def __init__(self,
morphology=None,
model=None,
threshold=None,
refractory=False,
reset=None,
events=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', 'constant over dt')
})
#: The original equations as specified by the user (i.e. before
#: inserting point-currents into the membrane equation, before adding
#: all the internally used variables and constants, etc.).
self.user_equations = model
# Separate subexpressions depending whether they are considered to be
# constant over a time step or not (this would also be done by the
# NeuronGroup initializer later, but this would give incorrect results
# for the linearity check)
model, constant_over_dt = extract_constant_subexpressions(model)
# Extract membrane equation
if 'Im' in model:
if len(model['Im'].flags):
raise TypeError(
'Cannot specify any flags for the transmembrane '
'current Im.')
membrane_expr = model['Im'].expr # the membrane equation
else:
raise TypeError('The transmembrane current Im must be defined')
model_equations = []
# Insert point currents in the membrane equation
for eq in model.itervalues():
if eq.varname == 'Im':
continue # ignore -- handled separately
if 'point current' in eq.flags:
fail_for_dimension_mismatch(
eq.dim, amp,
"Point current " + eq.varname + " should be in amp")
membrane_expr = Expression(
str(membrane_expr.code) + '+' + eq.varname + '/area')
eq = SingleEquation(
eq.type,
eq.varname,
eq.dim,
expr=eq.expr,
flags=list(set(eq.flags) - set(['point current'])))
model_equations.append(eq)
model_equations.append(
SingleEquation(SUBEXPRESSION,
'Im',
dimensions=(amp / meter**2).dim,
expr=membrane_expr))
model_equations.append(SingleEquation(PARAMETER, 'v', volt.dim))
model = Equations(model_equations)
###### Process model equations (Im) to extract total conductance and the remaining current
# Expand expressions in the membrane equation
for var, expr in model.get_substituted_expressions(
include_subexpressions=True):
if var == 'Im':
Im_expr = expr
break
else:
raise AssertionError('Model equations did not contain Im!')
# Differentiate Im with respect to v
Im_sympy_exp = str_to_sympy(Im_expr.code)
v_sympy = sp.Symbol('v', real=True)
diffed = sp.diff(Im_sympy_exp, v_sympy)
unevaled_derivatives = diffed.atoms(sp.Derivative)
if len(unevaled_derivatives):
raise TypeError(
'Cannot take the derivative of "{Im}" with respect '
'to v.'.format(Im=Im_expr.code))
gtot_str = sympy_to_str(sp.simplify(-diffed))
I0_str = sympy_to_str(sp.simplify(Im_sympy_exp - diffed * v_sympy))
if gtot_str == '0':
gtot_str += '*siemens/meter**2'
if I0_str == '0':
I0_str += '*amp/meter**2'
gtot_str = "gtot__private=" + gtot_str + ": siemens/meter**2"
I0_str = "I0__private=" + I0_str + ": amp/meter**2"
model += Equations(gtot_str + "\n" + I0_str)
# Insert morphology (store a copy)
self.morphology = copy.deepcopy(morphology)
# Flatten the morphology
self.flat_morphology = FlatMorphology(morphology)
# 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("""
length : meter (constant)
distance : meter (constant)
area : meter**2 (constant)
volume : meter**3
Ic : amp/meter**2
diameter : meter (constant)
Cm : farad/meter**2 (constant)
Ri : ohm*meter (constant, shared)
r_length_1 : meter (constant)
r_length_2 : meter (constant)
time_constant = Cm/gtot__private : second
space_constant = (2/pi)**(1.0/3.0) * (area/(1/r_length_1 + 1/r_length_2))**(1.0/6.0) /
(2*(Ri*gtot__private)**(1.0/2.0)) : meter
""")
if self.flat_morphology.has_coordinates:
eqs_constants += Equations('''
x : meter (constant)
y : meter (constant)
z : meter (constant)
''')
NeuronGroup.__init__(self,
morphology.total_compartments,
model=model + eqs_constants,
threshold=threshold,
refractory=refractory,
reset=reset,
events=events,
method=method,
dt=dt,
clock=clock,
order=order,
namespace=namespace,
dtype=dtype,
name=name)
# Parameters and intermediate variables for solving the cable equations
# Note that some of these variables could have meaningful physical
# units (e.g. _v_star is in volt, _I0_all is in amp/meter**2 etc.) but
# since these variables should never be used in user code, we don't
# assign them any units
self.variables.add_arrays(
[
'_ab_star0',
'_ab_star1',
'_ab_star2',
'_a_minus0',
'_a_minus1',
'_a_minus2',
'_a_plus0',
'_a_plus1',
'_a_plus2',
