From 1c87bcd22b74b103963a027c4845fcd0ab422b9e Mon Sep 17 00:00:00 2001
From: jaimerzp <jaimerz011235813@gmal.com>
Date: Tue, 17 Sep 2024 12:14:15 +0100
Subject: [PATCH] Turing tests

---
 Manifest.toml            | 842 ++++++++++++++++++++++++++++++++++++++-
 Project.toml             |   1 +
 src/MicroCanonicalHMC.jl |   2 +-
 test/turing.jl           |   2 +-
 4 files changed, 844 insertions(+), 3 deletions(-)

diff --git a/Manifest.toml b/Manifest.toml
index 8ba99f9..5472e45 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -2,7 +2,7 @@
 
 julia_version = "1.10.3"
 manifest_format = "2.0"
-project_hash = "c885513dd31088f4f7a94be8a194a058ba6e289c"
+project_hash = "8d5d365aa071b44ea9dddeccf081ff5d62da916a"
 
 [[deps.ADTypes]]
 git-tree-sha1 = "99a6f5d0ce1c7c6afdb759daa30226f71c54f6b0"
@@ -76,6 +76,62 @@ weakdeps = ["StaticArrays"]
     [deps.Adapt.extensions]
     AdaptStaticArraysExt = "StaticArrays"
 
+[[deps.AdvancedHMC]]
+deps = ["AbstractMCMC", "ArgCheck", "DocStringExtensions", "InplaceOps", "LinearAlgebra", "LogDensityProblems", "LogDensityProblemsAD", "ProgressMeter", "Random", "Requires", "Setfield", "SimpleUnPack", "Statistics", "StatsBase", "StatsFuns"]
+git-tree-sha1 = "dfa0e3508fc3df81d28624b328f3b937c1df8bc2"
+uuid = "0bf59076-c3b1-5ca4-86bd-e02cd72cde3d"
+version = "0.6.1"
+
+    [deps.AdvancedHMC.extensions]
+    AdvancedHMCCUDAExt = "CUDA"
+    AdvancedHMCMCMCChainsExt = "MCMCChains"
+    AdvancedHMCOrdinaryDiffEqExt = "OrdinaryDiffEq"
+
+    [deps.AdvancedHMC.weakdeps]
+    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+    MCMCChains = "c7f686f2-ff18-58e9-bc7b-31028e88f75d"
+    OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+
+[[deps.AdvancedMH]]
+deps = ["AbstractMCMC", "Distributions", "FillArrays", "LinearAlgebra", "LogDensityProblems", "Random", "Requires"]
+git-tree-sha1 = "fa4e8d6f9bae913aaa40224cf9407163e693d829"
+uuid = "5b7e9947-ddc0-4b3f-9b55-0d8042f74170"
+version = "0.8.2"
+weakdeps = ["DiffResults", "ForwardDiff", "MCMCChains", "StructArrays"]
+
+    [deps.AdvancedMH.extensions]
+    AdvancedMHForwardDiffExt = ["DiffResults", "ForwardDiff"]
+    AdvancedMHMCMCChainsExt = "MCMCChains"
+    AdvancedMHStructArraysExt = "StructArrays"
+
+[[deps.AdvancedPS]]
+deps = ["AbstractMCMC", "Distributions", "Random", "Random123", "Requires", "SSMProblems", "StatsFuns"]
+git-tree-sha1 = "5dcd3de7e7346f48739256e71a86d0f96690b8c8"
+uuid = "576499cb-2369-40b2-a588-c64705576edc"
+version = "0.6.0"
+weakdeps = ["Libtask"]
+
+    [deps.AdvancedPS.extensions]
+    AdvancedPSLibtaskExt = "Libtask"
+
+[[deps.AdvancedVI]]
+deps = ["ADTypes", "Bijectors", "DiffResults", "Distributions", "DistributionsAD", "DocStringExtensions", "ForwardDiff", "LinearAlgebra", "ProgressMeter", "Random", "Requires", "StatsBase", "StatsFuns", "Tracker"]
+git-tree-sha1 = "3e97de1a2ccce08978cd80570d8cbb9ff3f08bd3"
+uuid = "b5ca4192-6429-45e5-a2d9-87aec30a685c"
+version = "0.2.6"
+
+    [deps.AdvancedVI.extensions]
+    AdvancedVIEnzymeExt = ["Enzyme"]
+    AdvancedVIFluxExt = ["Flux"]
+    AdvancedVIReverseDiffExt = ["ReverseDiff"]
+    AdvancedVIZygoteExt = ["Zygote"]
+
+    [deps.AdvancedVI.weakdeps]
+    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+    Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
 [[deps.AliasTables]]
 deps = ["PtrArrays", "Random"]
 git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
@@ -91,9 +147,51 @@ version = "2.3.0"
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 version = "1.1.1"
 
+[[deps.ArnoldiMethod]]
+deps = ["LinearAlgebra", "Random", "StaticArrays"]
+git-tree-sha1 = "d57bd3762d308bded22c3b82d033bff85f6195c6"
+uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
+version = "0.4.0"
+
+[[deps.ArrayInterface]]
+deps = ["Adapt", "LinearAlgebra"]
+git-tree-sha1 = "3640d077b6dafd64ceb8fd5c1ec76f7ca53bcf76"
+uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
+version = "7.16.0"
+
+    [deps.ArrayInterface.extensions]
+    ArrayInterfaceBandedMatricesExt = "BandedMatrices"
+    ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
+    ArrayInterfaceCUDAExt = "CUDA"
+    ArrayInterfaceCUDSSExt = "CUDSS"
+    ArrayInterfaceChainRulesExt = "ChainRules"
+    ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
+    ArrayInterfaceReverseDiffExt = "ReverseDiff"
+    ArrayInterfaceSparseArraysExt = "SparseArrays"
+    ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
+    ArrayInterfaceTrackerExt = "Tracker"
+
+    [deps.ArrayInterface.weakdeps]
+    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+    CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e"
+    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+    GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
 [[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 
+[[deps.Atomix]]
+deps = ["UnsafeAtomics"]
+git-tree-sha1 = "c06a868224ecba914baa6942988e2f2aade419be"
+uuid = "a9b6321e-bd34-4604-b9c9-b65b8de01458"
+version = "0.1.0"
+
 [[deps.AxisAlgorithms]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "WoodburyMatrices"]
 git-tree-sha1 = "01b8ccb13d68535d73d2b0c23e39bd23155fb712"
@@ -136,6 +234,11 @@ git-tree-sha1 = "aebf55e6d7795e02ca500a689d326ac979aaf89e"
 uuid = "9718e550-a3fa-408a-8086-8db961cd8217"
 version = "0.1.1"
 
