def test_2_4_vectorization():
"""Testing vectorization functionality of ComputeGraph class.
See Also
--------
:method:`_vectorize`: Detailed documentation of vectorize method of `ComputeGraph` class.
"""
backends = ['tensorflow', 'numpy']
for b in backends:
# test whether vectorized networks produce same output as non-vectorized backend
################################################################################
# define simulation params
dt = 1e-2
sim_time = 10.
sim_steps = int(sim_time / dt)
inp = np.zeros((sim_steps, 2)) + 0.5
# set up networks
net_config0 = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net12").apply()
net_config1 = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net12").apply()
net0 = ComputeGraph(net_config=net_config0,
name='net0',
vectorization='none',
dt=dt,
build_in_place=False,
backend=b)
net1 = ComputeGraph(net_config=net_config1,
name='net1',
vectorization='nodes',
dt=dt,
build_in_place=False,
backend=b)
# simulate network behaviors
results0 = net0.run(sim_time,
outputs={
'a': 'pop0/op7/a',
'b': 'pop1/op7/a'
},
inputs={'all/op7/inp': inp})
results1 = net1.run(sim_time,
outputs={
'a': 'pop0/op7/a',
'b': 'pop1/op7/a'
},
inputs={'all/op7/inp': inp},
out_dir='/tmp/log')
error1 = nmrse(results0.values, results1.values)
assert np.sum(results1.values) > 0.
assert np.mean(error1) == pytest.approx(0., rel=1e-6, abs=1e-6)
def test_2_5_solver():
"""Testing different numerical solvers of pyrates.
See Also
--------
:method:`_solve`: Detailed documentation of how to numerical integration is performed by the `NumpyBackend`.
:method:`run`: Detailed documentation of the method that needs to be called to solve differential equations in the
`NumpyBackend`.
"""
backend = 'numpy'
# define input
dt = 1e-3
sim_time = 100.
sim_steps = int(np.round(sim_time / dt, decimals=0))
inp = np.zeros((sim_steps, 1)) + 0.5
# standard euler solver (trusted)
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net13").apply(
label='net0')
net = net_config.compile(vectorization=True,
step_size=dt,
backend=backend,
solver='euler')
results = net.run(sim_time,
outputs={
'a1': 'p1/op9/a',
'a2': 'p2/op9/a'
},
inputs={'p1/op9/I_ext': inp})
net.clear()
# scipy solver (tested)
net_config2 = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net13").apply(
label='net1')
net2 = net_config2.compile(vectorization=True,
step_size=dt,
backend=backend,
solver='scipy')
results2 = net2.run(sim_time,
outputs={
'a1': 'p1/op9/a',
'a2': 'p2/op9/a'
},
inputs={'p1/op9/I_ext': inp},
method='RK23')
net2.clear()
assert np.mean(results.loc[:, 'a2'].values -
results2.loc[:, 'a2'].values) == pytest.approx(0.,
rel=1e-4,
abs=1e-4)
def test_op_caching_nodes():
"""Test the case that two operator templates are identical up to variable definitions, where one inherits from the
other"""
from pyrates.frontend import CircuitTemplate
circuit = CircuitTemplate.from_yaml("model_templates.test_resources.test_operator_caching_templates.TestCircuit1").apply()
# access nodes
node1 = circuit["node1"]
node2 = circuit["node2"]
# verify that operator labels and contents are identical
op1, op1_dict = next(iter(node1.op_graph.nodes(data=True)))
op2, op2_dict = next(iter(node2.op_graph.nodes(data=True)))
assert op1 == op2
assert op1_dict == op2_dict
assert op1_dict["operator"] is op2_dict["operator"]
# verify that values in nodes are indeed different (but refer to same operator)
assert node1.values["TestOpLin0"]["c"] == 0
assert node2.values["TestOpLin0"]["c"] == 1
# now do the vectorization step
circuit = circuit.optimize_graph_in_place()
def eval_fitness(self, genes: list, gene_map: list, loss_func: callable,
loss_kwargs: Optional[dict] = None, run_func: Optional[callable] = None,
template: Optional[str] = None, compile_kwargs: Optional[dict] = None,
run_kwargs: Optional[dict] = None) -> float:
"""Performs simulation in PyRates of the model defined by `template` and calculates the fitness based on the
resulting timeseries of that simulation.
Parameters
----------
genes
List of model parameters
gene_map
List of string-based variable pointers that indicate which gene refers to which variable in the model.
loss_func
loss_kwargs
run_func
User-specified run function that can be specified instead of a template, to run user-specified routines.
template
compile_kwargs
run_kwargs
Returns
-------
"""
if run_func is None:
attempts = 1
while attempts < 100:
try:
# load model template
model_id = self.get_unique_id(int(attempts*1e6))
if type(template) is str:
template = CircuitTemplate.from_yaml(template)
model = deepcopy(template).apply(label=f'model_{model_id}')
# apply new parameters to model template
params, param_map = dict(), dict()
for i, (p, key) in enumerate(zip(genes, gene_map)):
params[i] = p
param_map[i] = key
adapt_circuit(model, params=params, param_map=param_map)
# compile model into backend
model_compiled = model.compile(**compile_kwargs)
# define run func
run_func = model_compiled.run
break
except (FileExistsError, FileNotFoundError):
attempts += 1
continue
results = run_func(**run_kwargs)
return loss_func(results, **loss_kwargs)
References
^^^^^^^^^^
.. [1] B.H. Jansen & V.G. Rit (1995) *Electroencephalogram and visual evoked potential generation in a mathematical
model of coupled cortical columns.* Biological Cybernetics, 73(4): 357-366.
