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Add tests for PiecewiseLegendrePolyVector (#55)
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* Add StableRNGs

* Increase tests for poly.jl

* Use ≈ (isapprox)

* Format matrix data

* Use all

* Update reference data

* Add tests for PiecewiseLegendrePolyVector
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@terasakisatoshi
terasakisatoshi authored Nov 17, 2024
1 parent fe1f56a commit a610813
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1 change: 1 addition & 0 deletions test/Project.toml
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Expand Up @@ -4,4 +4,5 @@ name = "SparseIR Tests"
Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
Logging = "56ddb016-857b-54e1-b83d-db4d58db5568"
Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
StableRNGs = "860ef19b-820b-49d6-a774-d7a799459cd3"
Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
376 changes: 376 additions & 0 deletions test/poly.jl
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@@ -1,10 +1,301 @@
using Test
using SparseIR
using SparseIR.LinearAlgebra
using StableRNGs: StableRNG

isdefined(Main, :sve_logistic) || include("_conftest.jl")

@testset "poly.jl" begin
@testset "StableRNG" begin
# Useful for porting poly.jl to C++
# https://github.com/SpM-lab/SparseIR.jl/issues/51
rng = StableRNG(2024)
data = rand(rng, 3, 3)
knots = rand(rng, size(data, 2) + 1) |> sort
@test data == [
0.8177021060277301 0.7085670484724618 0.5033588232863977;
0.3804323567786363 0.7911959541742282 0.8268504271915096;
0.5425813266814807 0.38397463704084633 0.21626598379927042
]
@test knots == [
0.507134318967235, 0.5766150365607372, 0.7126662232433161, 0.7357313003784003
]
@assert issorted(knots)

drng = StableRNG(999)
randsymm = rand(drng, 1:10)
randsymm == 9
ddata = rand(drng, 3, 3)
ddata == [
0.5328437345518631 0.8443074122979211 0.6722336389122814;
0.1799506228788046 0.6805545318460489 0.17641780726469292;
0.13124858727993338 0.2193663343416914 0.7756615110113394
]
end

@testset "PiecewiseLegendrePoly(data::Matrix, knots::Vector, l::Int)" begin
rng = StableRNG(2024)
data = rand(rng, 3, 3)
knots = rand(rng, size(data, 2) + 1) |> sort
l = 3

pwlp = SparseIR.PiecewiseLegendrePoly(data, knots, l)
@test pwlp.data == data
@test pwlp.xmin == first(knots)
@test pwlp.xmax == last(knots)
@test pwlp.knots == knots
@test pwlp.polyorder == size(data, 1)
@test pwlp.symm == 0
end

@testset "PiecewiseLegendrePoly(data, p::PiecewiseLegendrePoly; symm=symm(p))" begin
rng = StableRNG(2024)
data = rand(rng, 3, 3)
knots = rand(rng, size(data, 2) + 1) |> sort
l = 3

pwlp = SparseIR.PiecewiseLegendrePoly(data, knots, l)

drng = StableRNG(999)
randsymm = rand(drng, Int)
ddata = rand(drng, 3, 3)
ddata_pwlp = SparseIR.PiecewiseLegendrePoly(ddata, pwlp; symm=randsymm)

@test ddata_pwlp.data == ddata
@test ddata_pwlp.symm == randsymm
for n in fieldnames(SparseIR.PiecewiseLegendrePoly)
n === :data && continue
n === :symm && continue
@test getfield(pwlp, n) == getfield(ddata_pwlp, n)
end
end

@testset "PiecewiseLegendrePolyVector" begin
#=
julia> # The following data and knots are generated by
julia> using SparseIR
julia> sve_result = SparseIR.SVEResult(LogisticKernel(1.0))
julia> data1 = sve_result.u[1].data
julia> data2 = sve_result.u[2].data
julia> data3 = sve_result.u[3].data
julia> knots1 = sve_result.u[1].knots
julia> knots2 = sve_result.u[2].knots
julia> knots3 = sve_result.u[3].knots
julia> l1 = sve_result.u[1].l
julia> l2 = sve_result.u[2].l
julia> l3 = sve_result.u[3].l
=#
begin
data1 = reshape(
[
0.49996553669802485
-0.009838135710548356
0.003315915376286483
-2.4035906967802686e-5
3.4824832610792906e-6
-1.6818592059096e-8
1.5530850593697272e-9
-5.67191158452736e-12
3.8438802553084145e-13
-1.12861464373688e-15
-1.4028528586225198e-16
5.199431653846204e-18
-3.490774002228127e-16
4.339342349553959e-18
-8.247505551908268e-17
7.379549188001237e-19
0.49996553669802485
0.009838135710548356
0.003315915376286483
2.4035906967802686e-5
3.4824832610792906e-6
1.6818592059096e-8
1.5530850593697272e-9
5.67191158452736e-12
3.8438802553084145e-13
1.12861464373688e-15
-1.4028528586225198e-16
-5.199431653846204e-18
-3.490774002228127e-16
-4.339342349553959e-18
-8.247505551908268e-17
-7.379549188001237e-19
],
16,
2,
)

