Merge branch 'master' into constants2

Author: lamorton

.github/workflows/Downstream.yml

@@ -25,6 +25,7 @@ jobs:
           - {user: SciML, repo: DataDrivenDiffEq.jl, group: Standard}
           - {user: SciML, repo: StructuralIdentifiability.jl, group: All}
           - {user: SciML, repo: ModelingToolkitStandardLibrary.jl}
+          - {user: SciML, repo: ModelOrderReduction.jl, group: All}
     steps:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@v1

Project.toml

@@ -1,7 +1,7 @@
 name = "ModelingToolkit"
 uuid = "961ee093-0014-501f-94e3-6117800e7a78"
 authors = ["Yingbo Ma <[email protected]>", "Chris Rackauckas <[email protected]> and contributors"]
-version = "8.21.0"
+version = "8.29.1"
 
 [deps]
 AbstractTrees = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
@@ -70,7 +70,7 @@ NonlinearSolve = "0.3.8"
 RecursiveArrayTools = "2.3"
 Reexport = "0.2, 1"
 RuntimeGeneratedFunctions = "0.4.3, 0.5"
-SciMLBase = "1.54"
+SciMLBase = "1.58.0"
 Setfield = "0.7, 0.8, 1"
 SpecialFunctions = "0.7, 0.8, 0.9, 0.10, 1.0, 2"
 StaticArrays = "0.10, 0.11, 0.12, 1.0"
@@ -93,9 +93,9 @@ OptimizationOptimJL = "36348300-93cb-4f02-beb5-3c3902f8871e"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 ReferenceTests = "324d217c-45ce-50fc-942e-d289b448e8cf"
+SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
-SafeTestsets = "1bc83da4-3b8d-516f-aca4-4fe02f6d838f"
 SteadyStateDiffEq = "9672c7b4-1e72-59bd-8a11-6ac3964bc41f"
 StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"

docs/pages.jl

@@ -17,6 +17,7 @@ pages = [
                     "basics/Variable_metadata.md",
                     "basics/Composition.md",
                     "basics/Events.md",
+                    "basics/Linearization.md",
                     "basics/Validation.md",
                     "basics/DependencyGraphs.md",
                     "basics/FAQ.md"],

docs/src/basics/Linearization.md

@@ -0,0 +1,64 @@
+# [Linearization](@id linearization)
+A nonlinear dynamical system with state (differential and algebraic) ``x`` and input signals ``u``
+```math
+M \dot x = f(x, u)
+```
+can be linearized using the function [`linearize`](@ref) to produce a linear statespace system on the form
+```math
+\begin{aligned}
+\dot x &= Ax + Bu\\
+y &= Cx + Du
+\end{aligned}
+```
+
+The `linearize` function expects the user to specify the inputs ``u`` and the outputs ``u`` using the syntax shown in the example below:
+
+## Example
+```@example LINEARIZE
+using ModelingToolkit
+@variables t x(t)=0 y(t)=0 u(t)=0 r(t)=0
+@parameters kp = 1
+D = Differential(t)
+
+eqs = [u ~ kp * (r - y) # P controller
+       D(x) ~ -x + u    # First-order plant
+       y ~ x]           # Output equation
+
+@named sys = ODESystem(eqs, t)
+matrices, simplified_sys = linearize(sys, [r], [y]) # Linearize from r to y
+matrices
+```
+The named tuple `matrices` contains the matrices of the linear statespace representation, while `simplified_sys` is an `ODESystem` that, amongst other things, indicates the state order in the linear system through
+```@example LINEARIZE
+using ModelingToolkit: inputs, outputs
+[states(simplified_sys); inputs(simplified_sys); outputs(simplified_sys)]
+```
+
+## Operating point
+The operating point to linearize around can be specified with the keyword argument `op` like this: `op = Dict(x => 1, r => 2)`. 
+
+## Batch linearization and algebraic variables
+If linearization is to be performed around multiple operating points, the simplification of the system has to be carried out a single time only. To facilitate this, the lower-level function [`ModelingToolkit.linearization_function`](@ref) is available. This function further allows you to obtain separate Jacobians for the differential and algebraic parts of the model. For ODE models without algebraic equations, the statespace representation above is available from the output of `linearization_function` as `A, B, C, D = f_x, f_u, h_x, h_u`.
+
+
+## Input derivatives
+Physical systems are always *proper*, i.e., they do not differentiate causal inputs. However, ModelingToolkit allows you to model non-proper systems, such as inverse models, and may sometimes fail to find a realization of a proper system on proper form. In these situations, `linearize` may throw an error mentioning
+```
+Input derivatives appeared in expressions (-g_z\g_u != 0)
+```
+This means that to simulate this system, some order of derivatives of the input is required. To allow `linearize` to proceed in this situation, one may pass the keyword argument `allow_input_derivatives = true`, in which case the resulting model will have twice as many inputs, ``2n_u``, where the last ``n_u`` inputs correspond to ``\dot u``. 
+
+If the modeled system is actually proper (but MTK failed to find a proper realization), further numerical simplification can be applied to the resulting statespace system to obtain a proper form. Such simplification is currently available in the experimental package [ControlSystemsMTK](https://github.com/baggepinnen/ControlSystemsMTK.jl#internals-transformation-of-non-proper-models-to-proper-statespace-form).
+
+
+## Tools for linear analysis
+[ModelingToolkitStandardLibrary](http://mtkstdlib.sciml.ai/dev/API/linear_analysis/) contains a set of [tools for more advanced linear analysis](http://mtkstdlib.sciml.ai/dev/API/linear_analysis/). These can be used to make it easier to work with and analyze causal models, such as control and signal-processing systems. 
+
+```@index
+Pages = ["Linearization.md"]
+```
+
+```@docs
+linearize
+ModelingToolkit.linearization_function
+```

