def setup_model(self):
"""
Function to setup model.
"""
class DriftCoherence(ddm.models.Drift):
name = "Drift depends linearly on coherence"
# Parameter that should be included in the ddm
required_parameters = ["driftcoherence"]
# Task Parameter, i.e. coherence
required_conditions = ["coherence"]
# Define the get_drift function
def get_drift(self, conditions, **kwargs):
return self.driftcoherence * conditions['coherence']
# Set up Model with Drift depending on Coherence
model = Model(
name='Noise Model - Drift varies with coherence',
drift=DriftCoherence(driftcoherence=Fittable(minval=0, maxval=20)),
noise=NoiseConstant(noise=1),
bound=BoundConstant(B=Fittable(minval=.1, maxval=1.5)),
overlay=OverlayChain(overlays=[
OverlayNonDecision(nondectime=Fittable(minval=0, maxval=.4)),
OverlayPoissonMixture(pmixturecoef=.02, rate=1)
]),
dx=.01,
dt=.01,
T_dur=2)
return model
def make_model(sample, model_settings):
# model components:
z = make_z(sample=sample,
z_depends_on=model_settings['depends_on']['z'])
drift = make_drift(sample=sample,
drift_bias=model_settings['drift_bias'],
v_depends_on=model_settings['depends_on']['v'],
b_depends_on=model_settings['depends_on']['b'])
a = make_a(sample=sample,
urgency=model_settings['urgency'],
a_depends_on=model_settings['depends_on']['a'],
u_depends_on=model_settings['depends_on']['u'])
t = make_t(sample=sample,
t_depends_on=model_settings['depends_on']['t'])
T_dur = model_settings['T_dur']
# limits:
ranges = {
'z':(0.05,0.95), # starting point
'v':(0,5), # drift rate
'b':(-5,5), # drift bias
'a':(0.1,5), # bound
# 'u':(-T_dur*10,T_dur*10), # hyperbolic collapse
'u':(0.01,T_dur*10), # hyperbolic collapse
't':(0,2), # non-decision time
}
# put together:
if model_settings['start_bias']:
initial_condition = z(**{param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in z.required_parameters})
else:
initial_condition = z(**{'z':0.5})
model = Model(name='stimulus coding model / collapsing bound',
IC=initial_condition,
drift=drift(**{param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in drift.required_parameters}),
bound=a(**{param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in a.required_parameters}),
overlay=OverlayChain(overlays=[t(**{param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in t.required_parameters}),
OverlayUniformMixture(umixturecoef=0)]),
# OverlayPoissonMixture(pmixturecoef=.01, rate=1)]),
noise=NoiseConstant(noise=1),
dx=.005, dt=.01, T_dur=T_dur)
return model
def DDM_FIT(RT, ANSWER):
df = []
# RT is scalles to seconds, the function takes seconds
df = pd.DataFrame({'RT': RT / 1000, 'correct': ANSWER})
df.head()
sample = Sample.from_pandas_dataframe(df,
rt_column_name="RT",
correct_column_name="correct")
model = Model(
name='Model',
drift=DriftConstant(drift=Fittable(minval=6, maxval=25)),
noise=NoiseConstant(
noise=1.5), #(noise=Fittable(minval=0.5, maxval=2.5)),
bound=BoundConstant(B=2.5),
overlay=OverlayChain(overlays=[
OverlayNonDecision(nondectime=Fittable(minval=0, maxval=.8)),
OverlayPoissonMixture(pmixturecoef=.02, rate=1)
]),
dx=.001,
dt=.01,
T_dur=2)
# Fitting this will also be fast because PyDDM can automatically
# determine that DriftCoherence will allow an analytical solution.
fit_model = fit_adjust_model(sample=sample,
model=model,
fitting_method="differential_evolution",
lossfunction=LossRobustBIC,
verbose=False)
param = fit_model.get_model_parameters()
Drift = np.asarray(param[0])
Delay = np.asarray(param[1])
return Drift, Delay
# Define a model which uses our new DriftCoherence defined above.
from ddm import Model, Fittable
from ddm.functions import fit_adjust_model, display_model
from ddm.models import NoiseConstant, BoundConstant, OverlayChain, OverlayNonDecision, OverlayPoissonMixture
