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# ==============================================================================
# -*- coding: utf-8 -*-
from typing import Callable
import brainstate
import braintools
import jax
import jax.numpy as jnp
import numpy as np
import saiunit as u
from brainstate.typing import ArrayLike, Size
from brainstate.util import DotDict
from ._base import NESTNeuron
from ._utils import is_tracer, validate_aeif_overflow, AdaptiveRungeKuttaStep
__all__ = [
'aeif_cond_alpha',
]
class aeif_cond_alpha(NESTNeuron):
r"""NEST-compatible ``aeif_cond_alpha`` neuron model.
Conductance-based adaptive exponential integrate-and-fire neuron with
alpha-shaped synaptic conductances.
Parameters
----------
in_size : Size
Population shape. States are broadcast/initialized over
``self.varshape`` derived from ``in_size``.
V_peak, V_reset, V_th, E_ex, E_in, E_L, Delta_T : ArrayLike
Voltage-like parameters in mV, each broadcastable to ``self.varshape``.
t_ref, tau_w, tau_syn_ex, tau_syn_in : ArrayLike
Time constants in ms, broadcastable to ``self.varshape``.
g_L, a : ArrayLike
Conductances in nS, broadcastable to ``self.varshape``.
C_m : ArrayLike
Membrane capacitance in pF, broadcastable to ``self.varshape``.
b, I_e : ArrayLike
Currents in pA, broadcastable to ``self.varshape``.
gsl_error_tol : ArrayLike
Unitless local RKF45 error tolerance, broadcastable and strictly positive.
V_initializer, g_ex_initializer, g_in_initializer, w_initializer : Callable
Initializer callables used by :meth:`init_state` and :meth:`reset_state`.
spk_fun : Callable
Surrogate spike function used by :meth:`get_spike`.
spk_reset : str
Reset mode inherited from :class:`~brainpy_state._base.Neuron`.
ref_var : bool
If ``True``, allocate and expose ``self.refractory`` state.
name : str | None
Optional node name.
Parameter Mapping
-----------------
.. list-table:: Parameter mapping to model symbols
:header-rows: 1
:widths: 17 25 15 20 43
* - Parameter
- Type / shape / unit
- Default
- Math symbol
- Semantics
* - ``in_size``
- :class:`~brainstate.typing.Size`; scalar or tuple
- required
- --
- Population shape defining ``self.varshape``.
* - ``V_peak``
- ArrayLike, broadcastable to ``self.varshape`` (mV)
- ``0.0 * u.mV``
- :math:`V_\mathrm{peak}`
- Spike detection threshold when ``Delta_T > 0`` and RHS clamp limit \
via :math:`\min(V, V_{\mathrm{peak}})`.
* - ``V_reset``
- ArrayLike, broadcastable (mV)
- ``-60.0 * u.mV``
- :math:`V_\mathrm{reset}`
- Membrane reset value and refractory clamp voltage.
* - ``t_ref``
- ArrayLike, broadcastable (ms)
- ``0.0 * u.ms``
- :math:`t_\mathrm{ref}`
- Absolute refractory duration converted to integer step counts using \
``ceil(t_ref / dt)``.
* - ``g_L`` and ``C_m``
- ArrayLike, broadcastable (nS, pF)
- ``30.0 * u.nS``, ``281.0 * u.pF``
- :math:`g_L`, :math:`C_m`
- Leak conductance and membrane capacitance in the AdEx membrane ODE.
* - ``E_ex``, ``E_in``, and ``E_L``
- ArrayLike, broadcastable (mV)
- ``0.0 * u.mV``, ``-85.0 * u.mV``, ``-70.6 * u.mV``
- :math:`E_\mathrm{ex}`, :math:`E_\mathrm{in}`, :math:`E_L`
- Excitatory, inhibitory, and leak reversal potentials.
* - ``Delta_T`` and ``V_th``
- ArrayLike, broadcastable (mV)
- ``2.0 * u.mV``, ``-50.4 * u.mV``
- :math:`\Delta_T`, :math:`V_\mathrm{th}`
- Exponential spike-initiation slope and soft-threshold location.
