# Variables and indices¶

## Introduction¶

To be able to generate the proper code out of abstract code statements, the code generation process has to have access to information about the variables (their type, size, etc.) as well as to the indices that should be used for indexing arrays (e.g. a state variable of a NeuronGroup will be indexed differently in the NeuronGroup state updater and in synaptic propagation code). Most of this information is stored in the variables attribute of a VariableOwner (this includes NeuronGroup, Synapses, PoissonGroup and everything else that has state variables). The variables attribute can be accessed as a (read-only) dictionary, mapping variable names to Variable objects storing the information about the respective variable. However, it is not a simple dictionary but an instance of the Variables class. Let’s have a look at its content for a simple example:

 >>> tau = 10*ms
>>> G = NeuronGroup(10, 'dv/dt = -v / tau : volt')
>>> for name, var in G.variables.items():
...     print('%r : %s' % (name, var))
...
'_spikespace' : <ArrayVariable(unit=Unit(1),  dtype=<type 'numpy.int32'>, scalar=False, constant=False, read_only=False)>
'i' : <ArrayVariable(unit=Unit(1),  dtype=<type 'numpy.int32'>, scalar=False, constant=True, read_only=True)>
'N' : <Constant(unit=Unit(1),  dtype=<type 'numpy.int64'>, scalar=True, constant=True, read_only=True)>
't' : <ArrayVariable(unit=second,  dtype=<type 'numpy.float64'>, scalar=True, constant=False, read_only=True)>
'v' : <ArrayVariable(unit=volt,  dtype=<type 'numpy.float64'>, scalar=False, constant=False, read_only=False)>
'dt' : <ArrayVariable(unit=second,  dtype=<type 'float'>, scalar=True, constant=True, read_only=True)>


The state variable v we specified for the NeuronGroup is represented as an ArrayVariable, all the other variables were added automatically. By convention, internal names for variables that should not be directly accessed by the user start with an underscore, in the above example the only variable of this kind is '_spikespace', the internal datastructure used to store the spikes that occured in the current time step. There’s another array i, the neuronal indices (simply an array of integers from 0 to 9), that is used for string expressions involving neuronal indices. The constant N represents the total number of neurons. At the first sight it might be surprising that t, the current time of the clock and dt, its timestep, are ArrayVariable objects as well. This is because those values can change during a run (for t) or between runs (for dt), and storing them as arrays with a single value (note the scalar=True) is the easiest way to share this value – all code accessing it only needs a reference to the array and can access its only element.

The information stored in the Variable objects is used to do various checks on the level of the abstract code, i.e. before any programming language code is generated. Here are some examples of errors that are caught this way:

>>> G.v = 3*ms  # G.variables['v'].unit is volt
Traceback (most recent call last):
...
DimensionMismatchError: v should be set with a value with units volt, but got 3. ms (unit is second).
>>> G.N = 5  # G.variables['N'] is read-only
Traceback (most recent call last):
...
>>> G2 = NeuronGroup(10, 'dv/dt = -v / tau : volt', threshold='v')  #G2.variables['v'].is_bool is False
Traceback (most recent call last):
...
TypeError: Threshold condition "v" is not a boolean expression


## Creating variables¶

Each variable that should be accessible as a state variable and/or should be available for use in abstract code has to be created as a Variable. For this, first a Variables container with a reference to the group has to be created, individual variables can then be added using the various add_... methods:

self.variables = Variables(self)
self.variables.create_clock_variables(self.clock)


As an additional argument, array variables can be specified with a specific index (see Indices below).

## References¶

For each variable, only one Variable object exists even if it is used in different contexts. Let’s consider the following example:

G = NeuronGroup(5, 'dv/dt = -v / tau : volt')
subG = G[2:]
S = Synapses(G, G, on_pre='v+=1*mV')
S.connect()


All allow an access to the state variable v (note the different shapes, these arise from the different indices used, see below):

>>> G.v
<neurongroup.v: array([ 0.,  0.,  0.,  0.,  0.]) * volt>
>>> subG.v
<neurongroup_subgroup.v: array([ 0.,  0.,  0.]) * volt>
>>> S.v
<synapses.v: array([ 0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,
0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.,  0.]) * volt>


In all of these cases, the Variables object stores references to the same ArrayVariable object:

>>> id(G.variables['v'])
108610960
>>> id(subG.variables['v'])
108610960
>>> id(S.variables['v'])
108610960


Such a reference can be added using Variables.add_reference, note that the name used for the reference is not necessarily the same as in the original group, e.g. in the above example S.variables also stores references to v under the names v_pre and v_post.

