API Reference
This section contains the complete API reference for BallArithmetic.jl, organized by functionality.
Pages
- Core Types - Ball, BallArray, BallMatrix, BallVector, and norm bounds
- Linear Systems - Verified linear system solvers
- Eigenvalues & SVD - Eigenvalue and singular value computation
- CertifScripts - Pseudospectra certification
- NumericalTest - Testing utilities
BallArithmetic.AdaptiveSVDResultBallArithmetic.BallBallArithmetic.BallArrayBallArithmetic.BallComplexF64BallArithmetic.BallF64BallArithmetic.BallMatrixBallArithmetic.BallVectorBallArithmetic.CertifScripts.CertificationCircleBallArithmetic.DeterminantResultBallArithmetic.GEVResultBallArithmetic.GaussianEliminationResultBallArithmetic.HBRResultBallArithmetic.IterativeResultBallArithmetic.MiyajimaVBDResultBallArithmetic.OgitaSVDRefinementResultBallArithmetic.Oishi2023ResultBallArithmetic.OverdeterminedResultBallArithmetic.PreconditionerResultBallArithmetic.PreconditionerTypeBallArithmetic.RegularityResultBallArithmetic.RigorousBlockSchurResultBallArithmetic.RigorousEigenvaluesResultBallArithmetic.RigorousGeneralizedEigenvaluesResultBallArithmetic.RigorousSVDResultBallArithmetic.RigorousSpectralProjectorsResultBallArithmetic.Rump2022aResultBallArithmetic.RumpLange2023ResultBallArithmetic.RumpOishi2024ResultBallArithmetic.SchurRefinementResultBallArithmetic.SchurSpectralProjectorResultBallArithmetic.ShavingResultBallArithmetic.VerifiedLinearSystemResultBallArithmetic.CertifScripts._bf_ogita_cache_statsBallArithmetic.CertifScripts._clear_bf_ogita_cache!BallArithmetic.CertifScripts._clear_ogita_cache!BallArithmetic.CertifScripts._clear_parametric_cache!BallArithmetic.CertifScripts._compute_schur_and_error_bigfloatBallArithmetic.CertifScripts._compute_schur_bigfloat_directBallArithmetic.CertifScripts._compute_schur_bigfloat_refinedBallArithmetic.CertifScripts._evaluate_sample_ogita_bigfloatBallArithmetic.CertifScripts._evaluate_sample_parametricBallArithmetic.CertifScripts._evaluate_sample_with_ogita_cacheBallArithmetic.CertifScripts._ogita_cache_statsBallArithmetic.CertifScripts._parametric_cache_statsBallArithmetic.CertifScripts._set_center_svd_cache!BallArithmetic.CertifScripts.adaptive_arcs!BallArithmetic.CertifScripts.bound_res_originalBallArithmetic.CertifScripts.bound_resolvent_schurBallArithmetic.CertifScripts.choose_snapshot_to_loadBallArithmetic.CertifScripts.compute_schur_and_errorBallArithmetic.CertifScripts.configure_certification!BallArithmetic.CertifScripts.doworkBallArithmetic.CertifScripts.dowork_ogitaBallArithmetic.CertifScripts.dowork_ogita_bigfloatBallArithmetic.CertifScripts.dowork_parametricBallArithmetic.CertifScripts.points_onBallArithmetic.CertifScripts.poly_from_rootsBallArithmetic.CertifScripts.run_certificationBallArithmetic.CertifScripts.run_certification_ogitaBallArithmetic.CertifScripts.run_certification_parametricBallArithmetic.CertifScripts.save_snapshot!BallArithmetic.CertifScripts.schur_to_original_resolventBallArithmetic.CertifScripts.set_parametric_config!BallArithmetic.CertifScripts.set_schur_matrix!BallArithmetic.NumericalTest.rounding_testBallArithmetic.adaptive_ogita_svdBallArithmetic.apply_preconditionerBallArithmetic.backward_singular_value_boundBallArithmetic.