Add bigraph conversion and pretty printing for debugging

Co-authored-by: "Shashi Gowda" <gowda@mit.edu>
Co-authored-by: "Yingbo Ma" <mayingbo5@gmail.com>

Author: YingboMa

src/systems/diffeqs/index_reduction.jl

@@ -12,3 +12,52 @@ function sys2bigraph(sys)
         push!(data, es)
     end
 end
+
+function get_vnodes(sys)
+    diffnodes = []
+    diffedges = Tuple{Int, Int}[]
+    for (i, eq) in enumerate(sys.eqs)
+        if !(eq.lhs isa Constant)
+            # Make sure that the LHS is a first order derivative of a var.
+            @assert eq.lhs.op isa Differential
+            @assert !(eq.lhs.args[1] isa Differential) # first order
+
+            push!(diffnodes, eq.lhs)
+            # For efficiency we note down the diff edges here
+            push!(diffedges, (i, length(diffnodes)))
+        end
+    end
+
+    diffvars = (first ∘ var_from_nested_derivative).(diffnodes)
+    algvars  = setdiff(states(sys), diffvars)
+    return diffnodes, diffedges, algvars
+end
+
+function sys2bigraph2(sys)
+    diffvars, edges, algvars = get_vnodes(sys)
+    varnumber_offset = length(diffvars)
+
+    for (i, eq) in enumerate(sys.eqs)
+        # T or D(x):
+        # We assume no derivatives appear on the RHS at this point
+        vs = vars(eq.rhs)
+        for v in vs
+            for (j, target_v) in enumerate(algvars)
+                if v == target_v
+                    push!(edges, (i, j+varnumber_offset))
+                end
+            end
+        end
+    end
+    vcat(diffvars, algvars), edges
+end
+
+print_bigraph(sys, vars, edges) = print_bigraph(stdout, sys, vars, edges)
+function print_bigraph(io::IO, sys, vars, edges)
+    println(io, "Equations:")
+    foreach(x->println(io, x), [i => sys.eqs[i] for i in 1:length(sys.eqs)])
+    println(io)
+    for (i, j) in edges
+        println(io, "Eq $i has $(vars[j])")
+    end
+end

test/index_reduction.jl

@@ -30,4 +30,6 @@ eqs = [D(x) ~ w,
        0 ~ x^2 + y^2 - L^2]
 pendulum = ODESystem(eqs, t, [x, y, w, z, T], [L, g], name=:pendulum)
 
+# V-nodes D(x), D(y), D(w), D(z), T
+# E-nodes
 sys2bigraph(pendulum)