knots1 = [-1.0, 0.0, 1.0]
l1 = 0
end

begin
data2 = reshape(
[
-0.43195475509329695
0.436151579050162
-0.005257007544885257
0.0010660519696441624
-6.611545612452212e-6
7.461310619506964e-7
-3.2179499894475862e-9
2.5166526274315926e-10
-8.387341925898803e-13
5.008268649326024e-14
3.7750894390998034e-17
-2.304983535459561e-16
3.0252856483620636e-16
-1.923751082183687e-16
7.201014354168769e-17
-3.2715804561902326e-17
0.43195475509329695
0.436151579050162
0.005257007544885257
0.0010660519696441624
6.611545612452212e-6
7.461310619506964e-7
3.2179499894475862e-9
2.5166526274315926e-10
8.387341925898803e-13
5.008268649326024e-14
-3.7750894390998034e-17
-2.304983535459561e-16
-3.0252856483620636e-16
-1.923751082183687e-16
-7.201014354168769e-17
-3.2715804561902326e-17
],
16,
2,
)

knots2 = [-1.0, 0.0, 1.0]
l2 = 1
end

begin
data3 = reshape(
[
-0.005870438661638806
-0.8376202388555938
0.28368166184926036
-0.0029450618222246236
0.0004277118923277169
-2.4101642603229184e-6
2.2287962786878678e-7
-8.875091544426018e-10
6.021488924175155e-11
-1.8705305570705647e-13
9.924398482443944e-15
4.299521053905097e-16
-1.0697019178666955e-16
3.6972269778329906e-16
-8.848885164903329e-17
6.327687614609368e-17
-0.005870438661638806
0.8376202388555938
0.28368166184926036
0.0029450618222246236
0.0004277118923277169
2.4101642603229184e-6
2.2287962786878678e-7
8.875091544426018e-10
6.021488924175155e-11
1.8705305570705647e-13
9.924398482443944e-15
-4.299521053905097e-16
-1.0697019178666955e-16
-3.6972269778329906e-16
-8.848885164903329e-17
-6.327687614609368e-17
],
16,
2,
)

knots3 = [-1.0, 0.0, 1.0]
l3 = 2
end

pwlp1 = SparseIR.PiecewiseLegendrePoly(data1, knots1, l1)
pwlp2 = SparseIR.PiecewiseLegendrePoly(data2, knots2, l2)
pwlp3 = SparseIR.PiecewiseLegendrePoly(data3, knots3, l3)

polys = SparseIR.PiecewiseLegendrePolyVector([pwlp1, pwlp2, pwlp3])

@test length(polys) == 3

polys = SparseIR.PiecewiseLegendrePolyVector(
[
SparseIR.PiecewiseLegendrePoly(data1, knots1, l1)
SparseIR.PiecewiseLegendrePoly(data2, knots2, l2)
SparseIR.PiecewiseLegendrePoly(data3, knots3, l3)
],
)

@test SparseIR.xmin(polys) == SparseIR.xmin(pwlp1)
@test SparseIR.xmax(polys) == SparseIR.xmax(pwlp1)
@test SparseIR.knots(polys) == SparseIR.knots(pwlp1)
@test SparseIR.Δx(polys) == SparseIR.Δx(pwlp1)
@test SparseIR.polyorder(polys) == SparseIR.polyorder(pwlp1)
@test SparseIR.norms(polys) == SparseIR.norms(pwlp1)
@test SparseIR.symm(polys) == SparseIR.symm.([pwlp1, pwlp2, pwlp3])

@testset "polys(x::Float64)" begin
x = rand(StableRNG(42))
@test polys(x) == [pwlp1(x), pwlp2(x), pwlp3(x)]
@test SparseIR.data(polys) ==
cat(SparseIR.data.([pwlp1, pwlp2, pwlp3])..., dims = 3)
end

@testset "polys(x::Array)" begin
x = rand(StableRNG(42), 2, 1, 4)
tar = polys(x)
@test size(tar) == (3, 2, 1, 4)
ref = reshape(vcat([[pwlp1(e), pwlp2(e), pwlp3(e)] for e in x]...), 3, 2, 1, 4)
@test tar == ref
end

