEstimates.mean_curvature
        • ComplexityEstimates.curvature_std
        • ComplexityEstimates.winding_number
        • ComplexityEstimates.total_arc_length
        • ComplexityEstimates.log_deriv_variation
        • ComplexityEstimates.arg_deriv_variation
        • ComplexityEstimates.min_jacobian
        • ComplexityEstimates.max_jacobian
        • ComplexityEstimates.jacobian_ratio
        • ComplexityEstimates.inversion_difficulty
        • ComplexityEstimates.sampling_density_factor
        • ComplexityEstimates.newton_convergence_factor
        • ComplexityEstimates.to_dict()
        • ComplexityEstimates.from_dict()
        • ComplexityEstimates.summary()
        • ComplexityEstimates.__init__()
      • compute_log_bijection()
      • compute_cesaro_form()
      • compute_whewell_form()
      • estimate_complexity()
      • IntrinsicCurveAnalysis
        • IntrinsicCurveAnalysis.log_data
        • IntrinsicCurveAnalysis.cesaro
        • IntrinsicCurveAnalysis.whewell
        • IntrinsicCurveAnalysis.complexity
        • IntrinsicCurveAnalysis.to_dict()
        • IntrinsicCurveAnalysis.from_dict()
        • IntrinsicCurveAnalysis.summary()
        • IntrinsicCurveAnalysis.__init__()
      • analyze_bijection()
      • suggest_inversion_config()
      • ContourPreCheckResult
        • ContourPreCheckResult.ok
        • ContourPreCheckResult.proceed
        • ContourPreCheckResult.is_closed
        • ContourPreCheckResult.is_simple
        • ContourPreCheckResult.has_sufficient_points
        • ContourPreCheckResult.has_reasonable_aspect
        • ContourPreCheckResult.has_reasonable_curvature
        • ContourPreCheckResult.num_points
        • ContourPreCheckResult.perimeter
        • ContourPreCheckResult.bounding_box
        • ContourPreCheckResult.aspect_ratio
        • ContourPreCheckResult.estimated_diameter
        • ContourPreCheckResult.min_segment_length
        • ContourPreCheckResult.max_segment_length
        • ContourPreCheckResult.max_turning_angle
        • ContourPreCheckResult.warnings
        • ContourPreCheckResult.errors
        • ContourPreCheckResult.estimated_difficulty
        • ContourPreCheckResult.estimated_fit_time_seconds
        • ContourPreCheckResult.to_dict()
        • ContourPreCheckResult.__init__()
      • precheck_contour()
      • precheck_contour_from_spline_export()
    • Logging Config Module
      • TaskStatus
        • TaskStatus.PENDING
        • TaskStatus.IN_PROGRESS
        • TaskStatus.COMPLETED
        • TaskStatus.FAILED
        • TaskStatus.SKIPPED
        • TaskStatus.__new__()
      • TaskProgress
        • TaskProgress.task_id
        • TaskProgress.name
        • TaskProgress.status
        • TaskProgress.progress
        • TaskProgress.message
        • TaskProgress.started_at
        • TaskProgress.completed_at
        • TaskProgress.error
        • TaskProgress.metadata
        • TaskProgress.to_dict()
        • TaskProgress.__init__()
      • PipelineSession
        • PipelineSession.session_id
        • PipelineSession.created_at
        • PipelineSession.expression
        • PipelineSession.curve_data
        • PipelineSession.zeros
        • PipelineSession.poles
        • PipelineSession.tasks
        • PipelineSession.result
        • PipelineSession.status
        • PipelineSession.to_dict()
        • PipelineSession.__init__()
      • PipelineLogger
        • PipelineLogger.__new__()
        • PipelineLogger.__init__()
        • PipelineLogger.register_progress_callback()
        • PipelineLogger.unregister_progress_callback()
        • PipelineLogger.compute_input_hash()
        • PipelineLogger.find_resumable_session()
        • PipelineLogger.start_session()
        • PipelineLogger.update_session_stage()
        • PipelineLogger.get_session()
        • PipelineLogger.list_sessions()
        • PipelineLogger.start_task()
        • PipelineLogger.update_task()
        • PipelineLogger.complete_task()
        • PipelineLogger.cache_computation()
        • PipelineLogger.get_cached_computation()
        • PipelineLogger.end_session()
        • PipelineLogger.get_current_progress()
        • PipelineLogger.debug()
        • PipelineLogger.info()
        • PipelineLogger.warning()
        • PipelineLogger.error()
      • get_logger()
    • Progress Module
      • StageInfo
        • StageInfo.id
        • StageInfo.name
        • StageInfo.description
        • StageInfo.status
        • StageInfo.progress
        • StageInfo.message
        • StageInfo.substeps_total
        • StageInfo.substeps_done
