class Synapses(NeuronGroup): # This way we inherit a lot of useful stuff
'''Set of synapses between two neuron groups
Initialised with arguments:
``source``
The source :class:`NeuronGroup`.
``target=None``
The target :class:`NeuronGroup`. By default, target=source.
``model=None``
The equations that defined the synaptic variables, as an Equations object or a string.
The syntax is the same as for a :class:`NeuronGroup`.
``pre=None``
The code executed when presynaptic spikes arrive at the synapses.
There can be multiple presynaptic codes, passed as a list or tuple of strings.
``post=None``
The code executed when postsynaptic spikes arrive at the synapses.
``max_delay=0*ms``
The maximum pre and postsynaptic delay. This is only useful if the delays can change
during the simulation.
``level=0``
See :class:`Equations` for details.
``clock=None``
The clock for updating synaptic state variables according to ``model``.
Currently, this must be identical to both the source and target clocks.
``compile=False``
Whether or not to attempt to compile the differential equation
solvers (into Python code). Typically, for best performance, both ``compile``
and ``freeze`` should be set to ``True`` for nonlinear differential equations.
``freeze=False``
If True, parameters are replaced by their values at the time
of initialization.
``method=None``
If not None, the integration method is forced. Possible values are
linear, nonlinear, Euler, exponential_Euler (overrides implicit and order
keywords).
``unit_checking=True``
Set to ``False`` to bypass unit-checking.
``order=1``
The order to use for nonlinear differential equation solvers.
TODO: more details.
``implicit=False``
Whether to use an implicit method for solving the differential
equations. TODO: more details.
``code_namespace=None``
Namespace for the pre and post codes.
**Methods**
.. method:: state(var)
Returns the vector of values for state
variable ``var``, with length the number of synapses. The
vector is an instance of class :class:`SynapticVariable`.
.. method:: synapse_index(i)
Returns the synapse indexes correspond to i, which can be a tuple or a slice.
If i is a tuple (m,n), m and n can be an integer, an array, a slice or a subgroup.
The following usages are also possible for a Synapses object ``S``:
``len(S)``
Returns the number of synapses in ``S``.
Attributes:
``delay``
The presynaptic delays for all synapses (synapse->delay). If there are multiple
presynaptic delays (multiple pre codes), this is a list.
``delay_pre``
Same as ``delay``.
``delay_post``
The postsynaptic delays for all synapses (synapse->delay post).
``lastupdate``
The time of last update of all synapses (synapse->last update). This
only exists if there are dynamic synaptic variables.
Internal attributes:
``source``
The source neuron group.
``target``
The target neuron group.
``_S``
The state matrix (a 2D dynamical array with values of synaptic variables).
At run time, it is transformed into a static 2D array (with compress()).
``presynaptic``
The (dynamic) array of presynaptic neuron indexes for all synapses (synapse->i).
``postsynaptic``
The array of postsynaptic neuron indexes for all synapses (synapse->j).
``synapses_pre``
A list of (dynamic) arrays giving the set of synapse indexes for each presynaptic neuron i
(i->synapses)
``synapses_post``
A list of (dynamic) arrays giving the set of synapse indexes for each postsynaptic neuron j
(j->synapses)
``queues``
List of SpikeQueues for pre and postsynaptic spikes.
``codes``
The compiled codes to be executed on pre and postsynaptic spikes.
``namespaces``
The namespaces for the pre and postsynaptic codes.
'''
def __init__(self, source, target = None, model = None, pre = None, post = None,
max_delay = 0*ms,
level = 0,
clock = None,code_namespace=None,
unit_checking = True, method = None, freeze = False, implicit = False, order = 1): # model (state updater) related
target=target or source # default is target=source
# Check clocks. For the moment we enforce the same clocks for all objects
clock = clock or source.clock
if source.clock!=target.clock:
raise ValueError,"Source and target groups must have the same clock"
if pre is None:
pre_list=[]
elif isSequenceType(pre) and not isinstance(pre,str): # a list of pre codes
pre_list=pre
else:
pre_list=[pre]
pre_list=[flattened_docstring(pre) for pre in pre_list]
if post is not None:
post=flattened_docstring(post)
# Pre and postsynaptic indexes (synapse -> pre/post)
self.presynaptic=DynamicArray1D(0,dtype=smallest_inttype(len(source))) # this should depend on number of neurons
self.postsynaptic=DynamicArray1D(0,dtype=smallest_inttype(len(target))) # this should depend on number of neurons
if not isinstance(model,SynapticEquations):
model=SynapticEquations(model,level=level+1)
# Insert the lastupdate variable if necessary (if it is mentioned in pre/post, or if there is event-driven code)
expr=re.compile(r'\blastupdate\b')
if (len(model._eventdriven)>0) or \
any([expr.search(pre) for pre in pre_list]) or \
(post is not None and expr.search(post) is not None):
model+='\nlastupdate : second\n'
pre_list=[pre+'\nlastupdate=t\n' for pre in pre_list]
if post is not None:
post=post+'\nlastupdate=t\n'
# Identify pre and post variables in the model string
# They are identified by _pre and _post suffixes
# or no suffix for postsynaptic variables
ids=set()
for RHS in model._string.itervalues():
ids.update(get_identifiers(RHS))
pre_ids = [id[:-4] for id in ids if id[-4:]=='_pre']
post_ids = [id[:-5] for id in ids if id[-5:]=='_post']
post_vars = [var for var in source.var_index if isinstance(var,str)] # postsynaptic variables
post_ids2 = list(ids.intersection(set(post_vars))) # post variables without the _post suffix
