Index

_

__call__() (AffineOperator method)

__repr__() (EquationGroup method), [1], [2]

A

AbstractNewtonSolver (class in bice.core.solvers) actions_after_newton_solve() (BifurcationConstraint method), [1] actions_before_evaluation() (BifurcationConstraint method), [1] active_branch (BifurcationDiagram attribute), [1], [2] adapt() (Equation method), [1], [2] (FiniteDifferencesEquation method), [1] (Problem method), [1], [2] (TimePeriodicOrbitHandler method), [1]

adapt_stepsize (PseudoArclengthContinuation attribute), [1] add_equation() (EquationGroup method), [1], [2] (Problem method), [1], [2] add_solution() (DeflationOperator method) add_solution_point() (Branch method), [1], [2] AffineOperator (class in bice.pde.finite_differences) always_locate_bifurcations (ProblemSettings attribute) approximate_jacobian (NewtonKrylovSolver attribute) atol (BDF attribute), [1]

B

bc (FiniteDifferencesEquation attribute), [1] bdf (BDF attribute) BDF (class in bice.time_steppers) (class in bice.time_steppers.bdf) BDF2 (class in bice.time_steppers) (class in bice.time_steppers.bdf) bice module bice.continuation module bice.continuation.bifurcations module bice.continuation.constraints module bice.continuation.continuation_steppers module bice.continuation.deflation module bice.continuation.timeperiodic module bice.core module bice.core.equation module bice.core.problem module bice.core.profiling module bice.core.solution module bice.core.solvers module bice.core.types module bice.demos module bice.measure module

bice.measure.lyapunov module bice.pde module bice.pde.finite_differences module bice.pde.pde module bice.pde.pseudospectral module bice.time_steppers module bice.time_steppers.bdf module bice.time_steppers.runge_kutta module bice.time_steppers.time_steppers module bifurcation_diagram (Problem attribute), [1], [2] bifurcation_type() (Solution method), [1], [2] BifurcationConstraint (class in bice.continuation) (class in bice.continuation.bifurcations) BifurcationDiagram (class in bice) (class in bice.core) (class in bice.core.solution) bifurcations() (Branch method), [1], [2] boundary_dx (PeriodicBC attribute) Branch (class in bice) (class in bice.core) (class in bice.core.solution) branch (Solution attribute), [1], [2] branches (BifurcationDiagram attribute), [1], [2] build_ddt_matrix() (TimePeriodicOrbitHandler method), [1] build_FD_matrices() (FiniteDifferencesEquation method), [1] build_FD_matrices_1d() (FiniteDifferencesEquation method), [1] build_kvectors() (PseudospectralEquation method), [1]

C

clear() (ProblemHistory method) clear_solutions() (DeflationOperator method) ConstraintEquation (class in bice.continuation) (class in bice.continuation.constraints) continuation_parameter (Problem attribute), [1], [2] continuation_parameter() (ProblemHistory method)

continuation_step() (Problem method), [1], [2] continuation_stepper (Problem attribute), [1], [2] ContinuationStepper (class in bice.continuation.continuation_steppers) convergence_tolerance (AbstractNewtonSolver attribute) (PseudoArclengthContinuation attribute), [1] current_solution() (BifurcationDiagram method), [1], [2]

D

D_operator() (DeflationOperator method) data (Solution attribute), [1], [2] data() (Branch method), [1], [2] ddx (FiniteDifferencesEquation attribute), [1] deflated_jacobian() (DeflationOperator method) deflated_rhs() (DeflationOperator method) DeflationOperator (class in bice.continuation.deflation) direction (TranslationConstraint attribute), [1] DirichletBC() (in module bice.pde.finite_differences) dot() (AffineOperator method)

ds (ContinuationStepper attribute) ds_decrease_factor (PseudoArclengthContinuation attribute), [1] ds_increase_factor (PseudoArclengthContinuation attribute), [1] ds_max (PseudoArclengthContinuation attribute), [1] ds_min (PseudoArclengthContinuation attribute), [1] dt (TimeStepper attribute) dt_max (BDF attribute), [1] du_dt() (PartialDifferentialEquation method), [1] du_dx() (FiniteDifferencesEquation method), [1] (PartialDifferentialEquation method), [1] DummyEquationGroup (class in bice.core.equation)

