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Add evaluation method for arrays of TaylorN (#364)
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* WIP: add `evaluate!` method for `TaylorN`s

* Update

* Small fix

* pow! fix for Julia 1.6

* Remove unused `@inbounds`

* Bump minor version

* Update README.md

* Small fix and add comments

* Update tests

* Update tests again
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@PerezHz
PerezHz authored Jul 21, 2024
1 parent bc87e50 commit e5b4989
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6 changes: 3 additions & 3 deletions 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 = "0.17.8"
version = "0.18.0"

[deps]
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
Expand All @@ -12,14 +12,14 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
[weakdeps]
IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
JLD2 = "033835bb-8acc-5ee8-8aae-3f567f8a3819"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"

[extensions]
TaylorSeriesIAExt = "IntervalArithmetic"
TaylorSeriesJLD2Ext = "JLD2"
TaylorSeriesSAExt = "StaticArrays"
TaylorSeriesRATExt = "RecursiveArrayTools"
TaylorSeriesSAExt = "StaticArrays"

[compat]
Aqua = "0.8"
Expand Down
8 changes: 4 additions & 4 deletions README.md
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Expand Up @@ -30,7 +30,7 @@ julia> t = Taylor1(Float64, 5)

julia> exp(t)
1.0 + 1.0 t + 0.5 t² + 0.16666666666666666 t³ + 0.041666666666666664 t⁴ + 0.008333333333333333 t⁵ + 𝒪(t⁶)

julia> log(1 + t)
1.0 t - 0.5 t² + 0.3333333333333333 t³ - 0.25 t⁴ + 0.2 t⁵ + 𝒪(t⁶)
```
Expand All @@ -40,7 +40,7 @@ julia> x, y = set_variables("x y", order=2);

julia> exp(x + y)
1.0 + 1.0 x + 1.0 y + 0.5 x² + 1.0 x y + 0.5 y² + 𝒪(‖x‖³)

