braincell.quad module

Numerical integrators for BrainCell.

Exposes get_integrator() plus every canonical solver name registered in braincell.quad._registry.

Note

This __init__.py deliberately performs side-effect imports of every _<backend>.py module. Each backend self-registers into the integrator registry at import time via @register_integrator. Do not lazily defer these imports — unresolved solver names would surface as ValueError: unknown integrator from get_integrator() at first call instead of at import time.

braincell.quad provides a mechanism to define coupled ordinary differential equations (ODEs) and solve them using various numerical integration methods. The integration methods are categorized into exponential integrators, Runge-Kutta methods, and implicit methods.

Defining Coupled ODEs

DiffEqState	A brainstate state that participates in numerical integration.
DiffEqModule	Mixin marking a module as integrable by braincell.quad.
IndependentIntegration	Mixin that opts a submodule out of its parent's integration loop.

Integrator Registry

IntegratorEntry	A single registered integrator and its metadata.
IntegratorRegistry	Mutable, observable registry of integrator step functions.
get_integrator	Resolve a numerical integrator from a string name or a callable.
get_registry	Return the process-wide IntegratorRegistry singleton.
register_integrator	Decorator: register the wrapped function in the global registry.
all_integrators	Backwards-compatible mapping view of the integrator registry.

Exponential Integrators

exp_euler_step(target, *args)	Advance one step with the (coupled) exponential Euler method.
exp_exp_euler_step(target, t, dt, *args)	Advance a cell with exponential cable and exponential Euler channels.
ind_exp_euler_step(target, *args[, ...])	Advance each DiffEqState independently with exponential Euler.

Runge-Kutta Integrators

euler_step(target, *args)	Advance one step with the explicit (forward) Euler method.
midpoint_step(target, *args)	Advance one step with the explicit midpoint (modified Euler) method.
rk2_step(target, *args)	Advance one step with a generic second-order Runge-Kutta method.
heun2_step(target, *args)	Advance one step with Heun's second-order Runge-Kutta method.
ralston2_step(target, *args)	Advance one step with Ralston's second-order Runge-Kutta method.
rk3_step(target, *args)	Advance one step with the classical third-order Runge-Kutta method.
heun3_step(target, *args)	Advance one step with Heun's third-order Runge-Kutta method.
ssprk3_step(target, *args)	Advance one step with the Strong-Stability-Preserving RK3 method.
ralston3_step(target, *args)	Advance one step with Ralston's third-order Runge-Kutta method.
rk4_step(target, *args)	Advance one step with the classical fourth-order Runge-Kutta method.
ralston4_step(target, *args)	Advance one step with Ralston's fourth-order Runge-Kutta method.

Implicit Integrators

backward_euler_step(target, *args[, ...])	Advance one step with the linearised backward (implicit) Euler method.
implicit_euler_step(target, t, dt, *args)	Advance one step with the implicit (backward) Euler method.
implicit_exp_euler_step(target, t, dt, *args)	Advance a cell with implicit Euler voltage and exponential Euler channels.
implicit_rk4_step(target, t, dt, *args)	Advance a cell with implicit Euler voltage and explicit RK4 channels.

Other Integrators

cn_exp_euler_step(target, t, dt, *args)	Advance a cell with Crank-Nicolson voltage and exponential Euler channels.
cn_rk4_step(target, t, dt, *args)	Advance a cell with Crank-Nicolson voltage and explicit RK4 channels.
splitting_step(target, t, dt, *args)	Advance a multi-compartment cell with operator-splitting.
staggered_step(target, *args)	Advance a multi-compartment cell by one staggered time step.