# Connection matricesΒΆ

A Connection object has an attribute W which is its connection matrix.

Brian’s system for connection matrices can be slightly confusing. The way it works is roughly as follows. There are two types of connection matrix data structures, ConstructionMatrix and ConnectionMatrix. The construction matrix types are used for building connectivity, and are optimised for insertion and deletion of elements, but access is slow. The connection matrix types are used when the simulation is running, and are optimised for fast access, but not for adding/removing or modifying elements. When a Connection object is created, it is given a construction matrix data type, and when the network is run, this matrix is converted to its corresponding connection matrix type. As well as this construction/connection matrix type distinction, there is also the distinction between dense/sparse/dynamic matrices, each of which have their own construction and connection versions.

The dense matrix structure is very simple, both the construction and connection types are basically just 2D numpy arrays.

The sparse and dynamic matrix structures are very different for construction and connection. Both the sparse and dynamic construction matrices are essentially just the scipy.lil_matrix sparse matrix type, however we add some slight improvements to scipy’s matrix data type to make it more efficient for our case.

The sparse and dynamic connection matrix structures are documented in more detail in the reference pages for SparseConnectionMatrix and DynamicConnectionMatrix.

For customised run-time modifications to sparse and dense connection matrices you have two options. You can modify the data structures directly using the information in the reference pages linked to in the paragraph above, or you can use the methods defined in the ConnectionMatrix class, which work for dense, sparse and dynamic matrix structures, and do not depend on implementation specific details. These methods provide element, row and column access. The row and column access methods use either DenseConnectionVector or SparseConnectionVector objects. The dense connection vector is just a 1D numpy array of length the size of the row/column. The sparse connection vector is slightly more complicated (but not much), see its documentation for details. The idea is that in most cases, both dense and sparse connection vectors can be operated on without having to know how they work, so for example if v is a ConnectionVector then 2*v is of the same type. So for a ConnectionMatrix W, this should work, whatever the structure of W:

```W.set_row(i, 2*W.get_row(i))
```

Or equivalently:

```W[i,:] = 2*W[i,:]
```

The syntax W[i,:], W[:,i] and W[i,j] is supported for integers i and j for (respectively) row, column and element access.

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