```
Differential and integral calculus on Taylor series:
```julia
Expand Down Expand Up @@ -95,6 +95,6 @@ We thank the participants of the course for putting up with the half-baked
material and contributing energy and ideas.

We acknowledge financial support from DGAPA-UNAM PAPIME grants
PE-105911 and PE-107114, and DGAPA-PAPIIT grants IG-101113,
IG-100616, and IG-100819.
PE-105911 and PE-107114, and DGAPA-PAPIIT grants IG-101113,
IG-100616, IG-100819 and IG-101122.
LB acknowledges support through a *Cátedra Moshinsky* (2013).
67 changes: 46 additions & 21 deletions src/arithmetic.jl
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Expand Up @@ -162,9 +162,7 @@ for T in (:Taylor1, :HomogeneousPolynomial, :TaylorN)
end

for T in (:Taylor1, :TaylorN)
@eval function zero(a::$T)
return $T(zero.(a.coeffs))
end
@eval zero(a::$T) = $T(zero.(a.coeffs))
@eval function one(a::$T)
b = zero(a)
b[0] = one(b[0])
Expand Down Expand Up @@ -539,25 +537,50 @@ for T in (:Taylor1, :TaylorN)
return nothing
end

@eval @inline function mul!(v::$T, a::$T, b::NumberNotSeries, k::Int)
@eval begin
if $T == Taylor1
@inbounds v[k] = a[k] * b
else
@inbounds for i in eachindex(v[k])
v[k][i] = a[k][i] * b
@inline function mul!(v::$T, a::$T, b::NumberNotSeries, k::Int)
@inbounds v[k] = a[k] * b
return nothing
end
@inline function mul!(v::$T, a::NumberNotSeries, b::$T, k::Int)
@inbounds v[k] = a * b[k]
return nothing
end
@inline function muladd!(v::$T, a::$T, b::NumberNotSeries, k::Int)
@inbounds v[k] += a[k] * b
return nothing
end
@inline function muladd!(v::$T, a::NumberNotSeries, b::$T, k::Int)
@inbounds v[k] += a * b[k]
return nothing
end
end
return nothing
end
@eval @inline function mul!(v::$T, a::NumberNotSeries, b::$T, k::Int)
if $T == Taylor1
@inbounds v[k] = a * b[k]
else
@inbounds for i in eachindex(v[k])
v[k][i] = a * b[k][i]
@inline function mul!(v::$T, a::$T, b::NumberNotSeries, k::Int)
@inbounds for i in eachindex(v[k])
v[k][i] = a[k][i] * b
end
return nothing
end
@inline function mul!(v::$T, a::NumberNotSeries, b::$T, k::Int)
@inbounds for i in eachindex(v[k])
v[k][i] = a * b[k][i]
end
return nothing
end
@inline function muladd!(v::$T, a::$T, b::NumberNotSeries, k::Int)
@inbounds for i in eachindex(v[k])
v[k][i] += a[k][i] * b
end
return nothing
end
@inline function muladd!(v::$T, a::NumberNotSeries, b::$T, k::Int)
@inbounds for i in eachindex(v[k])
v[k][i] += a * b[k][i]
end
return nothing
end
end
return nothing
end

@eval @inline function mul!(v::$T, a::$T, b::NumberNotSeries)
Expand Down Expand Up @@ -951,7 +974,8 @@ end

@inline function div!(c::Taylor1{T}, a::NumberNotSeries,
b::Taylor1{T}, k::Int) where {T<:Number}
iszero(a) && !iszero(b) && zero!(c, k)
zero!(c, k)
iszero(a) && !iszero(b) && return nothing
# order and coefficient of first factorized term
# In this case, since a[k]=0 for k>0, we can simplify to:
# ordfact, cdivfact = 0, a/b[0]
Expand All @@ -970,7 +994,8 @@ end

@inline function div!(c::Taylor1{TaylorN{T}}, a::NumberNotSeries,
b::Taylor1{TaylorN{T}}, k::Int) where {T<:NumberNotSeries}
iszero(a) && !iszero(b) && zero!(c, k)
zero!(c, k)
iszero(a) && !iszero(b) && return nothing
# order and coefficient of first factorized term
# In this case, since a[k]=0 for k>0, we can simplify to:
# ordfact, cdivfact = 0, a/b[0]
Expand Down Expand Up @@ -1141,14 +1166,14 @@ end
"""Division does not define a Taylor1 polynomial;
order k=$(ordfact) => coeff[$(ordfact)]=$(cdivfact).""") )

zero!(c, k)

if k == 0
# @inbounds c[0] = a[ordfact]/b[ordfact]
@inbounds div!(c[0], a[ordfact], b[ordfact])
return nothing
end

@inbounds zero!(c, k)

imin = max(0, k+ordfact-b.order)
@inbounds mul!(c[k], c[imin], b[k+ordfact-imin])
@inbounds for i = imin+1:k-1
Expand Down
105 changes: 70 additions & 35 deletions src/evaluate.jl
