Пример #1
0
def test_singlepop():

    # Settings:
    t0 = 0.
    dt = .001
    dv = .001
    v_min = -.01
    v_max = .02
    tf = .2
    verbose = False

    # Create simulation:
    b1 = ExternalPopulation(50)
    b2 = ExternalPopulation(50)
    i1 = InternalPopulation(v_min=v_min,
                            v_max=v_max,
                            dv=dv,
                            update_method='exact')
    b1_i1 = Connection(b1, i1, 1, weights=[.005], probs=[1.])
    b2_i1 = Connection(b2, i1, 1, weights=[.005], probs=[1.])
    simulation = Simulation([b1, b2, i1], [b1_i1, b2_i1], verbose=verbose)
    simulation.run(dt=dt, tf=tf, t0=t0)

    np.testing.assert_almost_equal(i1.t_record[-1], .2, 15)
    np.testing.assert_almost_equal(i1.firing_rate_record[-1],
                                   5.3550005434746355, 12)
    assert i1.n_bins == (v_max - v_min) / dv
    assert i1.n_edges - 1 == i1.n_bins
    assert len(simulation.population_list) == 3

    i1.plot_probability_distribution()
Пример #2
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def singlepop(steady_state, tau_m=.02, p0=((0.,),(1.,)), weights={'distribution':'delta', 'loc':.005}, bgfr=100, network_update_callback=lambda s: None, update_method='approx', simulation_configuration=None, tol=None):
    
    # Settings:
    t0 = 0.
    dt = .001
    dv = .001
    v_min = -.01
    v_max = .02
    tf = .1
    
    # Create simulation:
    b1 = ExternalPopulation(bgfr)
    i1 = InternalPopulation(v_min=v_min, tau_m=tau_m, v_max=v_max, dv=dv, update_method=update_method, p0=p0, tol=tol)
    b1_i1 = Connection(b1, i1, 1, weights=weights)
    network = Network([b1, i1], [b1_i1], update_callback=network_update_callback)
    if simulation_configuration is None:
        simulation_configuration = SimulationConfiguration(dt, tf, t0=t0)
    simulation = Simulation(network=network, simulation_configuration=simulation_configuration)
    simulation.run()
    b1.plot()
    
    i1.plot_probability_distribution()
    i1.plot()
    assert i1.n_edges == i1.n_bins+1 

    # Test steady-state:    
    np.testing.assert_almost_equal(i1.get_firing_rate(.05), steady_state, 12)
Пример #3
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def singlepop(steady_state, tau_m=.02, p0=((0.,),(1.,)), weights={'distribution':'delta', 'loc':.005}, bgfr=100, network_update_callback=lambda s: None, update_method='approx', simulation_configuration=None, tol=None, checkpoint_callback=None, nsyn=1):
    
    # Settings:
    t0 = 0.
    dt = .001
    dv = .001
    v_min = -.01
    v_max = .02
    tf = .1
    
    # Create simulation:
    b1 = ExternalPopulation(bgfr)
    i1 = InternalPopulation(v_min=v_min, tau_m=tau_m, v_max=v_max, dv=dv, update_method=update_method, p0=p0, tol=tol)
    b1_i1 = Connection(b1, i1, nsyn, weights=weights)
    network = Network([b1, i1], [b1_i1], update_callback=network_update_callback)
    if simulation_configuration is None:
        simulation_configuration = SimulationConfiguration(dt, tf, t0=t0)
    simulation = Simulation(network=network, simulation_configuration=simulation_configuration, checkpoint_callback=checkpoint_callback)
    simulation.run()
    b1.plot()
    
    i1.plot_probability_distribution()
    i1.plot()
    assert i1.n_edges == i1.n_bins+1 

    # Test steady-state:
    np.testing.assert_almost_equal(i1.get_firing_rate(.05), steady_state, 12)
Пример #4
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def test_network_df():
    p1 = ExternalPopulation(100, record=True)
    p2 = ExternalPopulation(200, record=False)
    p3 = InternalPopulation(v_min=0, v_max=.02, metadata={'X': 0})
    p4 = InternalPopulation(v_min=0, v_max=.01, metadata={'X': 0})
    n1 = Network(population_list=[p1, p2, p3, p4])

    print n1.to_df()
Пример #5
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def test_restart_interal():