+[[deps.Bijections]]
+git-tree-sha1 = "d8b0439d2be438a5f2cd68ec158fe08a7b2595b7"
+uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
+version = "0.1.9"
+
 [[deps.Bijectors]]
 deps = ["ArgCheck", "ChainRules", "ChainRulesCore", "ChangesOfVariables", "Compat", "Distributions", "DocStringExtensions", "Functors", "InverseFunctions", "IrrationalConstants", "LinearAlgebra", "LogExpFunctions", "MappedArrays", "Random", "Reexport", "Requires", "Roots", "SparseArrays", "Statistics"]
 git-tree-sha1 = "92edc3544607c4fda1b30357910597e2a70dc5ea"
@@ -162,6 +265,11 @@ version = "0.13.18"
     Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
     Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
+[[deps.CEnum]]
+git-tree-sha1 = "389ad5c84de1ae7cf0e28e381131c98ea87d54fc"
+uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
+version = "0.5.0"
+
 [[deps.Calculus]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
@@ -195,6 +303,11 @@ weakdeps = ["InverseFunctions", "Test"]
     ChangesOfVariablesInverseFunctionsExt = "InverseFunctions"
     ChangesOfVariablesTestExt = "Test"
 
+[[deps.Combinatorics]]
+git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
+uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
+version = "1.0.2"
+
 [[deps.CommonSolve]]
 git-tree-sha1 = "0eee5eb66b1cf62cd6ad1b460238e60e4b09400c"
 uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
@@ -206,6 +319,11 @@ git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
 uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
 version = "0.3.0"
 
+[[deps.CommonWorldInvalidations]]
+git-tree-sha1 = "ae52d1c52048455e85a387fbee9be553ec2b68d0"
+uuid = "f70d9fcc-98c5-4d4a-abd7-e4cdeebd8ca8"
+version = "1.0.0"
+
 [[deps.Compat]]
 deps = ["TOML", "UUIDs"]
 git-tree-sha1 = "b1c55339b7c6c350ee89f2c1604299660525b248"
@@ -221,6 +339,11 @@ deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 version = "1.1.1+0"
 
+[[deps.CompositeTypes]]
+git-tree-sha1 = "bce26c3dab336582805503bed209faab1c279768"
+uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657"
+version = "0.1.4"
+
 [[deps.CompositionsBase]]
 git-tree-sha1 = "802bb88cd69dfd1509f6670416bd4434015693ad"
 uuid = "a33af91c-f02d-484b-be07-31d278c5ca2b"
@@ -252,6 +375,12 @@ git-tree-sha1 = "249fe38abf76d48563e2f4556bebd215aa317e15"
 uuid = "a8cc5b0e-0ffa-5ad4-8c14-923d3ee1735f"
 version = "4.1.1"
 
+[[deps.DSP]]
+deps = ["Compat", "FFTW", "IterTools", "LinearAlgebra", "Polynomials", "Random", "Reexport", "SpecialFunctions", "Statistics"]
+git-tree-sha1 = "f7f4319567fe769debfcf7f8c03d8da1dd4e2fb0"
+uuid = "717857b8-e6f2-59f4-9121-6e50c889abd2"
+version = "0.7.9"
+
 [[deps.DataAPI]]
 git-tree-sha1 = "abe83f3a2f1b857aac70ef8b269080af17764bbe"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
@@ -277,12 +406,24 @@ git-tree-sha1 = "0fba8b706d0178b4dc7fd44a96a92382c9065c2c"
 uuid = "244e2a9f-e319-4986-a169-4d1fe445cd52"
 version = "0.1.2"
 
+[[deps.DelimitedFiles]]
+deps = ["Mmap"]
+git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
+uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
+version = "1.9.1"
+
 [[deps.DensityInterface]]
 deps = ["InverseFunctions", "Test"]
 git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
 uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
 version = "0.4.0"
 
+[[deps.Dictionaries]]
+deps = ["Indexing", "Random", "Serialization"]
+git-tree-sha1 = "35b66b6744b2d92c778afd3a88d2571875664a2a"
+uuid = "85a47980-9c8c-11e8-2b9f-f7ca1fa99fb4"
+version = "0.4.2"
+
 [[deps.DiffResults]]
 deps = ["StaticArraysCore"]
 git-tree-sha1 = "782dd5f4561f5d267313f23853baaaa4c52ea621"
@@ -311,12 +452,42 @@ weakdeps = ["ChainRulesCore", "DensityInterface", "Test"]
     DistributionsDensityInterfaceExt = "DensityInterface"
     DistributionsTestExt = "Test"
 
+[[deps.DistributionsAD]]
+deps = ["Adapt", "ChainRules", "ChainRulesCore", "Compat", "Distributions", "FillArrays", "LinearAlgebra", "PDMats", "Random", "Requires", "SpecialFunctions", "StaticArrays", "StatsFuns", "ZygoteRules"]
+git-tree-sha1 = "f4dd7727b07b4b7fff5ff4149118ee06e83dfab7"
+uuid = "ced4e74d-a319-5a8a-b0ac-84af2272839c"
+version = "0.6.55"
+
+    [deps.DistributionsAD.extensions]
+    DistributionsADForwardDiffExt = "ForwardDiff"
+    DistributionsADLazyArraysExt = "LazyArrays"
+    DistributionsADReverseDiffExt = "ReverseDiff"
+    DistributionsADTrackerExt = "Tracker"
+
+    [deps.DistributionsAD.weakdeps]
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    LazyArrays = "5078a376-72f3-5289-bfd5-ec5146d43c02"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
 [[deps.DocStringExtensions]]
 deps = ["LibGit2"]
 git-tree-sha1 = "2fb1e02f2b635d0845df5d7c167fec4dd739b00d"
 uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
 version = "0.9.3"
 