ball_hullBallArithmetic.certify_schur_decompositionBallArithmetic.clear_svd_cache!BallArithmetic.collatz_upper_bound_L2_opnormBallArithmetic.compute_beta_boundBallArithmetic.compute_block_sylvester_rhsBallArithmetic.compute_eigenspace_projectorBallArithmetic.compute_invariant_subspace_basisBallArithmetic.compute_preconditionerBallArithmetic.compute_schur_projectorBallArithmetic.compute_spectral_projector_hermitianBallArithmetic.compute_spectral_projector_schurBallArithmetic.contains_zeroBallArithmetic.det_cramerBallArithmetic.det_gershgorinBallArithmetic.det_hadamardBallArithmetic.estimate_block_separationBallArithmetic.evboxBallArithmetic.extract_cluster_blockBallArithmetic.gevboxBallArithmetic.hbr_methodBallArithmetic.hbr_method_simpleBallArithmetic.infBallArithmetic.intersect_ballBallArithmetic.interval_detBallArithmetic.interval_gauss_seidelBallArithmetic.interval_gaussian_eliminationBallArithmetic.interval_gaussian_elimination_detBallArithmetic.interval_jacobiBallArithmetic.interval_least_squaresBallArithmetic.interval_shavingBallArithmetic.is_regularBallArithmetic.is_regular_diagonal_dominanceBallArithmetic.is_regular_gaussian_eliminationBallArithmetic.is_regular_gershgorinBallArithmetic.is_regular_sufficient_conditionBallArithmetic.is_singular_sufficient_conditionBallArithmetic.is_well_preconditionedBallArithmetic.midBallArithmetic.midtypeBallArithmetic.miyajima_spectral_projectorsBallArithmetic.miyajima_vbdBallArithmetic.multi_jacobi_methodBallArithmetic.newton_schulz_orthogonalize!BallArithmetic.ogita_svd_refineBallArithmetic.oishi_2023_optimal_block_sizeBallArithmetic.oishi_2023_sigma_min_boundBallArithmetic.pi_normBallArithmetic.project_onto_eigenspaceBallArithmetic.project_onto_schur_subspaceBallArithmetic.project_vector_spectralBallArithmetic.projector_condition_numberBallArithmetic.psi_schur_factorBallArithmetic.qi_intervalsBallArithmetic.qi_sqrt_intervalsBallArithmetic.radBallArithmetic.radtypeBallArithmetic.refine_cluster_boundsBallArithmetic.refine_off_diagonal_blockBallArithmetic.refine_schur_decompositionBallArithmetic.refine_svd_bounds_with_vbdBallArithmetic.rigorous_block_schurBallArithmetic.rigorous_eigenvaluesBallArithmetic.rigorous_generalized_eigenvaluesBallArithmetic.rigorous_schur_bigfloatBallArithmetic.rigorous_svdBallArithmetic.rump_2022a_eigenvalue_boundsBallArithmetic.rump_lange_2023_cluster_boundsBallArithmetic.rump_oishi_2024_optimal_block_sizeBallArithmetic.rump_oishi_2024_sigma_min_boundBallArithmetic.rump_oishi_2024_triangular_boundBallArithmetic.set_svd_cache!BallArithmetic.sherman_morrison_inverse_updateBallArithmetic.subsquares_methodBallArithmetic.supBallArithmetic.svd_bound_L2_opnormBallArithmetic.svd_cache_statsBallArithmetic.svdboxBallArithmetic.sylvester_miyajima_enclosureBallArithmetic.triangular_sylvester_miyajima_enclosureBallArithmetic.upper_bound_L1_opnormBallArithmetic.upper_bound_L2_opnormBallArithmetic.upper_bound_L_inf_opnormBallArithmetic.upper_bound_normBallArithmetic.verified_linear_solve_hmatrixBallArithmetic.verified_project_onto_eigenspaceBallArithmetic.verify_block_schur_propertiesBallArithmetic.verify_generalized_eigenpairsBallArithmetic.verify_projector_propertiesBallArithmetic.verify_spectral_projector_properties