CSA

This module uses connection-set algebra to describe connectivity between two entities with a scalar (Double) value. The library build on the concept of M. Djurfeldt's Connection-Set Algebar [1]. The connection expressions can be compiled to a dependently typed AdjacencyMatrix from the Numeric.LinearAlgebra.Static package. Such a matrix can be used and exported as a regular n-dimensional vector.

Usage:

>>> toAdjacencyMatrix None :: L 2 2
(matrix
 [ 0.0, 0.0
 , 0.0, 0.0 ] :: L 2 2)

>>> toAdjacencyMatrix $ Minus (AllToAll 2) (OneToOne 1) :: L 2 2
(matrix
 [ 1.0, 2.0
 , 2.0, 1.0 ] :: L 2 2)

1: Mikael Djurfeldt. The Connection-set Algebra: a formalism for the representation of connectivity structure in neuronal network models, implementations in Python and C++, and their use in simulators, BMC Neuroscience, 2011. https://doi.org/10.1186/1471-2202-12-S1-P80

Documentation

type AdjacencyMatrix = L

An adjacency matrix describing connections in a directed graph

data Expr

An expression algebra tree (AST) that describes connections between two elements

Constructors

None

An empty connection (only 0s)

AllToAll ℝ

Full connectivity with the given value

OneToOne ℝ

One-to-one (diagonally) connectivity

Mask (ℝ -> ℝ -> ℝ)

A masked connectivity given by a function

Plus Expr Expr

Addition of two connectivity expressions

Minus Expr Expr

Subtraction of two connectivity expressions

toAdjacencyMatrix

Arguments

:: (KnownNat m, KnownNat n)

=> Expr

The expression to turn into a AdjacencyMatrix

-> AdjacencyMatrix m n

The resulting adjacency matrix

Converts an expression to an adjacency matrix by unrolling the expression tree from left to right