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GraphicalModels :: gaussianRing(Bigraph)

gaussianRing(Bigraph) -- ring of Gaussian correlations of a graphical model coming from a bigraph

Synopsis

Description

A gaussianRing of a bidirected graph is built as a gaussianRing of a mixed graph with only bidirected edges, see gaussianRing(MixedGraph).

i1 : G = bigraph {{a,{b,c}}, {b,{c,d}}, {c,{}}, {d,{}}};
i2 : R = gaussianRing G;
i3 : gens R

o3 = {p   , p   , p   , p   , p   , p   , p   , p   , s   , s   , s   , s   ,
       a,a   b,b   c,c   d,d   a,c   a,b   b,c   b,d   a,a   a,b   a,c   a,d 
     ------------------------------------------------------------------------
     s   , s   , s   , s   , s   , s   }
      b,b   b,c   b,d   c,c   c,d   d,d

o3 : List
i4 : covarianceMatrix R

o4 = | s_(a,a) s_(a,b) s_(a,c) s_(a,d) |
     | s_(a,b) s_(b,b) s_(b,c) s_(b,d) |
     | s_(a,c) s_(b,c) s_(c,c) s_(c,d) |
     | s_(a,d) s_(b,d) s_(c,d) s_(d,d) |

             4       4
o4 : Matrix R  <--- R
i5 : directedEdgesMatrix R

o5 = 0

             4       4
o5 : Matrix R  <--- R
i6 : bidirectedEdgesMatrix R

o6 = | p_(a,a) p_(a,b) p_(a,c) 0       |
     | p_(a,b) p_(b,b) p_(b,c) p_(b,d) |
     | p_(a,c) p_(b,c) p_(c,c) 0       |
     | 0       p_(b,d) 0       p_(d,d) |

             4       4
o6 : Matrix R  <--- R

See also