E

eigen_solver (Problem attribute), [1], [2] EigenSolver (class in bice) (class in bice.core) (class in bice.core.solvers) eigval_zero_tolerance (ProblemSettings attribute) epsilon (LyapunovExponentCalculator attribute), [1] eq (Problem attribute), [1], [2] Equation (class in bice) (class in bice.core) (class in bice.core.equation)

EquationGroup (class in bice) (class in bice.core) (class in bice.core.equation) equations (EquationGroup attribute), [1], [2] error_tolerance (RungeKuttaFehlberg45 attribute), [1] Euler (class in bice.time_steppers) (class in bice.time_steppers.time_steppers) execution_time (MethodProfile attribute) execution_times (Profiler attribute), [1], [2] exponents (LyapunovExponentCalculator property), [1]

F

factory_reset() (BDF method), [1] (ContinuationStepper method) fd_epsilon (PseudoArclengthContinuation attribute), [1] FDBoundaryConditions (class in bice.pde.finite_differences) FiniteDifferencesEquation (class in bice.pde) (class in bice.pde.finite_differences)

fixed_volume (VolumeConstraint attribute), [1] flattened_data() (MethodProfile method) floquet_multipliers() (TimePeriodicOrbitHandler method), [1] free_parameter (BifurcationConstraint attribute), [1]

G

G (AffineOperator attribute) (FDBoundaryConditions attribute) generate_bifurcation_diagram() (Problem method), [1], [2] generate_perturbation_vectors() (LyapunovExponentCalculator method), [1]

get_branch_by_ID() (BifurcationDiagram method), [1], [2] get_continuation_parameter() (Problem method), [1], [2] get_neighboring_solution() (Solution method), [1], [2] group (Equation attribute), [1], [2] (EquationGroup attribute), [1], [2]

H

history (Problem attribute), [1], [2]

I

id (Branch attribute), [1], [2] (Solution attribute), [1], [2] idx (EquationGroup attribute), [1], [2] ImplicitEuler (class in bice.time_steppers) (class in bice.time_steppers.time_steppers) is_active() (Profiler static method), [1], [2]

is_bifurcation() (Solution method), [1], [2] is_coupled (Equation attribute), [1], [2] (EquationGroup property), [1], [2] is_empty() (Branch method), [1], [2] is_linear() (AffineOperator method) is_stable() (Solution method), [1], [2]

J

jacobian() (BifurcationConstraint method), [1] (Equation method), [1], [2] (EquationGroup method), [1], [2] (FiniteDifferencesEquation method), [1] (Problem method), [1], [2] (TimePeriodicOrbitHandler method), [1] (TranslationConstraint method), [1] (VolumeConstraint method), [1]

K

k (PseudospectralEquation attribute), [1]

ksquare (PseudospectralEquation attribute)

L

laplace (FiniteDifferencesEquation attribute), [1] latest_eigenvalues (EigenSolver attribute), [1], [2] latest_eigenvectors (EigenSolver attribute), [1], [2] length (ProblemHistory property) list_equations() (EquationGroup method), [1], [2] (Problem method), [1], [2] load() (Equation method), [1], [2] (FiniteDifferencesEquation method), [1] (Problem method), [1], [2] (TimePeriodicOrbitHandler method), [1]

load_branch() (BifurcationDiagram method), [1], [2] locate_bifurcation() (Problem method), [1], [2] locate_bifurcation_using_constraint() (Problem method), [1], [2] log() (Problem method), [1], [2] LyapunovExponentCalculator (class in bice.measure) (class in bice.measure.lyapunov)

M

map_unknowns() (EquationGroup method), [1], [2] mass_matrix() (BifurcationConstraint method), [1] (ConstraintEquation method), [1] (Equation method), [1], [2] (EquationGroup method), [1], [2] (Problem method), [1], [2] max_dx (FiniteDifferencesEquation attribute), [1] max_iterations (AbstractNewtonSolver attribute) max_newton_iterations (PseudoArclengthContinuation attribute), [1] max_refinement_error (FiniteDifferencesEquation attribute), [1] max_rejections (RungeKuttaFehlberg45 attribute), [1] method (NewtonSolver attribute), [1], [2] MethodProfile (class in bice.core.profiling) min_dx (FiniteDifferencesEquation attribute), [1] min_refinement_error (FiniteDifferencesEquation attribute), [1] module bice bice.continuation bice.continuation.bifurcations bice.continuation.constraints bice.continuation.continuation_steppers bice.continuation.deflation bice.continuation.timeperiodic bice.core bice.core.equation bice.core.problem bice.core.profiling bice.core.solution bice.core.solvers bice.core.types bice.demos bice.measure bice.measure.lyapunov bice.pde bice.pde.finite_differences bice.pde.pde bice.pde.pseudospectral bice.time_steppers bice.time_steppers.bdf bice.time_steppers.runge_kutta bice.time_steppers.time_steppers