+[[deps.DomainSets]]
+deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "Random", "StaticArrays"]
+git-tree-sha1 = "490392af2c7d63183bfa2c8aaa6ab981c5ba7561"
+uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
+version = "0.7.14"
+
+    [deps.DomainSets.extensions]
+    DomainSetsMakieExt = "Makie"
+
+    [deps.DomainSets.weakdeps]
+    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+
 [[deps.Downloads]]
 deps = ["ArgTools", "FileWatching", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
@@ -350,6 +521,40 @@ version = "0.28.4"
     ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
     ZygoteRules = "700de1a5-db45-46bc-99cf-38207098b444"
 
+[[deps.DynamicPolynomials]]
+deps = ["Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Reexport", "Test"]
+git-tree-sha1 = "bbf1ace0781d9744cb697fb856bd2c3f6568dadb"
+uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
+version = "0.6.0"
+
+[[deps.Einsum]]
+deps = ["Compat"]
+git-tree-sha1 = "4a6b3eee0161c89700b6c1949feae8b851da5494"
+uuid = "b7d42ee7-0b51-5a75-98ca-779d3107e4c0"
+version = "0.4.1"
+
+[[deps.EllipticalSliceSampling]]
+deps = ["AbstractMCMC", "ArrayInterface", "Distributions", "Random", "Statistics"]
+git-tree-sha1 = "e611b7fdfbfb5b18d5e98776c30daede41b44542"
+uuid = "cad2338a-1db2-11e9-3401-43bc07c9ede2"
+version = "2.0.0"
+
+[[deps.EnumX]]
+git-tree-sha1 = "bdb1942cd4c45e3c678fd11569d5cccd80976237"
+uuid = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
+version = "1.0.4"
+
+[[deps.ExprTools]]
+git-tree-sha1 = "27415f162e6028e81c72b82ef756bf321213b6ec"
+uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
+version = "0.1.10"
+
+[[deps.Expronicon]]
+deps = ["MLStyle", "Pkg", "TOML"]
+git-tree-sha1 = "fc3951d4d398b5515f91d7fe5d45fc31dccb3c9b"
+uuid = "6b7a57c9-7cc1-4fdf-b7f5-e857abae3636"
+version = "0.8.5"
+
 [[deps.FFTW]]
 deps = ["AbstractFFTs", "FFTW_jll", "LinearAlgebra", "MKL_jll", "Preferences", "Reexport"]
 git-tree-sha1 = "4820348781ae578893311153d69049a93d05f39d"
@@ -377,6 +582,27 @@ weakdeps = ["PDMats", "SparseArrays", "Statistics"]
     FillArraysSparseArraysExt = "SparseArrays"
     FillArraysStatisticsExt = "Statistics"
 
+[[deps.FiniteDiff]]
+deps = ["ArrayInterface", "LinearAlgebra", "Setfield", "SparseArrays"]
+git-tree-sha1 = "f9219347ebf700e77ca1d48ef84e4a82a6701882"
+uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
+version = "2.24.0"
+
+    [deps.FiniteDiff.extensions]
+    FiniteDiffBandedMatricesExt = "BandedMatrices"
+    FiniteDiffBlockBandedMatricesExt = "BlockBandedMatrices"
+    FiniteDiffStaticArraysExt = "StaticArrays"
+
+    [deps.FiniteDiff.weakdeps]
+    BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+    BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+    StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+
+[[deps.Format]]
+git-tree-sha1 = "9c68794ef81b08086aeb32eeaf33531668d5f5fc"
+uuid = "1fa38f19-a742-5d3f-a2b9-30dd87b9d5f8"
+version = "1.3.7"
+
 [[deps.ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions"]
 git-tree-sha1 = "cf0fe81336da9fb90944683b8c41984b08793dad"
@@ -387,6 +613,17 @@ weakdeps = ["StaticArrays"]
     [deps.ForwardDiff.extensions]
     ForwardDiffStaticArraysExt = "StaticArrays"
 
+[[deps.FunctionWrappers]]
+git-tree-sha1 = "d62485945ce5ae9c0c48f124a84998d755bae00e"
+uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
+version = "1.1.3"
+
+[[deps.FunctionWrappersWrappers]]
+deps = ["FunctionWrappers"]
+git-tree-sha1 = "b104d487b34566608f8b4e1c39fb0b10aa279ff8"
+uuid = "77dc65aa-8811-40c2-897b-53d922fa7daf"
+version = "0.1.3"
+
 [[deps.Functors]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "64d8e93700c7a3f28f717d265382d52fac9fa1c1"
@@ -403,6 +640,12 @@ git-tree-sha1 = "ec632f177c0d990e64d955ccc1b8c04c485a0950"
 uuid = "46192b85-c4d5-4398-a991-12ede77f4527"
 version = "0.1.6"
 
+[[deps.Graphs]]
+deps = ["ArnoldiMethod", "Compat", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
+git-tree-sha1 = "ebd18c326fa6cee1efb7da9a3b45cf69da2ed4d9"
+uuid = "86223c79-3864-5bf0-83f7-82e725a168b6"
+version = "1.11.2"
+
 [[deps.HDF5]]
 deps = ["Compat", "HDF5_jll", "Libdl", "MPIPreferences", "Mmap", "Preferences", "Printf", "Random", "Requires", "UUIDs"]
 git-tree-sha1 = "e856eef26cf5bf2b0f95f8f4fc37553c72c8641c"
@@ -427,17 +670,49 @@ git-tree-sha1 = "ca0f6bf568b4bfc807e7537f081c81e35ceca114"
 uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
 version = "2.10.0+0"
 