    # Run part-way and serialize:
    b1 = ExternalPopulation('100', record=True)
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=.001)
    b1_i1 = Connection(b1, i1, 1, weights=.005, delays=0.0)
    simulation = Network([b1, i1], [b1_i1])
    simulation.run(dt=.001, tf=.01, t0=0)
    i1_str = i1.to_json()
    b1_str = b1.to_json()
    
    # Rehydrate and continue run:
    b2 = ExternalPopulation(**json.loads(b1_str))
    i2 = InternalPopulation(**json.loads(i1_str))
    simulation2 = Network([b2, i2], [Connection(b2, i2, 1, weights=.005, delays=0.0)])
    simulation2.run(dt=.001, tf=.02, t0=.01)
    
    # Run straight through, for comparison:
    b3 = ExternalPopulation('100', record=True)
    i3 = InternalPopulation(v_min=0, v_max=.02, dv=.001)
    simulation3 = Network([b3, i3], [Connection(b3, i3, 1, weights=.005, delays=0.0)])
    simulation3.run(dt=.001, tf=.02, t0=0)

    # Test:
    for y1, y2 in zip(i1.firing_rate_record, i3.firing_rate_record):
        np.testing.assert_almost_equal(y1, y2, 8) 

    b3.to_json(StringIO.StringIO())
    i3.to_json(StringIO.StringIO())
    b1_i1.to_json(StringIO.StringIO())
def get_simulation(dv=.001,
                   verbose=False,
                   update_method='approx',
                   approx_order=None,
                   tol=1e-8):
    import scipy.stats as sps

    # Create simulation:
    b1 = ExternalPopulation(100)
    i1 = InternalPopulation(v_min=0,
                            v_max=.02,
                            dv=dv,
                            update_method=update_method,
                            approx_order=approx_order,
                            tol=tol)
    b1_i1 = Connection(b1,
                       i1,
                       1,
                       delay=0.0,
                       distribution=sps.expon,
                       N=201,
                       scale=.005)
    simulation = Simulation([b1, i1], [b1_i1], verbose=verbose)

    return simulation
Пример #7
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def test_delay_doublepop():

    # Settings:
    t0 = 0.
    dt = .001
    tf = .010
    verbose = False

    # Create populations:
    b1 = ExternalPopulation(50)
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=.001, update_method='exact')
    i2 = InternalPopulation(v_min=0, v_max=.02, dv=.001, update_method='exact')

    # Create connections:
    b1_i1 = Connection(b1, i1, 2, weights=[.005], probs=[1.])
    i1_i2 = Connection(i1, i2, 20, weights=[.005], probs=[1.], delay=2 * dt)

    # Create and run simulation:
    simulation = Simulation([b1, i1, i2], [b1_i1, i1_i2], verbose=verbose)
    simulation.run(dt=dt, tf=tf, t0=t0)

    true_ans = np.array([
        0, 0.0, 0.0, 0.0, 1.9089656152757652e-13, 1.9787511418980406e-10,
        9.5007650186649266e-09, 1.3334881090883857e-07, 1.0103767575651715e-06,
        5.3604521936092067e-06, 2.2383604753409621e-05
    ])
    np.testing.assert_almost_equal(i2.firing_rate_record, true_ans, 12)
Пример #8
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def test_simulation_copy():
    b1 = ExternalPopulation(100)
    i1 = InternalPopulation(v_min=0, v_max=.02)
    b1_i1 = Connection(b1, i1, 2, weights=.005)
    o1 = Network([b1, i1], [b1_i1])
    o2 = o1.copy()
    compare(o1, o2)
Пример #9
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def get_singlepop_benchmark_network(scale=2):

    from dipde.internals.internalpopulation import InternalPopulation
    from dipde.internals.externalpopulation import ExternalPopulation
    from dipde.internals.network import Network
    from dipde.internals.connection import Connection as Connection

    # Settings:
    dv = .0001
    update_method = 'approx'
    approx_order = None
    tol = 1e-14

    # Run simulation:
    b_list = []
    i_list = []
    conn_list = []
    for _ in range(scale):
        b = ExternalPopulation(100, record=True)
        i = InternalPopulation(v_min=0,
                               v_max=.02,
                               dv=dv,
                               update_method=update_method,
                               approx_order=approx_order,
                               tol=tol)
        c = Connection(b, i, 1, weights=.005)
        b_list += [b]
        i_list += [i]
        conn_list += [c]
    return Network(b_list + i_list, conn_list)
Пример #10
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def get_matrices():

    dv = .001
    nsyn_bg = 1
    bgfr = 200
    we = .1
    wi = -.1
    nsyn_00, nsyn_01, nsyn_10, nsyn_11 = 5, 5, 2, 20

