Compatibility with IA v1 (#178)

* Initial fixes for compatibility with IA 1.0

* Update Project.toml

* Maaaany scattered fixes

* More fixes

* Upgrade TaylorSeries version, and other fixes

* Separate in a submodule validated integration stuff

* First round of substitution

* Fixes related to validated integration

* Fix test errors

* Further fixes

* Fix docs

* Fix a broken test

* Fixes in displaying TMs...

after upgrading IA to v0.23

* Small fixes

* Fix TM.bound_taylor1 (and broken tests)

* Use Bunger (2020) method to eval remainder of product

* Use pown(ii, n) instead of ii^n, for ii::Interval, n::Int, and fix tests

This avoids that the guarateed field of remainder is always false

* Use ii^interval(n) instead of pown(ii,n); saves allocs

* Bump IA to v1 :-)

* Keep compatibility with IA v0.22 and v0.23

---------

Co-authored-by: Benoît Richard <[email protected]>

Author: lbenet

.gitignore

@@ -4,3 +4,5 @@
 .DS_Store
 docs/build/
 docs/site/
+
+Manifest.toml

Project.toml

@@ -1,31 +1,35 @@
 name = "TaylorModels"
 uuid = "314ce334-5f6e-57ae-acf6-00b6e903104a"
 repo = "https://github.com/JuliaIntervals/TaylorModels.jl.git"
-version = "0.8.0"
+version = "0.9.0"
 
 [deps]
 IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 IntervalRootFinding = "d2bf35a9-74e0-55ec-b149-d360ff49b807"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
+Parameters = "d96e819e-fc66-5662-9728-84c9c7592b0a"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 Reexport = "189a3867-3050-52da-a836-e630ba90ab69"
+StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 TaylorIntegration = "92b13dbe-c966-51a2-8445-caca9f8a7d42"
 TaylorSeries = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
 
 [compat]
 Aqua = "0.8"
-IntervalArithmetic = "^0.20"
-IntervalRootFinding = "0.5"
-LinearAlgebra = "<0.0.1, 1"
-Markdown = "<0.0.1, 1"
-Random = "<0.0.1, 1"
+IntervalArithmetic = "0.22, 0.23, 1"
+IntervalRootFinding = "0.6"
+LinearAlgebra = "1"
+Markdown = "1"
+Parameters = "0.12.3"
+Random = "1"
 RecipesBase = "1"
 Reexport = "1"
-TaylorIntegration = "0.16"
-TaylorSeries = "0.18.4"
-Test = "<0.0.1, 1"
+StaticArrays = "1.9"
+TaylorIntegration = "0.17"
+TaylorSeries = "0.20"
+Test = "1"
 julia = "1.10"
 
 [extras]

benchmark/daisy/multivariate.jl

@@ -5,22 +5,22 @@ DAISY["himmilbeau"] = Dict("dom" => a×b,
     "numvars" => 2,
     "vars" => "x1 x2",
     "f" => ((x1, x2) -> (x1*x1 + x2 - 11)*(x1 * x1 + x2 - 11) + (x1 + x2*x2 - 7)*(x1 + x2*x2 - 7)),
-    "ref" => Interval(85.46830677734748, 221.7338939301446) # MOSEK deg 6
+    "ref" => interval(85.46830677734748, 221.7338939301446) # MOSEK deg 6
     )
 
 DAISY["kepler1"] = Dict("dom" => a×b×c×d×e×f,
     "numvars" => 6,
     "vars" => "x1 x2 x3 x4 x5 x6",
     "f" => ((x1, x2, x3, x4, x5, x6) -> x2 * x5 + x3 * x6 - x2 * x3 - x5 * x6 + x1 * (-x1 + x2 + x3 - x4 + x5 + x6)),
-    "ref" => Interval(-5.255935494810441, 7.321362422825775)  # MOSEK deg 6
+    "ref" => interval(-5.255935494810441, 7.321362422825775)  # MOSEK deg 6
     )
 
 DAISY["kepler2"] = Dict("dom" => a×b×c×d,
     "numvars" => 4,
     "vars" => "x1 x2 x3 x4",
     "f" => ((x1, x2, x3, x4) -> x1 * x4 * (-x1 + x2 + x3 - x4) +
                                 x2 * (x1 - x2 + x3 + x4) + x3 * (x1 + x2 - x3 + x4) -x2 * x3 * x4 - x1 * x3 - x1 * x2 - x4),
-    "ref" => Interval(-195.36974909125482, 78.3669520644375)  # MOSEK deg 6
+    "ref" => interval(-195.36974909125482, 78.3669520644375)  # MOSEK deg 6
     )
 
