Merge pull request #1411 from AayushSabharwal/as/arr-linear_expansion

feat: support array variables in `linear_expansion`

Author: ChrisRackauckas

Project.toml

@@ -25,6 +25,7 @@ LogExpFunctions = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
 MacroTools = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 NaNMath = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+OffsetArrays = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
 PrecompileTools = "aea7be01-6a6a-4083-8856-8a6e6704d82a"
 Primes = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
@@ -79,6 +80,7 @@ Lux = "1"
 MacroTools = "0.5"
 NaNMath = "1"
 Nemo = "0.46, 0.47, 0.48"
+OffsetArrays = "1.15.0"
 PreallocationTools = "0.4"
 PrecompileTools = "1"
 Primes = "0.5"

src/Symbolics.jl

@@ -47,6 +47,8 @@ import SymbolicLimits
 
 using ADTypes: ADTypes
 
+import OffsetArrays
+
 @reexport using SymbolicUtils
 RuntimeGeneratedFunctions.init(@__MODULE__)
 

src/linear_algebra.jl

@@ -276,6 +276,13 @@ function _linear_expansion(t, x)
     op, args = operation(t), arguments(t)
     expansion_check(op)
 
+    if iscall(x) && operation(x) == getindex
+        arrx, idxsx... = arguments(x)
+    else
+        arrx = nothing
+        idxsx = nothing
+    end
+
     if op === (+)
         a₁ = b₁ = 0
         islinear = true
@@ -318,15 +325,48 @@ function _linear_expansion(t, x)
         a₁, b₁, islinear = linear_expansion(args[1], x)
         # (a₁ x + b₁)/b₂
         return islinear ? (a₁ / b₂, b₁ / b₂, islinear) : (0, 0, false)
+    elseif op === getindex
+        arrt, idxst... = arguments(t)
+        isequal(arrt, arrx) && return (0, t, true)
+        shape(arrt) == Unknown() && return (0, t, true)
+
+        indexed_t = OffsetArrays.Origin(map(first, axes(arrt)))(Symbolics.scalarize(arrt))[idxst...]
+        # when indexing a registered function/callable symbolic
+        # scalarizing and indexing leads to the same symbolic variable
+        # which causes a StackOverflowError without this
+        isequal(t, indexed_t) && return (0, t, true)
+        return linear_expansion(Symbolics.scalarize(arrt)[idxst...], x)
     else
         for (i, arg) in enumerate(args)
+            isequal(arg, arrx) && return (0, 0, false)
+            if symbolic_type(arg) == NotSymbolic()
+                arg isa AbstractArray || continue
+                _occursin_array(x, arrx, arg) && return (0, 0, false)
+                continue
+            end
             a, b, islinear = linear_expansion(arg, x)
             (_iszero(a) && islinear) || return (0, 0, false)
         end
         return (0, t, true)
     end
 end
 
+"""
+    _occursin_array(sym, arrsym, arr)
+
+Check if `sym` (or, if `sym` is an element of an array symbolic, the array symbolic
+`arrsym`) occursin in the non-symbolic array `arr`.
+"""
+function _occursin_array(sym, arrsym, arr)
+    for el in arr
+        if symbolic_type(el) == NotSymbolic()
+            return el isa AbstractArray && _occursin_array(sym, arrsym, el)
+        else
+            return occursin(sym, el) || occursin(arrsym, el)
+        end
+    end
+end
+
 ###
 ### Utilities
 ###

test/linear_solver.jl

@@ -59,3 +59,26 @@ a, b, islinear = Symbolics.linear_expansion(D(x) - x, x)
 @test islinear
 @test isequal(a, -1)
 @test isequal(b, D(x))
+
+@testset "linear_expansion with array variables" begin
+    @variables x[1:2] y[1:2] z(..)
+    @test !Symbolics.linear_expansion(z(x) + x[1], x[1])[3]
+    @test !Symbolics.linear_expansion(z(x[1]) + x[1], x[1])[3]
+    a, b, islin = Symbolics.linear_expansion(z(x[2]) + x[1], x[1])
+    @test islin && isequal(a, 1) && isequal(b, z(x[2]))
+    a, b, islin = Symbolics.linear_expansion((x + x)[1], x[1])
+    @test islin && isequal(a, 2) && isequal(b, 0)
+    a, b, islin = Symbolics.linear_expansion(y[1], x[1])
+    @test islin && isequal(a, 0) && isequal(b, y[1])
+    @test !Symbolics.linear_expansion(z([x...]), x[1])[3]
+    @test !Symbolics.linear_expansion(z(collect(Symbolics.unwrap(x))), x[1])[3]
+    @test !Symbolics.linear_expansion(z([x, 2x]), x[1])[3]
+
+    @variables x[0:2]
+    a, b, islin = Symbolics.linear_expansion(x[0] - z(x[1]), z(x[1]))
+    @test islin && isequal(a, -1) && isequal(b, x[0])
+
+    @variables x::Vector{Real}
+    a, b, islin = Symbolics.linear_expansion(x[0] - z(x[1]), z(x[1]))
+    @test islin && isequal(a, -1) && isequal(b, x[0])
+end