def test_extract_subexpressions():
eqs = Equations("""dv/dt = -v / (10*ms) : 1
s1 = 2*v : 1
s2 = -v : 1 (constant over dt)
""")
variable, constant = extract_constant_subexpressions(eqs)
assert [var in variable for var in ['v', 's1', 's2']]
assert variable['s1'].type == SUBEXPRESSION
assert variable['s2'].type == PARAMETER
assert constant['s2'].type == SUBEXPRESSION
def test_extract_subexpressions():
eqs = Equations('''dv/dt = -v / (10*ms) : 1
s1 = 2*v : 1
s2 = -v : 1 (constant over dt)
''')
variable, constant = extract_constant_subexpressions(eqs)
assert [var in variable for var in ['v', 's1', 's2']]
assert variable['s1'].type == SUBEXPRESSION
assert variable['s2'].type == PARAMETER
assert constant['s2'].type == SUBEXPRESSION
def __init__(self,
N,
model,
method=('exact', 'euler', 'heun'),
method_options=None,
threshold=None,
reset=None,
refractory=False,
events=None,
namespace=None,
dtype=None,
dt=None,
clock=None,
order=0,
name='neurongroup*',
codeobj_class=None):
Group.__init__(self,
dt=dt,
clock=clock,
when='start',
order=order,
name=name)
if dtype is None:
dtype = {}
if isinstance(dtype, collections.MutableMapping):
dtype['lastspike'] = self._clock.variables['t'].dtype
self.codeobj_class = codeobj_class
try:
self._N = N = int(N)
except ValueError:
if isinstance(N, str):
raise TypeError(
"First NeuronGroup argument should be size, not equations."
)
raise
if N < 1:
raise ValueError("NeuronGroup size should be at least 1, was " +
str(N))
self.start = 0
self.stop = self._N
##### 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))
# Check flags
model.check_flags({
DIFFERENTIAL_EQUATION: ('unless refractory', ),
PARAMETER: ('constant', 'shared', 'linked'),
SUBEXPRESSION: ('shared', 'constant over dt')
})
# add refractoriness
#: The original equations as specified by the user (i.e. without
#: the multiplied `int(not_refractory)` term for equations marked as
#: `(unless refractory)`)
self.user_equations = model
if refractory is not False:
model = add_refractoriness(model)
uses_refractoriness = len(model) and any([
'unless refractory' in eq.flags
for eq in model.values() if eq.type == DIFFERENTIAL_EQUATION
])
# Separate subexpressions depending whether they are considered to be
# constant over a time step or not
model, constant_over_dt = extract_constant_subexpressions(model)
self.equations = model
self._linked_variables = set()
logger.diagnostic("Creating NeuronGroup of size {self._N}, "
"equations {self.equations}.".format(self=self))
if namespace is None:
namespace = {}
#: The group-specific namespace
self.namespace = namespace
# All of the following will be created in before_run
#: The refractory condition or timespan
self._refractory = refractory
if uses_refractoriness and refractory is False:
logger.warn(
'Model equations use the "unless refractory" flag but '
'no refractory keyword was given.', 'no_refractory')
#: The state update method selected by the user
self.method_choice = method
if events is None:
events = {}
if threshold is not None:
if 'spike' in events:
raise ValueError(("The NeuronGroup defines both a threshold "
"and a 'spike' event"))
events['spike'] = threshold
# Setup variables
# Since we have to create _spikespace and possibly other "eventspace"
# variables, we pass the supported events
self._create_variables(dtype, events=list(events.keys()))
#: Events supported by this group
self.events = events
#: Code that is triggered on events (e.g. reset)
self.event_codes = {}
#: Checks the spike threshold (or abitrary user-defined events)
self.thresholder = {}
#: Reset neurons which have spiked (or perform arbitrary actions for
#: user-defined events)
self.resetter = {}
for event_name in events.keys():
if not isinstance(event_name, basestring):
raise TypeError(('Keys in the "events" dictionary have to be '
'strings, not type %s.') % type(event_name))
if not _valid_event_name(event_name):
raise TypeError(("The name '%s' cannot be used as an event "
"name.") % event_name)
# By default, user-defined events are checked after the threshold
when = 'thresholds' if event_name == 'spike' else 'after_thresholds'
# creating a Thresholder will take care of checking the validity
# of the condition
thresholder = Thresholder(self, event=event_name, when=when)
self.thresholder[event_name] = thresholder
self.contained_objects.append(thresholder)
if reset is not None:
self.run_on_event('spike', reset, when='resets')
#: Performs numerical integration step
self.state_updater = StateUpdater(self, method, method_options)
self.contained_objects.append(self.state_updater)
#: Update the "constant over a time step" subexpressions
self.subexpression_updater = None
if len(constant_over_dt):
self.subexpression_updater = SubexpressionUpdater(
self, constant_over_dt)
self.contained_objects.append(self.subexpression_updater)
if refractory is not False:
# Set the refractoriness information
self.variables['lastspike'].set_value(-1e4 * second)
self.variables['not_refractory'].set_value(True)
# Activate name attribute access
self._enable_group_attributes()
def __init__(self, N, model,
method=('exact', 'euler', 'heun'),
method_options=None,
threshold=None,
reset=None,
refractory=False,
events=None,
namespace=None,
dtype=None,
dt=None,
clock=None,
order=0,
name='neurongroup*',
codeobj_class=None):
Group.__init__(self, dt=dt, clock=clock, when='start', order=order,
name=name)
if dtype is None:
dtype = {}
if isinstance(dtype, collections.MutableMapping):
dtype['lastspike'] = self._clock.variables['t'].dtype
self.codeobj_class = codeobj_class
try:
self._N = N = int(N)
except ValueError:
if isinstance(N, str):
raise TypeError("First NeuronGroup argument should be size, not equations.")
