This method returns the n × n matrix of direct causal effect indeterminates. This matrix has the parameter l(i,j) in the (i,j) position if there is a directed edge i →j, and 0 otherwise. Note that this matrix is not symmetric. The documentation of gaussianRing further describes the indeterminates l(i,j).
i1 : G = mixedGraph(digraph {{b,{c,d}},{c,{d}}},bigraph {{a,d}}) o1 = MixedGraph{Bigraph => Bigraph{a => {d}} } d => {a} Digraph => Digraph{b => {c, d}} c => {d} d => {} Graph => Graph{} o1 : MixedGraph |
i2 : R = gaussianRing G o2 = R o2 : PolynomialRing |
i3 : compactMatrixForm =false; |
i4 : directedEdgesMatrix R o4 = | 0 0 0 0 | | | | 0 0 l l | | b,c b,d | | | | 0 0 0 l | | c,d | | | | 0 0 0 0 | 4 4 o4 : Matrix R <--- R |
To obtain the directed edges matrix of a digraph, it should first be embedded into a mixed graph as follows.
i5 : D = digraph{{a,b},{c,d}} o5 = Digraph{a => {b}} b => {} c => {d} d => {} o5 : Digraph |
i6 : Dembedded = mixedGraph(D, bigraph{}) o6 = MixedGraph{Bigraph => Bigraph{} } Digraph => Digraph{a => {b}} b => {} c => {d} d => {} Graph => Graph{} o6 : MixedGraph |
i7 : directedEdgesMatrix gaussianRing Dembedded o7 = | 0 0 0 0 | | | | 0 0 l l | | b,c b,d | | | | 0 0 0 l | | c,d | | | | 0 0 0 0 | 4 4 o7 : Matrix R <--- R |