Merge pull request #680 from SciML/myb/fixes

Various fixes and scalar linear solve

Author: ChrisRackauckas

Project.toml

@@ -1,7 +1,7 @@
 name = "ModelingToolkit"
 uuid = "961ee093-0014-501f-94e3-6117800e7a78"
 authors = ["Chris Rackauckas <accounts@chrisrackauckas.com>"]
-version = "4.0.9"
+version = "4.1.0"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"

src/linearity.jl

@@ -27,7 +27,7 @@ for f in monadic_nonlinear
 end
 
 # 2-arg
-for f in [+, rem2pi, -, >, isless, <, isequal, max, min, convert]
+for f in [+, rem2pi, -, >, isless, <, isequal, max, min, convert, <=, >=]
     linearity_known_2[f] = true
     linearity_map_2[f] = (true, true, true)
 end

src/solve.jl

@@ -45,7 +45,7 @@ end
 # return the coefficient matrix `A` and a
 # vector of constants (possibly symbolic) `b` such that
 # A \ b will solve the equations for the vars
-function A_b(eqs, vars)
+function A_b(eqs::AbstractArray, vars::AbstractArray)
     exprs = rhss(eqs) .- lhss(eqs)
     for ex in exprs
         @assert islinear(ex, vars)
@@ -54,6 +54,13 @@ function A_b(eqs, vars)
     b = A * vars - exprs
     A, b
 end
+function A_b(eq, var)
+    ex = eq.rhs - eq.lhs
+    @assert islinear(ex, [var])
+    a = expand_derivatives(Differential(var)(ex))
+    b = a * var - ex
+    a, b
+end
 
 """
     solve_for(eqs::Vector, vars::Vector)
@@ -69,11 +76,12 @@ function solve_for(eqs, vars)
     _solve(A, b)
 end
 
-function _solve(A, b)
+function _solve(A::AbstractMatrix, b::AbstractArray)
     A = SymbolicUtils.simplify.(to_symbolic.(A), polynorm=true)
     b = SymbolicUtils.simplify.(to_symbolic.(b), polynorm=true)
     SymbolicUtils.simplify.(ldiv(sym_lu(A), b))
 end
+_solve(a, b) = value(SymbolicUtils.simplify(b/a, polynorm=true))
 
 # ldiv below
 

src/systems/abstractsystem.jl

@@ -230,6 +230,8 @@ end
 lhss(xs) = map(x->x.lhs, xs)
 rhss(xs) = map(x->x.rhs, xs)
 
+flatten(sys::AbstractSystem) = sys
+
 function equations(sys::ModelingToolkit.AbstractSystem)
     if isempty(sys.systems)
         return sys.eqs