* - ``tau_w``, ``a``, and ``b``
- ArrayLike, broadcastable (ms, nS, pA)
- ``144.0 * u.ms``, ``4.0 * u.nS``, ``80.5 * u.pA``
- :math:`\tau_w`, :math:`a`, :math:`b`
- Adaptation time constant, subthreshold coupling, and spike-triggered \
jump amplitude.
* - ``tau_syn_ex`` and ``tau_syn_in``
- ArrayLike, broadcastable (ms)
- ``0.2 * u.ms``, ``2.0 * u.ms``
- :math:`\tau_{\mathrm{syn,ex}}`, :math:`\tau_{\mathrm{syn,in}}`
- Alpha conductance time constants for excitatory/inhibitory channels.
* - ``I_e``
- ArrayLike, broadcastable (pA)
- ``0.0 * u.pA``
- :math:`I_e`
- Constant injected current added every substep.
* - ``gsl_error_tol``
- ArrayLike, broadcastable, unitless, ``> 0``
- ``1e-6``
- --
- Local absolute tolerance for the embedded RKF45 error estimate.
* - ``V_initializer``
- Callable
- ``Constant(-70.6 * u.mV)``
- --
- Initializer for membrane potential state ``V``.
* - ``g_ex_initializer`` and ``g_in_initializer``
- Callable
- ``Constant(0.0 * u.nS)``
- --
- Initializers for ``g_ex`` and ``g_in``; ``dg_ex`` and ``dg_in`` \
always start at zero.
* - ``w_initializer``
- Callable
- ``Constant(0.0 * u.pA)``
- --
- Initializer for adaptation current ``w``.
* - ``spk_fun``
- Callable
- ``ReluGrad()``
- --
- Surrogate spike nonlinearity used by :meth:`get_spike`.
* - ``spk_reset``
- str
- ``'hard'``
- --
- Reset policy inherited from :class:`~brainpy_state._base.Neuron`; \
hard reset matches NEST behavior.
* - ``ref_var``
- bool
- ``False``
- --
- If ``True``, expose boolean state ``self.refractory``.
* - ``name``
- str | None
- ``None``
- --
- Optional node name.
Returns
-------
out : Any
Configured neuron node. Each :meth:`update` call returns a binary spike
tensor (dtype ``float64``) with shape ``self.V.value.shape``.
Description
-----------
``aeif_cond_alpha`` follows NEST ``models/aeif_cond_alpha.{h,cpp}``.
The model combines:
- exponential spike-initiation current (AdEx),
- spike-triggered and subthreshold adaptation current ``w``,
- alpha-shaped excitatory/inhibitory conductances.
**1. Membrane, synapse, and adaptation dynamics**
Let :math:`V` be membrane voltage and :math:`w` adaptation current.
.. math::
C_m \frac{dV}{dt}
=
-g_L (V - E_L)
+ g_L \Delta_T \exp\!\left(\frac{V - V_{th}}{\Delta_T}\right)
- g_{ex}(V - E_{ex})
- g_{in}(V - E_{in})
- w + I_e + I_{stim}.
Adaptation dynamics:
.. math::
\tau_w \frac{dw}{dt} = a (V - E_L) - w.
Alpha conductance states (two states per channel):
.. math::
\frac{d\,dg_{ex}}{dt} = -\frac{dg_{ex}}{\tau_{syn,ex}},
\qquad
\frac{d g_{ex}}{dt} = dg_{ex} - \frac{g_{ex}}{\tau_{syn,ex}},
.. math::
\frac{d\,dg_{in}}{dt} = -\frac{dg_{in}}{\tau_{syn,in}},
\qquad
\frac{d g_{in}}{dt} = dg_{in} - \frac{g_{in}}{\tau_{syn,in}}.
Incoming spike weights are interpreted in nS and split by sign:
.. math::
dg_{ex} \leftarrow dg_{ex} + \frac{e}{\tau_{syn,ex}} w_+,
\qquad
dg_{in} \leftarrow dg_{in} + \frac{e}{\tau_{syn,in}} |w_-|.