model_rs = Model(
name='Roitman data, drift varies with coherence',
drift=DriftCoherence(driftcoh=Fittable(minval=0, maxval=20)),
noise=NoiseConstant(noise=1),
bound=BoundConstant(B=Fittable(minval=.1, maxval=1.5)),
# Since we can only have one overlay, we use
# OverlayChain to string together multiple overlays.
# They are applied sequentially in order. OverlayNonDecision
# implements a non-decision time by shifting the
# resulting distribution of response times by
# `nondectime` seconds.
overlay=OverlayChain(overlays=[
OverlayNonDecision(nondectime=Fittable(minval=0, maxval=.4)),
OverlayPoissonMixture(pmixturecoef=.02, rate=1)
]),
dx=.001,
dt=.01,
T_dur=2)
# Fitting this will also be fast because PyDDM can automatically
# determine that DriftCoherence will allow an analytical solution.
fit_model_rs = fit_adjust_model(sample=roitman_sample,
model=model_rs,
verbose=False)
display_model(fit_model_rs)
# Simple demonstration of PyDDM.
# Create a simple model with constant drift, noise, and bounds.
from ddm import Model
from ddm.models import DriftConstant, NoiseConstant, BoundConstant, OverlayNonDecision, ICPointSourceCenter
from ddm.functions import fit_adjust_model, display_model
model = Model(name='Simple model',
drift=DriftConstant(drift=2.2),
noise=NoiseConstant(noise=1.5),
bound=BoundConstant(B=1.1),
overlay=OverlayNonDecision(nondectime=.1),
dx=.001, dt=.01, T_dur=2)
# Solve the model, i.e. simulate the differential equations to
# generate a probability distribution solution.
display_model(model)
sol = model.solve()
# Now, sample from the model solution to create a new generated
# sample.
samp = sol.resample(1000)
# Fit a model identical to the one described above on the newly
# generated data so show that parameters can be recovered.
from ddm import Fittable, Fitted
from ddm.models import LossRobustBIC
from ddm.functions import fit_adjust_model
model_fit = Model(name='Simple model (fitted)',
drift=DriftConstant(drift=Fittable(minval=0, maxval=4)),
noise=NoiseConstant(noise=Fittable(minval=.5, maxval=4)),
# End canvas initialization
##### DDM SCHEMATIC #####
# Begin default unit
c.add_unit("absolute2", Vector(1, 1, "absolute"), Point(0, 1, "absolute"))
c.set_default_unit("absolute2")
# End default unit
# Begin other axes
c.add_axis("ddm", Point(0.3, 6.5), Point(3.7, 7.6))
c.add_axis("evidence", Point(0.3, 6.2), Point(3.7, 6.4))
# End other axes
# Begin model simulation
model = Model(drift=DriftConstant(drift=0.8), dt=0.01, dx=0.01)
sim_trial = model.simulate_trial(seed=8)
sim_trial[20:] = -sim_trial[20:] * 1.6
sim_trial = sim_trial[0:38]
# End model simulation
# Begin ddm plot
ax = c.ax("ddm")
ax.plot(model.t_domain()[0:len(sim_trial)], sim_trial, c="k")
ax.axhline(1, c=color_bound, clip_on=False)
ax.axhline(-1, c=color_bound, clip_on=False)
ax.set_ylabel("Decision variable")
set_up_plot(ax)
# End ddm plot
# Begin ddm annotate
def make_model_one_accumulator(sample, model_settings):