"""
# %%
# Part 1: Translating a model definition into an intermediate representation
# --------------------------------------------------------------------------
#
# First, we will need to load a model template into PyRates. We choose to load a YAML-based model definition, but this
# can be done just as well from a Python-based model definition.
from pyrates.frontend import CircuitTemplate
jr_template = CircuitTemplate.from_yaml(
"model_templates.jansen_rit.simple_jansenrit.JRC")
print(jr_template.nodes)
print(jr_template.edges)
# %%
# As demonstrated by the :code:`print()` calls above, the :code:`CircuitTemplate` contains fields for nodes and edges,
# which contain list of :code:`NodeTemplate` and :code:`EdgeTemplate` instances with :code:`OperatorTemplate` instances
# defined on them that contain the underlying model equations. This template can be transformed into an intermediate
# representation via the :code:`apply()` method defined for each template class:
jr_ir = jr_template.apply()
print(jr_ir.nodes)
print(jr_ir.edges)
dt = 1e-3
dts = 1e-2
cutoff = 100.0
T = 200.0 + cutoff
start = int((0 + cutoff) / dt)
dur = int(5 / (0.6 * dt))
steps = int(T / dt)
inp = np.zeros((steps, 1))
inp[start:start + dur] = 0.6
# target: delayed biexponential response of the alpha or renshaw neuron
path = "../config/spinal_cord/sc"
neuron = 'alpha'
target_var = 'I_ampa'
model = CircuitTemplate.from_yaml(path).apply().compile(backend='numpy',
step_size=dt,
solver='euler')
r1 = model.run(simulation_time=T,
sampling_step_size=dts,
inputs={'m1/m1_dummy/m_in': inp},
outputs={neuron: f'{neuron}/{neuron}_op/{target_var}'})
model.clear()
r1.plot()
plt.show()
# approximation: gamma-distributed feedback
source = 'm1'
param_grid = {
'd': np.asarray([1.5, 2.0, 2.5]),
's': np.asarray([0.4, 0.6, 0.8, 1.0])
}
def test_2_1_operator():
"""Testing operator functionality of compute graph class:
See Also
--------
:method:`add_operator`: Detailed documentation of method for adding operations to instance of `ComputeGraph`.
"""
backends = ["tensorflow", "numpy"]
accuracy = 1e-4
for b in backends:
# test correct numerical evaluation of operator with two coupled simple, linear equations
#########################################################################################
# create net config from YAML file
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net0").apply()
# instantiate compute graph from net config
dt = 1e-1
net = ComputeGraph(net_config=net_config,
name='net0',
vectorization=True,
backend=b)
# simulate operator behavior
sim_time = 10.0
results = net.run(simulation_time=sim_time,
step_size=dt,
outputs={'a': 'pop0/op0/a'})
net.clear()
# generate target values
sim_steps = int(sim_time / dt)
update0_1 = lambda x: x * 0.5
update0_0 = lambda x: x + 2.0
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = targets[i, 0] + dt * update0_0(targets[i, 1])
targets[i + 1, 1] = targets[i, 1] + dt * update0_1(targets[i, 0])
# compare results with target values
diff = results['a'].values[:, 0] - targets[1:, 1]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
# test correct numerical evaluation of operator with a single differential equation and external input
######################################################################################################
# set up operator in pyrates
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net1").apply()
net = ComputeGraph(net_config=net_config,
name='net1',
vectorization=True,
backend=b)
# define input
inp = np.zeros((sim_steps, )) + 0.5
# simulate operator behavior
results = net.run(sim_time,
step_size=dt,
inputs={'pop0/op1/u': inp},
outputs={'a': 'pop0/op1/a'})
net.clear()
# calculate operator behavior from hand
update1 = lambda x, y: x + dt * (y - x)
targets = np.zeros((sim_steps + 1, 1), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1] = update1(targets[i], inp[i])
diff = results['a'].values[:, 0] - targets[1:, 0]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
# test correct numerical evaluation of operator with two coupled equations (1 ODE, 1 non-DE eq.)
################################################################################################
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net2").apply()
net = ComputeGraph(net_config=net_config,
name='net2',
vectorization=True,
backend=b)
results = net.run(sim_time, outputs={'a': 'pop0/op2/a'}, step_size=dt)
net.clear()
# calculate operator behavior from hand
update2 = lambda x: 1. / (1. + np.exp(-x))
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 1] = update2(targets[i, 0])
targets[i + 1, 0] = update1(targets[i, 0], targets[i + 1, 1])
diff = results['a'].values[:, 0] - targets[1:, 0]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
# test correct numerical evaluation of operator with a two coupled DEs
######################################################################
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net3").apply()
net = ComputeGraph(net_config=net_config,
name='net3',
vectorization=True,
backend=b)
results = net.run(sim_time,
outputs={'b': 'pop0/op3/b'},
inputs={'pop0/op3/u': inp},
out_dir="/tmp/log",
step_size=dt)
net.clear()
# calculate operator behavior from hand
update3_0 = lambda a, b, u: a + dt * (-10. * a + b**2 + u)
update3_1 = lambda b, a: b + dt * 0.1 * a
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = update3_0(targets[i, 0], targets[i, 1], inp[i])
targets[i + 1, 1] = update3_1(targets[i, 1], targets[i, 0])
diff = results['b'].values[:, 0] - targets[1:, 1]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
from pyrates.utility.visualization import Interactive2DParamPlot
# parameter definition
dt = 1e-3
dts = 1e-2
cutoff = 100.0
T = 150.0 + cutoff
start = int((0 + cutoff)/dt)
dur = int(5/(0.6*dt))
steps = int(T/dt)
inp = np.zeros((steps, 1))
inp[start:start+dur] = 0.6
# model setup
path = "../config/spinal_cord/sc"
template = CircuitTemplate.from_yaml(path).apply()
plot_network_graph(template)
model = template.compile(backend='numpy', solver='scipy', step_size=dt)
# simulation
results = model.run(simulation_time=T, step_size=dt, sampling_step_size=dts,
inputs={'m1/m1_dummy/m_in': inp},
outputs={
'psp': 'muscle/muscle_op/I_acc',
'alpha_exc': 'alpha/alpha_op/I_ampa',
'alpha_inh': 'alpha/alpha_op/I_glycin',
'renshaw': 'renshaw/renshaw_op/I_acc'
}
)
def test_2_3_edge():
"""Testing edge functionality of compute graph class.
