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GraphicalModels :: directedEdgesMatrix

directedEdgesMatrix -- the matrix corresponding to the directed edges of a mixed graph

Synopsis

Usage:
L = directedEdgesMatrix(R,G)
Inputs:
- R, a ring, which should be a gaussianRing
- G, an object of class MixedGraph, mixed graph with directed and bidirected edges
Outputs:
- L, a matrix, the n x n matrix of symbols where we have l_(i,j) if there is a directed edge i-->j, and 0 otherwise.

Description

Note that this matrix is NOT symmetric in the symbols.

i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}})

o1 = MixedGraph{Bigraph => Bigraph{a => set {d}}   }
                                   d => set {a}
                Digraph => Digraph{b => set {c, d}}
                                   c => set {d}
                                   d => set {}
                Graph => Graph{}

o1 : MixedGraph

i2 : R = gaussianRing G

o2 = R

o2 : PolynomialRing

i3 : S = directedEdgesMatrix(R,G)

o3 = | 0 0 0       0       |
     | 0 0 l_(b,c) l_(b,d) |
     | 0 0 0       l_(c,d) |
     | 0 0 0       0       |

             4       4
o3 : Matrix R  <--- R

See also

gaussianRing -- ring of gaussian correlations on n random variables
gaussianParametrization -- the parametrization of the covariance matrix in terms of treks
covarianceMatrix -- the covariance matrix of a gaussian graphical model
bidirectedEdgesMatrix -- the matrix corresponding to the bidirected edges of a mixed graph

Ways to use `directedEdgesMatrix` :

directedEdgesMatrix(Ring,MixedGraph)