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use IntervalMatrices

Browse Source 
IntervalMatrices use Rump algorithm to matrix multiplication
This brings time to Qint'*Qint down to ~40s which is
5-8 × slower than Q'*Q (for size n=2^13).

The naive version is ~100 × slower than Q'*Q even for n = 2^10.
This commit is contained in:
Marek Kaluba 2023-04-06 13:17:52 +02:00
parent 17274f895f
commit 58f0ccb141
No known key found for this signature in database
GPG Key ID: 8BF1A3855328FC15
4 changed files with 34 additions and 156 deletions
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174
Manifest.toml
View File

@ -2,7 +2,7 @@
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@ -34,20 +17,9 @@ version = "1.1.1"
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@ -279,9 +206,9 @@ version = "0.21.3"
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@ -537,9 +439,9 @@ version = "0.2.0"
[[deps.StaticArrays]]
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@ -552,7 +454,7 @@ uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
[[deps.SymbolicWedderburn]]
deps = ["Cyclotomics", "GroupsCore", "LinearAlgebra", "PermutationGroups", "Primes", "SparseArrays", "StarAlgebras"]
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repo-rev = "enh/towards_simple_projections"
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@ -563,18 +465,6 @@ deps = ["Dates"]
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@ -614,12 +492,6 @@ deps = ["Libdl"]
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2
Project.toml
View File

@ -6,6 +6,7 @@ version = "0.4.0"
[deps]
Groups = "5d8bd718-bd84-11e8-3b40-ad14f4a32557"
IntervalArithmetic = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
IntervalMatrices = "5c1f47dc-42dd-5697-8aaa-4d102d140ba9"
JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
@ -17,6 +18,7 @@ SymbolicWedderburn = "858aa9a9-4c7c-4c62-b466-2421203962a2"
COSMO = "0.8"
Groups = "0.7"
IntervalArithmetic = "0.20"
IntervalMatrices = "0.8"
JuMP = "1.3"
ProgressMeter = "1.7"
SCS = "1.1"

1
src/PropertyT.jl
View File

@ -3,7 +3,6 @@ module PropertyT
using LinearAlgebra
using SparseArrays
using IntervalArithmetic
using JuMP
using Groups

13
src/certify.jl
View File

@ -1,3 +1,6 @@
import IntervalArithmetic
import IntervalMatrices
function augment_columns!(Q::AbstractMatrix)
for c in eachcol(Q)
c .-= sum(c) ./ length(c)
@ -63,7 +66,7 @@ function sufficient_λ(residual::StarAlgebras.AlgebraElement, λ; halfradius)
suff_λ = λ - 2.0^(2ceil(log2(halfradius))) * L1_norm
eq_sign = let T = eltype(residual)
if T <: Interval
if T <: IntervalArithmetic.Interval
"∈"
elseif T <: Union{Rational,Integer}
"="
@ -119,8 +122,10 @@ function certify_solution(
return false, λ_flpoint
end
λ_int = @interval(λ)
Q_int = [@interval(q) for q in Q]
λ_int = IntervalArithmetic.@interval(λ)
Q_int = IntervalMatrices.IntervalMatrix([
IntervalArithmetic.@interval(q) for q in Q
])
check, sos_int = @time if should_we_augment
@info("Projecting columns of Q to the augmentation ideal...")
@ -141,5 +146,5 @@ function certify_solution(
λ_certified =
sufficient_λ(elt, orderunit, λ_int, sos_int; halfradius = halfradius)
return check && inf(λ_certified) > 0.0, λ_certified
return check && IntervalArithmetic.inf(λ_certified) > 0.0, λ_certified
end