See Also
--------
:method:`add_edge`: Detailed documentation of add_edge method of `ComputeGraph`class.
"""
backends = ['numpy', 'tensorflow']
accuracy = 1e-4
for b in backends:
# test correct numerical evaluation of graph with 1 source projecting unidirectional to 2 target nodes
######################################################################################################
# set up edge in pyrates
dt = 1e-1
sim_time = 10.
sim_steps = int(sim_time / dt)
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net8").apply()
net = ComputeGraph(net_config=net_config,
name='net0',
vectorization=True,
backend=b)
# calculate edge behavior from hand
update0 = lambda x, y: x + dt * y * 0.5
update1 = lambda x, y: x + dt * (y + 2.0)
update2 = lambda x, y: x + dt * (y - x)
targets = np.zeros((sim_steps + 1, 4), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = update0(targets[i, 0], targets[i, 1])
targets[i + 1, 1] = update1(targets[i, 1], targets[i, 0])
targets[i + 1, 2] = update2(targets[i, 2], targets[i, 0] * 2.0)
targets[i + 1, 3] = update2(targets[i, 3], targets[i, 0] * 0.5)
# simulate edge behavior
results = net.run(sim_time,
outputs={
'a': 'pop1/op1/a',
'b': 'pop2/op1/a'
},
step_size=dt)
net.clear()
diff = np.mean(np.abs(results['a'].values[:, 0] - targets[1:, 2])) + \
np.mean(np.abs(results['b'].values[:, 0] - targets[1:, 3]))
assert diff == pytest.approx(0., rel=accuracy, abs=accuracy)
# test correct numerical evaluation of graph with 2 bidirectionaly coupled nodes
################################################################################
# define input
inp = np.zeros((sim_steps, 1)) + 0.5
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net9").apply()
net = ComputeGraph(net_config=net_config,
name='net1',
vectorization=True,
backend=b)
results = net.run(sim_time,
outputs={
'a': 'pop0/op1/a',
'b': 'pop1/op7/a'
},
inputs={'pop1/op7/inp': inp},
step_size=dt)
net.clear()
# calculate edge behavior from hand
update3 = lambda x, y, z: x + dt * (y + z - x)
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = update2(targets[i, 0], targets[i, 1] * 0.5)
targets[i + 1, 1] = update3(targets[i, 1], targets[i, 0] * 2.0,
inp[i])
diff = np.mean(np.abs(results['a'].values[:, 0] - targets[1:, 0])) + \
np.mean(np.abs(results['b'].values[:, 0] - targets[1:, 1]))
assert diff == pytest.approx(0., rel=accuracy, abs=accuracy)
# test correct numerical evaluation of graph with 2 bidirectionally delay-coupled nodes
#######################################################################################
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net10").apply()
net = ComputeGraph(net_config=net_config,
name='net2',
vectorization=True,
backend=b,
step_size=dt)
results = net.run(sim_time,
outputs={
'a': 'pop0/op8/a',
'b': 'pop1/op8/a'
},
step_size=dt)
net.clear()
# calculate edge behavior from hand
delay0 = int(0.5 / dt)
delay1 = int(1. / dt)
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
update4 = lambda x, y: x + dt * (2.0 + y)
for i in range(sim_steps):
inp0 = 0. if i < delay0 else targets[i - delay0, 1]
inp1 = 0. if i < delay1 else targets[i - delay1, 0]
targets[i + 1, 0] = update4(targets[i, 0], inp0 * 0.5)
targets[i + 1, 1] = update4(targets[i, 1], inp1 * 2.0)
diff = np.mean(np.abs(results['a'].values[:, 0] - targets[1:, 0])) + \
np.mean(np.abs(results['b'].values[:, 0] - targets[1:, 1]))
assert diff == pytest.approx(0., rel=accuracy, abs=accuracy)
# test correct numerical evaluation of graph with 2 unidirectionally, multi-delay-coupled nodes
###############################################################################################
# define input
inp = np.zeros((sim_steps, 1)) + 0.5
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net9").apply()
net = ComputeGraph(net_config=net_config,
name='net3',
vectorization=True,
step_size=dt,
backend=b)
results = net.run(sim_time,
step_size=dt,
outputs={
'a': 'pop0/op1/a',
'b': 'pop1/op7/a'
},
inputs={'pop1/op7/inp': inp})
net.clear()
# calculate edge behavior from hand
update3 = lambda x, y, z: x + dt * (y + z - x)
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = update2(targets[i, 0], targets[i, 1] * 0.5)
targets[i + 1, 1] = update3(targets[i, 1], targets[i, 0] * 2.0,
inp[i])
diff = np.mean(np.abs(results['a'].values[:, 0] - targets[1:, 0])) + \
np.mean(np.abs(results['b'].values[:, 0] - targets[1:, 1]))
assert diff == pytest.approx(0., rel=accuracy, abs=accuracy)
# test correct numerical evaluation of graph with delay distributions
#####################################################################
# define input
dt = 1e-2
sim_time = 100.
sim_steps = int(np.round(sim_time / dt, decimals=0))
inp = np.zeros((sim_steps, 1)) + 0.5
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net13").apply(
label='net4')
net = net_config.compile(vectorization=True,
step_size=dt,
backend=b,
solver='euler')
results = net.run(sim_time,
outputs={
'a1': 'p1/op9/a',
'a2': 'p2/op9/a'
},
inputs={'p1/op9/I_ext': inp})
# TODO: add evaluation of network behavior by hand and compare results against that
net.clear()
# %%
# Part 1: Creating a PyAuto Instance
# ==================================
#
# In this first part, we will be concerned with how to create a model representation that is compatible with auto-07p,
# which is the software that is used for parameter continuations and bifurcation analysis in PyRates [2]_.
# %%
# Step 1: Load the model into PyRates
# -----------------------------------
#
# As a first step, we have to load the model into PyRates. This is done the usual way. If you are not familiar with
# this, check out the example galleries for model definitions.
from pyrates.frontend import CircuitTemplate
qif = CircuitTemplate.from_yaml("model_templates.montbrio.simple_montbrio.QIF_exc").apply(label='qif')
