Main code structure

Overview

Brian features can be broadly categorised into construction of the network, and running the network.

Constructing the network

The following objects need to be specified by the user explicitly or implicitly:

  • NeuronGroup
  • Connection
  • Monitors
  • Network

After that, the network needs to be prepared. Preparation of the network involves initialising objects’ data structures appropriately, in particular compressing the Connection matrices. Connection matrices are initially stored as instances of a ConstructionMatrix class (sparse, dense, etc.), and then later compressed into an instance of a ConnectionMatrix class. Two levels are necessary, because at construction time, all matrices have to be editable, whereas at runtime, for efficiency reasons, some matrix types are read-only or partially read-only. Data structures appropriate to the construction of a matrix, particularly sparse matrices, are not the most efficient for runtime access.

Constructing the NeuronGroup object is a rather complicated operation, involving the construction of many subsididary objects. The most complicated aspect is the creation, manipulation and analysis of an Equations object.

Running the network

The network is run by repeatedly evaluating the ‘update schedule’ and updating the clock or clocks. The ‘update schedule’ is user specifiable, but usually consists of the following sequence of operations (interspersed with optional user network operation calls):

  • Update state variables of NeuronGroup
  • Call thresholding function
  • Push spikes into SpikeContainer
  • Propagate spikes (possibly with delays) via Connection
  • Update state variables of Synapses (possibly includes updating the state of targeted NeuronGroup objects
  • Call reset function on neurons which have spiked

Details of network construction

Construction of NeuronGroup

The NeuronGroup object is responsible for storing the state variables of each of its neurons, for updating them each time step, generating spikes via a thresholding mechanism, storing spikes so that they can be accessed with a delay, and resetting state variables after spiking. State variable update is done by a StateUpdater class defined in brian/stateupdater.py. Thresholding is done by a Threshold class defined in brian/threshold.py and resetting is done by a Reset class defined in brian/reset.py. The __init__ method of NeuronGroup takes these objects as arguments, but it also has various additional keywords which can be used more intuitively. In this case, the appropriate object is selected automatically. For example, if you specify reset=0*mV in the keyword arguments, Brian generates a Reset(0*mV) object. The NeuronGroup.__init__() method code is rather complicated and deals with many special cases.

The most complicated aspect of this is the definition of the state variables and the update procedure. Typically, the user simply gives a list of differential equations, and Brian attempts to automatically extract the appropriate state variable definitions, and creates a differential equation solver appropriate to them (it needs some help in this at the moment, e.g. specifying the order or type of the solver). The main work in this is done by the magic_state_updater() function, which uses the Equations object (see next section).

Once the state variables are defined, various internal objects are created. The state variables are stored in the _S attribute of a NeuronGroup. This is an MxN matrix where M is the number of variables and N is the number of neurons.

The other major data structure generated is the LS attribute (last spikes). This is a SpikeContainer instance, a circular array used to contain spikes. See brian/utils/circular.py.

Finally note that the construction of many of these objects requires a Clock object, which can either be specified explicitly, or is guessed by the guess_clock() function which searches for clocks using the magic module (see below). EventClock objects are excluded from this guessing.

The magic_state_updater() function and the Equations object

This function returns an appropriate StateUpdater object and a list of the dynamic variables of an Equations object. It uses methods of the Equations object to do this (such as Equations.is_linear()).

The Equations object can be constructed in various ways. It can be constructed from a multi-line string or by adding (concatenating) other Equations objects. Construction by multi-line string is done by pattern matching. The four forms are:

  1. dx/dt = f : unit (differential equation)
  2. x = f : unit (equation)
  3. x = y (alias)
  4. x : unit (parameter)

Differential equations and parameters are dynamic variables, equations and aliases are just computed and substituted when necessary. The f patterns in the forms above are stored for differential equations and parameters. For the solution of nonlinear equations, these f patterns are executed as Python code in the evaluation of the state update. For example, the equations dV/dt = -V*V/(10*ms) : 1 and dW/dt = cos(W)/(20*ms) : 1 are numerically evaluated with an Euler method as the following code (generated from the list of dynamic variables and their defining strings):

V, W = P._S
V__tmp, W__tmp = P._dS
V__tmp[:] = -V*V/(10*ms)
W__tmp[:] = cos(W)/(20*ms)
P._S += dt*P._dS

This code generation is done by the Equations.forward_euler() family of methods.

In the case where the equations are linear, they are solved by a matrix exponential using the code in get_linear_equations() defined in brian/stateupdater.py.

Finally, note that equations strings can contain references to names of objects that are defined in the namespace of the string, and the Equations object can pick these out. It does this by inspecting the call stack, extracting the namespace for the appropriate level (which has to be kept track of), and plucking out the appropriate name. The level=... keywords you see dotted around Brian’s code are there to keep track of these levels for this reason.

