[Dyn] Fix alpha synapse bugs (#578)

* [dyn] fix alpha synapse bugs

* [docs] fix math expression

brainpy/_src/dyn/synapses/abstract_models.py

@@ -477,7 +477,7 @@ def return_info(self):
 DualExponV2.__doc__ = DualExponV2.__doc__ % (pneu_doc,)
 
 
-class Alpha(DualExpon):
+class Alpha(SynDyn):
   r"""Alpha synapse model.
 
   **Model Descriptions**
@@ -494,7 +494,7 @@ class Alpha(DualExpon):
   .. math::
 
       \begin{aligned}
-      &\frac{d g}{d t}=-\frac{g}{\tau}+h \\
+      &\frac{d g}{d t}=-\frac{g}{\tau}+\frac{h}{\tau} \\
       &\frac{d h}{d t}=-\frac{h}{\tau}+\delta\left(t_{0}-t\right)
       \end{aligned}
 
@@ -585,16 +585,41 @@ def __init__(
       tau_decay: Union[float, ArrayType, Callable] = 10.0,
   ):
     super().__init__(
-      tau_decay=tau_decay,
-      tau_rise=tau_decay,
-      method=method,
       name=name,
       mode=mode,
       size=size,
       keep_size=keep_size,
       sharding=sharding
     )
 
+    # parameters
+    self.tau_decay = self.init_param(tau_decay)
+
+    # integrator
+    self.integral = odeint(JointEq(self.dg, self.dh), method=method)
+
+    self.reset_state(self.mode)
+
+  def reset_state(self, batch_or_mode=None, **kwargs):
+    self.h = self.init_variable(bm.zeros, batch_or_mode)
+    self.g = self.init_variable(bm.zeros, batch_or_mode)
+
+  def dh(self, h, t):
+    return -h / self.tau_decay
+
+  def dg(self, g, t, h):
+    return -g / self.tau_decay + h / self.tau_decay
+
+  def update(self, x):
+    # update synaptic variables
+    self.g.value, self.h.value = self.integral(self.g.value, self.h.value, share['t'], dt=share['dt'])
+    self.h += x
+    return self.g.value
+
+  def return_info(self):
+    return self.g
+
+
 
 Alpha.__doc__ = Alpha.__doc__ % (pneu_doc,)
 

brainpy/_src/dynold/synapses/abstract_models.py

@@ -498,7 +498,7 @@ def update(self, pre_spike=None):
     return super().update(pre_spike, stop_spike_gradient=self.stop_spike_gradient)
 
 
-class Alpha(DualExponential):
+class Alpha(_TwoEndConnAlignPre):
   r"""Alpha synapse model.
 
   **Model Descriptions**
@@ -516,7 +516,7 @@ class Alpha(DualExponential):
 
       \begin{aligned}
       &g_{\mathrm{syn}}(t)= g_{\mathrm{max}} g \\
-      &\frac{d g}{d t}=-\frac{g}{\tau}+h \\
+      &\frac{d g}{d t}=-\frac{g}{\tau}+\frac{h}{\tau} \\
       &\frac{d h}{d t}=-\frac{h}{\tau}+\delta\left(t_{0}-t\right)
       \end{aligned}
 
@@ -593,20 +593,40 @@ def __init__(
       mode: bm.Mode = None,
       stop_spike_gradient: bool = False,
   ):
-    super(Alpha, self).__init__(pre=pre,
-                                post=post,
-                                conn=conn,
-                                comp_method=comp_method,
-                                delay_step=delay_step,
-                                g_max=g_max,
-                                tau_decay=tau_decay,
-                                tau_rise=tau_decay,
-                                method=method,
-                                output=output,
-                                stp=stp,
-                                name=name,
-                                mode=mode,
-                                stop_spike_gradient=stop_spike_gradient)
+    # parameters
+    self.stop_spike_gradient = stop_spike_gradient
+    self.comp_method = comp_method
+    self.tau_decay = tau_decay
+    if bm.size(self.tau_decay) != 1:
+      raise ValueError(f'"tau_decay" must be a scalar or a tensor with size of 1. '
+                       f'But we got {self.tau_decay}')
+
+    syn = synapses.Alpha(pre.size,
+                         pre.keep_size,
+                         mode=mode,
+                         tau_decay=tau_decay,
+                         method=method)
+
+    super().__init__(pre=pre,
+                     post=post,
+                     syn=syn,
+                     conn=conn,
+                     comp_method=comp_method,
+                     delay_step=delay_step,
+                     g_max=g_max,
+                     output=output,
+                     stp=stp,
+                     name=name,
+                     mode=mode,)
+
+    self.check_post_attrs('input')
+    # copy the references
+    self.g = syn.g
+    self.h = syn.h
+
+  def update(self, pre_spike=None):
+    return super().update(pre_spike, stop_spike_gradient=self.stop_spike_gradient)
+
 
 
 class NMDA(_TwoEndConnAlignPre):