# %%
# Step 2: Load the model into the backend
# ---------------------------------------
#
# Here, we will parse the model equations into the PyRates backend. If you are not familiar with this, check out the
# example galleries for model compilation and simulation. This step, however, differs slightly from the usual way.
# We need to use the :code:`FortranBackend`, since :code:`auto07-p` requires a fortran file with the model equations
# and initial values [2]_. Furthermore, we need to set the keyword argument :code:`auto_compat` of the :code:`compile()`
# method to :code:`True`, to indicate to the :code:`FortranBackend` that it should compile the model equations in a way
# that is compatible with auto-07p [2]_.
qif_compiled = qif.compile(backend='fortran', auto_compat=True)
# %%
from pyrates.utility.visualization import plot_timeseries, create_cmap
# additional imports
import numpy as np
import matplotlib.pyplot as plt
dt = 1e-3 # integration step size in s
dts = 1e-3 # variable storage sub-sampling step size in s
sub = int(dts/dt) # sub-sampling rate
T = 800.0 # total simulation time in s
#inp = np.zeros((int(T/dt), 1), dtype='float32') # external input to the population
#inp[int(20./dt):int((T-20.)/dt)] = 5.
circuit = CircuitTemplate.from_yaml("model_templates.montbrio.simple_montbrio.QIF_sfa_exp"
).apply(node_values={'p/Op_sfa_exp/eta': -3.96,
'p/Op_sfa_exp/J': 15.0*np.sqrt(2.0),
'p/Op_sfa_exp/alpha': 0.7}
)
compute_graph = circuit.compile(vectorization=True, backend='numpy', name='montbrio', solver='scipy')
result, t = compute_graph.run(T,
step_size=dt,
#inputs={"E/Op_e_adapt/inp": inp},
outputs={"r": "p/Op_sfa_exp/r",
"v": "p/Op_sfa_exp/v",
"A": "p/Op_sfa_exp/I_a"},
sampling_step_size=dts,
profile='t',
verbose=True,
method='LSODA'
)
def test_2_6_inputs_outputs():
"""Tests the input-output interface of the run method in circuits of different hierarchical depth.
See Also
-------
:method:`CircuitIR.run` detailed documentation of how to use the arguments `inputs` and `outputs`.
"""
backend = 'numpy'
dt = 1e-3
sim_time = 100.
sim_steps = int(np.round(sim_time / dt, decimals=0))
# define inputs and outputs for each population separately
##########################################################
# define input
inp1 = np.zeros((sim_steps, 1)) + 0.5
inp2 = np.zeros((sim_steps, 1)) + 0.2
# perform simulation
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net13").apply(
label='net1')
net = net_config.compile(vectorization=True,
step_size=dt,
backend=backend,
solver='scipy')
r1 = net.run(sim_time,
outputs={
'a1': 'p1/op9/a',
'a2': 'p2/op9/a'
},
inputs={
'p1/op9/I_ext': inp1,
'p2/op9/I_ext': inp2
})
net.clear()
# define input and output for both populations simultaneously
#############################################################
backend = 'numpy'
# define input
inp = np.zeros((sim_steps, 2))
inp[:, 0] = 0.5
inp[:, 1] = 0.2
# perform simulation
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net13").apply(
label='net2')
net = net_config.compile(vectorization=True,
step_size=dt,
backend=backend,
solver='scipy')
r2 = net.run(sim_time,
outputs={'a': 'all/op9/a'},
inputs={'all/op9/I_ext': inp})
net.clear()
assert np.mean(r1.values.flatten() - r2.values.flatten()) == pytest.approx(
0., rel=1e-4, abs=1e-4)
# repeat in a network with 2 hierarchical levels of node organization
#####################################################################
# define input
inp3 = np.zeros((sim_steps, 1)) + 0.1
inp4 = np.zeros((sim_steps, 1))
# perform simulation
nc1 = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net14").apply(
label='net3')
n1 = nc1.compile(vectorization=True,
step_size=dt,
backend=backend,
solver='scipy')
r1 = n1.run(sim_time,
outputs={
'a1': 'c1/p1/op9/a',
'a2': 'c1/p2/op9/a',
'a3': 'c2/p1/op9/a',
'a4': 'c2/p2/op9/a'
},
inputs={
'c1/p1/op9/I_ext': inp1,
'c1/p2/op9/I_ext': inp2,
'c2/p1/op9/I_ext': inp3,
'c2/p2/op9/I_ext': inp4
})
n1.clear()
# define input
inp = np.zeros((sim_steps, 4))
inp[:, 0] = 0.5
inp[:, 1] = 0.2
inp[:, 2] = 0.1
# perform simulation
nc2 = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net14").apply(
label='net4')
n2 = nc2.compile(vectorization=True,
step_size=dt,
backend=backend,
solver='scipy')
r2 = n2.run(sim_time,
outputs={'a': 'all/all/op9/a'},
inputs={'all/all/op9/I_ext': inp})
n2.clear()
assert np.mean(r1.values.flatten() - r2.values.flatten()) == pytest.approx(
0., rel=1e-4, abs=1e-4)
operators={qif_op: {
'tau': 3.0,
'J': -5.0,
'eta': -6.0
}})
qif_template = CircuitTemplate(name='net',
path=None,
nodes={
'pc': pc,
'ein': ein,
'iin': iin
},
edges=[('pc/qif/r', 'ein/qif/r_in', None, {
'weight': 5.0
}),
('ein/qif/r', 'pc/qif/r_in', None, {
'weight': 10.0
}),
('pc/qif/r', 'iin/qif/r_in', None, {
'weight': 5.0
}),
('iin/qif/r', 'pc/qif/r_in', None, {
'weight': -10.0
})])
T = 60.