# remember whether our equations refer to any variables in the pre- or
# postsynaptic group. This is important for the state-updater, e.g. the
# equations can no longer be solved as linear equations.
model.refers_others = (len(pre_ids) + len(post_ids) + len(post_ids2) > 0)
# Insert static equations for pre and post variables
S=self
for name in pre_ids:
model.add_eq(name+'_pre', 'S.source.'+name+'[S.presynaptic[:]]', source.unit(name),
global_namespace={'S':S})
for name in post_ids:
model.add_eq(name+'_post', 'S.target.'+name+'[S.postsynaptic[:]]', target.unit(name),
global_namespace={'S':S})
for name in post_ids2: # we have to change the name of the variable to avoid problems with equation processing
if name not in model._string: # check that it is not already defined
model.add_eq(name, 'S.target.state_(__'+name+')[S.postsynaptic[:]]', target.unit(name),
global_namespace={'S':S,'__'+name:name})
self.source=source
self.target=target
NeuronGroup.__init__(self, 0,model=model,clock=clock,level=level+1,unit_checking=unit_checking,method=method,freeze=freeze,implicit=implicit,order=order)
'''
At this point we have:
* a state matrix _S with all variables
* units, state dictionary with each value being a row of _S + the static equations
* subgroups of synapses
* link_var (i.e. we can link two synapses objects)
* __len__
* __setattr__: we can write S.w=array of values
* var_index is a dictionary from names to row index in _S
* num_states()
Things we have that we don't want:
* LS structure (but it will not be filled since the object does not spike)
* (from Group) __getattr_ needs to be rewritten
* a complete state updater, but we need to extract parameters and event-driven parts
* The state matrix is not dynamic
Things we may need to add:
* _pre and _post suffixes
'''
self._iscompressed=False # True if compress() has already been called
# Look for event-driven code in the differential equations
if use_sympy:
eqs=self._eqs # an Equations object
#vars=eqs._diffeq_names_nonzero # Dynamic variables
vars=eqs._eventdriven.keys()
var_set=set(vars)
for var,RHS in eqs._eventdriven.iteritems():
ids=get_identifiers(RHS)
if len(set(list(ids)+[var]).intersection(var_set))==1:
# no external dynamic variable
# Now we test if it is a linear equation
_namespace=dict.fromkeys(ids,1.) # there is a possibility of problems here (division by zero)
# plus units problems? (maybe not since these are identifiers too)
# another option is to use random numbers, but that doesn't solve all problems
_namespace[var]=AffineFunction()
try:
eval(RHS,eqs._namespace[var],_namespace)
except: # not linear
raise TypeError,"Cannot turn equation for "+var+" into event-driven code"
z=symbolic_eval(RHS)
symbol_var=sympy.Symbol(var)
symbol_t=sympy.Symbol('t')-sympy.Symbol('lastupdate')
b=z.subs(symbol_var,0)
a=sympy.simplify(z.subs(symbol_var,1)-b)
if a==0:
expr=symbol_var+b*symbol_t
else:
expr=-b/a+sympy.exp(a*symbol_t)*(symbol_var+b/a)
expr=var+'='+str(expr)
# Replace pre and post code
# N.B.: the differential equations are kept, we will probably want to remove them!
pre_list=[expr+'\n'+pre for pre in pre_list]
if post is not None:
post=expr+'\n'+post
else:
raise TypeError,"Cannot turn equation for "+var+" into event-driven code"
elif len(self._eqs._eventdriven)>0:
raise TypeError,"The Sympy package must be installed to produce event-driven code"
if len(self._eqs._diffeq_names_nonzero)==0:
self._state_updater=None
# Set last spike to -infinity
if 'lastupdate' in self.var_index:
self.lastupdate=-1e6
# _S is turned to a dynamic array - OK this is probably not good! we may lose references at this point
S=self._S
self._S=DynamicArray(S.shape)
self._S[:]=S
# Pre and postsynaptic delays (synapse -> delay_pre/delay_post)
self._delay_pre=[DynamicArray1D(len(self),dtype=np.int16) for _ in pre_list] # max 32767 delays
self._delay_post=DynamicArray1D(len(self),dtype=np.int16) # Actually only useful if there is a post code!
# Pre and postsynaptic synapses (i->synapse indexes)
max_synapses=2147483647 # it could be explicitly reduced by a keyword
# We use a loop instead of *, otherwise only 1 dynamic array is created
self.synapses_pre=[DynamicArray1D(0,dtype=smallest_inttype(max_synapses)) for _ in range(len(self.source))]
self.synapses_post=[DynamicArray1D(0,dtype=smallest_inttype(max_synapses)) for _ in range(len(self.target))]
# Code generation
self._binomial = lambda n,p:np.random.binomial(np.array(n,dtype=int),p)
self.contained_objects = []
self.codes=[]
self.namespaces=[]
self.queues=[]
for i,pre in enumerate(pre_list):
code,_namespace=self.generate_code(pre,level+1,code_namespace=code_namespace)
self.codes.append(code)
self.namespaces.append(_namespace)
self.queues.append(SpikeQueue(self.source, self.synapses_pre, self._delay_pre[i], max_delay = max_delay))
if post is not None:
code,_namespace=self.generate_code(post,level+1,direct=True,code_namespace=code_namespace)
self.codes.append(code)
self.namespaces.append(_namespace)
self.queues.append(SpikeQueue(self.target, self.synapses_post, self._delay_post, max_delay = max_delay))
self.queues_namespaces_codes = zip(self.queues,
self.namespaces,
self.codes)
self.contained_objects+=self.queues
def generate_code(self,code,level,direct=False,code_namespace=None):
'''
Generates pre and post code.
``code''
The code as a string.
``level''
The namespace level in which the code is executed.
``direct=False''
If True, the code is generated assuming that
postsynaptic variables are not modified. This makes the
code faster.