# # components:
# z = make_z_one_accumulator(sample=sample,
# a_depends_on=model_settings['depends_on']['a'])
# drift = make_drift_one_accumulator(sample=sample,
# drift_bias=model_settings['drift_bias'],
# leak=model_settings['leak'],
# v_depends_on=model_settings['depends_on']['v'],
# b_depends_on=model_settings['depends_on']['b'],
# k_depends_on=model_settings['depends_on']['k'],
# a_depends_on=model_settings['depends_on']['v'],)
# bound = BoundConstant
# t = NonDecisionTime
# n = NoisePulse(noise=1)
# # limits:
# ranges = {
# # 'v':(0.99,1.01), # drift rate
# # 'b':(-0.21,-0.19), # drift bias
# # 'k':(2.39,2.41), # leak
# # 'z':(0.75,0.999), # starting point --> translates into bound heigth 0-5
# 'v':(0,5), # drift rate
# 'b':(-5,5), # drift bias
# 'k':(0,5), # leak
# 'a':(0.1,5), # bound
# 't':(0,.1), # non-decision time
# }
# # initialize params:
# a_params = {param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in z.required_parameters}
# drift_params = {param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in drift.required_parameters if not 'a' in param}
# drift_params = {**drift_params, **a_params}
# # put together:
# model = Model(name='one accumulator model',
# IC=z(**a_params),
# drift=drift(**drift_params),
# bound=bound(B=10),
# overlay=OverlayChain(overlays=[t(**{param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in t.required_parameters}),
# # OverlayUniformMixture(umixturecoef=0)
# # OverlayUniformMixture(umixturecoef=0.01)
# OverlayPoissonMixture(pmixturecoef=.02, rate=1)
# ]),
# noise=n,
# dx=.01, dt=.01, T_dur=T_dur)
# parameters:
ranges = {
# 'v':(0.99,1.01), # drift rate
# 'b':(-0.21,-0.19), # drift bias
# 'k':(2.39,2.41), # leak
# 'z':(0.75,0.999), # starting point --> translates into bound heigth 0-5
'v': (0, 25), # drift rate
'b': (-5, 5), # drift bias
'k': (0, 5), # leak
'a': (0.1, 5), # bound
't': (0, .1), # non-decision time
'lapse': (0.001, 0.999), # lapse rate
'mixture': (0.001, 0.999), # mixture rate
}
a0_value = Fittable(minval=ranges['a'][0],
maxval=ranges['a'][1],
default=1)
a1_value = Fittable(minval=ranges['a'][0],
maxval=ranges['a'][1],
default=1)
v0_value = Fittable(minval=ranges['v'][0],
maxval=ranges['v'][1],
default=1)
v1_value = Fittable(minval=ranges['v'][0],
maxval=ranges['v'][1],
default=1)
if model_settings['drift_bias'] & (model_settings['depends_on']['b']
== ['reward']):
b0_value = Fittable(minval=ranges['b'][0],
maxval=ranges['b'][1],
default=0)
b1_value = Fittable(minval=ranges['b'][0],
maxval=ranges['b'][1],
default=0)
elif model_settings['drift_bias'] & (model_settings['depends_on']['b'] is
None):
b0_value = Fittable(minval=ranges['b'][0],
maxval=ranges['b'][1],
default=0)
b1_value = b0_value
else:
b0_value = 0
b1_value = 0
if model_settings['leak'] & (model_settings['depends_on']['k']
== ['reward']):
k0_value = Fittable(minval=ranges['k'][0],
maxval=ranges['k'][1],
default=1)
k1_value = Fittable(minval=ranges['k'][0],
maxval=ranges['k'][1],
default=1)
elif model_settings['leak'] & (model_settings['depends_on']['k'] is None):
k0_value = Fittable(minval=ranges['k'][0],
maxval=ranges['k'][1],
default=1)
k1_value = k0_value
else:
k0_value = 0
k1_value = 0
if model_settings['lapse'] & (model_settings['depends_on']['lapse']
== ['reward']):
lapse0_value = Fittable(minval=ranges['lapse'][0],
maxval=ranges['lapse'][1],
default=0.1)
lapse1_value = Fittable(minval=ranges['lapse'][0],
maxval=ranges['lapse'][1],
default=0.1)
elif model_settings['lapse'] & (model_settings['depends_on']['lapse'] is
None):
lapse0_value = Fittable(minval=ranges['lapse'][0],
maxval=ranges['lapse'][1],
default=0.1)
lapse1_value = lapse0_value
else:
lapse0_value = 0
lapse1_value = 0
if model_settings['mixture'] & (model_settings['depends_on']['mixture']
== ['reward']):
mixture0_value = Fittable(minval=ranges['mixture'][0],
maxval=ranges['mixture'][1],
default=0.1)
mixture1_value = Fittable(minval=ranges['mixture'][0],
