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Merged
lbenet merged 2 commits into from
May 13, 2025
Merged

More IntervalArithmetic v1.0 fixes #382

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091b4d6
More IAv1.0 fixes
lbenet May 13, 2025
7311610
Bump minor version
lbenet May 13, 2025
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2 changes: 1 addition & 1 deletion Project.toml
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Original file line number Diff line number Diff line change
@@ -1,7 +1,7 @@
name = "TaylorSeries"
uuid = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
repo = "https://github.com/JuliaDiff/TaylorSeries.jl.git"
version = "0.19.1"
version = "0.20.0"

[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Expand Down
149 changes: 72 additions & 77 deletions ext/TaylorSeriesIAExt.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -4,7 +4,8 @@ using TaylorSeries

import Base: ^, sqrt, log, asin, acos, acosh, atanh, iszero, ==

import TaylorSeries: _pow, pow!, evaluate, _evaluate, normalize_taylor, aff_normalize
import TaylorSeries: _pow, pow!, evaluate, _evaluate, _evaluate!,
normalize_taylor, aff_normalize

using IntervalArithmetic

Expand Down Expand Up @@ -751,7 +752,12 @@ for T in (:Taylor1, :TaylorN)
end


function evaluate(a::Taylor1{T}, dx::Interval{S}) where {T<:Real, S<:NumTypes}
function evaluate(a::Taylor1{Interval{T}}, dx::S) where {T<:NumTypes, S<:NumTypes}
dxI, _ = promote(dx, constant_term(a))
return evaluate(a, dxI)
end

function evaluate(a::Taylor1{T}, dx::Interval{T}) where {T<:NumTypes}
order = a.order
uno = one(dx)
dx2 = dx^2
Expand All @@ -771,16 +777,44 @@ function evaluate(a::Taylor1{T}, dx::Interval{S}) where {T<:Real, S<:NumTypes}
return sum_even + sum_odd*dx
end

function evaluate(a::TaylorN{T}, dx::AbstractVector{Interval{S}}) where
{T<:Real, S<:NumTypes}
@assert length(dx) == get_numvars()
suma = zero(constant_term(a)) + interval(zero(T))
@inbounds for homPol in reverse(eachindex(a))
suma += evaluate(a.coeffs[homPol+1], dx)
function evaluate(a::Taylor1{Interval{T}}, dx::Interval{T}) where {T<:NumTypes}
order = a.order
uno = one(dx)
dx2 = dx^2
if iseven(order)
kend = order-2
@inbounds sum_even = a[end]*uno
@inbounds sum_odd = a[end-1]*zero(dx)
else
kend = order-3
@inbounds sum_odd = a[end]*uno
@inbounds sum_even = a[end-1]*uno
end
return suma
@inbounds for k in kend:-2:0
sum_odd = sum_odd*dx2 + a[k+1]
sum_even = sum_even*dx2 + a[k]
end
return sum_even + sum_odd*dx
end

function evaluate(a::TaylorN{Interval{T}}, dx::AbstractVector{S}) where {T<:NumTypes, S<:NumTypes}
@assert length(dx) == get_numvars()
return evaluate(a, (dx...,); sorting=false)
end

function evaluate(a::TaylorN{T}, dx::AbstractVector{Interval{T}}) where {T<:NumTypes}
@assert length(dx) == get_numvars()
return evaluate(a, (dx...,); sorting=false)
end

function evaluate(a::TaylorN{Interval{T}}, dx::AbstractVector{Interval{T}}) where {T<:NumTypes}
@assert length(dx) == get_numvars()
return evaluate(a, (dx...,); sorting=false)
end

evaluate(a::TaylorN{T}, vals::AbstractVector{TaylorN{Interval{T}}}) where
{T<:NumTypes} = evaluate(a, (vals...,); sorting=false)

function evaluate(a::Taylor1{TaylorN{T}}, dx::Interval{S}) where {T<:Real, S<:Real}
order = a.order
uno = one(dx)
Expand Down Expand Up @@ -874,6 +908,17 @@ function TS._evaluate(a::TaylorN{T}, vals::NTuple{N,TaylorN{Interval{S}}}) where
return suma
end