``code_namespace''
Additional namespace (highest priority)
TODO:
* include static variables (substitution)
* have a list of variable names
'''
# Handle multi-line pre, post equations and multi-statement equations separated by ;
# (this should probably be factored)
if '\n' in code:
code = flattened_docstring(code)
elif ';' in code:
code = '\n'.join([line.strip() for line in code.split(';')])
# Create namespaces
_namespace = namespace(code, level = level + 1)
if code_namespace is not None:
_namespace.update(code_namespace)
_namespace['target'] = self.target # maybe we could save one indirection here
_namespace['unique'] = np.unique
_namespace['nonzero'] = np.nonzero
_namespace['empty'] = np.empty
_namespace['logical_not'] = np.logical_not
_namespace['not_equal'] = np.not_equal
_namespace['take'] = np.take
_namespace['extract'] = np.extract
_namespace['add'] = np.add
_namespace['hstack'] = np.hstack
code = re.sub(r'\b' + 'rand\(\)', 'rand(n)', code)
code = re.sub(r'\b' + 'randn\(\)', 'randn(n)', code)
# Generate the code
def update_code(code, indices, postinds):
res = code
# given the synapse indices, write the update code,
# this is here because in the code we generate we need to write this twice (because of the multiple presyn spikes for the same postsyn neuron problem)
# Replace synaptic variables by their value
for var in self.var_index: # static variables are not included here
if isinstance(var, str):
res = re.sub(r'\b' + var + r'\b', var + '['+indices+']', res) # synaptic variable, indexed by the synapse number
# Replace postsynaptic variables by their value
for postsyn_var in self.target.var_index: # static variables are not included here
if isinstance(postsyn_var, str):
#res = re.sub(r'\b' + postsyn_var + r'_post\b', 'target.' + postsyn_var + '['+postinds+']', res)# postsyn variable, indexed by post syn neuron numbers
#res = re.sub(r'\b' + postsyn_var + r'\b', 'target.' + postsyn_var + '['+postinds+']', res)# postsyn variable, indexed by post syn neuron numbers
res = re.sub(r'\b' + postsyn_var + r'_post\b', '_target_' + postsyn_var + '['+postinds+']', res)# postsyn variable, indexed by post syn neuron numbers
res = re.sub(r'\b' + postsyn_var + r'\b', '_target_' + postsyn_var + '['+postinds+']', res)# postsyn variable, indexed by post syn neuron numbers
_namespace['_target_' + postsyn_var] = self.target.state_(postsyn_var)
# Replace presynaptic variables by their value
for presyn_var in self.source.var_index: # static variables are not included here
if isinstance(presyn_var, str):
#res = re.sub(r'\b' + presyn_var + r'_pre\b', 'source.' + presyn_var + '[_pre['+indices+']]', res)# postsyn variable, indexed by post syn neuron numbers
res = re.sub(r'\b' + presyn_var + r'_pre\b', '_source_' + presyn_var + '[_pre['+indices+']]', res)# postsyn variable, indexed by post syn neuron numbers
_namespace['_source_' + presyn_var] = self.source.state_(presyn_var)
# Replace n by number of synapses being updated
res = re.sub(r'\bn\b','len('+indices+')', res)
return res
if direct: # direct update code, not caring about multiple accesses to postsynaptic variables
code_str = '_post_neurons = _post[_synapses]\n'+update_code(code, '_synapses', '_post_neurons') + "\n"
else:
algo = 3
if algo==0:
## Old version using numpy's unique()
code_str = "_post_neurons = _post[_synapses]\n" # not necessary to do a copy because _synapses is not a slice
code_str += "_u, _i = unique(_post_neurons, return_index = True)\n"
#code_str += update_code(code, '_synapses[_i]', '_u') + "\n"
code_str += update_code(code, '_synapses[_i]', '_post[_synapses[_i]]') + "\n"
code_str += "if len(_u) < len(_post_neurons):\n"
code_str += " _post_neurons[_i] = -1\n"
code_str += " while (len(_u) < len(_post_neurons)) & (_post_neurons>-1).any():\n" # !! the any() is time consuming (len(u)>=1??)
#code_str += " while (len(_u) < len(_post_neurons)) & (len(_u)>1):\n" # !! the any() is time consuming (len(u)>=1??)
code_str += " _u, _i = unique(_post_neurons, return_index = True)\n"
code_str += indent(update_code(code, '_synapses[_i[1:]]', '_post[_synapses[_i[1:]]]'),2) + "\n"
code_str += " _post_neurons[_i[1:]] = -1 \n"
elif algo==1:
code_str = "_post_neurons = _post[_synapses]\n" # not necessary to do a copy because _synapses is not a slice
code_str += "_perm = _post_neurons.argsort()\n"
code_str += "_aux = _post_neurons[_perm]\n"
code_str += "_flag = empty(len(_aux) + 1, dtype = bool)\n"
code_str += "_flag[0] = _flag[-1] = True\n"
code_str += "not_equal(_aux[1:], _aux[:-1], _flag[1:-1])\n"
code_str += "_F = _flag.nonzero()[0][:-1]\n"
code_str += "logical_not(_flag, _flag)\n"
code_str += "while len(_F):\n"
code_str += " _u = _aux[_F]\n"
code_str += " _i = _perm[_F]\n"
code_str += indent(update_code(code, '_synapses[_i]', '_u'), 1) + "\n"
code_str += " _F += 1\n"
code_str += " _F = _F[_flag[_F]]\n"
elif algo==2:
code_str = '''
_post_neurons = _post.data.take(_synapses)
_perm = _post_neurons.argsort()
_aux = _post_neurons.take(_perm)
_flag = empty(len(_aux)+1, dtype=bool)
_flag[0] = _flag[-1] = 1
not_equal(_aux[1:], _aux[:-1], _flag[1:-1])
if 0:#_flag.sum()==len(_aux)+1:
%(code1)s
else:
_F = _flag.nonzero()[0][:-1]
logical_not(_flag, _flag)
while len(_F):
_u = _aux.take(_F)
_i = _perm.take(_F)
%(code2)s
_F += 1
_F = extract(_flag.take(_F), _F)
'''
code_str = flattened_docstring(code_str) % {'code1': indent(update_code(code, '_synapses','_post_neurons'), 1),
'code2': indent(update_code(code, '_synapses[_i]', '_u'), 2)}
elif algo==3:
code_str = '''
_post_neurons = _post.data.take(_synapses)
_perm = _post_neurons.argsort()
_aux = _post_neurons.take(_perm)
_flag = empty(len(_aux)+1, dtype=bool)
_flag[0] = _flag[-1] = 1
not_equal(_aux[1:], _aux[:-1], _flag[1:-1])
_F = _flag.nonzero()[0][:-1]
logical_not(_flag, _flag)
while len(_F):
_u = _aux.take(_F)
_i = _perm.take(_F)
%(code)s
_F += 1
_F = extract(_flag.take(_F), _F)
'''
code_str = flattened_docstring(code_str) % {'code': indent(update_code(code, '_synapses[_i]', '_u'), 1)}
elif algo==4:
code_str = '''
_post_neurons = _post[_synapses]
_perm = _post_neurons.argsort()
_aux = _post_neurons[_perm]
_flag = empty(len(_aux)+1, dtype=bool)
_flag[0] = _flag[-1] = 1
not_equal(_aux[1:], _aux[:-1], _flag[1:-1])
_F = _flag.nonzero()[0][:-1]
logical_not(_flag, _flag)
while len(_F):
_u = _aux[_F]
_i = _perm[_F]
%(code)s
_F += 1
_F = _F[_flag[_F]]
'''
code_str = flattened_docstring(code_str) % {'code': indent(update_code(code, '_synapses[_i]', '_u'), 1)}
# print code_str
log_debug('brian.synapses', '\nCODE:\n'+code_str)
# Compile
compiled_code = compile(code_str, "Synaptic code", "exec")
_namespace['_original_code_string'] = code_str
return compiled_code,_namespace
def __setitem__(self, key, value):
'''
Creates new synapses.