maxval=ranges['mixture'][1],
default=0.1)
elif model_settings['mixture'] & (model_settings['depends_on']['mixture']
is None):
mixture0_value = Fittable(minval=ranges['mixture'][0],
maxval=ranges['mixture'][1],
default=0.1)
mixture1_value = mixture0_value
else:
mixture0_value = 0
mixture1_value = 0
# components:
starting_point_components = {'a0': a0_value, 'a1': a1_value}
drift_components = {
'v0': v0_value,
'v1': v1_value,
'k0': k0_value,
'k1': k1_value,
'b0': b0_value,
'b1': b1_value,
'a0': a0_value,
'a1': a1_value,
}
mixture_components = {
'mixture0': mixture0_value,
'mixture1': mixture1_value
}
lapse_components = {'lapse0': lapse0_value, 'lapse1': lapse1_value}
# build model:
from ddm.models import DriftConstant, NoiseConstant, BoundConstant, OverlayChain, OverlayNonDecision, OverlayPoissonMixture, OverlayUniformMixture, InitialCondition, ICPoint, ICPointSourceCenter, LossBIC
bound = BoundConstant
a = StartingPoint_reward
drift = DriftPulse_reward
t = NonDecisionTime
n = NoisePulse(noise=1)
model = Model(
name='one accumulator model',
IC=a(**starting_point_components),
drift=drift(**drift_components),
bound=bound(B=10),
overlay=OverlayChain(overlays=[
t(t=0),
# t(**{param:Fittable(minval=ranges[param[0]][0], maxval=ranges[param[0]][1]) for param in t.required_parameters}),
OverlayExGaussMixture(**mixture_components),
OverlayEvidenceLapse(**lapse_components),
]),
noise=n,
dx=model_settings['dx'],
dt=model_settings['dt'],
T_dur=model_settings['T_dur'])
# # fit:
# # model_fit = fit_adjust_model(sample=sample, model=model, lossfunction=LossLikelihood)
# try:
# model_fit = fit_adjust_model(sample=sample, model=model, lossfunction=LossLikelihoodGonogo, fitting_method="differential_evolution")
# # print('model: {}'.format(model_fit.solve({'stimulus':0}).prob_correct()))
# # print('data: {}'.format(df.loc[df['stimulus']==0, 'response'].mean()))
# # print()
# # print('model: {}'.format(model_fit.solve({'stimulus':1}).prob_correct()))
# # print('data: {}'.format(df.loc[df['stimulus']==1, 'response'].mean()))
# # # plot:
# # ddm.plot.plot_fit_diagnostics(model=model_fit, sample=sample)
# # get params:
# params = pd.DataFrame(np.atleast_2d([p.real for p in model_fit.get_model_parameters()]), columns=model_fit.get_model_parameter_names())
# params['bic'] = model_fit.fitresult.value()
# except Exception as e:
# print(e)
# params = pd.DataFrame(np.atleast_2d([np.nan, np.nan, np.nan, np.nan]), columns=model.get_model_parameter_names())
return model
wves = sqrt(
float(self.kves)**2 /
(float(self.kvis)**2 + float(self.kves)**2))
wvis = sqrt(
float(self.kvis)**2 /
(float(self.kvis)**2 + float(self.kves)**2))
return wves * mu_ves + wvis * mu_vis
from ddm import Model, Fittable
from ddm.functions import fit_adjust_model
from ddm.models import NoiseConstant, BoundConstant, OverlayNonDecision
model = Model(
name="3DMP Kiani09 Sim",
drift=DriftRate(kves=Fittable(minval=0, maxval=3),
kvis=Fittable(minval=3, maxval=6),
acc=acc,
vel=vel),
bound=BoundConstant(B=Fittable(minval=50, maxval=90)),
noise=NoiseConstant(noise=1),
overlay=OverlayNonDecision(nondectime=Fittable(minval=.1, maxval=.4)),
dx=.01,
dt=.001,
T_dur=2.0)
fit_model = fit_adjust_model(sample=sample, model=model)
#model_gui(model=model, sample=sample)
model_ic = ICPoint(x0=x0)
_overlay_map = OverlayMappingError(mappingcoef=mappingcoef)
_overlay_nondecision = OverlayNonDecision(nondectime=nondectime)