**2. Refractory and spike handling (NEST semantics)**
During refractory integration, NEST clamps effective membrane voltage to
``V_reset`` and sets :math:`dV/dt=0`. Otherwise the RHS uses
:math:`\min(V, V_{peak})` as effective voltage.
Threshold detection uses:
- ``V_peak`` if ``Delta_T > 0``,
- ``V_th`` if ``Delta_T == 0`` (iaf-like limit).
On each detected spike:
- ``V`` is reset to ``V_reset``,
- adaptation jump ``w <- w + b`` is applied immediately,
- refractory counter is set to ``refractory_counts + 1`` if refractory is enabled.
Spike handling occurs *inside* the adaptive RKF45 substep loop. Therefore,
with ``t_ref = 0`` multiple spikes can occur inside one simulation step,
matching NEST behavior.
**3. Update order per simulation step**
1. Integrate ODEs on :math:`(t, t+dt]` via adaptive RKF45.
2. Inside integration loop: apply refractory clamp and spike/reset/adaptation.
3. After loop: decrement refractory counter once.
4. Apply arriving spike weights to ``dg_ex``/``dg_in``.
5. Store external current input ``x`` into one-step delayed ``I_stim``.
Raises
------
ValueError
If parameters violate NEST-compatible constraints:
``V_reset < V_peak``, ``V_peak >= V_th``, ``Delta_T >= 0``,
``C_m > 0``, ``t_ref >= 0``, all time constants strictly positive,
and ``gsl_error_tol > 0``. Also raised when
``(V_peak - V_th) / Delta_T`` can overflow the exponential term, or if
runtime states exceed stability guards in :meth:`update`.
TypeError
If incompatible unitful/unitless values are passed and arithmetic
fails during parameter broadcasting or updates.
Attributes
----------
V : HiddenState
Membrane potential :math:`V_m` (mV).
dg_ex, dg_in : ShortTermState
Alpha auxiliary states stored as numeric values representing
:math:`\mathrm{nS}/\mathrm{ms}`.
g_ex, g_in : HiddenState
Excitatory and inhibitory conductances (nS).
w : HiddenState
Adaptation current (pA).
refractory_step_count : ShortTermState
Remaining refractory grid steps (``int32``).
integration_step : ShortTermState
Persistent RKF45 substep size estimate (ms).
I_stim : ShortTermState
One-step delayed injected current buffer (pA).
last_spike_time : ShortTermState
Last emitted spike time (ms); written as ``t + dt`` on spike.
refractory : ShortTermState
Optional boolean refractory indicator, available only when
``ref_var=True``.
See Also
--------
aeif_cond_exp : AdEx conductance model with exponential (single-state)
synaptic kernels.
aeif_cond_alpha_multisynapse : AdEx alpha-conductance model with
receptor-indexed ports.
aeif_psc_alpha : Current-based AdEx model with alpha PSCs.
Notes
-----
The two-state alpha formulation is equivalent to a causal alpha kernel.
With an event of effective conductance weight :math:`w` applied at
:math:`t=0` through ``dg += e w / \tau``, the resulting conductance is:
.. math::
g(t) = w \cdot \frac{t}{\tau} \exp\!\left(1-\frac{t}{\tau}\right),\quad t \ge 0.
Hence the kernel peaks at :math:`t=\tau` with amplitude exactly :math:`w`,
matching NEST's interpretation of weight magnitudes in nS.
Additional implementation implications:
- ``t_ref=0`` (default) allows multiple in-loop spikes within one grid step.
- Current input ``x`` is delayed by one step via ``I_stim`` (ring-buffer
semantics), while spike events are applied after ODE integration.
- Runtime is dominated by per-neuron adaptive RKF45 loops and therefore
scales with both population size and accepted substeps.
- Spike output is binary per simulation step even though multiple internal
spike/reset events can occur during a single ``dt`` integration window.
References
----------
.. [1] Brette R, Gerstner W (2005). Adaptive exponential integrate-and-fire
model as an effective description of neuronal activity.
