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GraphicalModels :: bidirectedEdgesMatrix

bidirectedEdgesMatrix -- the matrix corresponding to the bidirected edges of a mixed graph

Synopsis

Description

This method returns the n × n covariance matrix of the noise variables in the Gaussian graphical model. The diagonal in this matrix consists of the indeterminates p(i,i). Each off-diagonal entry is zero unless there is a bidirected edge between i and j in which case the corresponding entry in the matrix is the indeterminate p(i,j). The documentation of gaussianRing further describes the indeterminates p(i,j).

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 : compactMatrixForm =false;
i4 : bidirectedEdgesMatrix R

o4 = | p       0     0   p    |
     |  a,a               a,d |
     |                        |
     |   0   p       0     0  |
     |        b,b             |
     |                        |
     |   0     0   p       0  |
     |              c,c       |
     |                        |
     | p       0     0   p    |
     |  a,d               d,d |

             4       4
o4 : Matrix R  <--- R

See also

Ways to use bidirectedEdgesMatrix :

  • bidirectedEdgesMatrix(Ring)