## Indices¶

In subgroups and especially in synapses, the transformation of abstract code into executable code is not straightforward because it can involve variables from different contexts. Here is a simple example:

G = NeuronGroup(5, 'dv/dt = -v / tau : volt')
S = Synapses(G, G, 'w : volt', on_pre='v+=w')


The seemingly trivial operation v+=w involves the variable v of the NeuronGroup and the variable w of the Synapses object which have to be indexed in the appropriate way. Since this statement is executed in the context of S, the variable indices stored there are relevant:

>>> S.variables.indices['w']
'_idx'
>>> S.variables.indices['v']
'_postsynaptic_idx'


The index _idx has a special meaning and always refers to the “natural” index for a group (e.g. all neurons for a NeuronGroup, all synapses for a Synapses object, etc.). All other indices have to refer to existing arrays:

>>> S.variables['_postsynaptic_idx']
<DynamicArrayVariable(unit=Unit(1),  dtype=<type 'numpy.int32'>, scalar=False, constant=False, is_bool=False, read_only=False)>


In this case, _postsynaptic_idx refers to a dynamic array that stores the postsynaptic targets for each synapse (since it is an array itself, it also has an index. It is defined for each synapse so its index is _idx – in fact there is currently no support for an additional level of indirection in Brian: a variable representing an index has to have _idx as its own index). Using this index information, the following C++ code (slightly simplified) is generated:

for(int _spiking_synapse_idx=0;
_spiking_synapse_idx<_num_spiking_synapses;
_spiking_synapse_idx++)
{
const int _idx = _spiking_synapses[_spiking_synapse_idx];
const int _postsynaptic_idx = _ptr_array_synapses__synaptic_post[_idx];
const double w = _ptr_array_synapses_w[_idx];
double v = _ptr_array_neurongroup_v[_postsynaptic_idx];
v += w;
_ptr_array_neurongroup_v[_postsynaptic_idx] = v;
}


In this case, the “natural” index _idx iterates over all the synapses that received a spike (this is defined in the template) and _postsynaptic_idx refers to the postsynaptic targets for these synapses. The variables w and v are then pulled out of their respective arrays with these indices so that the statement v += w; does the right thing.

## Getting and setting state variables¶

When a state variable is accessed (e.g. using G.v), the group does not return a reference to the underlying array itself but instead to a VariableView object. This is because a state variable can be accessed in different contexts and indexing it with a number/array (e.g. obj.v[0]) or a string (e.g. obj.v['i>3']) can refer to different values in the underlying array depending on whether the object is the NeuronGroup, a Subgroup or a Synapses object.

The __setitem__ and __getitem__ methods in VariableView delegate to VariableView.set_item and VariableView.get_item respectively (which can also be called directly under special circumstances). They analyze the arguments (is the index a number, a slice or a string? Is the target value an array or a string expression?) and delegate the actual retrieval/setting of the values to a specific method:

• Getting with a numerical (or slice) index (e.g. G.v[0]): VariableView.get_with_index_array
• Getting with a string index (e.g. G.v['i>3']): VariableView.get_with_expression
• Setting with a numerical (or slice) index and a numerical target value (e.g. G.v[5:] = -70*mV): VariableView.set_with_index_array
• Setting with a numerical (or slice) index and a string expression value (e.g. G.v[5:] = (-70+i)*mV): VariableView.set_with_expression
• Setting with a string index and a string expression value (e.g. G.v['i>5'] = (-70+i)*mV): VariableView.set_with_expression_conditional

These methods are annotated with the device_override decorator and can therefore be implemented in a different way in certain devices. The standalone device, for example, overrides the all the getting functions and the setting with index arrays. Note that for standalone devices, the “setter” methods do not actually set the values but only note them down for later code generation.

The variables stored in the variables attribute of a VariableOwner can be used everywhere (e.g. in the state updater, in the threshold, the reset, etc.). Objects that depend on these variables, e.g. the Thresholder of a NeuronGroup add additional variables, in particular AuxiliaryVariables that are automatically added to the abstract code: a threshold condition v > 1 is converted into the statement _cond = v > 1; to specify the meaning of the variable _cond for the code generation stage (in particular, C++ code generation needs to know the data type) an AuxiliaryVariable object is created.
In some rare cases, a specific variable_indices dictionary is provided that overrides the indices for variables stored in the variables attribute. This is necessary for synapse creation because the meaning of the variables changes in this context: an expression v>0 does not refer to the v variable of all the connected postsynaptic variables, as it does under other circumstances in the context of a Synapses object, but to the v variable of all possible targets.