 DAISY["kepler3"] = Dict("dom" => a×b×c×d×e×f,
@@ -29,19 +29,19 @@ DAISY["kepler3"] = Dict("dom" => a×b×c×d×e×f,
     "f" => ((x1, x2, x3, x4, x5, x6) -> x1 * x4 * (-x1 + x2 + x3 - x4 + x5 + x6) +
                                         x2 * x5 * (x1 - x2 + x3 + x4 - x5 + x6) +x3* x6 * (x1 + x2 - x3 + x4 + x5 - x6) -
                                         x2 * x3 * x4 -x1* x3* x5 - x1 * x2 * x6 - x4 * x5 * x6),
-    "ref" => Interval(-309.8484155131222, 17.982082401462407) # MOSEK deg 6
+    "ref" => interval(-309.8484155131222, 17.982082401462407) # MOSEK deg 6
     )
 
 DAISY["Rigidbody1"] = Dict("dom" => a×b×c,
     "numvars" => 3,
     "vars" => "x1 x2 x3",
     "f" => ((x1, x2, x3) -> -x1*x2 - 2*x2*x3 - x1 - x3),
-    "ref" => Interval(-20.786552979420335, -0.540012836551535) # MOSEK deg 6
+    "ref" => interval(-20.786552979420335, -0.540012836551535) # MOSEK deg 6
     )
 
 DAISY["Rigidbody2"] = Dict("dom" => a×b×c,
     "numvars" => 3,
     "vars" => "x1 x2 x3",
     "f" => ((x1, x2, x3) -> 2*(x1*x2*x3) + (3*x3*x3) - x2*(x1*x2*x3) + (3*x3*x3) - x2),
-    "ref" => Interval(68.81138021006673, 359.98566570476504)  # MOSEK deg 6
+    "ref" => interval(68.81138021006673, 359.98566570476504)  # MOSEK deg 6
     )

benchmark/daisy/setup.jl

@@ -5,12 +5,12 @@
 # The following domains are used throughout the tests in Tables 3-5 in
 # [1] Althoff, M., Grebenyuk, D., & Kochdumper, N. (2018). Implementation of Taylor models in CORA 2018.
 #     In Proc. of the 5th International Workshop on Applied Verification for Continuous and Hybrid Systems.
-a = Interval(-4.5, -0.3)
-b = Interval(0.4, 0.9)
-c = Interval(3.8, 7.8)
-d = Interval(8.0, 10.0)
-e = Interval(-10.0, 8.0)
-f = Interval(1.0, 2.0)
+a = interval(-4.5, -0.3)
+b = interval(0.4, 0.9)
+c = interval(3.8, 7.8)
+d = interval(8.0, 10.0)
+e = interval(-10.0, 8.0)
+f = interval(1.0, 2.0)
 
 # ======================
 # Relative precision
@@ -27,7 +27,7 @@ function relative_precision(x, x_ref)
     x_ref_low, x_ref_high = inf(x_ref), sup(x_ref)
     rel_low = -(x_low - x_ref_low) / (x_ref_high - x_ref_low)
     rel_high = (x_high - x_ref_high) / (x_ref_high - x_ref_low)
-    return 100 * Interval(rel_low, rel_high)
+    return 100 * interval(rel_low, rel_high)
 end
 
 # ==========================
@@ -36,37 +36,38 @@ end
 
 # taylor model in one variable
 function bounds_TM(func::Function, dom::Interval, ord::Int)
-    x0 = Interval(mid(dom))
+    x0 = interval(mid(dom))
     x = TaylorModel1(ord, x0, dom)
     return evaluate(func(x), dom - x0)
 end
 
 # taylor model in N variables
-function bounds_TM(func::Function, dom::IntervalBox{N}, ord) where {N}
-    x0 = mid(dom)
+function bounds_TM(func::Function, dom::AbstractVector{<:Interval}, ord)
+    x0 = mid.(dom)
     set_variables(Float64, "x", order=2ord, numvars=N)
-    x = [TaylorModelN(i, ord, IntervalBox(x0), dom) for i=1:N]
+    x = [TaylorModelN(i, ord, x0, dom) for i in eachindex(dom)]
     return evaluate(func(x...), dom - x0)
 end
 
 # normalized taylor model in one variable
 function bounds_TM_NORM(func::Function, dom::Interval, ord::Int)
-    x0 = Interval(mid(dom))
+    x0 = interval(mid(dom))
     x = TaylorModel1(ord, x0, dom)
     xnorm = normalize_taylor(x.pol, dom - x0, true)
     xnormTM = TaylorModel1(xnorm, 0..0, 0..0, -1..1)
     return evaluate(func(xnormTM), -1..1)
 end
 