Journal of Neurophysiology, 94:3637-3642.
DOI: https://doi.org/10.1152/jn.00686.2005
.. [2] NEST source: ``models/aeif_cond_alpha.h`` and
``models/aeif_cond_alpha.cpp``.
Examples
--------
.. code-block:: python
>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> neuron = brainpy.state.aeif_cond_alpha(
... in_size=3,
... V_peak=0.0 * u.mV,
... t_ref=2.0 * u.ms,
... )
>>> neuron.init_state()
>>> with brainstate.environ.context(dt=0.1 * u.ms, t=0.0 * u.ms):
... spikes = neuron.update(x=120.0 * u.pA)
>>> spikes.shape
(3,)
"""
__module__ = 'brainpy.state'
_MIN_H = 1e-8 * u.ms # ms
_MAX_ITERS = 100000
def __init__(
self,
in_size: Size,
V_peak: ArrayLike = 0.0 * u.mV,
V_reset: ArrayLike = -60.0 * u.mV,
t_ref: ArrayLike = 0.0 * u.ms,
g_L: ArrayLike = 30.0 * u.nS,
C_m: ArrayLike = 281.0 * u.pF,
E_ex: ArrayLike = 0.0 * u.mV,
E_in: ArrayLike = -85.0 * u.mV,
E_L: ArrayLike = -70.6 * u.mV,
Delta_T: ArrayLike = 2.0 * u.mV,
tau_w: ArrayLike = 144.0 * u.ms,
a: ArrayLike = 4.0 * u.nS,
b: ArrayLike = 80.5 * u.pA,
V_th: ArrayLike = -50.4 * u.mV,
tau_syn_ex: ArrayLike = 0.2 * u.ms,
tau_syn_in: ArrayLike = 2.0 * u.ms,
I_e: ArrayLike = 0.0 * u.pA,
gsl_error_tol: ArrayLike = 1e-6,
V_initializer: Callable = braintools.init.Constant(-70.6 * u.mV),
g_ex_initializer: Callable = braintools.init.Constant(0.0 * u.nS),
g_in_initializer: Callable = braintools.init.Constant(0.0 * u.nS),
w_initializer: Callable = braintools.init.Constant(0.0 * u.pA),
spk_fun: Callable = braintools.surrogate.ReluGrad(),
spk_reset: str = 'hard',
ref_var: bool = False,
name: str = None,
):
super().__init__(in_size, name=name, spk_fun=spk_fun, spk_reset=spk_reset)
self.V_peak = braintools.init.param(V_peak, self.varshape)
self.V_reset = braintools.init.param(V_reset, self.varshape)
self.t_ref = braintools.init.param(t_ref, self.varshape)
self.g_L = braintools.init.param(g_L, self.varshape)
self.C_m = braintools.init.param(C_m, self.varshape)
self.E_ex = braintools.init.param(E_ex, self.varshape)
self.E_in = braintools.init.param(E_in, self.varshape)
self.E_L = braintools.init.param(E_L, self.varshape)
self.Delta_T = braintools.init.param(Delta_T, self.varshape)
self.tau_w = braintools.init.param(tau_w, self.varshape)
self.a = braintools.init.param(a, self.varshape)
self.b = braintools.init.param(b, self.varshape)
self.V_th = braintools.init.param(V_th, self.varshape)
self.tau_syn_ex = braintools.init.param(tau_syn_ex, self.varshape)
self.tau_syn_in = braintools.init.param(tau_syn_in, self.varshape)
self.I_e = braintools.init.param(I_e, self.varshape)
self.gsl_error_tol = gsl_error_tol
self.V_initializer = V_initializer
self.g_ex_initializer = g_ex_initializer
self.g_in_initializer = g_in_initializer
self.w_initializer = w_initializer
self.ref_var = ref_var
self._validate_parameters()
self.integrator = AdaptiveRungeKuttaStep(
method='RKF45',
vf=self._vector_field,
event_fn=self._event_fn,
min_h=self._MIN_H,
max_iters=self._MAX_ITERS,
atol=self.gsl_error_tol,
dt=brainstate.environ.get_dt()
)
# other variable
ditype = brainstate.environ.ditype()
dt = brainstate.environ.get_dt()
self.ref_count = u.math.asarray(u.math.ceil(self.t_ref / dt), dtype=ditype)
def _validate_parameters(self):
r"""Validate model parameters against NEST constraints.
