# -*- coding: utf-8 -*-
#
# brunel_exp_multisynapse_nest.py
#
# This file is part of NEST.
#
# Copyright (C) 2004 The NEST Initiative
#
# NEST is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 2 of the License, or
# (at your option) any later version.
#
# NEST is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with NEST.  If not, see <http://www.gnu.org/licenses/>.

'''
Random balanced network (exp synapses, multiple time constants)
---------------------------------------------------------------

This script simulates an excitatory and an inhibitory population on
the basis of the network used in

Brunel N, Dynamics of Sparsely Connected Networks of Excitatory and
Inhibitory Spiking Neurons, Journal of Computational Neuroscience 8,
183-208 (2000).

The example demonstrate the usage of the multisynapse neuron
model. Each spike arriving at the neuron triggers an exponential
PSP. The time constant associated with the PSP is defined in the
recepter type array tau_syn of each neuron. The receptor types of all
connections are uniformally distributed, resulting in uniformally
distributed time constants of the PSPs.

When connecting the network customary synapse models are used, which
allow for querying the number of created synapses. Using spike
detectors the average firing rates of the neurons in the populations
are established. The building as well as the simulation time of the
network are recorded.
'''

'''
Import all necessary modules for simulation, analysis and plotting.
'''

import nest
import nest.raster_plot

import time
from numpy import exp

nest.ResetKernel()

'''
Assigning the current time to a variable in order to determine the
build time of the network.
'''

startbuild = time.time()

'''
Assigning the simulation parameters to variables.
'''

dt = 0.1    # the resolution in ms
simtime = 1000.0  # Simulation time in ms
delay = 1.5    # synaptic delay in ms

'''
Definition of the parameters crucial for asynchronous irregular firing
of the neurons.
'''

g = 5.0  # ratio inhibitory weight/excitatory weight
eta = 2.0  # external rate relative to threshold rate
epsilon = 0.1  # connection probability

'''
Definition of the number of neurons in the network and the number of
neuron recorded from
'''

order = 2500
NE = 4 * order  # number of excitatory neurons
NI = 1 * order  # number of inhibitory neurons
N_neurons = NE + NI   # number of neurons in total
N_rec = 50      # record from 50 neurons

'''
Definition of connectivity parameter
'''

CE = int(epsilon * NE)  # number of excitatory synapses per neuron
CI = int(epsilon * NI)  # number of inhibitory synapses per neuron
C_tot = int(CI + CE)      # total number of synapses per neuron

'''
Initialization of the parameters of the integrate and fire neuron and
the synapses. The parameter of the neuron are stored in a dictionary.
'''

tauMem = 20.0  # time constant of membrane potential in ms
theta = 20.0  # membrane threshold potential in mV
J = 0.1   # postsynaptic amplitude in mV
nr_ports = 100  # number of receptor types
# Create array of synaptic time constants for each neuron,
# ranging from 0.1 to 1.09 ms.
tau_syn = [0.1 + 0.01 * i for i in range(nr_ports)]
neuron_params = {"C_m": 1.0,
                 "tau_m": tauMem,
                 "t_ref": 2.0,
                 "E_L": 0.0,
                 "V_reset": 0.0,
                 "V_m": 0.0,
                 "V_th": theta,
                 "tau_syn": tau_syn}
J_ex = J       # amplitude of excitatory postsynaptic current
J_in = -g * J_ex  # amplitude of inhibitory postsynaptic current

'''
Definition of threshold rate, which is the external rate needed to fix
the membrane potential around its threshold, the external firing rate
and the rate of the poisson generator which is multiplied by the
in-degree CE and converted to Hz by multiplication by 1000.
'''

nu_th = theta / (J * CE * tauMem)
nu_ex = eta * nu_th
p_rate = 1000.0 * nu_ex * CE

'''
Configuration of the simulation kernel by the previously defined time
resolution used in the simulation. Setting "print_time" to True prints
the already processed simulation time as well as its percentage of the
total simulation time.
'''

nest.SetKernelStatus({"resolution": dt, "print_time": True,
                      "overwrite_files": True})

print("Building network")

'''
Configuration of the model `iaf_psc_exp_multisynapse` and
`poisson_generator` using SetDefaults(). This function expects the
model to be the inserted as a string and the parameter to be specified
in a dictionary. All instances of theses models created after this
point will have the properties specified in the dictionary by default.
'''

nest.SetDefaults("iaf_psc_exp_multisynapse", neuron_params)
nest.SetDefaults("poisson_generator", {"rate": p_rate})

'''
Creation of the nodes using `Create`. We store the returned handles in
variables for later reference. Here the excitatory and inhibitory, as
well as the poisson generator and two spike detectors. The spike
detectors will later be used to record excitatory and inhibitory
spikes.
'''

nodes_ex = nest.Create("iaf_psc_exp_multisynapse", NE)
nodes_in = nest.Create("iaf_psc_exp_multisynapse", NI)
noise = nest.Create("poisson_generator")
espikes = nest.Create("spike_detector")
ispikes = nest.Create("spike_detector")

'''
Configuration of the spike detectors recording excitatory and
inhibitory spikes using `SetStatus`, which expects a list of node
handles and a list of parameter dictionaries. Setting the variable
"to_file" to True ensures that the spikes will be recorded in a .gdf
file starting with the string assigned to label. Setting "withtime"
and "withgid" to True ensures that each spike is saved to file by
stating the gid of the spiking neuron and the spike time in one line.
'''

nest.SetStatus(espikes, [{"label": "brunel-py-ex",
                          "withtime": True,
                          "withgid": True,
                          "to_file": True}])

nest.SetStatus(ispikes, [{"label": "brunel-py-in",
                          "withtime": True,
                          "withgid": True,
                          "to_file": True}])

print("Connecting devices")