_overlay_mix = OverlayExponentialRewardMixture(
pmixturecoef=pmixturecoef, ratehr=ratehr, ratelr=ratelr)
model_overlay = OverlayChain(
overlays=[_overlay_nondecision, _overlay_map, _overlay_mix])
modelparams = {"dx": 0.005, "dt": 0.002, "T_dur": 3.0}
modelname = "Shinn et al (2020) model (%s)" % (
"gain function" if URGENCY == "gain" else "collapsing bounds")
model = Model(name=modelname,
**modelparams,
drift=model_drift,
noise=model_noise,
bound=model_bounds,
IC=model_ic,
overlay=model_overlay)
ddm.plot.model_gui(model,
conditions={
"coherence": [50, 53, 60, 70],
"presample": [0, 400, 800],
"highreward": [0, 1]
})
# END demo
# This is just a temorary solution
if noise != 0:
return noise
else:
return noise + 0.001
from ddm import Model, Fittable
from ddm.functions import fit_adjust_model, display_model
from ddm.models import NoiseConstant, BoundConstant, OverlayChain, OverlayNonDecision, OverlayPoissonMixture
model_foodc = Model(
name='Data from Smith 2018 two food choice. Fit a regular DDM to it',
drift=DriftFoodc(d=Fittable(minval=0, maxval=0.001)),
noise=NoiseFoodc(sigma=Fittable(minval=0, maxval=0.05)),
bound=BoundConstant(B=1),
overlay=OverlayChain(overlays=[
OverlayNonDecision(nondectime=Fittable(minval=0, maxval=1)),
OverlayPoissonMixture(pmixturecoef=.02, rate=1)
]),
dx=.001,
dt=.01,
T_dur=10)
# Check if an analytical solution exists.
Model.has_analytical_solution(model_foodc)
# For the current model: True
### Fit the model to the dataset to find parameters
# Use the "differential_evolution" fitting method (default, recommanded fitting method)
fit_model_foodc = fit_adjust_model(sample=foodc_sample,
model=model_foodc,
def Fit_DDM_Group_JK_ib(domain='whole'):
# create a df to record the output data
column_names = ['domain', 'RS_level', 'sub_omit'] + model_rDDM.get_model_parameter_names() + \
['loss_func_value', 'criterion', 'sample_size', 'on_bound']
rDDM_fitting_jk = pd.DataFrame(columns=column_names)
# decide whether to fit rDDM on the whole dataset,
# the advantageous trials or disadvantageous trials
if domain == 'adv':
data_for_fit = data[data['domain_group'] == 1]
elif domain == 'dis':
data_for_fit = data[data['domain_group'] == 2]
else:
data_for_fit = data
# fit on groups of different RS levels
for group in np.sort(data_for_fit['RS_level'].unique()):
data_subgroup = data_for_fit[data_for_fit['RS_level'] == group]
# omit subjects one at a time
for sub_omit in np.sort(data_subgroup['subject'].unique()):
# find the current fitting parameters in the fit_ref
where = np.where((fit_ref['domain'] == domain)
& (fit_ref['RS_level'] == group)
& (fit_ref['sub_omit'] == str(sub_omit)))
where = int(where[0])
# allow for extra ranges from the best fitting results
extra = 0.05
extra_v_dis = 0.0005
extra_v_els = 0.005
if domain == 'dis':
vg_max = fit_ref.iloc[where]['vg_best'] + extra_v_dis
vg_min = fit_ref.iloc[where]['vg_best'] - extra_v_dis
vl_max = fit_ref.iloc[where]['vl_best'] + extra_v_dis
vl_min = fit_ref.iloc[where]['vl_best'] - extra_v_dis
else:
vg_max = fit_ref.iloc[where]['vg_best'] + extra_v_els
vg_min = fit_ref.iloc[where]['vg_best'] - extra_v_els
vl_max = fit_ref.iloc[where]['vl_best'] + extra_v_els
vl_min = fit_ref.iloc[where]['vl_best'] - extra_v_els
fixed_max = fit_ref.iloc[where]['fixed_best'] + extra
fixed_min = fit_ref.iloc[where]['fixed_best'] - extra
B_max = fit_ref.iloc[where]['B_best'] + extra
B_min = fit_ref.iloc[where]['B_best'] - extra