dt = 1e-3
dts = 1e-2
params = {'C': {'min': 1.0, 'max': 2.0}, 'J': {'min': 10.0, 'max': 15.0}}
# documentation can be found
# `here <https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.differential_evolution.html>`_. All
# arguments that :code:`scipy.optimize.differential_evolution` takes can also be provided as keyword arguments to the
# :code:`run()` method. By providing a :code:`template`, :code:`compile_kwargs` and :code:`run_kwargs`, the
# :code:`run()` method knows that it should use the provided model template, load it into the backend via
# :code:`CircuitIR.compile(**compile_kwargs)` and then simulate its behavior via :code:`CircuitIR.run(**run_kwargs)`.
# The resulting timeseries is then forwarded to the :code:`loss_func` together with the keyword arguments in
# :code:`loss_kwargs`.
#
# The return value of the :code:`run()` method contains the winning parameter set and its loss function value.
# Let's check out, whether this model parameter indeed produces the behavior we optimized for:
from pyrates.frontend import CircuitTemplate
from matplotlib.pyplot import show
jr_temp = CircuitTemplate.from_yaml(model_template).apply()
jr_temp.set_node_var('JRC/JRC_op/c', winner.at[0, 'C'])
jr_comp = jr_temp.compile(solver='scipy', backend='numpy', step_size=1e-4)
results = jr_comp.run(simulation_time=3.0,
sampling_step_size=1e-2,
outputs={
'V_pce': 'JRC/JRC_op/PSP_pc_e',
'V_pci': 'JRC/JRC_op/PSP_pc_i'
})
results = results['V_pce'] - results['V_pci']
results.plot()
jr_comp.clear()
show()
# %%
import matplotlib.pyplot as plt
import os
import numpy as np
# parameters
dt = 5e-4
T = 50.0
start = int(10.0 / dt)
stop = int(12.0 / dt)
dts = 1e-2
inp = np.zeros((int(T / dt), 1))
inp[start:stop] = 1.0
# target: delayed biexponential feedback
biexp = CircuitTemplate.from_yaml("config/stn_gpe/biexp_gamma")
r1 = biexp.run(simulation_time=T,
sampling_step_size=dts,
inputs={'n1/biexp_rate/I_ext': inp},
outputs={'r': 'n1/biexp_rate/r'},
backend='numpy',
step_size=dt,
solver='euler')
# fig, ax = plt.subplots()
# ax.plot(r1['r'])
# plt.show()
# approximation: gamma-distributed feedback
param_grid = {
'd': np.asarray([5.0, 6.0, 7.0]),
's': np.asarray([1.0, 1.5, 2.0])
# additional imports
import numpy as np
import matplotlib.pyplot as plt
dt = 1e-1 # integration step size in s
dts = 5e-1 # variable storage sub-sampling step size in s
sub = int(dts / dt) # sub-sampling rate
T = 1000.0 # total simulation time in ms
inp = np.zeros((int(T / dt), 1),
dtype='float32') # external input to the population
start = 200.0
stop = 400.0
inp[int(start / dt):int(stop / dt), :] = 10.0
circuit = CircuitTemplate.from_yaml(
"model_templates.wilson_cowan.simple_wilsoncowan.RC").apply()
compute_graph = ComputeGraph(circuit,
vectorization=True,
backend='numpy',
name='wc_net',
step_size=dt,
solver='scipy')
result, t = compute_graph.run(
T,
inputs={"P1/Op_rate/I_ext": inp},
outputs={
"r1": "P1/Op_rate/r",
"r2": "P2/Op_rate/r"
},
sampling_step_size=dts,
from pyrates.frontend import CircuitTemplate
# %%
# Step 2: Loading a model template from the `model_templates` library
# -------------------------------------------------------------------
#
# In the second step, we load a model template for the Jansen-Rit model that comes with PyRates via the
# :code:`from_yaml()` method of the :code:`CircuitTemplate`. This method returns a :code:`CircuitTemplate` instance
# which provides the method :code:`apply()` for turning it into a graph-based representation, i.e. a
# :code:`pyrates.ir.CircuitIR` instance. Have a look at the yaml definition of the model that can be found at the path
# used for the :code:`from_yaml()` method. You will see that all variables and parameters are already defined there.
# These are the basic steps you perform, if you want to load a model that is
# defined inside a yaml file. To check out the different model templates provided by PyRates, have a look at
# the :code:`PyRates.model_templates` module.
jrc = CircuitTemplate.from_yaml(
"model_templates.jansen_rit.simple_jansenrit.JRC_simple").apply()