'''
Definition of a synapse using `CopyModel`, which expects the model
name of a pre-defined synapse, the name of the customary synapse and
an optional parameter dictionary. The parameters defined in the
dictionary will be the default parameter for the customary
synapse. Here we define one synapse for the excitatory and one for the
inhibitory connections giving the previously defined weights and equal
delays.
'''

nest.CopyModel("static_synapse", "excitatory",
               {"weight": J_ex, "delay": delay})
nest.CopyModel("static_synapse", "inhibitory",
               {"weight": J_in, "delay": delay})

'''
Connecting the previously defined poisson generator to the excitatory
and inhibitory neurons using the excitatory synapse. Since the poisson
generator is connected to all neurons in the population the default
rule ('all_to_all') of Connect() is used. The synaptic properties are
pre-defined in a dictionary and inserted via syn_spec. As synaptic
model the pre-defined synapses "excitatory" and "inhibitory" are
choosen, thus setting weight and delay. The recepter type is drawn
from a distribution for each connection, which is specified in the
synapse properties by assigning a dictionary to the keyword
'receptor_type', which includes the specification of the distribution
and the associated parameter.
'''

syn_params_ex = {"model": "excitatory",
                 "receptor_type": {"distribution": "uniform_int",
                                   "low": 1, "high": nr_ports}
                 }
syn_params_in = {"model": "inhibitory",
                 "receptor_type": {"distribution": "uniform_int",
                                   "low": 1, "high": nr_ports}
                 }

nest.Connect(noise, nodes_ex, syn_spec=syn_params_ex)
nest.Connect(noise, nodes_in, syn_spec=syn_params_ex)

'''
Connecting the first N_rec nodes of the excitatory and inhibitory
population to the associated spike detectors using excitatory
synapses. Here the same shortcut for the specification of the synapse
as defined above is used.
'''

nest.Connect(nodes_ex[:N_rec], espikes, syn_spec="excitatory")
nest.Connect(nodes_in[:N_rec], ispikes, syn_spec="excitatory")

print("Connecting network")

print("Excitatory connections")

'''
Connecting the excitatory population to all neurons while distribution
the ports. Here we use the previously defined parameter dictionary
syn_params_ex. Beforehand, the connection parameter are defined in a
dictionary. Here we use the connection rule 'fixed_indegree', which
requires the definition of the indegree.
'''

conn_params_ex = {'rule': 'fixed_indegree', 'indegree': CE}
nest.Connect(nodes_ex, nodes_ex + nodes_in, conn_params_ex, syn_params_ex)

print("Inhibitory connections")

'''
Connecting the inhibitory population to all neurons while distribution
the ports. Here we use the previously defined parameter dictionary
syn_params_in.The connection parameter are defined analogously to the
connection from the excitatory population defined above.
'''

conn_params_in = {'rule': 'fixed_indegree', 'indegree': CI}
nest.Connect(nodes_in, nodes_ex + nodes_in, conn_params_in, syn_params_in)

'''
Storage of the time point after the buildup of the network in a
variable.
'''

endbuild = time.time()

'''
Simulation of the network.
'''

print("Simulating")

nest.Simulate(simtime)

'''
Storage of the time point after the simulation of the network in a
variable.
'''

endsimulate = time.time()

'''
Reading out the total number of spikes received from the spike
detector connected to the excitatory population and the inhibitory
population.
'''

events_ex = nest.GetStatus(espikes, "n_events")[0]
events_in = nest.GetStatus(ispikes, "n_events")[0]

'''
Calculation of the average firing rate of the excitatory and the
inhibitory neurons by dividing the total number of recorded spikes by
the number of neurons recorded from and the simulation time. The
multiplication by 1000.0 converts the unit 1/ms to 1/s=Hz.
'''

rate_ex = events_ex / simtime * 1000.0 / N_rec
rate_in = events_in / simtime * 1000.0 / N_rec

'''
Reading out the number of connections established using the excitatory
and inhibitory synapse model. The numbers are summed up resulting in
the total number of synapses.
'''

num_synapses = (nest.GetDefaults("excitatory")["num_connections"] +
                nest.GetDefaults("inhibitory")["num_connections"])

'''
Establishing the time it took to build and simulate the network by
taking the difference of the pre-defined time variables.
'''

build_time = endbuild - startbuild
sim_time = endsimulate - endbuild

'''
Printing the network properties, firing rates and building times.
'''

print("Brunel network simulation (Python)")
print("Number of neurons : {0}".format(N_neurons))
print("Number of synapses: {0}".format(num_synapses))
print("       Exitatory  : {0}".format(int(CE * N_neurons) + N_neurons))
print("       Inhibitory : {0}".format(int(CI * N_neurons)))
print("Excitatory rate   : %.2f Hz" % rate_ex)
print("Inhibitory rate   : %.2f Hz" % rate_in)
print("Building time     : %.2f s" % build_time)
print("Simulation time   : %.2f s" % sim_time)

'''
Plot a raster of the excitatory neurons and a histogram.
'''

nest.raster_plot.from_device(espikes, hist=True)