src/ModelingToolkit.jl

@@ -5,6 +5,7 @@ module ModelingToolkit
 using DocStringExtensions
 using AbstractTrees
 using DiffEqBase, SciMLBase, ForwardDiff, Reexport
+using SciMLBase: StandardODEProblem, StandardNonlinearProblem, handle_varmap
 using Distributed
 using StaticArrays, LinearAlgebra, SparseArrays, LabelledArrays
 using InteractiveUtils
@@ -110,6 +111,7 @@ function parameters end
 
 # this has to be included early to deal with depency issues
 include("structural_transformation/bareiss.jl")
+function complete end
 include("bipartite_graph.jl")
 using .BipartiteGraphs
 
@@ -147,6 +149,7 @@ include("systems/dependency_graphs.jl")
 include("systems/systemstructure.jl")
 using .SystemStructures
 
+include("debugging.jl")
 include("systems/alias_elimination.jl")
 include("structural_transformation/StructuralTransformations.jl")
 
@@ -176,7 +179,8 @@ export NonlinearSystem, OptimizationSystem
 export alias_elimination, flatten
 export connect, @connector, Connection, Flow, Stream, instream
 export isinput, isoutput, getbounds, hasbounds, isdisturbance, istunable, getdist, hasdist,
-       tunable_parameters, isirreducible, getdescription, hasdescription
+       tunable_parameters, isirreducible, getdescription, hasdescription, isbinaryvar,
+       isintegervar
 export ode_order_lowering, dae_order_lowering, liouville_transform
 export PDESystem
 export Differential, expand_derivatives, @derivatives
@@ -185,7 +189,7 @@ export Term, Sym
 export SymScope, LocalScope, ParentScope, GlobalScope
 export independent_variables, independent_variable, states, parameters, equations, controls,
        observed, structure, full_equations
-export structural_simplify, expand_connections, linearize, linear_statespace
+export structural_simplify, expand_connections, linearize, linearization_function
 export DiscreteSystem, DiscreteProblem
 
 export calculate_jacobian, generate_jacobian, generate_function
@@ -207,7 +211,9 @@ export toexpr, get_variables
 export simplify, substitute
 export build_function
 export modelingtoolkitize
+
 export @variables, @parameters, @constants
-export @named, @nonamespace, @namespace, extend, compose
+export @named, @nonamespace, @namespace, extend, compose, complete
+export debug_system
 
 end # module

src/bipartite_graph.jl

@@ -1,12 +1,14 @@
 module BipartiteGraphs
 
+import ModelingToolkit: complete
+
 export BipartiteEdge, BipartiteGraph, DiCMOBiGraph, Unassigned, unassigned,
        Matching, ResidualCMOGraph, InducedCondensationGraph, maximal_matching,
        construct_augmenting_path!, MatchedCondensationGraph
 
 export 𝑠vertices, 𝑑vertices, has_𝑠vertex, has_𝑑vertex, 𝑠neighbors, 𝑑neighbors,
        𝑠edges, 𝑑edges, nsrcs, ndsts, SRC, DST, set_neighbors!, invview,
-       complete, delete_srcs!, delete_dsts!
+       delete_srcs!, delete_dsts!
 