# %%
# Step 3: Loading the model into the backend
# ------------------------------------------
#
# In this example, we directly load the :code:`CircuitIR` instance into the backend via the :code:`compile()` method
# without any further changes to the graph. This way, a :code:`pyrates.backend.NumpyBackend` instance is created.
# After this step, structural modifications of the network are not possible anymore. Here, we choose scipy as a solver
# for our differential equation system. The default is the forward Euler method that is implemented in PyRates itself.
# Generally, the scipy solver is both more accurate and faster and thus the recommended solver in PyRates.
jrc_compiled = jrc.compile(backend='numpy', step_size=1e-4, solver='scipy')
# %%
# Step 4: Numerical simulation of a the model behavior in time
# simulations
#############
outputs = {
'stn': 'stn/stn_op/R',
'gpe-p': 'gpe_p/gpe_p_op/R',
'gpe-a': 'gpe_a/gpe_a_op/R',
'msn-d1': 'msn_d1/msn_d1_op/R',
'msn-d2': 'msn_d2/msn_d2_op/R',
'fsi': 'fsi/fsi_op/R',
}
for c_dict in deepcopy(conditions):
model = CircuitTemplate.from_yaml("config/stn_gpe_str/stn_gpe_str")
model = model.update_var(node_vars=node_updates, edge_vars=edge_updates)
results = model.run(simulation_time=T, step_size=dt, sampling_step_size=dts, outputs=outputs.copy(), solver='scipy',
verbose=True, method='RK23', atol=1e-5, rtol=1e-4, clear=True)
clear_frontend_caches()
fig, ax = plt.subplots(figsize=(6, 2.0), dpi=dpi)
results = results * 1e3
for key in outputs:
ax.plot(results.loc[:, key])
plt.legend(list(outputs.keys()))
ax.set_ylabel('Firing rate')
ax.set_xlabel('time (ms)')
# ax.set_xlim([4000.0, 5000.0])
# ax.set_ylim([0.0, 50.0])
ax.tick_params(axis='both', which='major', labelsize=9)
path=None,
operators={op_inh_syn: {
'tau': 2.0,
'eta': -0.5
}})
jrc_template = CircuitTemplate(
name='jrc_template',
path=None,
nodes={
'PCs': pcs,
'EINs': eins,
'IINs': iins
},
edges=[('PCs/Op_exc_syn/r', 'EINs/Op_exc_syn/r_exc', None, {
'weight': 13.5
}),
('EINs/Op_exc_syn/r', 'PCs/Op_exc_syn/r_exc', None, {
'weight': 0.8 * 13.5
}),
('PCs/Op_exc_syn/r', 'IINs/Op_inh_syn/r_exc', None, {
'weight': 0.25 * 13.5
}),
('IINs/Op_inh_syn/r', 'PCs/Op_exc_syn/r_inh', None, {
'weight': 1.75 * 13.5
})])
jrc_ir = jrc_template.apply()
dt = 1e-3 # integration step size in s
dts = 1e-2 # variable storage sub-sampling step size in s
T = 42.
def __init__(self, p, context):
super(PyRates_CNS_Model, self).__init__(p, context)
from pyrates.frontend import OperatorTemplate
from pyrates.frontend import NodeTemplate, CircuitTemplate
exc_syn = [
'd/dt * r = (delta/(PI*tau) + 2.*r*v) /tau',
'd/dt * v = (v^2 + eta + I_ext + (I_exc - I_inh)*tau - (PI*r*tau)^2) /tau',
'd/dt * I_exc = J*r + r_exc - I_exc/tau_exc',
'd/dt * I_inh = r_inh - I_inh/tau_inh'
]
inh_syn = [
'd/dt * r = (delta/(PI*tau) + 2.*r*v) /tau',
'd/dt * v = (v^2 + eta + I_ext + (I_exc - I_inh)*tau - (PI*r*tau)^2) /tau',
'd/dt * I_exc = r_exc - I_exc/tau_exc',
'd/dt * I_inh = J*r + r_inh - I_inh/tau_inh'
]
variables = {
'delta': {
'default': 1.0
},
'tau': {
'default': 1.0
},
'eta': {
'default': -2.5
},
'J': {
'default': 0.0
},
'tau_exc': {
'default': 1.0
},
'tau_inh': {
'default': 2.0
},
'r': {
'default': 'output'
},
'v': {
'default': 'variable'
},
'I_exc': {
'default': 'variable'
},
'I_inh': {
'default': 'variable'
},
'I_ext': {
'default': 'input'
},
'r_exc': {
'default': 'input'
},
'r_inh': {
'default': 'input'
},
}
op_exc_syn = OperatorTemplate(name='Op_exc_syn',
path=None,
equations=exc_syn,
variables=variables)
op_inh_syn = OperatorTemplate(name='Op_inh_syn',
path=None,
equations=inh_syn,
variables=variables)
pcs = NodeTemplate(name='PCs', path=None, operators=[op_exc_syn])
eins = NodeTemplate(name='EINs',
path=None,
operators={op_exc_syn: {
'eta': -0.5
}})
iins = NodeTemplate(name='IINs',
path=None,
operators={op_inh_syn: {
'tau': 2.0,
'eta': -0.5
}})
self.jrc_template = CircuitTemplate(
name='jrc_template',
path=None,
nodes={
'PCs': pcs,
'EINs': eins,
'IINs': iins
},
edges=[('PCs/Op_exc_syn/r', 'EINs/Op_exc_syn/r_exc', None, {
'weight': 13.5
}),
('EINs/Op_exc_syn/r', 'PCs/Op_exc_syn/r_exc', None, {
'weight': 0.8 * 13.5
}),
('PCs/Op_exc_syn/r', 'IINs/Op_inh_syn/r_exc', None, {
'weight': 0.25 * 13.5
}),
('IINs/Op_inh_syn/r', 'PCs/Op_exc_syn/r_inh', None, {
'weight': 1.75 * 13.5
})])
def grid_search(circuit_template: Union[CircuitTemplate, str],
param_grid: Union[dict, pd.DataFrame],
param_map: dict,
dt: float,
simulation_time: float,
inputs: dict,
outputs: dict,
sampling_step_size: Optional[float] = None,
permute_grid: bool = False,
init_kwargs: dict = None,
**kwargs) -> tuple:
"""Function that runs multiple parametrizations of the same circuit in parallel and returns a combined output.
Parameters
----------
circuit_template
Path to the circuit template.
param_grid
Key-value pairs for each circuit parameter that should be altered over different circuit parametrizations.
param_map
Key-value pairs that map the keys of param_grid to concrete circuit variables.
dt
Simulation step-size in s.
simulation_time
Simulation time in s.
inputs
Inputs as provided to the `run` method of `:class:ComputeGraph`.
outputs
Outputs as provided to the `run` method of `:class:ComputeGraph`.
sampling_step_size
Sampling step-size as provided to the `run` method of `:class:ComputeGraph`.
permute_grid
If true, all combinations of the provided param_grid values will be realized. If false, the param_grid values
will be traversed pairwise.
kwargs
Additional keyword arguments passed to the `:class:ComputeGraph` initialization.
Returns
-------
tuple
Simulation results stored in a multi-index data frame, the mapping between the data frame column names and the
parameter grid, the simulation time, and the memory consumption.