        • StageInfo.started_at
        • StageInfo.completed_at
        • StageInfo.error
        • StageInfo.to_dict()
        • StageInfo.__init__()
      • ProgressTracker
        • ProgressTracker.__init__()
        • ProgressTracker.stages
        • ProgressTracker.subscribe()
        • ProgressTracker.get_state()
        • ProgressTracker.start_stage()
        • ProgressTracker.update_stage()
        • ProgressTracker.complete_stage()
        • ProgressTracker.skip_stage()
        • ProgressTracker.sync_start_stage()
        • ProgressTracker.sync_update_stage()
        • ProgressTracker.sync_complete_stage()
      • format_cli_progress()
  • Space Adapter
    • Overview
    • TransformParams
      • TransformParams
        • TransformParams.offset_x
        • TransformParams.offset_y
        • TransformParams.scale_x
        • TransformParams.scale_y
        • TransformParams.scale_y_effective
        • TransformParams.is_uniform
        • TransformParams.to_dict()
        • TransformParams.from_dict()
        • TransformParams.from_view_bounds()
        • TransformParams.__init__()
      • Creating from View Bounds
    • SpaceAdapter
      • SpaceAdapter
        • SpaceAdapter.__init__()
        • SpaceAdapter.offset
        • SpaceAdapter.scale
        • SpaceAdapter.screen_to_logical()
        • SpaceAdapter.logical_to_screen()
        • SpaceAdapter.screen_to_complex()
        • SpaceAdapter.complex_to_screen()
        • SpaceAdapter.transform_point_to_logical()
        • SpaceAdapter.transform_point_to_screen()
        • SpaceAdapter.transform_points_to_logical()
        • SpaceAdapter.transform_points_to_screen()
        • SpaceAdapter.transform_spline_to_logical()
        • SpaceAdapter.transform_spline_to_screen()
        • SpaceAdapter.transform_spline_export_to_logical()
        • SpaceAdapter.screen_distance_to_logical()
        • SpaceAdapter.logical_distance_to_screen()
        • SpaceAdapter.with_params()
        • SpaceAdapter.zoom()
        • SpaceAdapter.pan()
        • SpaceAdapter.to_dict()
        • SpaceAdapter.from_dict()
      • Basic Usage
      • Working with Complex Numbers
      • Transforming Points and Splines
      • Zoom and Pan
      • Distance Conversion
  • Laurent Series Fitting
    • Mathematical Background
    • Configuration
      • LaurentFitConfig
        • LaurentFitConfig.N_min
        • LaurentFitConfig.N_max
        • LaurentFitConfig.m_samples
        • LaurentFitConfig.lambda_init
        • LaurentFitConfig.lambda_increase_factor
        • LaurentFitConfig.max_lambda_tries
        • LaurentFitConfig.reparam_iters
        • LaurentFitConfig.theta_search_grid
        • LaurentFitConfig.theta_refine_iters
        • LaurentFitConfig.fit_tol_max_factor
        • LaurentFitConfig.prefer_smallest_N
        • LaurentFitConfig.rho_in
        • LaurentFitConfig.rho_out
        • LaurentFitConfig.check_theta_grid
        • LaurentFitConfig.min_abs_deriv_factor
        • LaurentFitConfig.min_sep_factor
        • LaurentFitConfig.poly_eps_factor
        • LaurentFitConfig.from_pipeline_config()
        • LaurentFitConfig.__init__()
    • Results
      • LaurentMapResult
        • LaurentMapResult.N
        • LaurentMapResult.a0
        • LaurentMapResult.a
        • LaurentMapResult.b
        • LaurentMapResult.eval()
        • LaurentMapResult.eval_array()
        • LaurentMapResult.deriv()
        • LaurentMapResult.deriv_array()
        • LaurentMapResult.to_laurent_map()
        • LaurentMapResult.from_laurent_map()
        • LaurentMapResult.__init__()
      • FitResult
        • FitResult.ok
        • FitResult.failure_reason
        • FitResult.curve_scale
        • FitResult.polyline_used
        • FitResult.laurent_map
        • FitResult.fit_max_err
        • FitResult.fit_rms_err
        • FitResult.simple_on_unit_circle
        • FitResult.min_abs_deriv_unit
        • FitResult.min_sep_unit
        • FitResult.min_sep_in
        • FitResult.min_sep_out
        • FitResult.__init__()
    • Main Fitting Function
      • fit_laurent_map()
      • Basic Usage
      • Custom Configuration
    • Utility Functions
      • load_polyline_from_export()
      • estimate_diameter()
    • Quality Checks
  • Meromorphic Functions
    • Mathematical Background
    • Singularity Class
      • Singularity
        • Singularity.x
        • Singularity.y
        • Singularity.multiplicity
        • Singularity.z
        • Singularity.to_dict()
        • Singularity.from_dict()
        • Singularity.from_point()
        • Singularity.__init__()
