def __init__(self, morphology=None, model=None, threshold=None,
refractory=False, reset=None,
threshold_location=None,
dt=None, clock=None, order=0, Cm=0.9 * uF / cm ** 2, Ri=150 * ohm * cm,
name='spatialneuron*', dtype=None, namespace=None,
method=('linear', 'exponential_euler', 'rk2', 'milstein')):
# #### Prepare and validate equations
if isinstance(model, basestring):
model = Equations(model)
if not isinstance(model, Equations):
raise TypeError(('model has to be a string or an Equations '
'object, is "%s" instead.') % type(model))
# Insert the threshold mechanism at the specified location
if threshold_location is not None:
if hasattr(threshold_location,
'_indices'): # assuming this is a method
threshold_location = threshold_location._indices()
# for now, only a single compartment allowed
if len(threshold_location) == 1:
threshold_location = threshold_location[0]
else:
raise AttributeError(('Threshold can only be applied on a '
'single location'))
threshold = '(' + threshold + ') and (i == ' + str(threshold_location) + ')'
# Check flags (we have point currents)
model.check_flags({DIFFERENTIAL_EQUATION: ('point current',),
PARAMETER: ('constant', 'shared', 'linked', 'point current'),
SUBEXPRESSION: ('shared', 'point current')})
# Add the membrane potential
model += Equations('''
v:volt # membrane potential
''')
# Extract membrane equation
if 'Im' in model:
membrane_eq = model['Im'] # the membrane equation
else:
raise TypeError('The transmembrane current Im must be defined')
# Insert point currents in the membrane equation
for eq in model.itervalues():
if 'point current' in eq.flags:
fail_for_dimension_mismatch(eq.unit, amp,
"Point current " + eq.varname + " should be in amp")
eq.flags.remove('point current')
membrane_eq.expr = Expression(
str(membrane_eq.expr.code) + '+' + eq.varname + '/area')
###### Process model equations (Im) to extract total conductance and the remaining current
# Check conditional linearity with respect to v
# Match to _A*v+_B
var = sp.Symbol('v', real=True)
wildcard = sp.Wild('_A', exclude=[var])
constant_wildcard = sp.Wild('_B', exclude=[var])
pattern = wildcard * var + constant_wildcard
# Expand expressions in the membrane equation
membrane_eq.type = DIFFERENTIAL_EQUATION
for var, expr in model._get_substituted_expressions(): # this returns substituted expressions for diff eqs
if var == 'Im':
Im_expr = expr
membrane_eq.type = SUBEXPRESSION
# Factor out the variable
s_expr = sp.collect(Im_expr.sympy_expr.expand(), var)
matches = s_expr.match(pattern)
if matches is None:
raise TypeError, "The membrane current must be linear with respect to v"
a, b = (matches[wildcard],
matches[constant_wildcard])
# Extracts the total conductance from Im, and the remaining current
minusa_str, b_str = sympy_to_str(-a), sympy_to_str(b)
# Add correct units if necessary
if minusa_str == '0':
minusa_str += '*siemens/meter**2'
if b_str == '0':
b_str += '*amp/meter**2'
gtot_str = "gtot__private=" + minusa_str + ": siemens/meter**2"
I0_str = "I0__private=" + b_str + ": amp/meter**2"
model += Equations(gtot_str + "\n" + I0_str)
# Equations for morphology
# TODO: check whether Cm and Ri are already in the equations
# no: should be shared instead of constant
# yes: should be constant (check)
eqs_constants = Equations("""
diameter : meter (constant)
length : meter (constant)
x : meter (constant)
y : meter (constant)
z : meter (constant)
distance : meter (constant)
area : meter**2 (constant)
Cm : farad/meter**2 (constant)
Ri : ohm*meter (constant, shared)
space_constant = (diameter/(4*Ri*gtot__private))**.5 : meter # Not so sure about the name
### Parameters and intermediate variables for solving the cable equation
ab_star0 : siemens/meter**2
ab_plus0 : siemens/meter**2
ab_minus0 : siemens/meter**2
ab_star1 : siemens/meter**2
ab_plus1 : siemens/meter**2
ab_minus1 : siemens/meter**2
ab_star2 : siemens/meter**2
ab_plus2 : siemens/meter**2
ab_minus2 : siemens/meter**2
b_plus : siemens/meter**2
b_minus : siemens/meter**2
v_star : volt
u_plus : 1
u_minus : 1
""")
# Possibilities for the name: characteristic_length, electrotonic_length, length_constant, space_constant
# Insert morphology
self.morphology = morphology
# Link morphology variables to neuron's state variables
self.morphology_data = MorphologyData(len(morphology))
self.morphology.compress(self.morphology_data)
NeuronGroup.__init__(self, len(morphology), model=model + eqs_constants,
threshold=threshold, refractory=refractory,
reset=reset,
method=method, dt=dt, clock=clock, order=order,
namespace=namespace, dtype=dtype, name=name)