"""
# argument pre-processing
#########################
if not init_kwargs:
init_kwargs = {}
vectorization = init_kwargs.pop('vectorization', 'nodes')
if type(circuit_template) is str:
circuit_template = CircuitTemplate.from_yaml(circuit_template)
# linearize parameter grid if necessary
if type(param_grid) is dict:
param_grid = linearize_grid(param_grid, permute_grid)
# create grid-structure of network
##################################
# get parameter names and grid length
param_keys = list(param_grid.keys())
N = param_grid.shape[0]
# assign parameter updates to each circuit, combine them to unconnected network and remember their parameters
circuit = CircuitIR()
circuit_names = []
for idx in param_grid.index:
new_params = {}
for key in param_keys:
new_params[key] = param_grid[key][idx]
circuit_tmp = circuit_template.apply()
circuit_key = f'{circuit_tmp.label}_{idx}'
circuit_tmp = adapt_circuit(circuit_tmp, new_params, param_map)
circuit.add_circuit(circuit_key, circuit_tmp)
circuit_names.append(circuit_key)
param_grid.index = circuit_names
# create backend graph
net = circuit.compile(dt=dt, vectorization=vectorization, **init_kwargs)
# adjust input of simulation to combined network
for inp_key, inp in inputs.copy().items():
inputs[f"all/{inp_key}"] = np.tile(inp, (1, N))
inputs.pop(inp_key)
# adjust output of simulation to combined network
for out_key, out in outputs.items():
outputs[out_key] = f"all/{out}"
# simulate the circuits behavior
results = net.run(simulation_time=simulation_time,
inputs=inputs,
outputs=outputs,
sampling_step_size=sampling_step_size,
**kwargs) # type: pd.DataFrame
if 'profile' in kwargs:
results, duration = results
if 'profile' in kwargs:
return results, param_grid, duration
return results, param_grid
"model_templates.jansen_rit.simple_jansenrit.RPO_e_pc")
RPO_i = OperatorTemplate.from_yaml(
"model_templates.jansen_rit.simple_jansenrit.RPO_i")
pc = NodeTemplate(name='PC', path=None,
operators=[RPO_e_pc, RPO_i, PRO]) # Pyramidal cells (PC)
# Circuits (lists of nodes, coupled via edges)
""" Edges are defined by a list with four entries (1/2/3/4):
1) The source variable (PC/PRO/m_out refers to variable m_out in operator PRO of node PC) /
2) The target variable /
3) An edge template with additional operators (null means no particular edge template is used)
4) A dictionary of variables and values that are specific to this edge"""
circuit = CircuitTemplate(
name="JRC", nodes={'IIN': iin, 'EIN': ein, 'PC': pc},
edges = [ \
["PC/PRO/m_out", "IIN/RPO_e/m_in", None, {'weight': 33.75}],
["PC/PRO/m_out", "EIN/RPO_e/m_in", None, {'weight': 135.}],
["EIN/PRO/m_out", "PC/RPO_e_pc/m_in", None, {'weight': 108.}],
["IIN/PRO/m_out", "PC/RPO_i/m_in", None, {'weight': 33.75}]],
path=None)
# Instantiate (apply) circuit
circuit = circuit.apply()
# # ---------------------------------------------------
# # Visualise the network
# # ---------------------------------------------------
# pos = nx.spring_layout(circuit.graph)
# nx.draw_shell(circuit.graph, with_labels=True, node_size=2000, arrowsize=30)
# plt.show()
# ---------------------------------------------------
from pyrates.frontend import CircuitTemplate
# %%
# Step 2: Loading a model template from the `model_templates` library
# -------------------------------------------------------------------
#
# In the second step, we load the model template for an excitatory QIF population that comes with PyRates via the
# :code:`from_yaml()` method of the :code:`CircuitTemplate`. This method returns a :code:`CircuitTemplate` instance
# which provides the method :code:`apply()` for turning it into a graph-based representation, i.e. a
# :code:`pyrates.ir.CircuitIR` instance. Have a look at the yaml definition of the model that can be found at the path
# used for the :code:`from_yaml()` method. You will see that all variables and parameters are already defined there.
# These are the basic steps you perform, if you want to load a model that is
# defined inside a yaml file. To check out the different model templates provided by PyRates, have a look at
# the :code:`PyRates.model_templates` module.
qif_circuit = CircuitTemplate.from_yaml(
"model_templates.montbrio.simple_montbrio.QIF_exc").apply()
# %%
# Step 3: Loading the model into the backend
# ------------------------------------------
#
# In this example, we directly load the :code:`CircuitIR` instance into the backend via the :code:`compile()` method
# without any further changes to the graph. This way, a :code:`pyrates.backend.NumpyBackend` instance is created.
# After this step, structural modifications of the network are not possible anymore.
qif_compiled = qif_circuit.compile(backend='numpy', step_size=1e-3)
# %%
# Step 4: Numerical simulation of a the model behavior in time
# ------------------------------------------------------------
#
def test_2_2_node():
"""Testing node functionality of compute graph class.
See Also
--------
:method:`add_node`: Detailed documentation of method for adding nodes to instance of `ComputeGraph`.
"""
backends = ['numpy', 'tensorflow']
accuracy = 1e-4
for b in backends:
# test correct numerical evaluation of node with 2 operators, where op1 projects to op2
#######################################################################################
# set up node in pyrates
dt = 1e-1
sim_time = 10.
sim_steps = int(sim_time / dt)
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net4").apply()
net = ComputeGraph(net_config=net_config,
name='net0',
vectorization=True,
backend=b)
# simulate node behavior
results = net.run(sim_time, outputs={'a': 'pop0/op1/a'}, step_size=dt)
net.clear()
# calculate node behavior from hand
update0 = lambda x: x + dt * 2.
update1 = lambda x, y: x + dt * (y - x)
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = update0(targets[i, 0])
targets[i + 1, 1] = update1(targets[i, 1], targets[i + 1, 0])
diff = results['a'].values[:, 0] - targets[:-1, 1]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
# test correct numerical evaluation of node with 2 independent operators
########################################################################
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net5").apply()
net = ComputeGraph(net_config=net_config,
name='net1',
vectorization=True,
backend=b)
# simulate node behavior
results = net.run(sim_time, outputs={'a': 'pop0/op5/a'}, step_size=dt)
net.clear()
# calculate node behavior from hand
targets = np.zeros((sim_steps + 1, 2), dtype=np.float32)
for i in range(sim_steps):
targets[i + 1, 0] = update0(targets[i, 0])
targets[i + 1, 1] = update1(targets[i, 1], 0.)
