Specialize lu instead of inv

src/TaylorSeries.jl

@@ -23,10 +23,12 @@ using Markdown
 using Requires
 
 using LinearAlgebra: norm, mul!,
- lu, istriu, triu!, istril, tril!, UpperTriangular, LowerTriangular,
- LinearAlgebra.inv!, LinearAlgebra.checksquare
+ lu, lu!, LinearAlgebra.lutype, LinearAlgebra.copy_oftype,
+ LinearAlgebra.issuccess
+ # istriu, triu!, istril, tril!, UpperTriangular, LowerTriangular,
+ # LinearAlgebra.inv!, LinearAlgebra.checksquare
 
-import LinearAlgebra: norm, mul!
+import LinearAlgebra: norm, mul!, lu
 
 import Base: ==, +, -, *, /, ^
 

src/arithmetic.jl

@@ -566,18 +566,34 @@ end
 # licensed under MIT "Expat".
 # Specialize a method of `inv` for Matrix{Taylor1{T}}. Simply, avoid pivoting,
 # since the polynomial field is not an ordered one.
-function Base.inv(A::StridedMatrix{Taylor1{T}}) where T
- checksquare(A)
- S = Taylor1{typeof((one(T)*zero(T) + one(T)*zero(T))/one(T))}
- AA = convert(AbstractArray{S}, A)
- if istriu(AA)
- Ai = triu!(parent(inv(UpperTriangular(AA))))
- elseif istril(AA)
- Ai = tril!(parent(inv(LowerTriangular(AA))))
+# function Base.inv(A::StridedMatrix{Taylor1{T}}) where T
+# checksquare(A)
+# S = Taylor1{typeof((one(T)*zero(T) + one(T)*zero(T))/one(T))}
+# AA = convert(AbstractArray{S}, A)
+# if istriu(AA)
+# Ai = triu!(parent(inv(UpperTriangular(AA))))
+# elseif istril(AA)
+# Ai = tril!(parent(inv(LowerTriangular(AA))))
+# else
+# # Do not use pivoting !!
+# Ai = inv!(lu(AA, Val(false)))
+# Ai = convert(typeof(parent(Ai)), Ai)
+# end
+# return Ai
+# end
+
+# Adapted from (Julia v1.2) stdlib/v1.2/LinearAlgebra/src/lu.jl#240-253
+# and (Julia v1.4.0-dev) stdlib/LinearAlgebra/v1.4/src/lu.jl#270-274,
+# licensed under MIT "Expat".
+# Specialize a method of `lu` for Matrix{Taylor1{T}}, which avoids pivoting,
+# since the polynomial field is not an ordered one.
+# We can't assume an ordered field so we first try without pivoting
+function lu(A::AbstractMatrix{Taylor1{T}}; check::Bool = true) where T
+ S = Taylor1{lutype(T)}
+ F = lu!(copy_oftype(A, S), Val(false); check = false)
+ if issuccess(F)
+ return F
  else
- # Do not use pivoting !!
- Ai = inv!(lu(AA, Val(false)))
- Ai = convert(typeof(parent(Ai)), Ai)
+ return lu!(copy_oftype(A, S), Val(true); check = check)
  end
- return Ai
 end

test/onevariable.jl

@@ -506,22 +506,30 @@ end
 
 @testset "Test `inv` for `Matrix{Taylor1{Float64}}``" begin
  t = Taylor1(5)
-
  a = Diagonal(rand(0:10,3)) + rand(3, 3)
+ ainv = inv(a)
  b = Taylor1.(a, 5)
  binv = inv(b)
- @test norm(binv - inv(a), Inf) ≤ 1e-11
- @test norm(b*binv - I, Inf) ≤ 1e-11
- @test norm(binv*b - I, Inf) ≤ 1e-11
- @test norm(triu(b)*inv(UpperTriangular(b)) - I, Inf) ≤ 1e-11
- @test norm(inv(LowerTriangular(b))*tril(b) - I, Inf) ≤ 1e-11
-
- b .= b .+ t
- binv = inv(b)
- @test norm(b*binv - I, Inf) ≤ 1e-11
- @test norm(binv*b - I, Inf) ≤ 1e-11
- @test norm(triu(b)*inv(triu(b)) - I, Inf) ≤ 1e-11
- @test norm(inv(tril(b))*tril(b) - I, Inf) ≤ 1e-11
+ tol = 1.0e-11
+
+ for its = 1:10
+ a .= Diagonal(rand(2:12,3)) + rand(3, 3)
+ ainv .= inv(a)
+ b .= Taylor1.(a, 5)
+ binv .= inv(b)
+ @test norm(binv - ainv, Inf) ≤ tol
+ @test norm(b*binv - I, Inf) ≤ tol
+ @test norm(binv*b - I, Inf) ≤ tol
+ @test norm(triu(b)*inv(UpperTriangular(b)) - I, Inf) ≤ tol
+ @test norm(inv(LowerTriangular(b))*tril(b) - I, Inf) ≤ tol
+
+ b .= b .+ t
+ binv .= inv(b)
+ @test norm(b*binv - I, Inf) ≤ tol
+ @test norm(binv*b - I, Inf) ≤ tol
+ @test norm(triu(b)*inv(triu(b)) - I, Inf) ≤ tol
+ @test norm(inv(tril(b))*tril(b) - I, Inf) ≤ tol
+ end
 end
 
 @testset "Matrix multiplication for Taylor1" begin