+[[deps.HybridArrays]]
+deps = ["LinearAlgebra", "Requires", "StaticArrays"]
+git-tree-sha1 = "6c3e57bc26728b99f470b267a437f0d380eac4fc"
+uuid = "1baab800-613f-4b0a-84e4-9cd3431bfbb9"
+version = "0.4.16"
+
 [[deps.HypergeometricFunctions]]
 deps = ["DualNumbers", "LinearAlgebra", "OpenLibm_jll", "SpecialFunctions"]
 git-tree-sha1 = "f218fe3736ddf977e0e772bc9a586b2383da2685"
 uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
 version = "0.3.23"
 
+[[deps.IfElse]]
+git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
+uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
+version = "0.1.1"
+
+[[deps.Indexing]]
+git-tree-sha1 = "ce1566720fd6b19ff3411404d4b977acd4814f9f"
+uuid = "313cdc1a-70c2-5d6a-ae34-0150d3930a38"
+version = "1.1.1"
+
+[[deps.Inflate]]
+git-tree-sha1 = "d1b1b796e47d94588b3757fe84fbf65a5ec4a80d"
+uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
+version = "0.1.5"
+
 [[deps.InitialValues]]
 git-tree-sha1 = "4da0f88e9a39111c2fa3add390ab15f3a44f3ca3"
 uuid = "22cec73e-a1b8-11e9-2c92-598750a2cf9c"
 version = "0.3.1"
 
+[[deps.InplaceOps]]
+deps = ["LinearAlgebra", "Test"]
+git-tree-sha1 = "50b41d59e7164ab6fda65e71049fee9d890731ff"
+uuid = "505f98c9-085e-5b2c-8e89-488be7bf1f34"
+version = "0.3.0"
+
+[[deps.IntegerMathUtils]]
+git-tree-sha1 = "b8ffb903da9f7b8cf695a8bead8e01814aa24b30"
+uuid = "18e54dd8-cb9d-406c-a71d-865a43cbb235"
+version = "0.1.2"
+
 [[deps.IntelOpenMP_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "be50fe8df3acbffa0274a744f1a99d29c45a57f4"
@@ -481,6 +756,11 @@ weakdeps = ["Dates"]
     [deps.InverseFunctions.extensions]
     DatesExt = "Dates"
 
+[[deps.InvertedIndices]]
+git-tree-sha1 = "0dc7b50b8d436461be01300fd8cd45aa0274b038"
+uuid = "41ab1584-1d38-5bbf-9106-f11c6c58b48f"
+version = "1.3.0"
+
 [[deps.IrrationalConstants]]
 git-tree-sha1 = "630b497eafcc20001bba38a4651b327dcfc491d2"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
@@ -502,17 +782,99 @@ git-tree-sha1 = "7e5d6779a1e09a36db2a7b6cff50942a0a7d0fca"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
 version = "1.5.0"
 
+[[deps.KernelAbstractions]]
+deps = ["Adapt", "Atomix", "InteractiveUtils", "MacroTools", "PrecompileTools", "Requires", "StaticArrays", "UUIDs", "UnsafeAtomics", "UnsafeAtomicsLLVM"]
+git-tree-sha1 = "cb1cff88ef2f3a157cbad75bbe6b229e1975e498"
+uuid = "63c18a36-062a-441e-b654-da1e3ab1ce7c"
+version = "0.9.25"
+
+    [deps.KernelAbstractions.extensions]
+    EnzymeExt = "EnzymeCore"
+    LinearAlgebraExt = "LinearAlgebra"
+    SparseArraysExt = "SparseArrays"
+
+    [deps.KernelAbstractions.weakdeps]
+    EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
+    LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+
 [[deps.KernelDensity]]
 deps = ["Distributions", "DocStringExtensions", "FFTW", "Interpolations", "StatsBase"]
 git-tree-sha1 = "7d703202e65efa1369de1279c162b915e245eed1"
 uuid = "5ab0869b-81aa-558d-bb23-cbf5423bbe9b"
 version = "0.6.9"
 
+[[deps.Kronecker]]
+deps = ["LinearAlgebra", "NamedDims", "SparseArrays", "StatsBase"]
+git-tree-sha1 = "9253429e28cceae6e823bec9ffde12460d79bb38"
+uuid = "2c470bb0-bcc8-11e8-3dad-c9649493f05e"
+version = "0.5.5"
+
+[[deps.LBFGSB]]
+deps = ["L_BFGS_B_jll"]
+git-tree-sha1 = "e2e6f53ee20605d0ea2be473480b7480bd5091b5"
+uuid = "5be7bae1-8223-5378-bac3-9e7378a2f6e6"
+version = "0.4.1"
+
+[[deps.LLVM]]
+deps = ["CEnum", "LLVMExtra_jll", "Libdl", "Preferences", "Printf", "Requires", "Unicode"]
+git-tree-sha1 = "4ad43cb0a4bb5e5b1506e1d1f48646d7e0c80363"
+uuid = "929cbde3-209d-540e-8aea-75f648917ca0"
+version = "9.1.2"
+
+    [deps.LLVM.extensions]
+    BFloat16sExt = "BFloat16s"
+
+    [deps.LLVM.weakdeps]
+    BFloat16s = "ab4f0b2a-ad5b-11e8-123f-65d77653426b"
+
+[[deps.LLVMExtra_jll]]
+deps = ["Artifacts", "JLLWrappers", "LazyArtifacts", "Libdl", "TOML"]
+git-tree-sha1 = "05a8bd5a42309a9ec82f700876903abce1017dd3"
+uuid = "dad2f222-ce93-54a1-a47d-0025e8a3acab"
+version = "0.0.34+0"
+
+[[deps.LRUCache]]
+git-tree-sha1 = "b3cc6698599b10e652832c2f23db3cab99d51b59"
+uuid = "8ac3fa9e-de4c-5943-b1dc-09c6b5f20637"
+version = "1.6.1"
+weakdeps = ["Serialization"]
+
+    [deps.LRUCache.extensions]
+    SerializationExt = ["Serialization"]
+
+[[deps.L_BFGS_B_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "77feda930ed3f04b2b0fbb5bea89e69d3677c6b0"
+uuid = "81d17ec3-03a1-5e46-b53e-bddc35a13473"
+version = "3.0.1+0"
+
 [[deps.LaTeXStrings]]
 git-tree-sha1 = "50901ebc375ed41dbf8058da26f9de442febbbec"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
 version = "1.3.1"
 