monodromy_matrix() (TimePeriodicOrbitHandler method), [1] MyNewtonSolver (class in bice) (class in bice.core) (class in bice.core.solvers)

N

nabla (FiniteDifferencesEquation attribute), [1] name (MethodProfile attribute) NaturalContinuation (class in bice.continuation) (class in bice.continuation.continuation_steppers) ncalls (MethodProfile attribute) ndesired_newton_steps (PseudoArclengthContinuation attribute), [1] ndofs (Equation property), [1], [2] (EquationGroup property), [1], [2] (Problem property), [1], [2] neigenvalues_crossed (Solution property), [1], [2] neigs (ProblemSettings attribute) nested_profiles (MethodProfile attribute) NeumannBC() (in module bice.pde.finite_differences) new_branch() (BifurcationDiagram method), [1], [2] (Problem method), [1], [2] newton_solve() (Problem method), [1], [2] newton_solver (Problem attribute), [1], [2]

NewtonKrylovSolver (class in bice.core.solvers) NewtonSolver (class in bice) (class in bice.core) (class in bice.core.solvers) nexponents (LyapunovExponentCalculator attribute), [1] nimaginary_eigenvalues_crossed (Solution property), [1], [2] nintegration_steps (LyapunovExponentCalculator attribute), [1] niterations (AbstractNewtonSolver property) nnewton_iter_taken (PseudoArclengthContinuation attribute), [1] NoBoundaryConditions (class in bice.pde.finite_differences) norm (Solution attribute), [1], [2] norm() (AbstractNewtonSolver method) (Problem method), [1], [2] norm_name (BifurcationDiagram attribute), [1], [2] norm_vals() (Branch method), [1], [2] Nt (TimePeriodicOrbitHandler property), [1] nunstable_eigenvalues (Solution attribute), [1], [2] nunstable_imaginary_eigenvalues (Solution attribute), [1], [2]

O

operator() (DeflationOperator method) order (BDF2 attribute), [1] (PeriodicBC attribute)

original_jacobian() (BifurcationConstraint method), [1] orthonormalize() (LyapunovExponentCalculator method), [1]

P

p (DeflationOperator attribute) (Solution attribute), [1], [2] pad() (FDBoundaryConditions method) pad_x() (FDBoundaryConditions method) (NoBoundaryConditions method) (PeriodicBC method) parameter_arc_length_proportion (PseudoArclengthContinuation attribute), [1] parameter_name (BifurcationDiagram attribute), [1], [2] parameter_vals() (Branch method), [1], [2] PartialDifferentialEquation (class in bice.pde) (class in bice.pde.pde) PeriodicBC (class in bice.pde.finite_differences) perturbations (LyapunovExponentCalculator attribute) plot() (BifurcationConstraint method), [1] (BifurcationDiagram method), [1], [2] (ConstraintEquation method), [1] (Equation method), [1], [2] (Problem method), [1], [2] (TimePeriodicOrbitHandler method), [1]

print_stats() (MethodProfile method) print_summary() (Profiler static method), [1], [2] problem (BDF attribute), [1] Problem (class in bice) (class in bice.core) (class in bice.core.problem) problem (LyapunovExponentCalculator attribute), [1] ProblemHistory (class in bice.core.problem) ProblemSettings (class in bice.core.problem) profile() (in module bice) (in module bice.core) (in module bice.core.profiling) Profiler (class in bice) (class in bice.core) (class in bice.core.profiling) PseudoArclengthContinuation (class in bice.continuation) (class in bice.continuation.continuation_steppers) PseudospectralEquation (class in bice.pde) (class in bice.pde.pseudospectral)

Q

Q (AffineOperator attribute) (FDBoundaryConditions attribute)