    # Components:
    b0 = ExternalPopulation(bgfr, record=True)
    i0 = InternalPopulation(tau_m=.05,
                            v_min=0,
                            v_max=1,
                            dv=dv,
                            update_method='gmres')
    i1 = InternalPopulation(tau_m=.05,
                            v_min=0,
                            v_max=1,
                            dv=dv,
                            update_method='gmres')
    b0_i0 = Connection(b0, i0, nsyn_bg, weights=we, delays=0.0)
    b0_i1 = Connection(b0, i1, nsyn_bg, weights=we, delays=0.0)
    i0_i0 = Connection(i0, i0, nsyn_00, weights=we, delays=0.0)
    i0_i1 = Connection(i0, i1, nsyn_01, weights=we, delays=0.0)
    i1_i0 = Connection(i1, i0, nsyn_10, weights=wi, delays=0.0)
    i1_i1 = Connection(i1, i1, nsyn_11, weights=wi, delays=0.0)

    L = get_leak_matrix(i1)
    Se, te = get_connection_flux_matrices(b0_i0)
    Si, _ = get_connection_flux_matrices(i1_i0)

    return L, Se, Si, te
Пример #11
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def get_simulation(dt=.001, dv=.001, tf=.2, verbose=False, update_method='exact', approx_order=None, tol=1e-8):

    # Create simulation:
    b1 = ExternalPopulation('100')
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=dv, update_method=update_method, approx_order=approx_order, tol=tol)
    b1_i1 = Connection(b1, i1, 1, weights=[.005], probs=[1.], delay=0.0)
    simulation = Simulation([b1, i1], [b1_i1], dt=dt, tf=tf, verbose=verbose)

    return simulation
Пример #12
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def get_simulation(dv=.001, update_method='exact', approx_order=None, tol=1e-8):

    # Create simulation:
    b1 = ExternalPopulation('100+50*abs(sin(40*t))')
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=dv, update_method=update_method, approx_order=approx_order, tol=tol)
    b1_i1 = Connection(b1, i1, 1, weights=.005, delays=0.0)
    simulation = Network([b1, i1], [b1_i1])

    return simulation
def get_network(dv=.001, verbose=False, update_method='approx', approx_order=1, tol=1e-14):

    # Create network:
    b1 = ExternalPopulation('100')
    i1 = InternalPopulation(v_min=-.02, v_max=.02, dv=dv, update_method=update_method, approx_order=approx_order, tol=tol)
    b1_i1 = Connection(b1, i1, 1, weights=.005, delays=([.005, .01],[.5,.5]))
    b1_i1_2 = Connection(b1, i1, 1, weights=-.005, delays=sps.uniform(0,.01))
    network = Network([b1, i1], [b1_i1, b1_i1_2])
    
    return network
Пример #14
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def get_multipop_model():

    # Settings:
    dv = .001
    update_method = 'approx'
    approx_order = None
    tol = 1e-14
    
    
    # Create simulation:
    b1 = ExternalPopulation(100)
    b2 = ExternalPopulation(50)
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=dv, update_method=update_method, approx_order=approx_order, tol=tol)
    i2 = InternalPopulation(v_min=0, v_max=.02, dv=dv, update_method=update_method, approx_order=approx_order, tol=tol)
    b1_i1 = Connection(b1, i1, 1, weights=.005)
    i1_i2 = Connection(i1, i2, 20, weights=.005, delays=.001)
    b2_i2 = Connection(b2, i2, 2, weights=.005, delays=.002)
    simulation = Network([b1, b2, i1, i2], [b1_i1, i1_i2, b2_i2])
    simulation_dict = simulation.to_dict()
    
    return simulation_dict
Пример #15
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def get_network(dv=.001, update_method='exact', tol=1e-14):

    # Create simulation:
    b1 = ExternalPopulation('100', record=True)
    i1 = InternalPopulation(v_min=0,
                            v_max=.02,
                            dv=dv,
                            update_method=update_method,
                            tol=tol)
    b1_i1 = Connection(b1, i1, 1, weights=.005, delays=0.0)
    network = Network([b1, i1], [b1_i1])

    return network
Пример #16
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def get_simulation(dv=.001, update_method='approx', tol=1e-8):
    import scipy.stats as sps