+[[deps.LambertW]]
+git-tree-sha1 = "c5ffc834de5d61d00d2b0e18c96267cffc21f648"
+uuid = "984bce1d-4616-540c-a9ee-88d1112d94c9"
+version = "0.4.6"
+
+[[deps.Latexify]]
+deps = ["Format", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "OrderedCollections", "Requires"]
+git-tree-sha1 = "ce5f5621cac23a86011836badfedf664a612cee4"
+uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+version = "0.16.5"
+
+    [deps.Latexify.extensions]
+    DataFramesExt = "DataFrames"
+    SparseArraysExt = "SparseArrays"
+    SymEngineExt = "SymEngine"
+
+    [deps.Latexify.weakdeps]
+    DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    SymEngine = "123dc426-2d89-5057-bbad-38513e3affd8"
+
 [[deps.LazyArtifacts]]
 deps = ["Artifacts", "Pkg"]
 uuid = "4af54fe1-eca0-43a8-85a7-787d91b784e3"
@@ -550,10 +912,34 @@ version = "1.11.0+1"
 [[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
+[[deps.Libtask]]
+deps = ["FunctionWrappers", "LRUCache", "LinearAlgebra", "Statistics"]
+git-tree-sha1 = "ed1f362b3fd13f00b65e61d98669c652c17663ab"
+uuid = "6f1fad26-d15e-5dc8-ae53-837a1d7b8c9f"
+version = "0.8.7"
+
+[[deps.LineSearches]]
+deps = ["LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "Printf"]
+git-tree-sha1 = "e4c3be53733db1051cc15ecf573b1042b3a712a1"
+uuid = "d3d80556-e9d4-5f37-9878-2ab0fcc64255"
+version = "7.3.0"
+
 [[deps.LinearAlgebra]]
 deps = ["Libdl", "OpenBLAS_jll", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
+[[deps.LinearMaps]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "ee79c3208e55786de58f8dcccca098ced79f743f"
+uuid = "7a12625a-238d-50fd-b39a-03d52299707e"
+version = "3.11.3"
+weakdeps = ["ChainRulesCore", "SparseArrays", "Statistics"]
+
+    [deps.LinearMaps.extensions]
+    LinearMapsChainRulesCoreExt = "ChainRulesCore"
+    LinearMapsSparseArraysExt = "SparseArrays"
+    LinearMapsStatisticsExt = "Statistics"
+
 [[deps.LogDensityProblems]]
 deps = ["ArgCheck", "DocStringExtensions", "Random"]
 git-tree-sha1 = "f9a11237204bc137617194d79d813069838fcf61"
@@ -631,6 +1017,11 @@ git-tree-sha1 = "d2a45e1b5998ba3fdfb6cfe0c81096d4c7fb40e7"
 uuid = "e80e1ace-859a-464e-9ed9-23947d8ae3ea"
 version = "1.9.6"
 
+[[deps.MLStyle]]
+git-tree-sha1 = "bc38dff0548128765760c79eb7388a4b37fae2c8"
+uuid = "d8e11817-5142-5d16-987a-aa16d5891078"
+version = "0.4.17"
+
 [[deps.MPICH_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Hwloc_jll", "JLLWrappers", "LazyArtifacts", "Libdl", "MPIPreferences", "TOML"]
 git-tree-sha1 = "4099bb6809ac109bfc17d521dad33763bcf026b7"
@@ -655,6 +1046,67 @@ git-tree-sha1 = "2fa9ee3e63fd3a4f7a9a4f4744a52f4856de82df"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
 version = "0.5.13"
 