'_b_plus',
'_b_minus',
'_v_star',
'_u_plus',
'_u_minus',
'_v_previous',
# The following three are for solving the
# three tridiag systems in parallel
'_c1',
'_c2',
'_c3',
# The following two are only necessary for
# C code where we cannot deal with scalars
# and arrays interchangeably:
'_I0_all',
'_gtot_all'
],
size=self.N,
read_only=True)
self.Cm = Cm
self.Ri = Ri
# These explict assignments will load the morphology values from disk
# in standalone mode
self.distance_ = self.flat_morphology.distance
self.length_ = self.flat_morphology.length
self.area_ = self.flat_morphology.area
self.diameter_ = self.flat_morphology.diameter
self.r_length_1_ = self.flat_morphology.r_length_1
self.r_length_2_ = self.flat_morphology.r_length_2
if self.flat_morphology.has_coordinates:
self.x_ = self.flat_morphology.x
self.y_ = self.flat_morphology.y
self.z_ = self.flat_morphology.z
# Performs numerical integration step
self.add_attribute('diffusion_state_updater')
self.diffusion_state_updater = SpatialStateUpdater(self,
method,
clock=self.clock,
order=order)
# Update v after the gating variables to obtain consistent Ic and Im
self.diffusion_state_updater.order = 1
# Creation of contained_objects that do the work
self.contained_objects.extend([self.diffusion_state_updater])
if len(constant_over_dt):
self.subexpression_updater = SubexpressionUpdater(
self, constant_over_dt)
self.contained_objects.append(self.subexpression_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])
def __init__(self,
morphology=None,
model=None,
threshold=None,
refractory=False,
reset=None,
events=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():
if var == 'Im':
Im_expr = expr
membrane_eq.type = SUBEXPRESSION
# Factor out the variable
s_expr = sp.collect(str_to_sympy(Im_expr.code).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)
# Insert morphology (store a copy)
self.morphology = copy.deepcopy(morphology)
# Flatten the morphology
self.flat_morphology = FlatMorphology(morphology)
# 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("""
length : meter (constant)
distance : meter (constant)
area : meter**2 (constant)
volume : meter**3
diameter : meter (constant)
Cm : farad/meter**2 (constant)
Ri : ohm*meter (constant, shared)
r_length_1 : meter (constant)
r_length_2 : meter (constant)
time_constant = Cm/gtot__private : second
space_constant = (2/pi)**(1.0/3.0) * (area/(1/r_length_1 + 1/r_length_2))**(1.0/6.0) /
(2*(Ri*gtot__private)**(1.0/2.0)) : meter
""")
if self.flat_morphology.has_coordinates:
eqs_constants += Equations('''
x : meter (constant)
y : meter (constant)
z : meter (constant)
''')
NeuronGroup.__init__(self,
morphology.total_compartments,
model=model + eqs_constants,
threshold=threshold,
refractory=refractory,
reset=reset,
events=events,
method=method,
dt=dt,
clock=clock,
order=order,
namespace=namespace,
dtype=dtype,
name=name)
# Parameters and intermediate variables for solving the cable equations
# Note that some of these variables could have meaningful physical
# units (e.g. _v_star is in volt, _I0_all is in amp/meter**2 etc.) but
# since these variables should never be used in user code, we don't
# assign them any units
self.variables.add_arrays(
[
'_ab_star0',
'_ab_star1',
'_ab_star2',
'_a_minus0',
'_a_minus1',
'_a_minus2',
'_a_plus0',
'_a_plus1',
'_a_plus2',
'_b_plus',
'_b_minus',
'_v_star',
'_u_plus',
'_u_minus',
# The following three are for solving the
# three tridiag systems in parallel
'_c1',
'_c2',
'_c3',
# The following two are only necessary for
# C code where we cannot deal with scalars
# and arrays interchangeably:
'_I0_all',
'_gtot_all'
],
unit=1,
size=self.N,
read_only=True)
self.Cm = Cm
self.Ri = Ri
# These explict assignments will load the morphology values from disk
# in standalone mode
self.distance_ = self.flat_morphology.distance
self.length_ = self.flat_morphology.length
self.area_ = self.flat_morphology.area
self.diameter_ = self.flat_morphology.diameter
self.r_length_1_ = self.flat_morphology.r_length_1
self.r_length_2_ = self.flat_morphology.r_length_2
if self.flat_morphology.has_coordinates:
self.x_ = self.flat_morphology.x
self.y_ = self.flat_morphology.y
self.z_ = self.flat_morphology.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])