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Expand Up @@ -187,43 +187,42 @@ function _evaluate(a::HomogeneousPolynomial{T}, vals::NTuple) where {T}
return suma
end

function _evaluate(a::HomogeneousPolynomial{T}, vals::NTuple{N,<:TaylorN{T}}) where
{N,T<:NumberNotSeries}
# @assert length(vals) == get_numvars()
a.order == 0 && return a[1]*one(vals[1])
function _evaluate!(res::TaylorN{T}, a::HomogeneousPolynomial{T}, vals::NTuple{N,<:TaylorN{T}},
valscache::Vector{TaylorN{T}}, aux::TaylorN{T}) where {N,T<:NumberNotSeries}
ct = coeff_table[a.order+1]
suma = TaylorN(zero(T), vals[1].order)
#
# vv = power_by_squaring.(vals, ct[1])
vv = vals .^ ct[1]
tmp = zero(suma)
aux = one(suma)
for el in eachindex(valscache)
power_by_squaring!(valscache[el], vals[el], aux, ct[1][el])
end
for (i, a_coeff) in enumerate(a.coeffs)
iszero(a_coeff) && continue
# @inbounds vv .= power_by_squaring.(vals, ct[i])
vv .= vals .^ ct[i]
# tmp = prod( vv )
for ord in eachindex(tmp)
@inbounds one!(aux, vv[1], ord)
# valscache .= vals .^ ct[i]
@inbounds for el in eachindex(valscache)
power_by_squaring!(valscache[el], vals[el], aux, ct[i][el])
end
for j in eachindex(vv)
for ord in eachindex(tmp)
zero!(tmp, ord)
@inbounds mul!(tmp, aux, vv[j], ord)
end
for ord in eachindex(tmp)
identity!(aux, tmp, ord)
end
# aux = one(valscache[1])
for ord in eachindex(aux)
@inbounds one!(aux, valscache[1], ord)
end
# suma += a_coeff * tmp
for ord in eachindex(tmp)
for ordQ in eachindex(tmp[ord])
zero!(aux[ord], ordQ)
aux[ord][ordQ] = a_coeff * tmp[ord][ordQ]
suma[ord][ordQ] += aux[ord][ordQ]
end
for j in eachindex(valscache)
# aux *= valscache[j]
mul!(aux, valscache[j])
end
# res += a_coeff * aux
for ord in eachindex(aux)
muladd!(res, a_coeff, aux, ord)
end
end
return nothing
end

function _evaluate(a::HomogeneousPolynomial{T}, vals::NTuple{N,<:TaylorN{T}}) where
{N,T<:NumberNotSeries}
# @assert length(vals) == get_numvars()
a.order == 0 && return a[1]*one(vals[1])
suma = TaylorN(zero(T), vals[1].order)
valscache = [zero(val) for val in vals]
aux = zero(suma)
_evaluate!(suma, a, vals, valscache, aux)
return suma
end

Expand Down Expand Up @@ -319,6 +318,17 @@ _evaluate(a::TaylorN{T}, vals::NTuple, ::Val{true}) where {T<:NumberNotSeries} =
_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}
R = promote_type(T, TS.numtype(vals[1]))
res = TaylorN(zero(R), vals[1].order)
valscache = [zero(val) for val in vals]
aux = zero(res)
@inbounds for homPol in eachindex(a)
_evaluate!(res, a[homPol], vals, valscache, aux)
end
return res
end

function _evaluate(a::TaylorN{T}, vals::NTuple{N,<:Number}) where {N,T<:Number}
R = promote_type(T, typeof(vals[1]))
a_length = length(a)
Expand All @@ -329,13 +339,20 @@ function _evaluate(a::TaylorN{T}, vals::NTuple{N,<:Number}) where {N,T<:Number}
return suma
end

function _evaluate(a::TaylorN{T}, vals::NTuple{N,<:TaylorN}) where {N,T<:Number}
R = TaylorN{promote_type(T, TS.numtype(vals[1]))}
a_length = length(a)
suma = zeros(R, a_length)
function _evaluate!(res::Vector{TaylorN{T}}, a::TaylorN{T}, vals::NTuple{N,<:TaylorN},
valscache::Vector{TaylorN{T}}, aux::TaylorN{T}) where {N,T<:Number}
@inbounds for homPol in eachindex(a)
suma[homPol+1] = _evaluate(a[homPol], vals)
_evaluate!(res[homPol+1], a[homPol], vals, valscache, aux)
end
return nothing
end

function _evaluate(a::TaylorN{T}, vals::NTuple{N,<:TaylorN}) where {N,T<:Number}
R = promote_type(T, TS.numtype(vals[1]))
suma = [TaylorN(zero(R), vals[1].order) for _ in eachindex(a)]
valscache = [zero(val) for val in vals]
aux = zero(suma[1])
_evaluate!(suma, a, vals, valscache, aux)
return suma
end

Expand Down Expand Up @@ -486,6 +503,24 @@ function evaluate!(x::AbstractArray{TaylorN{T}}, δx::Array{TaylorN{T},1},
return nothing
end

function evaluate!(a::TaylorN{T}, vals::NTuple{N,TaylorN{T}}, dest::TaylorN{T}, valscache::Vector{TaylorN{T}}, aux::TaylorN{T}) where {N,T<:Number}