+[[deps.ManifoldDiff]]
+deps = ["LinearAlgebra", "ManifoldsBase", "Markdown", "Random", "Requires"]
+git-tree-sha1 = "62fccd67f9fb83526bff40a1432f63464eb6d282"
+uuid = "af67fdf4-a580-4b9f-bbec-742ef357defd"
+version = "0.3.12"
+
+    [deps.ManifoldDiff.extensions]
+    ManifoldDiffFiniteDiffExt = "FiniteDiff"
+    ManifoldDiffFiniteDifferencesExt = "FiniteDifferences"
+    ManifoldDiffForwardDiffExt = "ForwardDiff"
+    ManifoldDiffReverseDiffExt = "ReverseDiff"
+    ManifoldDiffZygoteExt = "Zygote"
+
+    [deps.ManifoldDiff.weakdeps]
+    FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+    FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
+[[deps.Manifolds]]
+deps = ["Distributions", "Einsum", "Graphs", "HybridArrays", "Kronecker", "LinearAlgebra", "ManifoldDiff", "ManifoldsBase", "Markdown", "MatrixEquations", "Quaternions", "Random", "RecursiveArrayTools", "Requires", "SimpleWeightedGraphs", "SpecialFunctions", "StaticArrays", "Statistics", "StatsBase"]
+git-tree-sha1 = "58eb09899273a3ed17aae1f56435f440669b810c"
+uuid = "1cead3c2-87b3-11e9-0ccd-23c62b72b94e"
+version = "0.9.20"
+
+    [deps.Manifolds.extensions]
+    ManifoldsBoundaryValueDiffEqExt = "BoundaryValueDiffEq"
+    ManifoldsNLsolveExt = "NLsolve"
+    ManifoldsOrdinaryDiffEqDiffEqCallbacksExt = ["DiffEqCallbacks", "OrdinaryDiffEq"]
+    ManifoldsOrdinaryDiffEqExt = "OrdinaryDiffEq"
+    ManifoldsRecipesBaseExt = ["Colors", "RecipesBase"]
+    ManifoldsTestExt = "Test"
+
+    [deps.Manifolds.weakdeps]
+    BoundaryValueDiffEq = "764a87c0-6b3e-53db-9096-fe964310641d"
+    Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
+    DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
+    NLsolve = "2774e3e8-f4cf-5e23-947b-6d7e65073b56"
+    OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
+    RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
+    Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+
+[[deps.ManifoldsBase]]
+deps = ["LinearAlgebra", "Markdown", "Printf", "Random", "Requires"]
+git-tree-sha1 = "3edd590e67c7bcf6e17104b7c5356d7bad2ca120"
+uuid = "3362f125-f0bb-47a3-aa74-596ffd7ef2fb"
+version = "0.15.16"
+
+    [deps.ManifoldsBase.extensions]
+    ManifoldsBasePlotsExt = "Plots"
+    ManifoldsBaseQuaternionsExt = "Quaternions"
+    ManifoldsBaseRecursiveArrayToolsExt = "RecursiveArrayTools"
+    ManifoldsBaseStatisticsExt = "Statistics"
+
+    [deps.ManifoldsBase.weakdeps]
+    Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
+    Quaternions = "94ee1d12-ae83-5a48-8b1c-48b8ff168ae0"
+    RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
+    Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+
 [[deps.MappedArrays]]
 git-tree-sha1 = "2dab0221fe2b0f2cb6754eaa743cc266339f527e"
 uuid = "dbb5928d-eab1-5f90-85c2-b9b0edb7c900"
@@ -664,6 +1116,12 @@ version = "0.4.2"
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
+[[deps.MatrixEquations]]
+deps = ["LinearAlgebra", "LinearMaps"]
+git-tree-sha1 = "f765b4eda3ea9be8e644b9127809ca5151f3d9ea"
+uuid = "99c1a7ee-ab34-5fd5-8076-27c950a045f4"
+version = "2.4.2"
+
 [[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
@@ -694,12 +1152,77 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 version = "2023.1.10"
 
+[[deps.MultivariatePolynomials]]
+deps = ["ChainRulesCore", "DataStructures", "LinearAlgebra", "MutableArithmetics"]
+git-tree-sha1 = "5c1d1d9361e1417e5a065e1f84dc3686cbdaea21"
+uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
+version = "0.5.6"
+
+[[deps.MutableArithmetics]]
+deps = ["LinearAlgebra", "SparseArrays", "Test"]
+git-tree-sha1 = "d0a6b1096b584a2b88efb70a92f8cb8c881eb38a"
+uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
+version = "1.4.6"
+
+[[deps.NLSolversBase]]
+deps = ["DiffResults", "Distributed", "FiniteDiff", "ForwardDiff"]
+git-tree-sha1 = "a0b464d183da839699f4c79e7606d9d186ec172c"
+uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
+version = "7.8.3"
+
+[[deps.NNlib]]
+deps = ["Adapt", "Atomix", "ChainRulesCore", "GPUArraysCore", "KernelAbstractions", "LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "4a83c2e01027a0bfcea28589222f2df60b2e20cb"
+uuid = "872c559c-99b0-510c-b3b7-b6c96a88d5cd"
+version = "0.9.23"
+
+    [deps.NNlib.extensions]
+    NNlibAMDGPUExt = "AMDGPU"
+    NNlibCUDACUDNNExt = ["CUDA", "cuDNN"]
+    NNlibCUDAExt = "CUDA"
+    NNlibEnzymeCoreExt = "EnzymeCore"
+    NNlibFFTWExt = "FFTW"
+    NNlibForwardDiffExt = "ForwardDiff"
+
+    [deps.NNlib.weakdeps]
+    AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e"
+    CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+    EnzymeCore = "f151be2c-9106-41f4-ab19-57ee4f262869"
+    FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    cuDNN = "02a925ec-e4fe-4b08-9a7e-0d78e3d38ccd"
+
 [[deps.NaNMath]]
 deps = ["OpenLibm_jll"]
 git-tree-sha1 = "0877504529a3e5c3343c6f8b4c0381e57e4387e4"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
 version = "1.0.2"
 
+[[deps.NamedArrays]]
+deps = ["Combinatorics", "DataStructures", "DelimitedFiles", "InvertedIndices", "LinearAlgebra", "Random", "Requires", "SparseArrays", "Statistics"]
+git-tree-sha1 = "58e317b3b956b8aaddfd33ff4c3e33199cd8efce"
+uuid = "86f7a689-2022-50b4-a561-43c23ac3c673"
+version = "0.10.3"
+
+[[deps.NamedDims]]
+deps = ["LinearAlgebra", "Pkg", "Statistics"]
+git-tree-sha1 = "90178dc801073728b8b2d0d8677d10909feb94d8"
+uuid = "356022a1-0364-5f58-8944-0da4b18d706f"
+version = "1.2.2"
+
+    [deps.NamedDims.extensions]
+    AbstractFFTsExt = "AbstractFFTs"
+    ChainRulesCoreExt = "ChainRulesCore"
+    CovarianceEstimationExt = "CovarianceEstimation"
+    TrackerExt = "Tracker"
+
+    [deps.NamedDims.weakdeps]
+    AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    CovarianceEstimation = "587fd27a-f159-11e8-2dae-1979310e6154"
+    Requires = "ae029012-a4dd-5104-9daa-d747884805df"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+
 [[deps.NaturalSort]]
 git-tree-sha1 = "eda490d06b9f7c00752ee81cfa451efe55521e21"
 uuid = "c020b1a1-e9b0-503a-9c33-f039bfc54a85"
@@ -746,6 +1269,62 @@ git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 version = "0.5.5+0"
 
