Merge pull request #825 from SciML/myb/symbolics

Use Symbolics

Author: YingboMa

Project.toml

@@ -1,7 +1,7 @@
 name = "ModelingToolkit"
 uuid = "961ee093-0014-501f-94e3-6117800e7a78"
 authors = ["Chris Rackauckas <accounts@chrisrackauckas.com>"]
-version = "5.9.1"
+version = "5.10.0"
 
 [deps]
 ArrayInterface = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
@@ -33,6 +33,7 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 TreeViews = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
 UnPack = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
@@ -62,7 +63,8 @@ SciMLBase = "1.3"
 Setfield = "0.7"
 SpecialFunctions = "0.7, 0.8, 0.9, 0.10, 1.0"
 StaticArrays = "0.10, 0.11, 0.12, 1.0"
-SymbolicUtils = "0.8"
+SymbolicUtils = "0.8.3"
+Symbolics = "0.1"
 TreeViews = "0.3"
 UnPack = "0.1, 1.0"
 Unitful = "1.1"

src/ModelingToolkit.jl

@@ -25,159 +25,45 @@ RuntimeGeneratedFunctions.init(@__MODULE__)
 using RecursiveArrayTools
 
 import SymbolicUtils
-import SymbolicUtils: Term, Add, Mul, Pow, Sym, FnType,
-                      @rule, Rewriters, substitute, similarterm,
-                      promote_symtype
-
+import SymbolicUtils: istree, arguments, operation, similarterm, promote_symtype,
+                      Symbolic, Term, Add, Mul, Pow, Sym, FnType,
+                      @rule, Rewriters, substitute
+using SymbolicUtils.Code
 import SymbolicUtils.Code: toexpr
-
 import SymbolicUtils.Rewriters: Chain, Postwalk, Prewalk, Fixpoint
+
+using Reexport
+@reexport using Symbolics
+export @derivatives
+using Symbolics: _parse_vars, value, makesym, @derivatives, get_variables,
+                 exprs_occur_in, solve_for, build_expr
+import Symbolics: rename, get_variables!, _solve, hessian_sparsity,
+                  jacobian_sparsity, islinear, _iszero, _isone,
+                  tosymbol, lower_varname, diff2term, var_from_nested_derivative,
+                  BuildTargets, JuliaTarget, StanTarget, CTarget, MATLABTarget,
+                  ParallelForm, SerialForm, MultithreadedForm, build_function,
+                  unflatten_long_ops
+
 import DiffEqBase: @add_kwonly
-using LinearAlgebra: LU, BlasInt
 
 import LightGraphs: SimpleDiGraph, add_edge!
 
 import TreeViews
 
 using Requires
 
-export Num, Variable
-"""
-$(TYPEDEF)
-
-Wrap anything in a type that is a subtype of Real
-"""
-struct Num <: Real
-    val
-end
-
-const show_numwrap = Ref(false)
-
-Num(x::Num) = x # ideally this should never be called
-(n::Num)(args...) = Num(value(n)(map(value,args)...))
-value(x) = x
-value(x::Num) = x.val
-
-SciMLBase.issymbollike(::Num) = true
-SciMLBase.issymbollike(::SymbolicUtils.Symbolic) = true
-
-SymbolicUtils.@number_methods(Num,
-                              Num(f(value(a))),
-                              Num(f(value(a), value(b))))
-
-for C in [Complex, Complex{Bool}]
+for fun in [:toexpr]
     @eval begin
-        Base.:*(x::Num, z::$C) = Complex(x * real(z), x * imag(z))
-        Base.:*(z::$C, x::Num) = Complex(real(z) * x, imag(z) * x)
-    end
-end
-
-Base.:+(x::Num, z::Complex) = Complex(x + real(z), imag(z))
-Base.:+(z::Complex, x::Num) = Complex(real(z) + x, imag(z))
-Base.:-(x::Num, z::Complex) = Complex(x - real(z), -imag(z))
-Base.:-(z::Complex, x::Num) = Complex(real(z) - x, imag(z))
-
-function Base.inv(z::Complex{Num})
-    a, b = reim(z)
-    den = a^2 + b^2
-    Complex(a/den, -b/den)
-end
-function Base.:/(x::Complex{Num}, y::Complex{Num})
-    a, b = reim(x)
-    c, d = reim(y)
-    den = c^2 + d^2
-    Complex((a*c + b*d)/den, (b*c - a*d)/den)
-end
+        function $fun(eq::Equation; kw...)
+            Expr(:(=), $fun(eq.lhs; kw...), $fun(eq.rhs; kw...))
+        end
 