 using DocStringExtensions
 using UnPack
@@ -63,7 +65,17 @@ end
 function Base.setindex!(m::Matching{U}, v::Union{Integer, U}, i::Integer) where {U}
     if m.inv_match !== nothing
         oldv = m.match[i]
-        isa(oldv, Int) && (m.inv_match[oldv] = unassigned)
+        # TODO: maybe default Matching to always have an `inv_match`?
+
+        # To maintain the invariant that `m.inv_match[m.match[i]] == i`, we need
+        # to unassign the matching at `m.inv_match[v]` if it exists.
+        if v isa Int && (iv = m.inv_match[v]) isa Int
+            m.match[iv] = unassigned
+        end
+        if isa(oldv, Int)
+            @assert m.inv_match[oldv] == i
+            m.inv_match[oldv] = unassigned
+        end
         isa(v, Int) && (m.inv_match[v] = i)
     end
     return m.match[i] = v
@@ -191,14 +203,54 @@ end
 # Matrix whose only purpose is to pretty-print the bipartite graph
 struct BipartiteAdjacencyList
     u::Union{Vector{Int}, Nothing}
+    highligh_u::Union{Set{Int}, Nothing}
+    match::Union{Int, Bool, Unassigned}
+end
+function BipartiteAdjacencyList(u::Union{Vector{Int}, Nothing})
+    BipartiteAdjacencyList(u, nothing, unassigned)
+end
+
+struct HighlightInt
+    i::Int
+    highlight::Union{Symbol, Nothing}
+end
+Base.typeinfo_implicit(::Type{HighlightInt}) = true
+
+function Base.show(io::IO, hi::HighlightInt)
+    if hi.highlight !== nothing
+        printstyled(io, hi.i, color = hi.highlight)
+    else
+        print(io, hi.i)
+    end
 end
+
 function Base.show(io::IO, l::BipartiteAdjacencyList)
+    if l.match === true
+        printstyled(io, "∫ ", color = :light_blue, bold = true)
+    end
     if l.u === nothing
         printstyled(io, '⋅', color = :light_black)
     elseif isempty(l.u)
         printstyled(io, '∅', color = :light_black)
-    else
+    elseif l.highligh_u === nothing
         print(io, l.u)
+    else
+        match = l.match
+        isa(match, Bool) && (match = unassigned)
+        function choose_color(i)
+            i in l.highligh_u ? (i == match ? :light_yellow : :green) :
+            (i == match ? :yellow : nothing)
+        end
+        if !isempty(setdiff(l.highligh_u, l.u))
+            # Only for debugging, shouldn't happen in practice
+            print(io, map(union(l.u, l.highligh_u)) do i
+                      HighlightInt(i, !(i in l.u) ? :light_red : choose_color(i))
+                  end)
+        else
+            print(io, map(l.u) do i
+                      HighlightInt(i, choose_color(i))
+                  end)
+        end
     end
 end
 
@@ -262,7 +314,8 @@ function BipartiteGraph(nsrcs::T, ndsts::T, backedge::Val{B} = Val(true);
 end
 
 function Base.copy(bg::BipartiteGraph)
-    BipartiteGraph(bg.ne, copy(bg.fadjlist), copy(bg.badjlist), deepcopy(bg.metadata))
+    BipartiteGraph(bg.ne, map(copy, bg.fadjlist), map(copy, bg.badjlist),
+                   deepcopy(bg.metadata))
 end
 Base.eltype(::Type{<:BipartiteGraph{I}}) where {I} = I
 function Base.empty!(g::BipartiteGraph)
@@ -435,19 +488,23 @@ function set_neighbors!(g::BipartiteGraph, i::Integer, new_neighbors)
         for n in old_neighbors
             @inbounds list = g.badjlist[n]
             index = searchsortedfirst(list, i)
-            deleteat!(list, index)
+            if 1 <= index <= length(list) && list[index] == i
+                deleteat!(list, index)
+            end
         end
         for n in new_neighbors
             @inbounds list = g.badjlist[n]
             index = searchsortedfirst(list, i)
-            insert!(list, index, i)
+            if !(1 <= index <= length(list) && list[index] == i)
+                insert!(list, index, i)
+            end
         end
     end
     if iszero(new_nneighbors) # this handles Tuple as well
         # Warning: Aliases old_neighbors
         empty!(g.fadjlist[i])
     else
-        g.fadjlist[i] = copy(new_neighbors)
+        g.fadjlist[i] = unique!(sort(new_neighbors))
     end
 end
 

src/debugging.jl

@@ -0,0 +1,36 @@
+const LOGGED_FUN = Set([log, sqrt, (^), /, inv])
+is_legal(::typeof(/), a, b) = is_legal(inv, b)
+is_legal(::typeof(inv), a) = !iszero(a)
+is_legal(::Union{typeof(log), typeof(sqrt)}, a) = a isa Complex || a >= zero(a)
+is_legal(::typeof(^), a, b) = a isa Complex || b isa Complex || isinteger(b) || a >= zero(a)
+
+struct LoggedFun{F}
+    f::F
+    args::Any
+end
+Base.nameof(lf::LoggedFun) = nameof(lf.f)
+SymbolicUtils.promote_symtype(::LoggedFun, Ts...) = Real
+function (lf::LoggedFun)(args...)
+    f = lf.f
+    symbolic_args = lf.args
+    if is_legal(f, args...)
+        f(args...)
+    else
+        args_str = join(string.(symbolic_args .=> args), ", ", ", and ")
+        throw(DomainError(args, "$(lf.f) errors with input(s): $args_str"))
+    end
+end
+
+function logged_fun(f, args...)
+    # Currently we don't really support complex numbers
+    term(LoggedFun(f, args), args..., type = Real)
+end
+
+debug_sub(eq::Equation) = debug_sub(eq.lhs) ~ debug_sub(eq.rhs)
+function debug_sub(ex)
+    istree(ex) || return ex
+    f = operation(ex)
+    args = map(debug_sub, arguments(ex))
+    f in LOGGED_FUN ? logged_fun(f, args...) :
+    similarterm(ex, f, args, metadata = metadata(ex))
+end