/
erp_variability_model.py
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erp_variability_model.py
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import sys
sys.path.insert(0, 'old/scalingproject')
sys.path.insert(0, 'util')
from numpy import pi, dot, zeros, ndarray, transpose, identity, sqrt, newaxis
from numpy.random import multivariate_normal, uniform
from matplotlib import pyplot
from lead_field import Lead_Field
from generator_configuration import random_generator_placement
from topographicmap import plot_topographic_map, plot_topographic_map_array
from variability_visualization import plot_covariance_matrix
#TODO sigma should be sigma_sq_ throghout, or var, because it's variance, so
# sigma squared
class ERP_Variability_Model():
def __init__(self, n_sub, n_gen, variability_electrodes='none',
variability_generators='none',
variability_connections='none'):
self.n_gen = n_gen # generators
self.n_sub = n_sub # subjects
self.n_el = 60 # Hard-coded to use a specific electrode set
self.up_to_date = {}
self.set_parameter_limits()
self.gen_conf = None
self.lf = Lead_Field()
self.set_variability_type(variability_electrodes,
variability_generators,
variability_connections)
self.sigma_e = 0
self.sigma_g = zeros(self.n_gen)
self.sigma_c = zeros((self.n_gen, self.n_gen))
def print_model(self, topographies=False):
print('ERP Model Parameters')
print('====================')
print('Number of generators: ' + str(self.n_gen) + '\n')
print('Variability')
print('-----------')
print('* Electrodes (self.sigma_e)')
print self.sigma_e
print('* Generators (self.cov_gen)')
print self.cov_gen
print('* Final covariance matrix (self.cov)')
print self.cov
for gen in range(self.n_gen):
print('\nGenerator ' + str(gen+1))
print('-------------------')
print('LOCATION, Depth: ' + str(self.gen_conf[gen]['depth']))
print('LOCATION, Theta: ' + str(self.gen_conf[gen]['theta']))
print('LOCATION, Phi: ' + str(self.gen_conf[gen]['phi']))
print('ORIENTATION: ' + str(self.gen_conf[gen]['orientation']))
print('ORIENTATION, Phi: ' + str(self.gen_conf[gen]['orientation_phi']))
print('MAGNITUDE: ' + str(self.gen_conf[gen]['magnitude']))
if topographies:
pyplot.figure()
plot_topographic_map((self.gen_conf[gen]['magnitude'] *
self.lf.calculate(
[self.gen_conf[gen]]))[:,0])
def plot_model(self, to_plot):
for one_plot in to_plot:
if one_plot == 'mean':
plot_topographic_map(self.mean)
pyplot.title('Topographic map of mean')
# Individual generator means
pyplot.figure()
for i in range(self.n_gen):
pyplot.subplot(1,self.n_gen,i)
plot_topographic_map(self.mean)
pyplot.figtext(0.5, 0.75, 'Topographic maps of means of each generator',
ha='center')
if one_plot == 'variance':
pyplot.figure()
plot_topographic_map(self.cov.diagonal())
pyplot.title('Topographic map of variance')
# Individual generator variances
pyplot.figure()
for i in range(self.n_gen):
pyplot.subplot(1,self.n_gen,i)
single_cov = dot(transpose(self.lead_field[:,i][newaxis]),
self.lead_field[:,i][newaxis])
if self.variability_generators == 'constant':
single_cov = self.sigma_g * single_cov
elif self.variability_generators == 'individual':
single_cov = self.sigma_g[i] * single_cov
plot_topographic_map(single_cov.diagonal())
pyplot.figtext(0.5, 0.75, 'Topographic maps of variance of each generator',
ha='center')
if one_plot == 'covariance matrix':
pyplot.figure()
plot_covariance_matrix(self.data,self.cov)
pyplot.title('Covariance matrix')
def set_parameter_limits(self):
# Parameter bounds for randomizing model parameters
self.limits = {}
# Location and orientation
self.limits['depth']= (4.49,7.05) # roughly the cortex
self.limits['phi'] = (0,2*pi)
self.limits['theta'] = (0,pi/2)
self.limits['orientation'] = (0, pi/2) # cortex
self.limits['orientation_phi'] = (0,2*pi)
# Magnitude
self.limits['magnitude'] = (0, 1000)
# Variability
self.limits['generator_variance'] = [0, 1000000]
self.limits['electrode_variance'] = [0, 20]
# Covariance needs no limits becuase it is limited by the variance of
# the two generators in question
#self.limits['generator_covariance'] = [0, 1000000]
# Constant number of generators
self.limits['n_gen'] = (self.n_gen, self.n_gen)
def set_variability_type(self, variability_electrodes,
variability_generators, variability_connections):
if variability_electrodes not in ['constant', 'individual', 'none']:
raise ValueError
else:
self.variability_electrodes = variability_electrodes