raise
if N < 1:
raise ValueError("NeuronGroup size should be at least 1, was " + str(N))
self.start = 0
self.stop = self._N
##### 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))
# Check flags
model.check_flags({DIFFERENTIAL_EQUATION: ('unless refractory',),
PARAMETER: ('constant', 'shared', 'linked'),
SUBEXPRESSION: ('shared',
'constant over dt')})
# add refractoriness
#: The original equations as specified by the user (i.e. without
#: the multiplied `int(not_refractory)` term for equations marked as
#: `(unless refractory)`)
self.user_equations = model
if refractory is not False:
model = add_refractoriness(model)
uses_refractoriness = len(model) and any(
['unless refractory' in eq.flags
for eq in model.itervalues()
if eq.type == DIFFERENTIAL_EQUATION])
# Separate subexpressions depending whether they are considered to be
# constant over a time step or not
model, constant_over_dt = extract_constant_subexpressions(model)
self.equations = model
self._linked_variables = set()
logger.diagnostic("Creating NeuronGroup of size {self._N}, "
"equations {self.equations}.".format(self=self))
if namespace is None:
namespace = {}
#: The group-specific namespace
self.namespace = namespace
# All of the following will be created in before_run
#: The refractory condition or timespan
self._refractory = refractory
if uses_refractoriness and refractory is False:
logger.warn('Model equations use the "unless refractory" flag but '
'no refractory keyword was given.', 'no_refractory')
#: The state update method selected by the user
self.method_choice = method
if events is None:
events = {}
if threshold is not None:
if 'spike' in events:
raise ValueError(("The NeuronGroup defines both a threshold "
"and a 'spike' event"))
events['spike'] = threshold
# Setup variables
# Since we have to create _spikespace and possibly other "eventspace"
# variables, we pass the supported events
self._create_variables(dtype, events=events.keys())
#: Events supported by this group
self.events = events
#: Code that is triggered on events (e.g. reset)
self.event_codes = {}
#: Checks the spike threshold (or abitrary user-defined events)
self.thresholder = {}
#: Reset neurons which have spiked (or perform arbitrary actions for
#: user-defined events)
self.resetter = {}
for event_name in events.iterkeys():
if not isinstance(event_name, basestring):
raise TypeError(('Keys in the "events" dictionary have to be '
'strings, not type %s.') % type(event_name))
if not _valid_event_name(event_name):
raise TypeError(("The name '%s' cannot be used as an event "
"name.") % event_name)
# By default, user-defined events are checked after the threshold
when = 'thresholds' if event_name == 'spike' else 'after_thresholds'
# creating a Thresholder will take care of checking the validity
# of the condition
thresholder = Thresholder(self, event=event_name, when=when)
self.thresholder[event_name] = thresholder
self.contained_objects.append(thresholder)
if reset is not None:
self.run_on_event('spike', reset, when='resets')
#: Performs numerical integration step
self.state_updater = StateUpdater(self, method, method_options)
self.contained_objects.append(self.state_updater)
#: Update the "constant over a time step" subexpressions
self.subexpression_updater = None
if len(constant_over_dt):
self.subexpression_updater = SubexpressionUpdater(self,
constant_over_dt)
self.contained_objects.append(self.subexpression_updater)
if refractory is not False:
# Set the refractoriness information
self.variables['lastspike'].set_value(-1e4*second)
self.variables['not_refractory'].set_value(True)
# Activate name attribute access
self._enable_group_attributes()
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, 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.unit, 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.unit, expr=eq.expr,
flags=list(set(eq.flags)-set(['point current'])))
model_equations.append(eq)
model_equations.append(SingleEquation(SUBEXPRESSION, 'Im',
unit=amp/meter**2,
expr=membrane_expr))
model_equations.append(SingleEquation(PARAMETER, 'v', unit=volt))
model = Equations(model_equations)
###### 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
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!')
# 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])
if len(constant_over_dt):
self.subexpression_updater = SubexpressionUpdater(self,
constant_over_dt)
self.contained_objects.append(self.subexpression_updater)