@testset "PiecewiseLegendrePolyVector(polys::PiecewiseLegendrePolyVector, knots::AbstractVector)" begin
new_knots = [-1.0, 0.0, 1.0]

new_polys = SparseIR.PiecewiseLegendrePolyVector(
polys, new_knots,
symm=zeros(Int, size(SparseIR.data(polys), 3)),
)

@test SparseIR.data(new_polys) == SparseIR.data(polys)
@test SparseIR.knots(new_polys) == SparseIR.knots(new_polys)
@test SparseIR.Δx(new_polys) == diff(new_knots)
end
end

@testset "deriv" begin
# independent from sve.jl
# https://github.com/SpM-lab/SparseIR.jl/issues/51
rng = StableRNG(2024)

data = rand(rng, 3, 3)
knots = rand(rng, size(data, 2) + 1) |> sort
l = 3
pwlp = SparseIR.PiecewiseLegendrePoly(data, knots, l)

n = 1
ddata = SparseIR.legder(pwlp.data, n)
ddata .*= pwlp.inv_xs'

deriv_pwlp = SparseIR.deriv(pwlp)

@test deriv_pwlp.data == ddata
@test deriv_pwlp.symm == 0

for n in fieldnames(SparseIR.PiecewiseLegendrePoly)
n === :data && continue
n === :symm && continue
@test getfield(pwlp, n) == getfield(deriv_pwlp, n)
end
end

@testset "shape" begin
u, s, v = SparseIR.part(sve_logistic[42])
l = length(s)
Expand Down Expand Up @@ -64,6 +355,91 @@ isdefined(Main, :sve_logistic) || include("_conftest.jl")
@test all(isapprox.(overlap(u[1], u), ref; rtol=0, atol))
end

@testset "overlap(poly::PiecewiseLegendrePoly, f::F)" begin
# independent from sve.jl
# https://github.com/SpM-lab/SparseIR.jl/issues/51
rng = StableRNG(2024)

data = rand(rng, 3, 3)
knots = rand(rng, size(data, 2) + 1) |> sort
l = 3
pwlp = SparseIR.PiecewiseLegendrePoly(data, knots, l)

if Sys.isapple() && Sys.ARCH === :aarch64
# On macOS (arm64-apple-darwin22.4.0), we get
∫pwlp, ∫pwlp_err = (0.4934184996836404, 8.326672684688674e-17)
else
∫pwlp, ∫pwlp_err = (0.4934184996836403, 2.7755575615628914e-17)
end

@test overlap(pwlp, identity) ≈ ∫pwlp
@test all(overlap(pwlp, identity, return_error=true) .≈ (∫pwlp, ∫pwlp_err))
end

@testset "roots(poly::PiecewiseLegendrePoly; tol=1e-10, alpha=Val(2))" begin
# https://github.com/SpM-lab/SparseIR.jl/issues/51
#=
The following data and knots are generated by
julia> using SparseIR
julia> using Test
julia> Λ = 1.0
julia> sve_result = SparseIR.SVEResult(SparseIR.LogisticKernel(Λ))
julia> basis = SparseIR.FiniteTempBasis{SparseIR.Fermionic}(1, Λ; sve_result)
=#

data = reshape([
0.16774734206553019
0.49223680914312595
-0.8276728567928646
0.16912891046582143
-0.0016231275318572044
0.00018381683946452256
-9.699355027805034e-7
7.60144228530804e-8
-2.8518324490258146e-10
1.7090590205708293e-11
-5.0081401126025e-14
2.1244236198427895e-15
2.0478095258000225e-16
-2.676573801530628e-16
2.338165820094204e-16
-1.2050663212312096e-16
-0.16774734206553019
0.49223680914312595
0.8276728567928646
0.16912891046582143
0.0016231275318572044
0.00018381683946452256
9.699355027805034e-7
7.60144228530804e-8
2.8518324490258146e-10
1.7090590205708293e-11
5.0081401126025e-14
2.1244236198427895e-15
-2.0478095258000225e-16
-2.676573801530628e-16
-2.338165820094204e-16
-1.2050663212312096e-16
], 16, 2)

knots = [0.0, 0.5, 1.0]
l = 3

# expected behavior
#=
julia> @test basis.u[4].data == data
julia> @test basis.u[4].knots == knots
julia> @test basis.u[4].l == l
=#

pwlp = SparseIR.PiecewiseLegendrePoly(data, knots, l)
@test SparseIR.roots(pwlp) == [
0.1118633448586015
0.4999999999999998
0.8881366551413985
]
end

@testset "eval unique" begin
u, s, v = SparseIR.part(sve_logistic[42])
û = SparseIR.PiecewiseLegendreFTVector(u, Fermionic())
Expand Down

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