if variability_generators not in ['constant', 'individual', 'none']:
raise ValueError
else:
self.variability_generators = variability_generators
if variability_connections not in ['individual', 'none']:
raise ValueError
else:
self.variability_connections = variability_connections
def set_gen_conf(self, gen_conf):
self.gen_conf = gen_conf
self.n_gen = len(gen_conf)
def set_random(self):
self.set_random_locations_orientations()
self.set_random_magnitudes()
self.set_random_variability()
def set_random_locations_orientations(self):
self.gen_conf = random_generator_placement(self.limits)
self.up_to_date['lead field'] = False
self.up_to_date['mean'] = False
self.up_to_date['covariance generators'] = False
self.up_to_date['covariance'] = False
def set_random_magnitudes(self):
limits = self.limits['magnitude']
for i in range(self.n_gen):
self.gen_conf[i]['magnitude'] = limits[0] + uniform(limits[1] - limits[0])
self.up_to_date['mean'] = False
def set_random_variability(self):
self.set_random_variability_electrodes()
self.set_random_variability_generators()
self.set_random_variability_connections()
def set_random_variability_electrodes(self):
limits = self.limits['electrode_variance']
if self.variability_electrodes == 'none':
self.sigma_e = 0
elif self.variability_electrodes == 'constant':
self.sigma_e = limits[0] + uniform(limits[1] - limits[0])
elif self.variability_electrodes == 'individual':
self.sigma_e = []
for i in range(self.n_el):
self.sigma_e.append(limits[0] + uniform(limits[1] - limits[0]))
def set_random_variability_generators(self):
limits = self.limits['generator_variance']
if self.variability_generators == 'none':
self.sigma_g = 0
elif self.variability_generators == 'constant':
self.sigma_g = limits[0] + uniform(limits[1] - limits[0])
elif self.variability_generators == 'individual':
self.sigma_g = []
for i in range(self.n_gen):
self.sigma_g.append(limits[0] + uniform(limits[1] - limits[0]))
def set_random_variability_connections(self):
if self.variability_connections == 'none':
self.sigma_c = zeros((self.n_gen, self.n_gen))
elif self.variability_connections == 'individual':
self.sigma_c = zeros((self.n_gen, self.n_gen))
for row in range(self.n_gen):
for column in range(self.n_gen):
if row < column:
sigma_c = uniform(sqrt(self.sigma_g[row] *
self.sigma_g[column]))
self.sigma_c[row, column] = sigma_c
self.sigma_c[column, row] = sigma_c
def calculate_lead_field(self):
self.lead_field = self.lf.calculate(self.gen_conf)
self.up_to_date['lead field'] = True
self.up_to_date['mean'] = False
self.up_to_date['covariance generators'] = False
self.up_to_date['covariance'] = False
return self.lead_field
def calculate_mean(self):
if not self.up_to_date['lead field']: self.calculate_lead_field()
gen_amplitudes = []
for i in range(self.n_gen):
gen_amplitudes.append(self.gen_conf[i]['magnitude'])
self.mean = dot(self.lead_field, gen_amplitudes)
self.up_to_date['mean'] = True
return self.mean
def calculate_cov_gen(self):
if not self.up_to_date['lead field']: self.calculate_lead_field()
self.cov_gen = zeros((self.n_gen, self.n_gen))
for row in range(self.n_gen):
for column in range(self.n_gen):
if row == column:
if self.variability_generators == 'individual':
self.cov_gen[row,column] = self.sigma_g[row]
elif self.variability_generators == 'constant':
self.cov_gen[row,column] = self.sigma_g
elif column > row:
if self.variability_connections == 'individual':
self.cov_gen[row,column] = self.sigma_c[row,column]
self.cov_gen[column,row] = self.sigma_c[row,column]
self.up_to_date['covariance generators'] = True
self.up_to_date['covariance'] = False
return self.cov_gen
def calculate_cov(self):
if not self.up_to_date['lead field']: self.calculate_lead_field()
if not self.up_to_date['covariance generators']:
self.calculate_cov_gen()
# TODO: Make it work for individual electrode variance as well
self.cov = dot(dot(self.lead_field, self.cov_gen),
transpose(self.lead_field)) + self.sigma_e *\
identity(self.n_el)
self.up_to_date['covariance'] = True
return self.cov
def simulate(self):
self.data = multivariate_normal(self.mean,self.cov,self.n_sub)
return self.data
def recalculate_model(self):
self.up_to_date['lead field'] = False
self.up_to_date['mean'] = False
self.up_to_date['covariance generators'] = False
self.up_to_date['covariance'] = False
self.calculate_lead_field()
self.calculate_mean()
self.calculate_cov()
self.simulate()