Construction of Connection

Connection objects provide methods for storing weight matrices and propagating spikes. Spike propagation is done via the Connection.do_propagate() and Connection.propagate() methods. Weight matrices are stored in the W attribute. Initially, weight matrices are ConstructionMatrix objects and are converted by the Connection.compress() method, via the matrices’ connection_matrix() methods to ConnectionMatrix objects. The idea is to have two data structures, one appropriate to the construction of a matrix, supporting adding and removing new synapses, and one appropriate to runtime behaviour, focussing on fast row access above all else. There are three matrix structures, ‘dense’, ‘sparse’ and ‘dynamic’ (and ‘computed’ may be added later). The ‘dense’ matrix is just a full 2D array, and the matrix objects just reproduce the functionality of numpy arrays. The ‘sparse’ and ‘dynamic’ structures are sparse matrices. The first doesn’t allow you to add or remove elements at runtime and is very optimised, the second does allow you to and is less optimised. Both are more optimised than scipy’s sparse matrices, which are used as the basis for the construction phase.

Connection objects can handle homogeneous delays (all synapses with the same delay) by pulling spikes from NeuronGroup’s LS object with a delay. Heterogeneous delays (each synapse with a different delay) are done by the DelayConnection object, which stores a _delayvec attribute alongside the W attribute. The delay matrix is of the same type as the weight matrix and in the case of sparse matrices must have nonzero elements at the same places. The Connection object automatically turns itself into a DelayConnection object if heterogeneous delays are requested, so that the user doesn’t even need to know of the existence of DelayConnection.

The Connection object also provides methods for initialising the weight matrices either fully, randomly, etc. (See the user docs.)

Construction of monitors

The SpikeMonitor class of monitors derive from Connection. Rather than propagating spikes to another group, they store them in a list. The work is done in the SpikeMonitor.propagate() method.

The StateMonitor class of monitors derive from NetworkOperation. Network operations are called once every time step and execute arbitrary Python code. The StateMonitor class of monitors record state variables each time step to a list.

Construction of Network

When the user calls the function run(), a MagicNetwork object is created, and the Network.run() method is called. MagicNetwork gathers, using the magic module, a list of all appropriate objects and runs them together. Alternatively, the user can specify their own list of objects using a Network object. Each time an object is added to a Network either via the initialiser or the Network.add() method, it checks to see if it has an attribute contained_objects, and if so it adds all the objects in that to the network too. This allows, for example, the STDP object to contained NeuronGroup and Connection objects which the user doesn’t see, but are used to implement the STDP functionality.

The Network.run() method calls the Connection.compress() method on every Connection object to convert construction matrices to connection matrices. It also builds an update schedule (see below).

The magic module

The magic module is used for tracking instances of objects. A class that derives from the magic.InstanceTracker class can be tracked in this way, including NeuronGroup, Connection, NetworkOperation and Clock. The find_instances() function can be used to search for instances. Note that find_instances() will only return instances which were instantiated in the same execution frame as the find_instances() calling frame, or (if the level keyword is used) one of the frames higher up in the call stack. The idea is that you may have modular code with objects defined in different places, but that you don’t want to use all objects that exist at all in the network. This system causes a bit of trouble, but seems unavoidable. See the user manual section Projects with multiple files or functions for details on getting around this.

Details of network running

Update schedules

An update schedule gives the sequence of operations to be carried out each time step of the simulation. Typically this is: state update and threshold; propagation; reset, although an option is available for switching propagation and reset around. Network operations can be weaved in anywhere amongst these basic steps. See the reference documentation for the Network object for more details.

Simulation proceeds by choosing the clock with the lowest current time, selecting all objects which have that clock as their clock, and performing the update schedule on those objects, before applying the Clock.tick() method to increment the clock time by dt.

Network operations

A NetworkOperation object is called as if it were a function, i.e. the __call__() method is called with no arguments. The network_operation() decorator exists to convert a function into a suitable NetworkOperation object. This technique is used for the internal functioning of many of Brian’s features (such as StateMonitor).

NeuronGroup update

The NeuronGroup.update() method does the following three things. First of all it calls the StateUpdater to update the state variables. Then it calls its Threshold object if one exists to extract the indices of the spiking neurons. Finally it pushes these into the LS attribute for extraction by any Connection objects.

NeuronGroup reset

The Reset.__call__() method pulls spike from the NeuronGroup’s LS attribute and then resets the state variables for those.

Spike propagation

The Connection.do_propagate() method does two things, it gets the spike indices to propagate (with homogeneous delays if chosen) from the LS attribute of the NeuronGroup and then passes these to its Connection.propagate() method. This method extracts a list of connection matrix rows using the ConnectionMatrix.get_rows() method. This method returns a list of ConnectionVector instances. There are two types of ConnectionVector, dense and sparse. Dense ones are simply numpy arrays, sparse ones consist of two numpy arrays, an array of values and an array of corresponding column indices. The SparseConnectionVector class has some methods which make this distinction seamless to the user in most instances, although developers need to be aware of it. Finally, the Connection.propagate() method goes through this list applying the row vectors one by one. The pure Python version of this is straightforward, but there is also a C++ accelerated version which uses the scipy Weave package if the user has a suitable compiler on their system. This version is much more efficient, but the code is rather dense and difficult to understand.