Raises
------
ValueError
If parameter inequalities or positivity constraints are violated,
or if the exponential term can overflow at spike time for the
configured ``V_peak``, ``V_th``, and ``Delta_T``.
"""
v_reset = self.V_reset
v_peak = self.V_peak
v_th = self.V_th
delta_t = self.Delta_T / u.mV
# Skip validation when parameters are JAX tracers (e.g. during jit).
if any(is_tracer(v) for v in (v_reset, v_peak, v_th, delta_t)):
return
if np.any(v_reset >= v_peak):
raise ValueError('Ensure that: V_reset < V_peak .')
if np.any(delta_t < 0.0):
raise ValueError('Delta_T must be positive.')
if np.any(v_peak < v_th):
raise ValueError('V_peak >= V_th required.')
if np.any(self.C_m <= 0.0 * u.pF):
raise ValueError('Capacitance must be strictly positive.')
if np.any(self.t_ref < 0.0 * u.ms):
raise ValueError('Refractory time cannot be negative.')
if np.any(self.tau_syn_ex <= 0.0 * u.ms):
raise ValueError('All time constants must be strictly positive.')
if np.any(self.tau_syn_in <= 0.0 * u.ms):
raise ValueError('All time constants must be strictly positive.')
if np.any(self.tau_w <= 0.0 * u.ms):
raise ValueError('All time constants must be strictly positive.')
if np.any(self.gsl_error_tol <= 0.0):
raise ValueError('The gsl_error_tol must be strictly positive.')
# Mirror NEST overflow guard for exponential term at spike time.
validate_aeif_overflow(v_peak, v_th, delta_t)
[docs]
def init_state(self, **kwargs):
r"""Initialize persistent and short-term state variables.
Parameters
----------
**kwargs
Unused compatibility parameters accepted by the base-state API.
Raises
------
ValueError
If an initializer cannot be broadcast to requested shape.
TypeError
If initializer outputs have incompatible units/dtypes for the
corresponding state variables.
"""
ditype = brainstate.environ.ditype()
dftype = brainstate.environ.dftype()
dt = brainstate.environ.get_dt()
g_ex = braintools.init.param(self.g_ex_initializer, self.varshape)
g_in = braintools.init.param(self.g_in_initializer, self.varshape)
V = braintools.init.param(self.V_initializer, self.varshape)
zeros = u.math.zeros(self.varshape, dtype=V.dtype) * (u.nS / u.ms)
w = braintools.init.param(self.w_initializer, self.varshape)
self.dg_ex = brainstate.ShortTermState(zeros)
self.dg_in = brainstate.ShortTermState(zeros)
self.g_ex = brainstate.HiddenState(g_ex)
self.g_in = brainstate.HiddenState(g_in)
self.V = brainstate.HiddenState(V)
self.w = brainstate.HiddenState(w)
self.last_spike_time = brainstate.ShortTermState(u.math.full(self.varshape, -1e7 * u.ms))
self.refractory_step_count = brainstate.ShortTermState(u.math.full(self.varshape, 0, dtype=ditype))
self.integration_step = brainstate.ShortTermState.init(braintools.init.Constant(dt), self.varshape)
self.I_stim = brainstate.ShortTermState(u.math.full(self.varshape, 0.0 * u.pA, dtype=dftype))
if self.ref_var:
refractory = braintools.init.param(braintools.init.Constant(False), self.varshape)
self.refractory = brainstate.ShortTermState(refractory)
[docs]
def get_spike(self, V: ArrayLike = None):
r"""Evaluate surrogate spike output from membrane voltage.