function TS._evaluate(a::TaylorN{Interval{T}}, vals::NTuple{N,TaylorN{Interval{T}}}) where
{N, T<:NumTypes}
@assert get_numvars() == N
a_length = length(a)
suma = zeros(T, a_length)
@inbounds for homPol in 1:a_length
suma[homPol] = TS._evaluate(a.coeffs[homPol], vals)
end
return suma
end

function TS._evaluate(a::HomogeneousPolynomial{T},
vals::NTuple{N,TaylorN{Interval{S}}}) where {N, T<:Real, S<:NumTypes}
ct = TS.coeff_table[a.order+1]
Expand Down Expand Up @@ -907,80 +952,30 @@ are mapped by an affine transformation to the intervals `-1..1`
normalize_taylor(a::TaylorN, I::AbstractVector{Interval{T}},
symI::Bool=true) where {T<:NumTypes} = _normalize(a, I, Val(symI))

aff_normalize(x, I::Interval, ::Val{true}) = interval(mid(I)) + x*interval(radius(I))
aff_normalize(x, I::Interval, ::Val{false}) = interval(inf(I)) + x*interval(diam(I))

# I -> -1..1
function _normalize(a::Taylor1, I::Interval{T}, ::Val{true}) where {T<:NumTypes}
t = Taylor1(TS.numtype(a), get_order(a))
return a(aff_normalize(t, I, Val(true)))
end
aff_normalize(x, I::Interval, ::Val{true}) = interval(mid(I)) + x * interval(radius(I))
aff_normalize(x, I::Interval, ::Val{false}) = interval(inf(I)) + x * interval(diam(I))

# function _normalize(a::Taylor1{Interval{T}}, I::Interval{T}, ::Val{true}) where
# {T<:NumTypes}
# t = Taylor1(TS.numtype(a), get_order(a))
# return a(aff_normalize(t, I, Val(true)))
# end

# I -> 0..1
function _normalize(a::Taylor1, I::Interval{T}, ::Val{false}) where {T<:NumTypes}
t = Taylor1(TS.numtype(a), get_order(a))
return a(aff_normalize(t, I, Val(false)))
end

# function _normalize(a::Taylor1{Interval{T}}, I::Interval{T}, ::Val{false}) where
# {T<:NumTypes}
# t = Taylor1(TS.numtype(a), get_order(a))
# return a(aff_normalize(t, I, Val(false)))
# end

# I -> IntervalBox(-1..1, Val(N))
function _normalize(a::TaylorN, I::AbstractVector{Interval{T}},
::Val{true}) where {T<:NumTypes}
order = get_order(a)
x = Vector{typeof(a)}(undef, length(I))
@inbounds for ind in eachindex(x)
# x[ind] = mid(I[ind]) + TaylorN(ind, order=order)*radius(I[ind])
x[ind] = aff_normalize(TaylorN(ind, order=order), I[ind], Val(true))
for bb in (:true, :false)
@eval function _normalize(a::Taylor1, I::Interval{T}, ::Val{$bb}) where {T<:NumTypes}
S = promote_type(TS.numtype(a), Interval{T})
t = Taylor1(S, get_order(a))
return a(aff_normalize(t, I, Val($bb)))
end
return a(x)
end

# function _normalize(a::TaylorN{Interval{T}}, I::AbstractVector{Interval{T}},
# ::Val{true}) where {T<:NumTypes}
# order = get_order(a)
# x = Vector{typeof(a)}(undef, length(I))
# @inbounds for ind in eachindex(x)
# # x[ind] = interval(mid(I[ind])) +
# # TaylorN(ind, order=order)*interval(radius(I[ind]))
# x[ind] = aff_normalize(TaylorN(ind, order=order), I[ind], Val(true))
# end
# return a(x)
# end