Synapse indexes are created such that synapses with the same presynaptic neuron
and delay have contiguous indexes.
Caution:
1) there is no deletion
2) synapses are added, not replaced (e.g. S[1,2]=True;S[1,2]=True creates 2 synapses)
TODO:
* S[:,:]=array (boolean or int)
'''
if self._iscompressed:
raise AttributeError,"Synapses cannot be added after they have been run"
if not isinstance(key, tuple): # we should check that number of elements is 2 as well
raise AttributeError,'Synapses behave as 2-D objects'
pre,post=key # pre and post indexes (can be slices)
'''
Each of these sets of statements creates:
* synapses_pre: a mapping from presynaptic neuron to synapse indexes
* synapses_post: same
* presynaptic: an array of presynaptic neuron indexes (synapse->pre)
* postsynaptic: same
'''
pre_slice = self.presynaptic_indexes(pre)
post_slice = self.postsynaptic_indexes(post)
# Bound checks
if pre_slice[-1]>=len(self.source):
raise ValueError('Presynaptic index %d greater than number of '\
'presynaptic neurons (%d)'
% (pre_slice[-1], len(self.source)))
if post_slice[-1]>=len(self.target):
raise ValueError('Postsynaptic index %d greater than number of '\
'postsynaptic neurons (%d)'
% (post_slice[-1], len(self.target)))
if isinstance(value,float):
self.connect_random(pre,post,value)
return
elif isinstance(value, (int, bool)): # ex. S[1,7]=True
# Simple case, either one or multiple synapses between different neurons
if value is False:
raise ValueError('Synapses cannot be deleted')
elif value is True:
nsynapses = 1
else:
nsynapses = value
postsynaptic,presynaptic=np.meshgrid(post_slice,pre_slice) # synapse -> pre, synapse -> post
# Flatten
presynaptic.shape=(presynaptic.size,)
postsynaptic.shape=(postsynaptic.size,)
# pre,post -> synapse index, relative to last synapse
# (that's a complex vectorised one!)
synapses_pre=np.arange(len(presynaptic)).reshape((len(pre_slice),len(post_slice)))
synapses_post=np.ones((len(post_slice),1),dtype=int)*np.arange(0,len(presynaptic),len(post_slice))+\
np.arange(len(post_slice)).reshape((len(post_slice),1))
# Repeat
if nsynapses>1:
synapses_pre=np.hstack([synapses_pre+k*len(presynaptic) for k in range(nsynapses)]) # could be vectorised
synapses_post=np.hstack([synapses_post+k*len(presynaptic) for k in range(nsynapses)]) # could be vectorised
presynaptic=np.tile(presynaptic,nsynapses)
postsynaptic=np.tile(postsynaptic,nsynapses)
# Make sure the type is correct
synapses_pre=np.array(synapses_pre,dtype=self.synapses_pre[0].dtype)
synapses_post=np.array(synapses_post,dtype=self.synapses_post[0].dtype)
# Turn into dictionaries
synapses_pre=dict(zip(pre_slice,synapses_pre))
synapses_post=dict(zip(post_slice,synapses_post))
elif isinstance(value,str): # string code assignment
# For subgroups, origin of i and j are shifted to subgroup origin
if isinstance(pre,NeuronGroup):
pre_shift=pre_slice[0]
else:
pre_shift=0
if isinstance(post,NeuronGroup):
post_shift=post_slice[0]
else:
post_shift=0
code = re.sub(r'\b' + 'rand\(\)', 'rand(n)', value) # replacing rand()
code = re.sub(r'\b' + 'randn\(\)', 'randn(n)', code) # replacing randn()
_namespace = namespace(value, level=1)
_namespace.update({'j' : post_slice-post_shift,
'n' : len(post_slice),
'rand': np.random.rand,
'randn': np.random.randn})
# try: # Vectorise over all indexes: not faster!
# post,pre=np.meshgrid(post_slice-post_shift,pre_slice-pre_shift)
# pre=pre.flatten()
# post=post.flatten()
# _namespace['i']=array(pre,dtype=self.presynaptic.dtype)
# _namespace['j']=array(post,dtype=self.postsynaptic.dtype)
# _namespace['n']=len(post)
# result = eval(code, _namespace) # mask on synapses
# if result.dtype==float: # random number generation
# result=rand(len(post))<result
# indexes=result.nonzero()[0]
# presynaptic=pre[indexes]
# postsynaptic=post[indexes]
# dtype=self.synapses_pre[0].dtype
# synapses_pre={}
# nsynapses=0
# for i in pre_slice:
# n=sum(result[i*len(post_slice):(i+1)*len(post_slice)])
# synapses_pre[i]=array(nsynapses+np.arange(n),dtype=dtype)
# nsynapses+=n
# except MemoryError: # If not possible, vectorise over postsynaptic indexes
# log_info("synapses","Construction of synapses cannot be fully vectorised (too big)")
#del pre
#del post
#_namespace['i']=None
#_namespace['j']=post_slice-post_shift
#_namespace['n']=len(post_slice)
synapses_pre={}
nsynapses=0
presynaptic,postsynaptic=[],[]
for i in pre_slice:
_namespace['i']=i-pre_shift # maybe an array rather than a scalar?