Parameters
----------
V : ArrayLike, optional
Voltage values with shape broadcastable to ``self.varshape`` and
units compatible with mV. If ``None``, uses current state
``self.V.value``.
Returns
-------
ArrayLike
Surrogate spike activation produced by
``spk_fun((V - V_th) / (V_th - V_reset))``.
"""
V = self.V.value if V is None else V
v_scaled = (V - self.V_th) / (self.V_th - self.V_reset)
return self.spk_fun(v_scaled)
def _vector_field(self, state, extra):
"""Unit-aware vectorized RHS for all neurons simultaneously.
Parameters
----------
state : DotDict
Keys: V, dg_ex, g_ex, dg_in, g_in, w — ODE state variables.
extra : DotDict
Keys: spike_mask, r, unstable, i_stim, v_peak_detect — mutable
auxiliary data carried through the integrator.
Returns
-------
DotDict with same keys as ``state``, containing time derivatives.
"""
is_refractory = extra.r > 0
v_eff = u.math.where(is_refractory, self.V_reset, u.math.minimum(state.V, self.V_peak))
i_syn_exc = state.g_ex * (v_eff - self.E_ex)
i_syn_inh = state.g_in * (v_eff - self.E_in)
delta_t_safe = u.math.where(self.Delta_T == 0.0 * u.mV, 1.0 * u.mV, self.Delta_T)
exp_arg = u.math.clip((v_eff - self.V_th) / delta_t_safe, -500.0, 500.0)
i_spike = self.g_L * self.Delta_T * u.math.exp(exp_arg)
dV_raw = (
-self.g_L * (v_eff - self.E_L) + i_spike
- i_syn_exc - i_syn_inh - state.w + self.I_e + extra.i_stim
) / self.C_m
dV = u.math.where(is_refractory, u.math.zeros_like(dV_raw), dV_raw)
ddg_ex = -state.dg_ex / self.tau_syn_ex
dg_ex_dt = state.dg_ex - state.g_ex / self.tau_syn_ex
ddg_in = -state.dg_in / self.tau_syn_in
dg_in_dt = state.dg_in - state.g_in / self.tau_syn_in
dw = (self.a * (v_eff - self.E_L) - state.w) / self.tau_w
return DotDict(V=dV, dg_ex=ddg_ex, g_ex=dg_ex_dt, dg_in=ddg_in, g_in=dg_in_dt, w=dw)
def _event_fn(self, state, extra, accept):
"""In-loop spike detection, reset, and refractory handling.
Parameters
----------
state : DotDict
Keys: V, dg_ex, g_ex, dg_in, g_in, w — ODE state variables.
extra : DotDict
Keys: spike_mask, r, unstable, i_stim, v_peak_detect.
accept : array, bool
Mask of neurons whose RK substep was accepted.
Returns
-------
(new_state, new_extra) DotDicts with updated spike/reset/refractory info.
"""
unstable = extra.unstable | jnp.any(
accept & ((state.V < -1e3 * u.mV) | (state.w < -1e6 * u.pA) | (state.w > 1e6 * u.pA))
)
refr_accept = accept & (extra.r > 0)
new_V = u.math.where(refr_accept, self.V_reset, state.V)
spike_now = accept & (extra.r <= 0) & (new_V >= extra.v_peak_detect)
spike_mask = extra.spike_mask | spike_now
new_V = u.math.where(spike_now, self.V_reset, new_V)
new_w = u.math.where(spike_now, state.w + self.b, state.w)
r = u.math.where(spike_now & (self.ref_count > 0), self.ref_count + 1, extra.r)
new_state = DotDict({**state, 'V': new_V, 'w': new_w})
new_extra = DotDict({**extra, 'spike_mask': spike_mask, 'r': r, 'unstable': unstable})
return new_state, new_extra
[docs]
def update(self, x=0.0 * u.pA):
r"""Advance the neuron by one simulation step.
Parameters
----------
x : ArrayLike, optional
Continuous external current input in pA, broadcastable to
``self.varshape``. This value is stored into ``I_stim`` and applied
at the next simulation step (one-step delay).
