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feat: support array variables in linear_expansion #1320

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feat: support array variables in linear_expansion #1320

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39 changes: 39 additions & 0 deletions src/linear_algebra.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -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
Expand Down Expand Up @@ -318,15 +325,47 @@ 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)

indexed_t = 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
###
Expand Down
15 changes: 15 additions & 0 deletions test/linear_solver.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -59,3 +59,18 @@ 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]
end
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