result = eval(code, _namespace) # mask on synapses
if result.dtype==float: # random number generation
result=rand(len(post_slice))<result
indexes=result.nonzero()[0]
n=len(indexes)
synapses_pre[i]=np.array(nsynapses+np.arange(n),dtype=self.synapses_pre[0].dtype)
presynaptic.append(i*np.ones(n,dtype=int))
postsynaptic.append(post_slice[indexes])
nsynapses+=n
# Make sure the type is correct
presynaptic=np.array(np.hstack(presynaptic),dtype=self.presynaptic.dtype)
postsynaptic=np.array(np.hstack(postsynaptic),dtype=self.postsynaptic.dtype)
synapses_post=None
elif isinstance(value, np.ndarray):
raise NotImplementedError
nsynapses = np.array(value, dtype = int)
# Now create the synapses
self.create_synapses(presynaptic,postsynaptic,synapses_pre,synapses_post)
def create_synapses(self,presynaptic,postsynaptic,synapses_pre=None,synapses_post=None):
'''
Create new synapses.
* synapses_pre: a mapping from presynaptic neuron to synapse indexes
* synapses_post: same
* presynaptic: an array of presynaptic neuron indexes (synapse->pre)
* postsynaptic: same
If synapses_pre or synapses_post is not specified, it is calculated from
presynaptic or postsynaptic.
'''
# Resize dynamic arrays and push new values
newsynapses=len(presynaptic) # number of new synapses
nvars,nsynapses_all=self._S.shape
self._S.resize((nvars,nsynapses_all+newsynapses))
self.presynaptic.resize(nsynapses_all+newsynapses)
self.presynaptic[nsynapses_all:]=presynaptic
self.postsynaptic.resize(nsynapses_all+newsynapses)
self.postsynaptic[nsynapses_all:]=postsynaptic
for delay_pre in self._delay_pre:
delay_pre.resize(nsynapses_all+newsynapses)
self._delay_post.resize(nsynapses_all+newsynapses)
if synapses_pre is None:
synapses_pre=invert_array(presynaptic,dtype=self.synapses_post[0].dtype)
for i,synapses in synapses_pre.iteritems():
nsynapses=len(self.synapses_pre[i])
self.synapses_pre[i].resize(nsynapses+len(synapses))
self.synapses_pre[i][nsynapses:]=synapses+nsynapses_all # synapse indexes are shifted
if synapses_post is None:
synapses_post=invert_array(postsynaptic,dtype=self.synapses_post[0].dtype)
for j,synapses in synapses_post.iteritems():
nsynapses=len(self.synapses_post[j])
self.synapses_post[j].resize(nsynapses+len(synapses))
self.synapses_post[j][nsynapses:]=synapses+nsynapses_all
def __getattr__(self, name):
if name == 'var_index':
raise AttributeError
if not hasattr(self, 'var_index'):
raise AttributeError
if (name=='delay_pre') or (name=='delay'): # default: delay is presynaptic delay
if len(self._delay_pre)>1:
return [SynapticDelayVariable(delay_pre,self,name) for delay_pre in self._delay_pre]
else:
return SynapticDelayVariable(self._delay_pre[0],self,name)
elif name=='delay_post':
return SynapticDelayVariable(self._delay_post,self,name)
try:
x=self.state(name)
return SynapticVariable(x,self,name)
except KeyError:
return NeuronGroup.__getattr__(self,name)
def __setattr__(self, name, val):
if (name=='delay_pre') or (name=='delay'):
if len(self._delay_pre)==1:
SynapticDelayVariable(self._delay_pre[0],self,name)[:]=val
else:
raise NotImplementedError,"Cannot assign multiple delays at the same time"
elif name=='delay_post':
SynapticDelayVariable(self._delay_post,self,name)[:]=val
else: # copied from Group
origname = name
if len(name) and name[-1] == '_':
origname = name[:-1]
if not hasattr(self, 'var_index') or (name not in self.var_index and origname not in self.var_index):
object.__setattr__(self, name, val)
else:
if name in self.var_index:
x=self.state(name)
else:
x=self.state_(origname)
SynapticVariable(x,self,name).__setitem__(slice(None,None,None),val,level=2)
def update(self): # this is called at every timestep
'''
Updates the synaptic variables.
TODO:
* Deal with static variables
'''
if self._state_updater is not None:
self._state_updater(self)
for queue, _namespace, code in zip(self.queues, self.namespaces, self.codes):
synaptic_events = queue.peek()
if len(synaptic_events):
# Build the namespace - Here we don't consider static equations
_namespace['_synapses'] = synaptic_events
_namespace['t'] = self.clock._t
exec code in _namespace
queue.next()
def connect_one_to_one(self,pre=None,post=None):
'''
Connects each neuron in the ``pre'' group to each corresponding one
in the ``post'' group.
'''
if pre is None:
pre = self.source
if post is None:
post = self.target
pre, post = self.presynaptic_indexes(pre), self.postsynaptic_indexes(post)
if len(pre) != len(post):
raise TypeError,"Source and target groups do not have the same size"
for i,j in zip(pre,post):
self[i,j]=True
def connect_random(self,pre=None,post=None,sparseness=None):
'''
Creates random connections between pre and post neurons
(default: all neurons).
This is equivalent to::
S[pre,post]=sparseness
``pre=None''
The set of presynaptic neurons, defined as an integer, an array, a slice or a subgroup.
``post=None''
The set of presynaptic neurons, defined as an integer, an array, a slice or a subgroup.