    # Create simulation:
    b1 = ExternalPopulation(50)
    b2 = ExternalPopulation(1000)
    i1 = InternalPopulation(v_min=-.04,
                            v_max=.02,
                            dv=dv,
                            update_method=update_method,
                            tol=tol)
    b1_i1 = Connection(b1,
                       i1,
                       1,
                       delays=0.0,
                       weights=(sps.expon(0, .00196), 301))
    b2_i1 = Connection(b2,
                       i1,
                       1,
                       delays=0.0,
                       weights=(sps.expon(0, .001), 301))
    simulation = Network([b1, b2, i1], [b1_i1, b2_i1])

    return simulation
Пример #17
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def test_delay_singlepop():

    # Settings:
    t0 = 0.
    dt = .001
    tf = .005
    verbose = False
    
    # Create simulation:
    b1 = ExternalPopulation('Heaviside(t)*100')
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=.001, update_method='exact')
    b1_i1 = Connection(b1, i1, 1, weights=[.005], probs=[1.], delay=2*dt)
    simulation = Simulation([b1, i1], [b1_i1], verbose=verbose)
    simulation.run(dt=dt, tf=tf, t0=t0)
    
    true_ans = np.array([0, 0.0, 0.0, 0.00066516669656511084, 0.025842290308637855, 0.08117342489138904])
    np.testing.assert_almost_equal(i1.firing_rate_record, true_ans, 12)
Пример #18
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def test_get_J():

    # Settings:
    bgfr=100
    update_method='approx'
    weights={'distribution':'delta', 'loc':.005}
    p0=((0.,),(1.,)) 
    tau_m=.02
    dv = .001
    v_min = -.01
    v_max = .02
    
    # Create simulation:
    b1 = ExternalPopulation(bgfr)
    i1 = InternalPopulation(v_min=v_min, tau_m=tau_m, v_max=v_max, dv=dv, update_method=update_method, p0=p0)
    b1_i1 = Connection(b1, i1, 1, weights=weights)
    network = Network([b1, i1], [b1_i1])
    network.get_total_flux_matrix(i1,.001)
Пример #19
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    def get_simulation(dv=.001,
                       verbose=False,
                       update_method='exact',
                       approx_order=None,
                       tol=1e-8):

        # Create simulation:
        f = RequestFiringRateFunction(5555)
        b1 = ExternalPopulation(f, record=True, name='b1')
        i1 = InternalPopulation(v_min=0,
                                v_max=.02,
                                dv=dv,
                                update_method=update_method,
                                approx_order=approx_order,
                                tol=tol)
        b1_i1 = Connection(b1, i1, 1, weights=.005, delay=0.0)
        simulation = Network([b1, i1], [b1_i1], verbose=verbose)

        return simulation
Пример #20
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def test_delay_distribution():

    # Settings:
    t0 = 0.
    dt = .001
    tf = .1
    
    # Create populations:
    b1 = ExternalPopulation('100*Heaviside(t)')
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=.001, update_method='exact')
    
    # Create connections:
    b1_i1 = Connection(b1, i1, 1, weights=.005, delays=((0,.05),(.5,.5)))
    
    # Create and run simulation:
    simulation = Network([b1, i1], [b1_i1])
    simulation.run(dt=dt, tf=tf, t0=t0)
    
    true_ans = np.array([0.38560647739319964, 5.229266329159536])
    np.testing.assert_almost_equal(np.array(i1.get_firing_rate([.04, .09])), true_ans, 8)
Пример #21
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def test_delay_singlepop():

    # Settings:
    t0 = 0.
    dt = .001
    tf = .005
    
    # Create simulation:
    b1 = ExternalPopulation('Heaviside(t)*100')
    i1 = InternalPopulation(v_min=0, v_max=.02, dv=.001, update_method='exact')
    b1_i1 = Connection(b1, i1, 1, weights=.005, delays=2*dt, delay_queue=[0,0,50])
    
#     # DEBUG:
#     b1_i1 = Connection(b1, i1, 1, weights=.005, delays=((0,.001, .002),(0,0,1.)), delay_queue=[0,0,50])
    
    
    simulation = Network([b1, i1], [b1_i1])
    simulation.run(dt=dt, tf=tf, t0=t0)
    
    true_ans = np.array([0, 0.0, 0.0, 0.00066516669656511084, 0.025842290308637855, 0.08117342489138904])
    np.testing.assert_almost_equal(i1.firing_rate_record, true_ans, 12)
Пример #22
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def get_simulation(dv=.001,
                   update_method='approx',
                   approx_order=None,
                   tol=1e-8):
    import scipy.stats as sps