+[[deps.Optim]]
+deps = ["Compat", "FillArrays", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "SparseArrays", "StatsBase"]
+git-tree-sha1 = "d9b79c4eed437421ac4285148fcadf42e0700e89"
+uuid = "429524aa-4258-5aef-a3af-852621145aeb"
+version = "1.9.4"
+
+    [deps.Optim.extensions]
+    OptimMOIExt = "MathOptInterface"
+
+    [deps.Optim.weakdeps]
+    MathOptInterface = "b8f27783-ece8-5eb3-8dc8-9495eed66fee"
+
+[[deps.Optimisers]]
+deps = ["ChainRulesCore", "Functors", "LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "6572fe0c5b74431aaeb0b18a4aa5ef03c84678be"
+uuid = "3bd65402-5787-11e9-1adc-39752487f4e2"
+version = "0.3.3"
+
+[[deps.Optimization]]
+deps = ["ADTypes", "ArrayInterface", "ConsoleProgressMonitor", "DocStringExtensions", "LBFGSB", "LinearAlgebra", "Logging", "LoggingExtras", "OptimizationBase", "Printf", "ProgressLogging", "Reexport", "SciMLBase", "SparseArrays", "TerminalLoggers"]
+git-tree-sha1 = "0b2a631276dc92ab147535689fa43f1e22a657b8"
+uuid = "7f7a1694-90dd-40f0-9382-eb1efda571ba"
+version = "3.28.0"
+
+[[deps.OptimizationBase]]
+deps = ["ADTypes", "ArrayInterface", "DocStringExtensions", "LinearAlgebra", "PDMats", "Reexport", "Requires", "SciMLBase", "SparseArrays", "SymbolicAnalysis", "SymbolicIndexingInterface", "Symbolics"]
+git-tree-sha1 = "3e5e5e8cbe572200dcd94a6084a63ca68fe76279"
+uuid = "bca83a33-5cc9-4baa-983d-23429ab6bcbb"
+version = "1.5.0"
+
+    [deps.OptimizationBase.extensions]
+    OptimizationEnzymeExt = "Enzyme"
+    OptimizationFiniteDiffExt = "FiniteDiff"
+    OptimizationForwardDiffExt = "ForwardDiff"
+    OptimizationMTKExt = "ModelingToolkit"
+    OptimizationReverseDiffExt = "ReverseDiff"
+    OptimizationSparseDiffExt = ["SparseDiffTools", "ReverseDiff"]
+    OptimizationTrackerExt = "Tracker"
+    OptimizationZygoteExt = "Zygote"
+
+    [deps.OptimizationBase.weakdeps]
+    Enzyme = "7da242da-08ed-463a-9acd-ee780be4f1d9"
+    FiniteDiff = "6a86dc24-6348-571c-b903-95158fe2bd41"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    ModelingToolkit = "961ee093-0014-501f-94e3-6117800e7a78"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
+[[deps.OptimizationOptimJL]]
+deps = ["Optim", "Optimization", "Reexport", "SparseArrays"]
+git-tree-sha1 = "43870d726f883a47d158beebb1fc3c9fab1da9d6"
+uuid = "36348300-93cb-4f02-beb5-3c3902f8871e"
+version = "0.3.2"
+
 [[deps.OrderedCollections]]
 git-tree-sha1 = "dfdf5519f235516220579f949664f1bf44e741c5"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
@@ -757,11 +1336,41 @@ git-tree-sha1 = "949347156c25054de2db3b166c52ac4728cbad65"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
 version = "0.11.31"
 
+[[deps.Parameters]]
+deps = ["OrderedCollections", "UnPack"]
+git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
+uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
+version = "0.12.3"
+
 [[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "FileWatching", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 version = "1.10.0"
 
+[[deps.Polynomials]]
+deps = ["LinearAlgebra", "RecipesBase", "Requires", "Setfield", "SparseArrays"]
+git-tree-sha1 = "1a9cfb2dc2c2f1bd63f1906d72af39a79b49b736"
+uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
+version = "4.0.11"
+
+    [deps.Polynomials.extensions]
+    PolynomialsChainRulesCoreExt = "ChainRulesCore"
+    PolynomialsFFTWExt = "FFTW"
+    PolynomialsMakieCoreExt = "MakieCore"
+    PolynomialsMutableArithmeticsExt = "MutableArithmetics"
+
+    [deps.Polynomials.weakdeps]
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
+    MakieCore = "20f20a25-4f0e-4fdf-b5d1-57303727442b"
+    MutableArithmetics = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
+
+[[deps.PositiveFactorizations]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "17275485f373e6673f7e7f97051f703ed5b15b20"
+uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
+version = "0.2.4"
+
 [[deps.PrecompileTools]]
 deps = ["Preferences"]
 git-tree-sha1 = "5aa36f7049a63a1528fe8f7c3f2113413ffd4e1f"
@@ -780,6 +1389,12 @@ git-tree-sha1 = "88b895d13d53b5577fd53379d913b9ab9ac82660"
 uuid = "08abe8d2-0d0c-5749-adfa-8a2ac140af0d"
 version = "2.3.1"
 
+[[deps.Primes]]
+deps = ["IntegerMathUtils"]
+git-tree-sha1 = "cb420f77dc474d23ee47ca8d14c90810cafe69e7"
+uuid = "27ebfcd6-29c5-5fa9-bf4b-fb8fc14df3ae"
+version = "0.5.6"
+
 [[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
@@ -807,6 +1422,12 @@ git-tree-sha1 = "9b23c31e76e333e6fb4c1595ae6afa74966a729e"
 uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 version = "2.9.4"
 
