# 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:

`dx/dt = f : unit`

(differential equation)`x = f : unit`

(equation)`x = y`

(alias)`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.