 # normalized taylor model in N variables
-function bounds_TM_NORM(func::Function, dom::IntervalBox{N}, ord::Int) where {N}
-    x0 = mid(dom)
+function bounds_TM_NORM(func::Function, dom::AbstractVector{<:Interval}, ord::Int)
+    x0 = mid.(dom)
+    N = length(dom)
     set_variables(Float64, "x", order=2ord, numvars=N)
 
-    zeroBox = IntervalBox(0..0, N)
-    symBox = IntervalBox(-1..1, N)
+    zeroBox = fill(0..0, N)
+    symBox = fill(-1..1, N)
 
-    x = [TaylorModelN(i, ord, IntervalBox(x0), dom) for i=1:N]
+    x = [TaylorModelN(i, ord, x0, dom) for i in eachindex(dom)]
     xnorm = [normalize_taylor(xi.pol, dom - x0, true) for xi in x]
     xnormTM = [TaylorModelN(xi_norm, 0..0, zeroBox, symBox) for xi_norm in xnorm]
     return evaluate(func(xnormTM...), symBox)

benchmark/daisy/univariate.jl

@@ -6,29 +6,29 @@
 DAISY["sine"] = Dict("dom" => a,
     "numvars" => 1,
     "f" => (x -> sin(x)),
-    "ref" => Interval(-1.0, 0.977530117665097) # (*)
+    "ref" => interval(-1.0, 0.977530117665097) # (*)
     )
 
 DAISY["bspline0"] = Dict("dom" => a,
     "numvars" => 1,
     "f" => (x -> (1 - x) * (1 - x) * (1 - x) / 6.0),
-    "ref" => Interval(0.36616666666666675, 27.729166666666668) # (*)
+    "ref" => interval(0.36616666666666675, 27.729166666666668) # (*)
     )
 
 DAISY["bspline1"] = Dict("dom" => a,
    "numvars" => 1,
     "f" => (x -> (3*x*x*x - 6*x*x + 4) / 6.0),
-    "ref" => Interval(-65.14583333333333, 0.5631666666666667) # (*)
+    "ref" => interval(-65.14583333333333, 0.5631666666666667) # (*)
     )
 
 DAISY["bspline2"] = Dict("dom" => a,
     "numvars" => 1,
     "f" => (x -> (-3*x*x*x  + 3*x*x + 3*x + 1) / 6.0),
-    "ref" => Interval(0.07516666666666667, 53.604166666666664) # (*)
+    "ref" => interval(0.07516666666666667, 53.604166666666664) # (*)
     )
 
 DAISY["bspline3"] = Dict("dom" => a,
     "numvars" => 1,
     "f" => (x -> -x*x*x / 6.0),
-    "ref" => Interval(0.0045, 15.1875) # (*)
+    "ref" => interval(0.0045, 15.1875) # (*)
     )

docs/src/api.md

@@ -4,5 +4,5 @@
 ```
 
 ```@autodocs
-Modules = [TaylorModels]
+Modules = [TaylorModels, TaylorModels.ValidatedInteg]
 ```

src/TaylorModels.jl

@@ -1,11 +1,12 @@
 module TaylorModels
 
 using Reexport
-@reexport using TaylorSeries, IntervalArithmetic
-@reexport using TaylorIntegration
+@reexport using TaylorSeries, IntervalArithmetic, IntervalArithmetic.Symbols
+# @reexport using TaylorIntegration
 
 using IntervalRootFinding
-using LinearAlgebra: norm, mul!, cond, isposdef
+using LinearAlgebra: norm, isposdef
+using StaticArrays
 
 using RecipesBase
 
@@ -29,22 +30,23 @@ import LinearAlgebra: norm
 export TaylorModel1, RTaylorModel1, TaylorModelN, TMSol
 
 export remainder, polynomial, domain, expansion_point, flowpipe, get_xTM,
-    rpa, fp_rpa, bound_remainder, centered_dom,
-    validated_integ, validated_integ2
+    rpa, fp_rpa, bound_remainder, centered_dom, symmetric_box
 
 export linear_dominated_bounder, quadratic_fast_bounder
 
+
+setdisplay(:full)
+
 include("constructors.jl")
 include("auxiliary.jl")
 include("promotion.jl")
 include("bounds.jl")
 include("evaluate.jl")
-include("rpa_functions.jl")
 include("arithmetic.jl")
+include("rpa_functions.jl")
 include("integration.jl")
 include("show.jl")
-include("valid_integ/validated_integ.jl")
-include("valid_integ/validated_integ2.jl")
+include("valid_integ/ValidatedInteg.jl")
 include("recipe.jl")