self.Cm = Cm
self.Ri = Ri
# TODO: View instead of copy for runtime?
self.diameter_ = self.morphology_data.diameter
self.distance_ = self.morphology_data.distance
self.length_ = self.morphology_data.length
self.area_ = self.morphology_data.area
self.x_ = self.morphology_data.x
self.y_ = self.morphology_data.y
self.z_ = self.morphology_data.z
# Performs numerical integration step
self.add_attribute('diffusion_state_updater')
self.diffusion_state_updater = SpatialStateUpdater(self, method,
clock=self.clock,
order=order)
# Creation of contained_objects that do the work
self.contained_objects.extend([self.diffusion_state_updater])
def __init__(self,
morphology=None,
model=None,
threshold=None,
refractory=False,
reset=None,
threshold_location=None,
dt=None,
clock=None,
order=0,
Cm=0.9 * uF / cm**2,
Ri=150 * ohm * cm,
name='spatialneuron*',
dtype=None,
namespace=None,
method=('linear', 'exponential_euler', 'rk2', 'heun')):
# #### Prepare and validate equations
if isinstance(model, basestring):
model = Equations(model)
if not isinstance(model, Equations):
raise TypeError(('model has to be a string or an Equations '
'object, is "%s" instead.') % type(model))
# Insert the threshold mechanism at the specified location
if threshold_location is not None:
if hasattr(threshold_location,
'_indices'): # assuming this is a method
threshold_location = threshold_location._indices()
# for now, only a single compartment allowed
if len(threshold_location) == 1:
threshold_location = threshold_location[0]
else:
raise AttributeError(('Threshold can only be applied on a '
'single location'))
threshold = '(' + threshold + ') and (i == ' + str(
threshold_location) + ')'
# Check flags (we have point currents)
model.check_flags({
DIFFERENTIAL_EQUATION: ('point current', ),
PARAMETER: ('constant', 'shared', 'linked', 'point current'),
SUBEXPRESSION: ('shared', 'point current')
})
# Add the membrane potential
model += Equations('''
v:volt # membrane potential
''')
# Extract membrane equation
if 'Im' in model:
membrane_eq = model['Im'] # the membrane equation
else:
raise TypeError('The transmembrane current Im must be defined')
# Insert point currents in the membrane equation
for eq in model.itervalues():
if 'point current' in eq.flags:
fail_for_dimension_mismatch(
eq.unit, amp,
"Point current " + eq.varname + " should be in amp")
eq.flags.remove('point current')
membrane_eq.expr = Expression(
str(membrane_eq.expr.code) + '+' + eq.varname + '/area')
###### Process model equations (Im) to extract total conductance and the remaining current
# Check conditional linearity with respect to v
# Match to _A*v+_B
var = sp.Symbol('v', real=True)
wildcard = sp.Wild('_A', exclude=[var])
constant_wildcard = sp.Wild('_B', exclude=[var])
pattern = wildcard * var + constant_wildcard
# Expand expressions in the membrane equation
membrane_eq.type = DIFFERENTIAL_EQUATION
for var, expr in model._get_substituted_expressions(
): # this returns substituted expressions for diff eqs
if var == 'Im':
Im_expr = expr
membrane_eq.type = SUBEXPRESSION
# Factor out the variable
s_expr = sp.collect(Im_expr.sympy_expr.expand(), var)
matches = s_expr.match(pattern)
if matches is None:
raise TypeError, "The membrane current must be linear with respect to v"
a, b = (matches[wildcard], matches[constant_wildcard])
# Extracts the total conductance from Im, and the remaining current
minusa_str, b_str = sympy_to_str(-a), sympy_to_str(b)
# Add correct units if necessary
if minusa_str == '0':
minusa_str += '*siemens/meter**2'
if b_str == '0':
b_str += '*amp/meter**2'
gtot_str = "gtot__private=" + minusa_str + ": siemens/meter**2"
I0_str = "I0__private=" + b_str + ": amp/meter**2"
model += Equations(gtot_str + "\n" + I0_str)
# Equations for morphology
# TODO: check whether Cm and Ri are already in the equations
# no: should be shared instead of constant
# yes: should be constant (check)
eqs_constants = Equations("""
diameter : meter (constant)
length : meter (constant)
x : meter (constant)
y : meter (constant)
z : meter (constant)
distance : meter (constant)
area : meter**2 (constant)
Cm : farad/meter**2 (constant)
Ri : ohm*meter (constant, shared)
space_constant = (diameter/(4*Ri*gtot__private))**.5 : meter # Not so sure about the name
### Parameters and intermediate variables for solving the cable equation
ab_star0 : siemens/meter**2
ab_plus0 : siemens/meter**2
ab_minus0 : siemens/meter**2
ab_star1 : siemens/meter**2
ab_plus1 : siemens/meter**2
ab_minus1 : siemens/meter**2
ab_star2 : siemens/meter**2
ab_plus2 : siemens/meter**2
ab_minus2 : siemens/meter**2
b_plus : siemens/meter**2
b_minus : siemens/meter**2
v_star : volt
u_plus : 1
u_minus : 1
# The following two are only necessary for C code where we cannot deal
# with scalars and arrays interchangeably
gtot_all : siemens/meter**2
I0_all : amp/meter**2
""")
# Possibilities for the name: characteristic_length, electrotonic_length, length_constant, space_constant
# Insert morphology
self.morphology = morphology
# Link morphology variables to neuron's state variables
self.morphology_data = MorphologyData(len(morphology))
self.morphology.compress(self.morphology_data)
NeuronGroup.__init__(self,
len(morphology),
model=model + eqs_constants,
threshold=threshold,
refractory=refractory,
reset=reset,
method=method,
dt=dt,
clock=clock,
order=order,
namespace=namespace,
dtype=dtype,
name=name)
self.Cm = Cm
self.Ri = Ri
# TODO: View instead of copy for runtime?
self.diameter_ = self.morphology_data.diameter
self.distance_ = self.morphology_data.distance
self.length_ = self.morphology_data.length
self.area_ = self.morphology_data.area
self.x_ = self.morphology_data.x
self.y_ = self.morphology_data.y
self.z_ = self.morphology_data.z
# Performs numerical integration step
self.add_attribute('diffusion_state_updater')
self.diffusion_state_updater = SpatialStateUpdater(self,
method,
clock=self.clock,
order=order)
# Creation of contained_objects that do the work
self.contained_objects.extend([self.diffusion_state_updater])