``sparseness=None''
The probability of connection of a pair of pre/post-synaptic neurons.
'''
if pre is None:
pre=self.source
if post is None:
post=self.target
pre,post=self.presynaptic_indexes(pre),self.postsynaptic_indexes(post)
m=len(post)
synapses_pre={}
nsynapses=0
presynaptic,postsynaptic=[],[]
for i in pre: # vectorised over post neurons
k = binomial(m, sparseness, 1)[0] # number of postsynaptic neurons
synapses_pre[i]=nsynapses+np.arange(k)
presynaptic.append(i*np.ones(k,dtype=int))
# Not significantly faster to generate all random numbers in one pass
# N.B.: the sample method is implemented in Python and it is not in Scipy
postneurons = sample(xrange(m), k)
#postneurons.sort() # sorting is unnecessary
postsynaptic.append(post[postneurons])
nsynapses+=k
presynaptic=np.hstack(presynaptic)
postsynaptic=np.hstack(postsynaptic)
synapses_post=None # we ask for automatic calculation of (post->synapse)
# this is more or less given by unique
self.create_synapses(presynaptic,postsynaptic,synapses_pre,synapses_post)
def presynaptic_indexes(self,x):
'''
Returns the array of presynaptic neuron indexes corresponding to x,
which can be a integer, an array, a slice or a subgroup.
'''
return neuron_indexes(x,self.source)
def postsynaptic_indexes(self,x):
'''
Returns the array of postsynaptic neuron indexes corresponding to x,
which can be a integer, an array, a slice or a subgroup.
'''
return neuron_indexes(x,self.target)
def compress(self):
'''
* Checks that the object is not empty.
* Make the state array non-dynamical (important for the state updater).
* Updates namespaces of pre and post code.
'''
if hasattr(self, '_iscompressed') and self._iscompressed:
return
self._iscompressed = True
# Check that the object is not empty
if len(self)==0:
warnings.warn("Empty Synapses object")
self._S=self._S[:,:]
# Update namespaces of pre/post code
for _namespace in self.namespaces:
for var,i in self.var_index.iteritems(): # no static variables here
if isinstance(var, str):
_namespace[var]=self._S[i,:]
for var,i in self.source.var_index.iteritems():
if isinstance(var, str):
_namespace[var+'_pre']=self.source._S[i,:]
for var,i in self.target.var_index.iteritems():
if isinstance(var, str):
_namespace[var+'_post']=self.target._S[i,:]
_namespace[var]=self.target._S[i,:]
_namespace['_pre']=self.presynaptic
_namespace['_post']=self.postsynaptic
_namespace['np']=np
_namespace['binomial']=self._binomial
_namespace['rand']=rand
_namespace['randn']=randn
_namespace['zeros']=np.zeros
_namespace['sum']=sum
self._iscompressed=True
def synapse_index(self,i):
'''
Returns the synapse indexes correspond to i, which is a tuple.
If i is a tuple (m,n), m and n can be an integer, an array, a slice or a subgroup.
Searching synapse indexes for synapse (i,j) is implemented as follows.
If i or j is an integer or a slice, they are converted to a boolean test.
Then the following is executed:
1) get indexes of target synapses of presynaptic neuron(s) i
2) test whether postsynaptic neurons of these synapses correspond to j
3) return synapses that passed the test
or the symmetrical operations (depending on what is possible and faster).
Otherwise, the following is executed:
1) get indexes of target synapses of presynaptic neuron(s) i
2) get indexes of source synapses of postsynaptic neuron(s) j
3) calculate the intersection
This will generally be ok for vectorised searches, but not for searching
single elements (i,j). In this case, one might want to use
a dictionary (i,j)->synapse index (not implemented). This is fast
but 1) cannot be vectorised, 2) is very memory expensive.
'''
if not isinstance(i,tuple): # we assume it is directly a synapse index
return i
if len(i)==2:
i,j=i
# We use boolean tests if possible (faster)
if isinstance(i,slice) or isinstance(i,int):
test_i=slice_to_test(i)
else:
test_i=None
if isinstance(j,slice) or isinstance(j,int):
test_j=slice_to_test(j)
else:
test_j=None
i=neuron_indexes(i,self.source)
j=neuron_indexes(j,self.target)
synapsetype=self.synapses_pre[0].dtype
if (test_i is None) and (test_j is None): # no speed-up is possible
synapses_pre=np.array(np.hstack([self.synapses_pre[k] for k in i]),dtype=synapsetype)
synapses_post=np.array(np.hstack([self.synapses_post[k] for k in j]),dtype=synapsetype)
return np.intersect1d(synapses_pre, synapses_post,assume_unique=True)
elif ((len(i)<len(j)) and (test_j is not None)) or (test_i is None): # test synapses of presynaptic neurons
synapses_pre=np.array(np.hstack([self.synapses_pre[k] for k in i]),dtype=synapsetype)
return synapses_pre[test_j(self.postsynaptic[synapses_pre])]
else: # test synapses of postsynaptic neurons
synapses_post=np.array(np.hstack([self.synapses_post[k] for k in j]),dtype=synapsetype)
return synapses_post[test_i(self.presynaptic[synapses_post])]
elif len(i)==3: # 3rd coordinate is synapse number
if np.isscalar(i[0]) and np.isscalar(i[1]):
return self.synapse_index(i[:2])[i[2]]
else:
raise NotImplementedError,"The first two coordinates must be integers"
return i
def __repr__(self):
return 'Synapses object with '+ str(len(self))+ ' synapses'
def test_dynamicarray():