    • Building Expressions
      • build_meromorphic_expression()
      • meromorphic_from_points()
    • MeromorphicBuilder Class
      • MeromorphicBuilder
        • MeromorphicBuilder.__init__()
        • MeromorphicBuilder.zeros
        • MeromorphicBuilder.poles
        • MeromorphicBuilder.add_zero()
        • MeromorphicBuilder.add_pole()
        • MeromorphicBuilder.add_zero_from_screen()
        • MeromorphicBuilder.add_pole_from_screen()
        • MeromorphicBuilder.clear()
        • MeromorphicBuilder.remove_zero()
        • MeromorphicBuilder.remove_pole()
        • MeromorphicBuilder.build_expression()
        • MeromorphicBuilder.to_dict()
        • MeromorphicBuilder.from_dict()
      • Adding from Screen Coordinates
      • Modifying the Builder
      • Serialization
    • Expression Format
  • Analytic Continuation
    • Pipeline Overview
    • Pole Class
      • Pole
        • Pole.z
        • Pole.multiplicity
        • Pole.__init__()
    • Holomorphic Checking (Stage 4)
      • Configuration
        • HolomorphicCheckConfig
      • Result
        • HolomorphicCheckResult
      • Main Function
        • check_f_holomorphic_on_annulus()
    • Inversion (Stage 5)
      • Configuration
        • InvertConfig
      • Result
        • InvertResult
      • Main Function
        • invert_z()
    • Composition (Stage 6)
      • Result
        • CompositionResult
      • Main Functions
        • compute_composition()
        • compute_continuation_grid()
    • Workflow Example
  • Intrinsic Curve Analysis
    • Mathematical Background
    • Representations
      • CesaroRepresentation
        • CesaroRepresentation.arc_lengths
        • CesaroRepresentation.curvatures
        • CesaroRepresentation.total_arc_length
        • CesaroRepresentation.samples
        • CesaroRepresentation.arc_lengths
        • CesaroRepresentation.curvatures
        • CesaroRepresentation.total_arc_length
        • CesaroRepresentation.samples
        • CesaroRepresentation.kappa_at()
        • CesaroRepresentation.to_dict()
        • CesaroRepresentation.from_dict()
        • CesaroRepresentation.__init__()
      • WhewellRepresentation
        • WhewellRepresentation.arc_lengths
        • WhewellRepresentation.tangent_angles
        • WhewellRepresentation.total_arc_length
        • WhewellRepresentation.winding_number
        • WhewellRepresentation.samples
        • WhewellRepresentation.arc_lengths
        • WhewellRepresentation.tangent_angles
        • WhewellRepresentation.total_arc_length
        • WhewellRepresentation.winding_number
        • WhewellRepresentation.samples
        • WhewellRepresentation.phi_at()
        • WhewellRepresentation.to_dict()
        • WhewellRepresentation.from_dict()
        • WhewellRepresentation.__init__()
    • Computation Functions
      • compute_cesaro_form()
      • compute_whewell_form()
    • Log Bijection Analysis
      • LogBijectionData
        • LogBijectionData.laurent_N
        • LogBijectionData.laurent_a0
        • LogBijectionData.laurent_a
        • LogBijectionData.laurent_b
        • LogBijectionData.curve_scale
        • LogBijectionData.theta_samples
        • LogBijectionData.log_z_samples
        • LogBijectionData.z_samples
        • LogBijectionData.log_derivative_samples
        • LogBijectionData.to_dict()
        • LogBijectionData.from_dict()
        • LogBijectionData.__init__()
      • compute_log_bijection()
    • Complexity Estimation
      • ComplexityEstimates
        • ComplexityEstimates.total_curvature
        • ComplexityEstimates.curvature_variation
        • ComplexityEstimates.max_curvature
        • ComplexityEstimates.mean_curvature
        • ComplexityEstimates.curvature_std
        • ComplexityEstimates.winding_number
        • ComplexityEstimates.total_arc_length
        • ComplexityEstimates.log_deriv_variation
        • ComplexityEstimates.arg_deriv_variation
        • ComplexityEstimates.min_jacobian
        • ComplexityEstimates.max_jacobian
        • ComplexityEstimates.jacobian_ratio
        • ComplexityEstimates.inversion_difficulty
        • ComplexityEstimates.sampling_density_factor
        • ComplexityEstimates.newton_convergence_factor
        • ComplexityEstimates.to_dict()
        • ComplexityEstimates.from_dict()
        • ComplexityEstimates.summary()
        • ComplexityEstimates.__init__()
      • estimate_complexity()
    • Inversion Configuration
      • suggest_inversion_config()
    • Complete Analysis
      • IntrinsicCurveAnalysis
        • IntrinsicCurveAnalysis.log_data
