def __init__(self,
f_cell,
f_type='continuous',
f_loss_batch=None,
verbose=True):
self.verbose = verbose
if f_type not in ['discrete', 'continuous']:
raise AnalyzerError(
f'Only support "continuous" (continuous derivative function) or '
f'"discrete" (discrete update function), not {f_type}.')
# functions
self.f_cell = f_cell
if f_loss_batch is None:
if f_type == 'discrete':
self.f_loss = bm.jit(lambda h: bm.mean((h - f_cell(h))**2))
self.f_loss_batch = bm.jit(lambda h: bm.mean(
(h - bm.vmap(f_cell, auto_infer=False)(h))**2, axis=1))
if f_type == 'continuous':
self.f_loss = bm.jit(lambda h: bm.mean(f_cell(h)**2))
self.f_loss_batch = bm.jit(lambda h: bm.mean(
(bm.vmap(f_cell, auto_infer=False)(h))**2, axis=1))
else:
self.f_loss_batch = f_loss_batch
self.f_loss = bm.jit(lambda h: bm.mean(f_cell(h)**2))
self.f_jacob_batch = bm.jit(bm.vmap(bm.jacobian(f_cell)))
# essential variables
self._losses = None
self._fixed_points = None
self._selected_ids = None
self.opt_losses = None
def F_vmap_jacobian(self):
if C.F_vmap_jacobian not in self.analyzed_results:
f1 = lambda xy, *args: jnp.array([self.F_fx(xy[0], xy[1], *args),
self.F_fy(xy[0], xy[1], *args)])
f2 = bm.jit(bm.vmap(bm.jacobian(f1)), device=self.jit_device)
self.analyzed_results[C.F_vmap_jacobian] = f2
return self.analyzed_results[C.F_vmap_jacobian]
def find_fps_with_opt_solver(self, candidates, opt_method=None):
"""Optimize fixed points with nonlinear optimization solvers.
Parameters
----------
candidates
opt_method: function, callable
"""
assert bm.ndim(candidates) == 2 and isinstance(
candidates, (bm.JaxArray, jax.numpy.ndarray))
if opt_method is None:
opt_method = lambda f, x0: minimize(f, x0, method='BFGS')
if self.verbose:
print(f"Optimizing to find fixed points:")
f_opt = bm.jit(bm.vmap(lambda x0: opt_method(self.f_loss, x0)))
res = f_opt(bm.as_device_array(candidates))
valid_ids = jax.numpy.where(res.success)[0]
self._fixed_points = np.asarray(res.x[valid_ids])
self._losses = np.asarray(res.fun[valid_ids])
self._selected_ids = np.asarray(valid_ids)
if self.verbose:
print(
f' '
f'Found {len(valid_ids)} fixed points from {len(candidates)} initial points.'
)
def get_sign2(f, *xyz, args=()): in_axes = tuple(range(len(xyz))) + tuple([None] * len(args)) f = bm.jit(bm.vmap(f_without_jaxarray_return(f), in_axes=in_axes)) xyz = tuple((v.value if isinstance(v, bm.JaxArray) else v) for v in xyz) XYZ = jnp.meshgrid(*xyz) XYZ = tuple(jnp.moveaxis(v, 1, 0).flatten() for v in XYZ) shape = (len(v) for v in xyz) return jnp.sign(f(*(XYZ + args))).reshape(shape)
def roots_of_1d_by_xy(f, starts, ends, args): f = f_without_jaxarray_return(f) f_opt = bm.jit(bm.vmap(jax_brentq(f))) res = f_opt(starts, ends, (args,)) valid_idx = jnp.where(res['status'] == ECONVERGED)[0] xs = res['root'][valid_idx] ys = args[valid_idx] return xs, ys
def brentq_roots(f, starts, ends, *vmap_args, args=()):
in_axes = (0, 0, tuple([0] * len(vmap_args)) + tuple([None] * len(args)))
vmap_f_opt = bm.jit(bm.vmap(jax_brentq(f), in_axes=in_axes))
all_args = vmap_args + args
if len(all_args):
res = vmap_f_opt(starts, ends, all_args)
else:
res = vmap_f_opt(starts, ends, )
valid_idx = jnp.where(res['status'] == ECONVERGED)[0]
roots = res['root'][valid_idx]
vmap_args = tuple(a[valid_idx] for a in vmap_args)
return roots, vmap_args
def roots_of_1d_by_x(f, candidates, args=()):
"""Find the roots of the given function by numerical methods.
"""
f = f_without_jaxarray_return(f)
candidates = candidates.value if isinstance(candidates, bm.JaxArray) else candidates
args = tuple(a.value if isinstance(candidates, bm.JaxArray) else a for a in args)
vals = f(candidates, *args)
signs = jnp.sign(vals)
zero_sign_idx = jnp.where(signs == 0)[0]
fps = candidates[zero_sign_idx]
candidate_ids = jnp.where(signs[:-1] * signs[1:] < 0)[0]
if len(candidate_ids) <= 0:
return fps
starts = candidates[candidate_ids]
ends = candidates[candidate_ids + 1]
f_opt = bm.jit(bm.vmap(jax_brentq(f), in_axes=(0, 0, None)))
res = f_opt(starts, ends, args)
valid_idx = jnp.where(res['status'] == ECONVERGED)[0]
fps2 = res['root'][valid_idx]
return jnp.concatenate([fps, fps2])
def F_vmap_dfxdx(self):
if C.F_vmap_dfxdx not in self.analyzed_results:
f = bm.jit(bm.vmap(bm.vector_grad(self.F_fx, argnums=0)), device=self.jit_device)
self.analyzed_results[C.F_vmap_dfxdx] = f
return self.analyzed_results[C.F_vmap_dfxdx]
def F_vmap_brentq_fy(self):
if C.F_vmap_brentq_fy not in self.analyzed_results:
f_opt = bm.jit(bm.vmap(utils.jax_brentq(self.F_fy)))
self.analyzed_results[C.F_vmap_brentq_fy] = f_opt
return self.analyzed_results[C.F_vmap_brentq_fy]
cann = CANN2D(length=512, k=0.1)
cann.show_conn()
# encoding
Iext, length = bp.inputs.section_input(
values=[cann.get_stimulus_by_pos([0., 0.]), 0.],
durations=[10., 20.],
return_length=True)
runner = bp.StructRunner(cann,
inputs=['input', Iext, 'iter'],
monitors=['r'],
dyn_vars=cann.vars())
runner.run(length)
bp.visualize.animate_2D(values=runner.mon.r,
net_size=(cann.length, cann.length))
# tracking
length = 20
positions = bp.inputs.ramp_input(-bm.pi, bm.pi, duration=length, t_start=0)
positions = bm.stack([positions, positions]).T
Iext = bm.vmap(cann.get_stimulus_by_pos)(positions)
runner = bp.StructRunner(cann,
inputs=['input', Iext, 'iter'],
monitors=['r'],
dyn_vars=cann.vars())
runner.run(length)
bp.visualize.animate_2D(values=runner.mon.r,
net_size=(cann.length, cann.length))