diff = results['a'].values[:, 0] - targets[:-1, 1]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
# test correct numerical evaluation of node with 2 independent operators projecting to the same target operator
###############################################################################################################
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net6").apply()
net = ComputeGraph(net_config=net_config,
name='net2',
vectorization=True,
backend=b)
results = net.run(sim_time, outputs={'a': 'pop0/op1/a'}, step_size=dt)
net.clear()
# calculate node behavior from hand
targets = np.zeros((sim_steps + 1, 3), dtype=np.float32)
update2 = lambda x: x + dt * (4. + np.tanh(0.5))
for i in range(sim_steps):
targets[i + 1, 0] = update0(targets[i, 0])
targets[i + 1, 1] = update2(targets[i, 1])
targets[i + 1, 2] = update1(targets[i, 2],
targets[i + 1, 0] + targets[i + 1, 1])
diff = results['a'].values[:, 0] - targets[:-1, 2]
assert np.mean(np.abs(diff)) == pytest.approx(0.,
rel=accuracy,
abs=accuracy)
# test correct numerical evaluation of node with 1 source operator projecting to 2 independent targets
######################################################################################################
net_config = CircuitTemplate.from_yaml(
"model_templates.test_resources.test_backend.net7").apply()
net = ComputeGraph(net_config=net_config,
name='net3',
vectorization=True,
backend=b)
results = net.run(sim_time,
outputs={
'a': 'pop0/op1/a',
'b': 'pop0/op3/b'
},
step_size=dt)
# calculate node behavior from hand
targets = np.zeros((sim_steps + 1, 4), dtype=np.float32)
update3 = lambda a, b, u: a + dt * (-10. * a + b**2 + u)
update4 = lambda x, y: x + dt * 0.1 * y
for i in range(sim_steps):
targets[i + 1, 0] = update0(targets[i, 0])
targets[i + 1, 1] = update1(targets[i, 1], targets[i + 1, 0])
targets[i + 1, 2] = update3(targets[i, 2], targets[i, 3],
targets[i + 1, 0])
targets[i + 1, 3] = update4(targets[i, 3], targets[i, 2])
diff = np.mean(np.abs(results['a'].values[:, 0] - targets[:-1, 1])) + \
np.mean(np.abs(results['b'].values[:, 0] - targets[:-1, 3]))
assert diff == pytest.approx(0., rel=accuracy, abs=accuracy)
# ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
#
# In the case of the Jansen-Rit model, this translates to connecting the PC, EIN and IIN populations via simple, linear
# edges that can be set up within the :code:`CircuitTemplate` as follows:
from pyrates.frontend import CircuitTemplate
jrc = CircuitTemplate(name="JRC",
nodes={
'PC': pc,
'EIN': ein,
'IIN': iin
},
edges=[("PC/PRO/m_out", "IIN/RPO_e/m_in", None, {
'weight': 33.75
}),
("PC/PRO/m_out", "EIN/RPO_e/m_in", None, {
'weight': 135.
}),
("EIN/PRO/m_out", "PC/RPO_e/m_in", None, {
'weight': 108.
}),
("IIN/PRO/m_out", "PC/RPO_i/m_in", None, {
'weight': 33.75
})],
path=None)
# %%
# A circuit template requires the definition of 2 fields: :code:`nodes` and :code:`edges`.
#
# :code:`nodes`
# - can either be a list of all nodes that this circuit is composed of
def benchmark(Ns, Ps, T, dt, init_kwargs, run_kwargs, disable_gpu=False):
"""Function that will run a benchmark simulation for each combination of N and P.
Each benchmark simulation simulates the behavior of a neural population network, where the Jansen-Rit model is used for each of the N nodes and
connections are drawn randomly, such that on overall coupling density of P is established.
Parameters
----------
Ns
Vector with network sizes.
Ps
Vector with coupling densities.
T
Overall simulation time.
dt
Integration step-size.
init_kwargs
Additional key-word arguments for the model initialization.
run_kwargs
Additional key-word arguments for running the simulation.
disable_gpu
If true, GPU devices will be disabled, so the benchmark will be run on the CPU only.
Returns
-------
tuple
Simulation times, peak memory consumptions
"""
if disable_gpu:
os.environ['CUDA_VISIBLE_DEVICES'] = '-1'
else:
os.environ['CUDA_VISIBLE_DEVICES'] = '0'
times = np.zeros((len(Ns), len(Ps)))
for i, n in enumerate(Ns):
for j, p in enumerate(Ps):
print(f'Running benchmark for n = {n} and p = {p}.')
print("Setting up the network in PyRates...")
# define inter-JRC connectivity
C = np.random.uniform(size=(n, n))
C[C > p] = 0.
c_sum = np.sum(C, axis=1)
for k in range(C.shape[0]):
if c_sum[k] != 0.:
C[k, :] /= c_sum[k]
conns = DataFrame(
np.round(C, 3),
columns=[f'jrc_{idx}/PC/PRO/m_out' for idx in range(n)])
conns.index = [f'jrc_{idx}/PC/RPO_e_pc/m_in' for idx in range(n)]
# define input
inp = 220 + np.asarray(np.random.randn(int(T / dt), n),
dtype=np.float32) * 22.
# set up template
template = CircuitTemplate.from_yaml(
"model_templates.jansen_rit.simple_jansenrit.JRC")
# set up intermediate representation
circuits = {}
for idx in range(n):
circuits[f'jrc_{idx}'] = deepcopy(template)
circuit = CircuitIR.from_circuits(label='net',
circuits=circuits,
connectivity=conns)
# set up compute graph
net = circuit.compile(dt=dt, **init_kwargs)
print("Starting the benchmark simulation...")
# run simulations
_, t = net.run(T,
inputs={'all/PC/RPO_e_pc/u': inp},
outputs={'V': 'all/PC/OBS/V'},
verbose=False,
**run_kwargs)
times[i, j] = t
print("Finished!")
print(f'simulation time: {t} s.')
return times