# Perform the test mentioned in the docstring of the DynamicArray class.
# TODO: This could be a doctest directly...
x = DynamicArray((2, 3), dtype=int)
x[:] = 1
x.resize((3, 3))
x[:] += 1
x.resize((3, 4))
x[:] += 1
x.resize((4, 4))
x[:] += 1
x.data[:] = x.data**2
# Do a resize that changes nothing
x.resize((4, 4))
# This is the expected result
y = array([[16, 16, 16, 4], [16, 16, 16, 4], [9, 9, 9, 4], [1, 1, 1, 1]])
assert (len(x) == len(y))
assert (len(x[0]) == len(y[0]))
assert (x.shape == (4, 4))
assert ((x == y).all())
# Do the same with use_numpy_resize=True
x = DynamicArray((2, 3), dtype=int, use_numpy_resize=True)
x[:] = 1
x.resize((3, 3))
x[:] += 1
x.resize((3, 4))
x[:] += 1
x.resize((4, 4))
x[:] += 1
x.data[:] = x.data**2
# Do a resize that changes nothing
x.resize((4, 4))
y = array([[16, 16, 16, 4], [16, 16, 16, 4], [9, 9, 9, 4], [1, 1, 1, 1]])
assert (len(x) == len(y))
assert (len(x[0]) == len(y[0]))
assert (x.shape == (4, 4))
assert ((x == y).all())
# Test shrinking
x = DynamicArray((2, 3), dtype=int)
x[:] = 1
x.shrink((1, 2))
# This should not do anything
x.shrink((2, 3))
y = array([[1, 1]])
assert (x.shape == y.shape)
assert ((x == y).all())
# Test DynamicArray1D
x = DynamicArray1D(2, dtype=int)
x[:] = 1
x.resize(3)
x[:] += 1
x.resize(4)
x.data[:] = x.data**2
# Expected result
y = array([4, 4, 1, 0])
assert (len(x) == len(y))
assert (x.shape == y.shape)
assert ((x == y).all())
# Test DynamicArray1D with use_numpy_resize=True
x = DynamicArray1D(2, dtype=int, use_numpy_resize=True)
x[:] = 1
x.resize(3)
x[:] += 1
x.resize(4)
x.data[:] = x.data**2
# Expected result
y = array([4, 4, 1, 0])
assert (len(x) == len(y))
assert (x.shape == y.shape)
assert ((x == y).all())
def __init__(self, source, target = None, model = None, pre = None, post = None,
max_delay = 0*ms,
level = 0,
clock = None,code_namespace=None,
unit_checking = True, method = None, freeze = False, implicit = False, order = 1): # model (state updater) related
target=target or source # default is target=source
# Check clocks. For the moment we enforce the same clocks for all objects
clock = clock or source.clock
if source.clock!=target.clock:
raise ValueError,"Source and target groups must have the same clock"
if pre is None:
pre_list=[]
elif isSequenceType(pre) and not isinstance(pre,str): # a list of pre codes
pre_list=pre
else:
pre_list=[pre]
pre_list=[flattened_docstring(pre) for pre in pre_list]
if post is not None:
post=flattened_docstring(post)
# Pre and postsynaptic indexes (synapse -> pre/post)
self.presynaptic=DynamicArray1D(0,dtype=smallest_inttype(len(source))) # this should depend on number of neurons
self.postsynaptic=DynamicArray1D(0,dtype=smallest_inttype(len(target))) # this should depend on number of neurons
if not isinstance(model,SynapticEquations):
model=SynapticEquations(model,level=level+1)
# Insert the lastupdate variable if necessary (if it is mentioned in pre/post, or if there is event-driven code)
expr=re.compile(r'\blastupdate\b')
if (len(model._eventdriven)>0) or \
any([expr.search(pre) for pre in pre_list]) or \
(post is not None and expr.search(post) is not None):
model+='\nlastupdate : second\n'
pre_list=[pre+'\nlastupdate=t\n' for pre in pre_list]
if post is not None:
post=post+'\nlastupdate=t\n'
# Identify pre and post variables in the model string
# They are identified by _pre and _post suffixes
# or no suffix for postsynaptic variables
ids=set()
for RHS in model._string.itervalues():
ids.update(get_identifiers(RHS))
pre_ids = [id[:-4] for id in ids if id[-4:]=='_pre']
post_ids = [id[:-5] for id in ids if id[-5:]=='_post']
post_vars = [var for var in source.var_index if isinstance(var,str)] # postsynaptic variables
post_ids2 = list(ids.intersection(set(post_vars))) # post variables without the _post suffix
# remember whether our equations refer to any variables in the pre- or
# postsynaptic group. This is important for the state-updater, e.g. the
# equations can no longer be solved as linear equations.
model.refers_others = (len(pre_ids) + len(post_ids) + len(post_ids2) > 0)
# Insert static equations for pre and post variables
S=self
for name in pre_ids:
model.add_eq(name+'_pre', 'S.source.'+name+'[S.presynaptic[:]]', source.unit(name),
global_namespace={'S':S})
for name in post_ids:
model.add_eq(name+'_post', 'S.target.'+name+'[S.postsynaptic[:]]', target.unit(name),
global_namespace={'S':S})
for name in post_ids2: # we have to change the name of the variable to avoid problems with equation processing
if name not in model._string: # check that it is not already defined
model.add_eq(name, 'S.target.state_(__'+name+')[S.postsynaptic[:]]', target.unit(name),
global_namespace={'S':S,'__'+name:name})
self.source=source
self.target=target
NeuronGroup.__init__(self, 0,model=model,clock=clock,level=level+1,unit_checking=unit_checking,method=method,freeze=freeze,implicit=implicit,order=order)
'''
At this point we have:
* a state matrix _S with all variables
* units, state dictionary with each value being a row of _S + the static equations
* subgroups of synapses
* link_var (i.e. we can link two synapses objects)
* __len__
* __setattr__: we can write S.w=array of values
* var_index is a dictionary from names to row index in _S
* num_states()
Things we have that we don't want:
* LS structure (but it will not be filled since the object does not spike)
* (from Group) __getattr_ needs to be rewritten
* a complete state updater, but we need to extract parameters and event-driven parts
* The state matrix is not dynamic
Things we may need to add:
* _pre and _post suffixes
'''
self._iscompressed=False # True if compress() has already been called
# Look for event-driven code in the differential equations
if use_sympy:
eqs=self._eqs # an Equations object
#vars=eqs._diffeq_names_nonzero # Dynamic variables
vars=eqs._eventdriven.keys()
var_set=set(vars)
for var,RHS in eqs._eventdriven.iteritems():
ids=get_identifiers(RHS)
if len(set(list(ids)+[var]).intersection(var_set))==1:
# no external dynamic variable
# Now we test if it is a linear equation
_namespace=dict.fromkeys(ids,1.) # there is a possibility of problems here (division by zero)
# plus units problems? (maybe not since these are identifiers too)
# another option is to use random numbers, but that doesn't solve all problems
_namespace[var]=AffineFunction()
try:
eval(RHS,eqs._namespace[var],_namespace)
except: # not linear
raise TypeError,"Cannot turn equation for "+var+" into event-driven code"
z=symbolic_eval(RHS)
symbol_var=sympy.Symbol(var)
symbol_t=sympy.Symbol('t')-sympy.Symbol('lastupdate')
b=z.subs(symbol_var,0)
a=sympy.simplify(z.subs(symbol_var,1)-b)
if a==0:
expr=symbol_var+b*symbol_t
else:
expr=-b/a+sympy.exp(a*symbol_t)*(symbol_var+b/a)
expr=var+'='+str(expr)