-function Base.show(io::IO, z::Complex{<:Num})
-    r, i = reim(z)
-    compact = get(io, :compact, false)
-    show(io, r)
-    print(io, (compact ? "+" : " + ") * "(")
-    show(io, i)
-    print(io, ")*im")
-end
-
-SymbolicUtils.simplify(n::Num; kw...) = Num(SymbolicUtils.simplify(value(n); kw...))
-
-SymbolicUtils.symtype(n::Num) = symtype(n.val)
-
-function Base.iszero(x::Num)
-    _x = SymbolicUtils.to_mpoly(value(x))[1]
-    return (_x isa Number || _x isa SymbolicUtils.MPoly) && iszero(_x)
-end
-
-import SymbolicUtils: <ₑ, Symbolic, Term, operation, arguments
-
-Base.show(io::IO, n::Num) = show_numwrap[] ? print(io, :(Num($(value(n))))) : Base.show(io, value(n))
-
-Base.promote_rule(::Type{<:Number}, ::Type{<:Num}) = Num
-Base.promote_rule(::Type{<:Symbolic{<:Number}}, ::Type{<:Num}) = Num
-function Base.getproperty(t::Union{Add, Mul, Pow, Term}, f::Symbol)
-    if f === :op
-        Base.depwarn("`x.op` is deprecated, use `operation(x)` instead", :getproperty, force=true)
-        operation(t)
-    elseif f === :args
-        Base.depwarn("`x.args` is deprecated, use `arguments(x)` instead", :getproperty, force=true)
-        arguments(t)
-    else
-        getfield(t, f)
-    end
-end
-<ₑ(s::Num, x) = value(s) <ₑ value(x)
-<ₑ(s, x::Num) = value(s) <ₑ value(x)
-<ₑ(s::Num, x::Num) = value(s) <ₑ value(x)
-
-for T in (Integer, Rational)
-    @eval Base.:(^)(n::Num, i::$T) = Num(value(n)^i)
-end
-
-macro num_method(f, expr, Ts=nothing)
-    if Ts === nothing
-        Ts = [Any]
-    else
-        @assert Ts.head == :tuple
-        # e.g. a tuple or vector
-        Ts = Ts.args
+        $fun(eqs::AbstractArray; kw...) = map(eq->$fun(eq; kw...), eqs)
+        $fun(x::Integer; kw...) = x
+        $fun(x::AbstractFloat; kw...) = x
     end
-
-    ms = [quote
-              $f(a::$T, b::$Num) = $expr
-              $f(a::$Num, b::$T) = $expr
-          end for T in Ts]
-    quote
-        $f(a::$Num, b::$Num) = $expr
-        $(ms...)
-    end |> esc
 end
 
-"""
-    tosymbolic(a::Union{Sym,Num}) -> Sym{Real}
-    tosymbolic(a::T) -> T
-"""
-tosymbolic(a::Num) = tosymbolic(value(a))
-tosymbolic(a::Sym) = tovar(a)
-tosymbolic(a) = a
-@num_method Base.isless  (val = isless(tosymbolic(a), tosymbolic(b)); val isa Bool ? val : Num(val)) (Real,)
-@num_method Base.:(<)    (val = tosymbolic(a) < tosymbolic(b)       ; val isa Bool ? val : Num(val)) (Real,)
-@num_method Base.:(<=)   (val = tosymbolic(a) <= tosymbolic(b)      ; val isa Bool ? val : Num(val)) (Real,)
-@num_method Base.:(>)    (val = tosymbolic(a) > tosymbolic(b)       ; val isa Bool ? val : Num(val)) (Real,)
-@num_method Base.:(>=)   (val = tosymbolic(a) >= tosymbolic(b)      ; val isa Bool ? val : Num(val)) (Real,)
-@num_method Base.:(==)   (val = tosymbolic(a) == tosymbolic(b)      ; val isa Bool ? val : Num(val)) (AbstractFloat,Number)
-@num_method Base.isequal isequal(tosymbolic(a), tosymbolic(b)) (AbstractFloat, Number, Symbolic)
-
-Base.hash(x::Num, h::UInt) = hash(value(x), h)
-
-Base.convert(::Type{Num}, x::Symbolic{<:Number}) = Num(x)
-Base.convert(::Type{Num}, x::Number) = Num(x)
-Base.convert(::Type{Num}, x::Num) = x
-
-Base.convert(::Type{<:Array{Num}}, x::AbstractArray) = map(Num, x)
-Base.convert(::Type{<:Array{Num}}, x::AbstractArray{Num}) = x
-Base.convert(::Type{Sym}, x::Num) = value(x) isa Sym ? value(x) : error("cannot convert $x to Sym")
-
-LinearAlgebra.lu(x::Array{Num}; check=true, kw...) = sym_lu(x; check=check)
-
 """
 $(TYPEDEF)
 
@@ -211,16 +97,10 @@ include("bipartite_graph.jl")
 using .BipartiteGraphs
 
 include("variables.jl")
-include("context_dsl.jl")
-include("differentials.jl")
+include("parameters.jl")
 
-include("equations.jl")
 include("utils.jl")
-include("linearity.jl")
-include("solve.jl")
-include("direct.jl")
 include("domains.jl")
-include("register_function.jl")
 
 include("systems/abstractsystem.jl")
 
@@ -252,10 +132,6 @@ include("systems/alias_elimination.jl")
 include("structural_transformation/StructuralTransformations.jl")
 @reexport using .StructuralTransformations
 
-include("latexify_recipes.jl")
-include("build_function.jl")
-include("extra_functions.jl")
-
 export ODESystem, ODEFunction, ODEFunctionExpr, ODEProblemExpr
 export SDESystem, SDEFunction, SDEFunctionExpr, SDESystemExpr
 export SystemStructure
@@ -296,7 +172,6 @@ export asgraph, asdigraph
 export toexpr, get_variables
 export simplify, substitute
 export build_function
-export @register
 export modelingtoolkitize
 export @variables, @parameters
 export @named