# I -> IntervalBox(0..1, Val(N))
function _normalize(a::TaylorN, I::AbstractVector{Interval{T}},
::Val{false}) where {T<:NumTypes}
order = get_order(a)
x = Vector{typeof(a)}(undef, length(I))
@inbounds for ind in eachindex(x)
# x[ind] = inf(I[ind]) + TaylorN(ind, order=order)*diam(I[ind])
x[ind] = aff_normalize(TaylorN(ind, order=order), I[ind], Val(false))
@eval function _normalize(a::TaylorN, I::AbstractVector{Interval{T}},
::Val{$bb}) where {T<:NumTypes}
order = get_order(a)
S = promote_type(TS.numtype(a), Interval{T})
x = Vector{TaylorN{S}}(undef, length(I))
@inbounds for ind in eachindex(x)
# x[ind] = mid(I[ind]) + TaylorN(ind, order=order)*radius(I[ind])
x[ind] = aff_normalize(TaylorN(S, ind, order=order), I[ind], Val($bb))
end
aa = convert(TaylorN{S}, a)
return evaluate(aa, x)
end
return a(x)
end

# function _normalize(a::TaylorN{Interval{T}}, I::AbstractVector{Interval{T}},
# ::Val{false}) where {T<:NumTypes}
# order = get_order(a)
# x = Vector{typeof(a)}(undef, length(I))
# @inbounds for ind in eachindex(x)
# # x[ind] = interval(inf(I[ind])) +
# # TaylorN(ind, order=order)*interval(diam(I[ind]))
# x[ind] = aff_normalize(TaylorN(ind, order=order), I[ind], Val(false))
# end
# return a(x)
# end

# Printing-related methods numbr2str
function TS.numbr2str(zz::Interval, ifirst::Bool=false)
Expand Down
14 changes: 7 additions & 7 deletions src/evaluate.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -277,13 +277,13 @@ function evaluate(a::TaylorN, vals::NTuple{N,<:AbstractSeries};
end

evaluate(a::TaylorN{T}, vals::AbstractVector{<:Number}; sorting::Bool=true) where
{T<:NumberNotSeries} = evaluate(a, (vals...,); sorting=sorting)
{T<:NumberNotSeries} = evaluate(a, (vals...,); sorting)

evaluate(a::TaylorN{T}, vals::AbstractVector{<:AbstractSeries}; sorting::Bool=false) where
{T<:NumberNotSeries} = evaluate(a, (vals...,); sorting=sorting)
{T<:NumberNotSeries} = evaluate(a, (vals...,); sorting)

evaluate(a::TaylorN{Taylor1{T}}, vals::AbstractVector{S};
sorting::Bool=false) where {T, S} = evaluate(a, (vals...,); sorting=sorting)
sorting::Bool=false) where {T, S} = evaluate(a, (vals...,); sorting)

function evaluate(a::TaylorN{T}, s::Symbol, val::S) where
{T<:Number, S<:NumberNotSeriesN}
Expand All @@ -292,8 +292,8 @@ function evaluate(a::TaylorN{T}, s::Symbol, val::S) where
return evaluate(a, ind, val)
end

function evaluate(a::TaylorN{T}, ind::Int, val::S) where
{T<:Number, S<:NumberNotSeriesN}
function evaluate(a::TaylorN{T}, ind::Int, val::S) where {T<:Number,
S<:NumberNotSeriesN}
@assert (1 ≤ ind ≤ get_numvars()) "Invalid `ind`; it must be between 1 and `get_numvars()`"
R = promote_type(T,S)
return _evaluate(convert(TaylorN{R}, a), ind, convert(R, val))
Expand Down Expand Up @@ -325,8 +325,8 @@ _evaluate(a::TaylorN{T}, vals::NTuple, ::Val{true}) where
_evaluate(a::TaylorN{T}, vals::NTuple, ::Val{false}) where {T<:Number} =
sum( _evaluate(a, vals) )

function _evaluate(a::TaylorN{T}, vals::NTuple{N,<:TaylorN},
::Val{false}) where {N,T<:Number}
function _evaluate(a::TaylorN{T}, vals::NTuple{N,<:TaylorN}, ::Val{false}) where
{N,T<:Number}
R = promote_type(T, TS.numtype(vals[1]))
res = TaylorN(zero(R), vals[1].order)
vvals = ntuple(i -> convert(TaylorN{R}, vals[i]), length(vals))
Expand Down
3 changes: 3 additions & 0 deletions test/runtests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -21,3 +21,6 @@ testfiles = (
for file in testfiles
include(file)
end

# Back to TaylorN default parameters
set_variables("x", order=6, numvars=2);
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