Returns
-------
jax.Array
Binary spike tensor with dtype ``jnp.float64`` and shape
``self.V.value.shape``. A value of ``1.0`` indicates at least one
internal spike event occurred during the integrated interval
:math:`(t, t+dt]`.
Raises
------
ValueError
If RKF45 integration enters a guarded unstable regime
(``V < -1e3 mV`` or ``|w| > 1e6 pA``), indicating divergent
dynamics for the current parameter/input regime.
Notes
-----
Integration is performed with an adaptive vectorized RKF45 loop,
including in-loop spike/reset/adaptation events and optional
multiple spikes per step. All arithmetic is unit-aware via
``saiunit.math``.
"""
t = brainstate.environ.get('t')
dt = brainstate.environ.get_dt()
dftype = brainstate.environ.dftype()
ditype = brainstate.environ.ditype()
# Read state variables with their natural units.
V = self.V.value # mV
dg_ex = self.dg_ex.value # nS/ms
g_ex = self.g_ex.value # nS
dg_in = self.dg_in.value # nS/ms
g_in = self.g_in.value # nS
w = self.w.value # pA
r = self.refractory_step_count.value # int
i_stim = self.I_stim.value # pA
h = self.integration_step.value # ms
# Spike detection threshold: V_peak if Delta_T > 0, else V_th.
v_peak_detect = u.math.where(self.Delta_T > 0.0 * u.mV, self.V_peak, self.V_th)
# Current input for next step (one-step delay).
new_i_stim = self.sum_current_inputs(x, self.V.value) # pA
# Adaptive RKF45 integration via generic integrator.
ode_state = DotDict(V=V, dg_ex=dg_ex, g_ex=g_ex, dg_in=dg_in, g_in=g_in, w=w)
extra = DotDict(
spike_mask=jnp.zeros(self.varshape, dtype=jnp.bool_),
r=r,
unstable=jnp.array(False),
i_stim=i_stim,
v_peak_detect=v_peak_detect,
)
ode_state, h, extra = self.integrator(state=ode_state, h=h, extra=extra)
V, dg_ex, g_ex = ode_state.V, ode_state.dg_ex, ode_state.g_ex
dg_in, g_in, w = ode_state.dg_in, ode_state.g_in, ode_state.w
spike_mask, r, unstable = extra.spike_mask, extra.r, extra.unstable
# Post-loop stability check.
brainstate.transform.jit_error_if(
jnp.any(unstable), 'Numerical instability in aeif_cond_alpha dynamics.'
)
# Decrement refractory counter.
r = u.math.where(r > 0, r - 1, r)
# Synaptic spike inputs (applied after integration).
w_ex = self.sum_delta_inputs(u.math.zeros_like(self.g_ex.value), label='w_ex')
w_in = self.sum_delta_inputs(u.math.zeros_like(self.g_in.value), label='w_in')
pscon_ex = np.e / self.tau_syn_ex # 1/ms
pscon_in = np.e / self.tau_syn_in # 1/ms
# Apply synaptic spike inputs.
dg_ex = dg_ex + pscon_ex * w_ex # nS/ms + 1/ms * nS = nS/ms
dg_in = dg_in + pscon_in * w_in # nS/ms + 1/ms * nS = nS/ms
# Write back state.
self.V.value = V
self.dg_ex.value = dg_ex
self.g_ex.value = g_ex
self.dg_in.value = dg_in
self.g_in.value = g_in
self.w.value = w
self.refractory_step_count.value = jnp.asarray(u.get_mantissa(r), dtype=ditype)
self.integration_step.value = h
self.I_stim.value = new_i_stim + u.math.zeros(self.varshape) * u.pA
last_spike_time = u.math.where(spike_mask, t + dt, self.last_spike_time.value)
self.last_spike_time.value = jax.lax.stop_gradient(last_spike_time)
if self.ref_var:
self.refractory.value = jax.lax.stop_gradient(self.refractory_step_count.value > 0)
return u.math.asarray(spike_mask, dtype=dftype)