# Replace pre and post code
# N.B.: the differential equations are kept, we will probably want to remove them!
pre_list=[expr+'\n'+pre for pre in pre_list]
if post is not None:
post=expr+'\n'+post
else:
raise TypeError,"Cannot turn equation for "+var+" into event-driven code"
elif len(self._eqs._eventdriven)>0:
raise TypeError,"The Sympy package must be installed to produce event-driven code"
if len(self._eqs._diffeq_names_nonzero)==0:
self._state_updater=None
# Set last spike to -infinity
if 'lastupdate' in self.var_index:
self.lastupdate=-1e6
# _S is turned to a dynamic array - OK this is probably not good! we may lose references at this point
S=self._S
self._S=DynamicArray(S.shape)
self._S[:]=S
# Pre and postsynaptic delays (synapse -> delay_pre/delay_post)
self._delay_pre=[DynamicArray1D(len(self),dtype=np.int16) for _ in pre_list] # max 32767 delays
self._delay_post=DynamicArray1D(len(self),dtype=np.int16) # Actually only useful if there is a post code!
# Pre and postsynaptic synapses (i->synapse indexes)
max_synapses=2147483647 # it could be explicitly reduced by a keyword
# We use a loop instead of *, otherwise only 1 dynamic array is created
self.synapses_pre=[DynamicArray1D(0,dtype=smallest_inttype(max_synapses)) for _ in range(len(self.source))]
self.synapses_post=[DynamicArray1D(0,dtype=smallest_inttype(max_synapses)) for _ in range(len(self.target))]
# Code generation
self._binomial = lambda n,p:np.random.binomial(np.array(n,dtype=int),p)
self.contained_objects = []
self.codes=[]
self.namespaces=[]
self.queues=[]
for i,pre in enumerate(pre_list):
code,_namespace=self.generate_code(pre,level+1,code_namespace=code_namespace)
self.codes.append(code)
self.namespaces.append(_namespace)
self.queues.append(SpikeQueue(self.source, self.synapses_pre, self._delay_pre[i], max_delay = max_delay))
if post is not None:
code,_namespace=self.generate_code(post,level+1,direct=True,code_namespace=code_namespace)
self.codes.append(code)
self.namespaces.append(_namespace)
self.queues.append(SpikeQueue(self.target, self.synapses_post, self._delay_post, max_delay = max_delay))
self.queues_namespaces_codes = zip(self.queues,
self.namespaces,
self.codes)
self.contained_objects+=self.queues
def test_dynamicarray():
# Perform the test mentioned in the docstring of the DynamicArray class.
# TODO: This could be a doctest directly...
x = DynamicArray((2, 3), dtype=int)
x[:] = 1
x.resize((3, 3))
x[:] += 1
x.resize((3, 4))
x[:] += 1
x.resize((4, 4))
x[:] += 1
x.data[:] = x.data**2
# Do a resize that changes nothing
x.resize((4, 4))
# This is the expected result
y = array([[16, 16, 16, 4],
[16, 16, 16, 4],
[ 9, 9, 9, 4],
[ 1, 1, 1, 1]])
assert(len(x) == len(y))
assert(len(x[0]) == len(y[0]))
assert(x.shape == (4, 4))
assert((x == y).all())
# Do the same with use_numpy_resize=True
x = DynamicArray((2, 3), dtype=int, use_numpy_resize=True)
x[:] = 1
x.resize((3, 3))
x[:] += 1
x.resize((3, 4))
x[:] += 1
x.resize((4, 4))
x[:] += 1
x.data[:] = x.data**2
# Do a resize that changes nothing
x.resize((4, 4))
y = array([[16, 16, 16, 4],
[16, 16, 16, 4],
[ 9, 9, 9, 4],
[ 1, 1, 1, 1]])
assert(len(x) == len(y))
assert(len(x[0]) == len(y[0]))
assert(x.shape == (4, 4))
assert((x == y).all())
# Test shrinking
x = DynamicArray((2, 3), dtype=int)
x[:] = 1
x.shrink((1, 2))
# This should not do anything
x.shrink((2, 3))
y = array([[1, 1]])
assert(x.shape == y.shape)
assert((x == y).all())
# Test DynamicArray1D
x = DynamicArray1D(2, dtype=int)
x[:] = 1
x.resize(3)
x[:] += 1
x.resize(4)
x.data[:] = x.data**2
# Expected result
y = array([4, 4, 1, 0])
assert(len(x) == len(y))
assert(x.shape == y.shape)
assert((x == y).all())
# Test DynamicArray1D with use_numpy_resize=True
x = DynamicArray1D(2, dtype=int, use_numpy_resize=True)
x[:] = 1
x.resize(3)
x[:] += 1
x.resize(4)
x.data[:] = x.data**2
# Expected result
y = array([4, 4, 1, 0])
assert(len(x) == len(y))
assert(x.shape == y.shape)
assert((x == y).all())