fix #99; provide documentation for FDE solvers

brainpy/integrators/fde/GL.py

@@ -146,11 +146,15 @@ def __init__(self, f, alpha, num_memory, inits, dt=None, name=None):
     # binomial coefficients
     bc = (1 - (1 + self.alpha.reshape((-1, 1))) / jnp.arange(1, num_memory + 1))
     bc = jnp.cumprod(jnp.vstack([jnp.ones_like(self.alpha), bc.T]), axis=0)
-    self.binomial_coef = jnp.flip(bc[1:], axis=0)
+    self._binomial_coef = jnp.flip(bc[1:], axis=0)
 
     # integral function
     self.set_integral(self._integral_func)
 
+  @property
+  def binomial_coef(self):
+    return bm.as_numpy(jnp.flip(self._binomial_coef, axis=0))
+
   def _integral_func(self, *args, **kwargs):
     # format arguments
     all_args = format_args(args, kwargs, self.arguments)
@@ -173,7 +177,7 @@ def _integral_func(self, *args, **kwargs):
     integrals = []
     idx = (self._idx + bm.arange(self.num_memory)) % self.num_memory
     for i, var in enumerate(self.variables):
-      summation = self.binomial_coef[:, i] @ self.delays[var][idx]
+      summation = self._binomial_coef[:, i] @ self.delays[var][idx]
       integral = (dt ** self.alpha[i]) * devs[var] - summation
       self.delays[var][self._idx[0]] = integral
       integrals.append(integral)

brainpy/integrators/fde/base.py

@@ -10,6 +10,11 @@
 from brainpy.errors import UnsupportedError
 
 
+__all__ = [
+  'FDEIntegrator'
+]
+
+
 class FDEIntegrator(Integrator):
   """Numerical integrator for fractional differential equations (FEDs).
 

docs/index.rst

@@ -58,6 +58,7 @@ The code of BrainPy is open-sourced at GitHub:
    tutorial_toolbox/ode_numerical_solvers
    tutorial_toolbox/sde_numerical_solvers
    tutorial_toolbox/dde_numerical_solvers
+   tutorial_toolbox/fde_numerical_solvers
    tutorial_toolbox/joint_equations
    tutorial_toolbox/synaptic_connections
    tutorial_toolbox/synaptic_weights