R

ref_eq (TranslationConstraint attribute), [1] (VolumeConstraint attribute), [1] refinement_error_estimate() (FiniteDifferencesEquation method), [1] rejection_count (RungeKuttaFehlberg45 attribute), [1] remove_branch_by_ID() (BifurcationDiagram method), [1], [2] remove_equation() (EquationGroup method), [1], [2] (Problem method), [1], [2] remove_solution() (DeflationOperator method) remove_solution_point() (Branch method), [1], [2] reshape() (Equation method), [1], [2] rhs() (BifurcationConstraint method), [1] (Equation method), [1], [2] (EquationGroup method), [1], [2] (Problem method), [1], [2] (TimePeriodicOrbitHandler method), [1] (TranslationConstraint method), [1] (VolumeConstraint method), [1]

RobinBC (class in bice.pde.finite_differences) rtol (BDF attribute), [1] RungeKutta4 (class in bice.time_steppers) (class in bice.time_steppers.runge_kutta) RungeKuttaFehlberg45 (class in bice.time_steppers) (class in bice.time_steppers.runge_kutta)

S

save() (Branch method), [1], [2] (Equation method), [1], [2] (FiniteDifferencesEquation method), [1] (Problem method), [1], [2] (TimePeriodicOrbitHandler method), [1] set_continuation_parameter() (Problem method), [1], [2] settings (Problem attribute), [1], [2] shape (Equation property), [1], [2] (EquationGroup property), [1], [2] shift (DeflationOperator attribute) (EigenSolver attribute), [1], [2] Solution (class in bice) (class in bice.core) (class in bice.core.solution) solutions (Branch attribute), [1], [2] (DeflationOperator attribute) solve() (AbstractNewtonSolver method) (EigenSolver method), [1], [2] (MyNewtonSolver method), [1], [2] (NewtonKrylovSolver method) (NewtonSolver method), [1], [2]

solve_eigenproblem() (Problem method), [1], [2] spatial_dimension (PartialDifferentialEquation property), [1] start() (Profiler static method), [1], [2] step() (BDF method), [1] (BDF2 method), [1] (ContinuationStepper method) (Euler method), [1] (ImplicitEuler method), [1] (LyapunovExponentCalculator method), [1] (NaturalContinuation method), [1] (PseudoArclengthContinuation method), [1] (RungeKutta4 method), [1] (RungeKuttaFehlberg45 method), [1] (TimeStepper method) step_size() (ProblemHistory method) switch_branch() (Problem method), [1], [2]

T

T (LyapunovExponentCalculator attribute), [1] (TimePeriodicOrbitHandler property), [1] t (TimePeriodicOrbitHandler property), [1] throw_no_convergence_error() (AbstractNewtonSolver method) time (Problem attribute), [1], [2] time() (ProblemHistory method) time_step() (Problem method), [1], [2]

time_stepper (Problem attribute), [1], [2] TimePeriodicOrbitHandler (class in bice.continuation) (class in bice.continuation.timeperiodic) TimeStepper (class in bice.time_steppers.time_steppers) tol (EigenSolver attribute), [1], [2] TranslationConstraint (class in bice.continuation) (class in bice.continuation.constraints) type (ProblemHistory attribute)

U

u (Equation attribute), [1], [2] (EquationGroup property), [1], [2] (Problem property), [1], [2] (TranslationConstraint attribute), [1] (VolumeConstraint attribute), [1] u() (ProblemHistory method) u_history (Equation attribute), [1], [2]

u_orbit() (TimePeriodicOrbitHandler method), [1] update() (FDBoundaryConditions method) (NoBoundaryConditions method) (PeriodicBC method) (ProblemHistory method) (RobinBC method) use_sparse_matrices (ProblemSettings attribute)

V

variable (TranslationConstraint attribute), [1] (VolumeConstraint attribute), [1] verbose (ProblemSettings attribute)

verbosity (AbstractNewtonSolver attribute) VolumeConstraint (class in bice.continuation) (class in bice.continuation.constraints)

X

x (FiniteDifferencesEquation attribute), [1] (PartialDifferentialEquation attribute), [1] (PseudospectralEquation attribute)

xlim (BifurcationDiagram attribute), [1], [2]

Y

ylim (BifurcationDiagram attribute), [1], [2]