    # Create simulation:
    b1 = ExternalPopulation(100)
    i1 = InternalPopulation(v_min=0,
                            v_max=.02,
                            dv=dv,
                            update_method=update_method,
                            approx_order=approx_order,
                            tol=tol)
    b1_i1 = Connection(b1,
                       i1,
                       1,
                       delays=0.0,
                       weights=(sps.expon(0, .005), 201))
    simulation = Network([b1, i1], [b1_i1])

    return simulation
Пример #23
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def test_enternalpopulation_copy():
    o1 = ExternalPopulation(100)
    o2 = o1.copy()
    compare(o1, o2)
Пример #24
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print 'NEST   Mean Exc rate: ', rate_ex, '[Hz]'
print 'NEST   Mean Inh rate: ', rate_in, '[Hz]'

###DipDe
# Settings:
t0 = 0.
dt = 0.0001
dv = 0.1
tf = 1.  #.1 #simulation duration.
update_method = 'approx'
approx_order = 1
tol = 1e-14
verbose = False

# Create simulation:
b1 = ExternalPopulation(p_rate, record=True)
i1 = InternalPopulation(tau_m=t_m * 1e-3,
                        v_min=-0.02,
                        v_max=u_th * 1e-3,
                        dv=dv,
                        update_method=update_method,
                        approx_order=approx_order,
                        tol=tol,
                        record=True,
                        curr_firing_rate=0.0,
                        norm='inf')
i2 = InternalPopulation(tau_m=t_m * 1e-3,
                        v_min=-0.02,
                        v_max=u_th * 1e-3,
                        dv=dv,
                        update_method=update_method,
Пример #25
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sstm = 90.0
sbase = 120.0

# Create visual stimuli
External_stimuli_dict = {}
for index, celltype in itertools.product([0,1],['bkg']):
    stm_tmp = np.zeros(np.int(tf/dt))
    stm_tmp[np.int(background_start[index,celltype]/dt):np.int(background_end[index,celltype]/dt)] = sstm
    stm_tmp += sbase
    External_stimuli_dict[index,celltype] = stm_tmp

# Create populations:
background_population_dict = {}
internal_population_dict = {}
for index, celltype in itertools.product([0,1], ['bkg']):    
    background_population_dict[index, celltype] = ExternalPopulation(External_stimuli[index,celltype],dt, record=False)
for index, celltype in itertools.product([0,1,2,3], ['e','i']):    
    internal_population_dict[index, celltype] = RecurrentPopulation(dt = dt,v_min=-1.0, v_max=1.0, dv=dv, update_method=update_method, approx_order=approx_order, tol=tol)

# Create background connections:
connection_list = []
for index, celltype in itertools.product([0], ['e', 'i']):
    source_population = background_population_dict[0,'bkg']
    target_population = internal_population_dict[layer, celltype]
    if celltype == 'e':
        background_delay = .005
    else:
        background_delay = 0.
    curr_connection = Connection(source_population, target_population, nsyn_background[layer, celltype], weights=[conn_weights['e']], probs=[1.], delay=background_delay) 
    connection_list.append(curr_connection)
Пример #26
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def test_enternalpopulation_df():
    e1 = ExternalPopulation(100)
    e2 = ExternalPopulation(**dict_from_df(e1.to_df()))
    compare_dicts(e1.to_dict(), e2.to_dict())
Пример #27
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def test_enternalpopulation_df():
    e1 = ExternalPopulation(100)
    e2 = ExternalPopulation(**dict_from_df(e1.to_df()))
    compare_dicts(e1.to_dict(), e2.to_dict())
Пример #28
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    b = np.zeros(A.shape[0])
    b[0] = 1
    f1_new = np.dot(npla.solve(A, b), (bgfr * nsyn_bg + nsyn_01 * f0) * te)

    return np.array([f0_new, f1_new])


# Compute steady state:
f0_ss, f1_ss = sopt.fixed_point(steady_state_function,
                                np.array([14, 9]),
                                args=(bgfr, nsyn_bg, nsyn_00, nsyn_01, nsyn_10,
                                      nsyn_11, delay))