        • IntrinsicCurveAnalysis.cesaro
        • IntrinsicCurveAnalysis.whewell
        • IntrinsicCurveAnalysis.complexity
        • IntrinsicCurveAnalysis.to_dict()
        • IntrinsicCurveAnalysis.from_dict()
        • IntrinsicCurveAnalysis.summary()
        • IntrinsicCurveAnalysis.__init__()
      • analyze_bijection()
    • Contour Pre-check (Stage 1)
      • ContourPreCheckResult
        • ContourPreCheckResult.ok
        • ContourPreCheckResult.proceed
        • ContourPreCheckResult.is_closed
        • ContourPreCheckResult.is_simple
        • ContourPreCheckResult.has_sufficient_points
        • ContourPreCheckResult.has_reasonable_aspect
        • ContourPreCheckResult.has_reasonable_curvature
        • ContourPreCheckResult.num_points
        • ContourPreCheckResult.perimeter
        • ContourPreCheckResult.bounding_box
        • ContourPreCheckResult.aspect_ratio
        • ContourPreCheckResult.estimated_diameter
        • ContourPreCheckResult.min_segment_length
        • ContourPreCheckResult.max_segment_length
        • ContourPreCheckResult.max_turning_angle
        • ContourPreCheckResult.warnings
        • ContourPreCheckResult.errors
        • ContourPreCheckResult.estimated_difficulty
        • ContourPreCheckResult.estimated_fit_time_seconds
        • ContourPreCheckResult.to_dict()
        • ContourPreCheckResult.__init__()
      • precheck_contour()
      • precheck_contour_from_spline_export()
    • Workflow Integration
  • Logging and Progress Tracking
    • Pipeline Logger
      • PipelineLogger
        • PipelineLogger.__new__()
        • PipelineLogger.__init__()
        • PipelineLogger.register_progress_callback()
        • PipelineLogger.unregister_progress_callback()
        • PipelineLogger.compute_input_hash()
        • PipelineLogger.find_resumable_session()
        • PipelineLogger.start_session()
        • PipelineLogger.update_session_stage()
        • PipelineLogger.get_session()
        • PipelineLogger.list_sessions()
        • PipelineLogger.start_task()
        • PipelineLogger.update_task()
        • PipelineLogger.complete_task()
        • PipelineLogger.cache_computation()
        • PipelineLogger.get_cached_computation()
        • PipelineLogger.end_session()
        • PipelineLogger.get_current_progress()
        • PipelineLogger.debug()
        • PipelineLogger.info()
        • PipelineLogger.warning()
        • PipelineLogger.error()
      • get_logger()
    • Task Status
      • TaskStatus
        • TaskStatus.PENDING
        • TaskStatus.IN_PROGRESS
        • TaskStatus.COMPLETED
        • TaskStatus.FAILED
        • TaskStatus.SKIPPED
        • TaskStatus.__new__()
      • TaskProgress
        • TaskProgress.task_id
        • TaskProgress.name
        • TaskProgress.status
        • TaskProgress.progress
        • TaskProgress.message
        • TaskProgress.started_at
        • TaskProgress.completed_at
        • TaskProgress.error
        • TaskProgress.metadata
        • TaskProgress.to_dict()
        • TaskProgress.__init__()
    • Pipeline Session
      • PipelineSession
        • PipelineSession.session_id
        • PipelineSession.created_at
        • PipelineSession.expression
        • PipelineSession.curve_data
        • PipelineSession.zeros
        • PipelineSession.poles
        • PipelineSession.tasks
        • PipelineSession.result
        • PipelineSession.status
        • PipelineSession.to_dict()
        • PipelineSession.__init__()
    • Progress Tracker
      • ProgressTracker
        • ProgressTracker.__init__()
        • ProgressTracker.stages
        • ProgressTracker.subscribe()
        • ProgressTracker.get_state()
        • ProgressTracker.start_stage()
        • ProgressTracker.update_stage()
        • ProgressTracker.complete_stage()
        • ProgressTracker.skip_stage()
        • ProgressTracker.sync_start_stage()
        • ProgressTracker.sync_update_stage()
        • ProgressTracker.sync_complete_stage()
    • Stage Information
      • StageInfo
        • StageInfo.id
        • StageInfo.name
        • StageInfo.description
        • StageInfo.status
        • StageInfo.progress
        • StageInfo.message
        • StageInfo.substeps_total
        • StageInfo.substeps_done
        • StageInfo.started_at
        • StageInfo.completed_at
        • StageInfo.error
        • StageInfo.to_dict()
        • StageInfo.__init__()
      • PIPELINE_STAGES
    • CLI Progress Formatting
      • format_cli_progress()
    • Integration Example
    • Callback-based Progress
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