@inbounds for homPol in eachindex(a)
_evaluate!(dest, a[homPol], vals, valscache, aux)
end
return nothing
end

function evaluate!(a::AbstractArray{TaylorN{T}}, vals::NTuple{N,TaylorN{T}}, dest::AbstractArray{TaylorN{T}}) where {N,T<:Number}
# initialize evaluation cache
valscache = [zero(val) for val in vals]
aux = zero(dest[1])
# loop over elements of `a`
for i in eachindex(a)
(!iszero(dest[i])) && zero!(dest[i])
evaluate!(a[i], vals, dest[i], valscache, aux)
end
return nothing
end

# In-place Horner methods, used when the result of an evaluation (substitution)
# is Taylor1{}
Expand Down
16 changes: 11 additions & 5 deletions src/functions.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -354,12 +354,18 @@ for T in (:Taylor1, :TaylorN)
return nothing
end

@inline function one!(c::$T{T}, a::$T{T}, k::Int) where {T<:Number}
zero!(c, k)
if k == 0
@inbounds c[0] = one(a[0])
if $T == Taylor1
@inline function one!(c::$T{T}, a::$T{T}, k::Int) where {T<:Number}
zero!(c, k)
(k == 0) && (@inbounds c[0] = one(constant_term(a)))
return nothing
end
else
@inline function one!(c::$T{T}, a::$T{T}, k::Int) where {T<:Number}
zero!(c, k)
(k == 0) && (@inbounds c[0][1] = one(constant_term(a)))
return nothing
end
return nothing
end

@inline function abs!(c::$T{T}, a::$T{T}, k::Int) where {T<:Number}
Expand Down
11 changes: 9 additions & 2 deletions src/power.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -62,8 +62,15 @@ end
# this method assumes `y`, `x` and `aux` are of same order
# TODO: add power_by_squaring! method for HomogeneousPolynomial and mixtures
for T in (:Taylor1, :TaylorN)
@eval function power_by_squaring!(y::$T{T}, x::$T{T}, aux::$T{T},
@eval @inline function power_by_squaring_0!(y::$T{T}, x::$T{T}) where {T<:NumberNotSeries}
for k in eachindex(y)
one!(y, x, k)
end
return nothing
end
@eval @inline function power_by_squaring!(y::$T{T}, x::$T{T}, aux::$T{T},
p::Integer) where {T<:NumberNotSeries}
(p == 0) && return power_by_squaring_0!(y, x)
t = trailing_zeros(p) + 1
p >>= t
# aux = x
Expand Down Expand Up @@ -272,7 +279,7 @@ exploits `k_0`, the order of the first non-zero coefficient of `a`.
isinteger(r) && r > 0 && (k > r*findlast(a)) && return nothing

if k == lnull
@inbounds c[k] = (a[l0])^r
@inbounds c[k] = (a[l0])^float(r)
return nothing
end

Expand Down
27 changes: 27 additions & 0 deletions test/manyvariables.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -821,6 +821,33 @@ end
@test float(TaylorN{Complex{Rational}}) == float(TaylorN{Complex{Float64}})
end

@testset "Test evaluate! method for arrays of TaylorN" begin
x = set_variables("x", order=2, numvars=4)
function radntn!(y)
for k in eachindex(y)
for l in eachindex(y[k])
y[k][l] = randn()
end
end
nothing
end
y = zero(x[1])
radntn!(y)
n = 10
v = [zero(x[1]) for _ in 1:n]
r = [zero(x[1]) for _ in 1:n] # output vector
radntn!.(v)
x1 = randn(4) .+ x
# warmup
TaylorSeries.evaluate!(v, (x1...,), r)
# call twice to make sure `r` is reset on second call
TaylorSeries.evaluate!(v, (x1...,), r)
r2 = evaluate.(v, Ref(x1))
@test r == r2
@test iszero(norm(r-r2, Inf))

end

end

@testset "Integrate for several variables" begin
Expand Down

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Registration pull request created: JuliaRegistries/General/111463

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Release notes:

## Breaking changes

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Tagging

After the above pull request is merged, it is recommended that a tag is created on this repository for the registered package version.

This will be done automatically if the Julia TagBot GitHub Action is installed, or can be done manually through the github interface, or via:

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