x0_max = fit_ref.iloc[where]['x0_best'] + extra
x0_min = fit_ref.iloc[where]['x0_best'] - extra
nondectime_max = fit_ref.iloc[where]['nondectime_best'] + extra
nondectime_min = fit_ref.iloc[where]['nondectime_best'] - extra
# create a DDM modell based on the current fitting range
model_rDDM_ib = Model(
name='Risk_DDM_individual_range_fit',
drift=Risk_Drift(vg=Fittable(minval=vg_min, maxval=vg_max),
vl=Fittable(minval=vl_min, maxval=vl_max),
fixed=Fittable(minval=fixed_min,
maxval=fixed_max)),
IC=Biased_Start(x0=Fittable(minval=x0_min, maxval=x0_max)),
noise=NoiseConstant(noise=1),
bound=BoundConstant(B=Fittable(minval=B_min, maxval=B_max)),
# Uniform Mixture Model
overlay=OverlayChain(overlays=[
OverlayNonDecision(nondectime=Fittable(
minval=nondectime_min, maxval=nondectime_max)),
OverlayUniformMixture(umixturecoef=.05)
]),
dx=0.001,
dt=0.001,
T_dur=10)
# dx=0.01, dt=0.01, T_dur=10)
data_jk = data_subgroup[data_subgroup['subject'] != sub_omit]
sample_size = data_jk.shape[0]
# create a sample and start fitting
data_jk_sample = Sample.from_pandas_dataframe(
data_jk, rt_column_name="RT", correct_column_name="accept")
fit_sample = fit_adjust_model(
sample=data_jk_sample,
model=model_rDDM_ib,
fitting_method='differential_evolution')
# sort out results
result_list = [[domain, group, sub_omit] + fit_sample.get_model_parameters() + \
[fit_sample.fitresult.value(), fit_sample.fitresult.loss, sample_size, 0]]
# 0 in the end is the place holder for the counts in the on_buond column
result_df = pd.DataFrame(result_list, columns=column_names)
# check whether the estimated results are on the limits of the fitting ranges
if result_df['vg'][0] == vg_min or result_df['vg'][0] == vg_max:
result_df['on_bound'][0] += 1
if result_df['vl'][0] == vl_min or result_df['vl'][0] == vl_max:
result_df['on_bound'][0] += 1
if result_df['fixed'][0] == fixed_min or result_df['fixed'][
0] == fixed_max:
result_df['on_bound'][0] += 1
if result_df['B'][0] == B_min or result_df['B'][0] == B_max:
result_df['on_bound'][0] += 1
if result_df['x0'][0] == x0_min or result_df['x0'][0] == x0_max:
result_df['on_bound'][0] += 1
if result_df['nondectime'][0] == nondectime_min or result_df[
'nondectime'][0] == nondectime_max:
result_df['on_bound'][0] += 1
# append the results
rDDM_fitting_jk = rDDM_fitting_jk.append(result_df,
ignore_index=True)
return rDDM_fitting_jk
required_conditions = ["gain", "loss"]
def get_drift(self, conditions, **kwargs):
valuation = self.vg * conditions['gain'] - self.vl * conditions['loss']
return valuation + self.fixed
model_rDDM = Model(
name='Risk_DDM',
drift=Risk_Drift(vg=Fittable(minval=0.001, maxval=0.06),
vl=Fittable(minval=0.001, maxval=0.06),
fixed=Fittable(minval=-1.6, maxval=0.8)),
IC=Biased_Start(x0=Fittable(minval=-0.55, maxval=0.55)),
noise=NoiseConstant(noise=1),
bound=BoundConstant(B=Fittable(minval=0.5, maxval=2)),
# Uniform Mixture Model
overlay=OverlayChain(overlays=[
OverlayNonDecision(nondectime=Fittable(minval=0, maxval=1.1)),
OverlayUniformMixture(umixturecoef=.05)
]),
dx=0.001,
dt=0.001,
T_dur=10)
# dx=0.01, dt=0.01, T_dur=10)
# Check if an analytical solution exists.
model_rDDM.has_analytical_solution()
model_rDDM.get_model_parameter_names()
model_rDDM.get_model_parameters()
import matplotlib.pyplot as plt
from ddm import Model
m = Model()
s = m.solve()
plt.plot(s.model.t_domain(), s.pdf_corr())
plt.savefig("helloworld.png")
plt.show()