# Compute initial guesses for eigenvector and eigenvalue:
# # Components:
b1 = ExternalPopulation(bgfr, record=True)
i1 = InternalPopulation(tau_m=.05,
                        v_min=0,
                        v_max=1,
                        dv=dv,
                        update_method='gmres')
b1_i1 = Connection(b1, i1, nsyn_bg, weights=we, delays=0.0)
i1_i1 = Connection(i1, i1, 0, weights=wi, delays=0.0)


def cheb(N):
    x = np.cos(np.pi * np.arange(N + 1) / N)
    c = np.array([2] + [1] *
                 (N - 1) + [2]) * np.array([(-1)**ii for ii in range(N + 1)])
    X = npm.repmat(x, 1, N + 1).reshape(N + 1, N + 1).T
    dX = X - X.T
Пример #29
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    def build(self, firing_rate):
        if firing_rate is not None:
            self._firing_rate = firing_rate

        self._dipde_obj = ExternalPopulation(firing_rate)
Пример #30
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# import matplotlib
# matplotlib.use('Qt4Agg')
# import matplotlib.pyplot as plt
from dipde.internals.internalpopulation import InternalPopulation
from dipde.internals.externalpopulation import ExternalPopulation
from dipde.internals.network import Network
from dipde.internals.connection import Connection as Connection
from dipde.visualization import visualize

dv = .0001
update_method = 'approx'
approx_order = 1
tol = 1e-14

b1 = ExternalPopulation('100', record=True)
i1 = InternalPopulation(v_min=0,
                        v_max=.02,
                        dv=dv,
                        update_method=update_method,
                        approx_order=approx_order,
                        tol=tol)
i2 = InternalPopulation(v_min=0,
                        v_max=.02,
                        dv=dv,
                        update_method=update_method,
                        approx_order=approx_order,
                        tol=tol)
b1_i1 = Connection(b1, i1, 1, weights=.005, delays=0.0)
b1_i2 = Connection(b1, i2, 2, weights=.005, delays=0.0)
network = Network([b1, i1, i2], [b1_i1, b1_i2])
Пример #31
0
 def __create_external_pop(self, params, rates):
     pop = ExternalPopulation(rates, record=False)
     return pop
    'tau_m': .01,
    'record': True
}

# Simulation settings:
t0 = 0.
dt = .0002
tf = .1
verbose = True
save = False

# Create populations:
background_population_dict = {}
internal_population_dict = {}
for layer, celltype in itertools.product([23, 4, 5, 6], ['e', 'i']):
    background_population_dict[layer, celltype] = ExternalPopulation(
        'Heaviside(t)*%s' % background_firing_rate, record=False)
    internal_population_dict[layer, celltype] = InternalPopulation(
        **internal_population_settings)

# Create background connections:
connection_list = []
for layer, celltype in itertools.product([23, 4, 5, 6], ['e', 'i']):
    source_population = background_population_dict[layer, celltype]
    target_population = internal_population_dict[layer, celltype]
    if celltype == 'e':
        background_delay = .005
    else:
        background_delay = 0.
    curr_connection = Connection(source_population,
                                 target_population,
                                 nsyn_background[layer, celltype],
"""This singlepop simulation provides a simple feedforward topology that uses
every major class in the core library. A single 100 Hz External population population
provides excitatory input. (Note that although here this frequencys specified as a
string, a floating point or integer specification will also work). This external
population is connected to an Internal population (modeled as a population density pde)
via a delta-distributed synaptic weight distribution, with 5 mV strength. The in-degree
(nsyn) of this Connection is set to 1 for this example. In general, this serves as a
multiplier of the input firing rate of the source population. The internal population
has a linearly binned voltage domain from v_min to v_max. No negative bins (i.e. v_min < 0)
are required here, because no negative synaptic inputs ('weights' in the Connection object)
are defined.
"""

# Create simulation
externalPopFreq = '50'
b1 = ExternalPopulation(externalPopFreq, record=True)
i1 = InternalPopulation(v_min=0,
                        v_max=.02,
                        dv=dv,
                        update_method=update_method,
                        approx_order=approx_order,
                        tol=tol)
b1_i1 = Connection(b1, i1, 1, weights=[.005], probs=[1.], delay=0.0)
simulation = Simulation([b1, i1], [b1_i1], verbose=verbose)

# Run simulation
simulation.run(dt=dt, tf=tf, t0=t0)

# Visualize results
i1 = simulation.population_list[1]
plt.figure(figsize=(3, 3))