+[[deps.Quaternions]]
+deps = ["LinearAlgebra", "Random", "RealDot"]
+git-tree-sha1 = "994cc27cdacca10e68feb291673ec3a76aa2fae9"
+uuid = "94ee1d12-ae83-5a48-8b1c-48b8ff168ae0"
+version = "0.7.6"
+
 [[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
@@ -815,6 +1436,18 @@ uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 deps = ["SHA"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
+[[deps.Random123]]
+deps = ["Random", "RandomNumbers"]
+git-tree-sha1 = "4743b43e5a9c4a2ede372de7061eed81795b12e7"
+uuid = "74087812-796a-5b5d-8853-05524746bad3"
+version = "1.7.0"
+
+[[deps.RandomNumbers]]
+deps = ["Random"]
+git-tree-sha1 = "c6ec94d2aaba1ab2ff983052cf6a606ca5985902"
+uuid = "e6cf234a-135c-5ec9-84dd-332b85af5143"
+version = "1.6.0"
+
 [[deps.RangeArrays]]
 git-tree-sha1 = "b9039e93773ddcfc828f12aadf7115b4b4d225f5"
 uuid = "b3c3ace0-ae52-54e7-9d0b-2c1406fd6b9d"
@@ -844,6 +1477,32 @@ git-tree-sha1 = "5c3d09cc4f31f5fc6af001c250bf1278733100ff"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 version = "1.3.4"
 
+[[deps.RecursiveArrayTools]]
+deps = ["Adapt", "ArrayInterface", "DocStringExtensions", "GPUArraysCore", "IteratorInterfaceExtensions", "LinearAlgebra", "RecipesBase", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
+git-tree-sha1 = "b034171b93aebc81b3e1890a036d13a9c4a9e3e0"
+uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
+version = "3.27.0"
+
+    [deps.RecursiveArrayTools.extensions]
+    RecursiveArrayToolsFastBroadcastExt = "FastBroadcast"
+    RecursiveArrayToolsForwardDiffExt = "ForwardDiff"
+    RecursiveArrayToolsMeasurementsExt = "Measurements"
+    RecursiveArrayToolsMonteCarloMeasurementsExt = "MonteCarloMeasurements"
+    RecursiveArrayToolsReverseDiffExt = ["ReverseDiff", "Zygote"]
+    RecursiveArrayToolsSparseArraysExt = ["SparseArrays"]
+    RecursiveArrayToolsTrackerExt = "Tracker"
+    RecursiveArrayToolsZygoteExt = "Zygote"
+
+    [deps.RecursiveArrayTools.weakdeps]
+    FastBroadcast = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    Measurements = "eff96d63-e80a-5855-80a2-b1b0885c5ab7"
+    MonteCarloMeasurements = "0987c9cc-fe09-11e8-30f0-b96dd679fdca"
+    ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+    SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
 [[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
@@ -887,10 +1546,64 @@ version = "2.2.1"
     SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
     SymPyPythonCall = "bc8888f7-b21e-4b7c-a06a-5d9c9496438c"
 
+[[deps.RuntimeGeneratedFunctions]]
+deps = ["ExprTools", "SHA", "Serialization"]
+git-tree-sha1 = "04c968137612c4a5629fa531334bb81ad5680f00"
+uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
+version = "0.5.13"
+
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 version = "0.7.0"
 
+[[deps.SSMProblems]]
+deps = ["AbstractMCMC"]
+git-tree-sha1 = "f640e4e8343c9d5f470e2f6ca6ce79f708ab6376"
+uuid = "26aad666-b158-4e64-9d35-0e672562fa48"
+version = "0.1.1"
+
+[[deps.SciMLBase]]
+deps = ["ADTypes", "Accessors", "ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "EnumX", "Expronicon", "FunctionWrappersWrappers", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "Markdown", "PrecompileTools", "Preferences", "Printf", "RecipesBase", "RecursiveArrayTools", "Reexport", "RuntimeGeneratedFunctions", "SciMLOperators", "SciMLStructures", "StaticArraysCore", "Statistics", "SymbolicIndexingInterface", "Tables"]
+git-tree-sha1 = "c96f81c3e98d5e2f0848fb42aba4383d772c3bb7"
+uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
+version = "2.53.1"
+
+    [deps.SciMLBase.extensions]
+    SciMLBaseChainRulesCoreExt = "ChainRulesCore"
+    SciMLBaseMakieExt = "Makie"
+    SciMLBasePartialFunctionsExt = "PartialFunctions"
+    SciMLBasePyCallExt = "PyCall"
+    SciMLBasePythonCallExt = "PythonCall"
+    SciMLBaseRCallExt = "RCall"
+    SciMLBaseZygoteExt = "Zygote"
+
+    [deps.SciMLBase.weakdeps]
+    ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+    ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+    Makie = "ee78f7c6-11fb-53f2-987a-cfe4a2b5a57a"
+    PartialFunctions = "570af359-4316-4cb7-8c74-252c00c2016b"
+    PyCall = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
+    PythonCall = "6099a3de-0909-46bc-b1f4-468b9a2dfc0d"
+    RCall = "6f49c342-dc21-5d91-9882-a32aef131414"
+    Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
+
+[[deps.SciMLOperators]]
+deps = ["Accessors", "ArrayInterface", "DocStringExtensions", "LinearAlgebra", "MacroTools"]
+git-tree-sha1 = "e39c5f217f9aca640c8e27ab21acf557a3967db5"
+uuid = "c0aeaf25-5076-4817-a8d5-81caf7dfa961"
+version = "0.3.10"
+weakdeps = ["SparseArrays", "StaticArraysCore"]
+
+    [deps.SciMLOperators.extensions]
+    SciMLOperatorsSparseArraysExt = "SparseArrays"
+    SciMLOperatorsStaticArraysCoreExt = "StaticArraysCore"
+
+[[deps.SciMLStructures]]
+deps = ["ArrayInterface"]
+git-tree-sha1 = "25514a6f200219cd1073e4ff23a6324e4a7efe64"
+uuid = "53ae85a6-f571-4167-b2af-e1d143709226"
+version = "1.5.0"
+
 [[deps.ScientificTypesBase]]
 git-tree-sha1 = "a8e18eb383b5ecf1b5e6fc237eb39255044fd92b"
 uuid = "30f210dd-8aff-4c5f-94ba-8e64358c1161"
@@ -909,11 +1622,23 @@ version = "1.1.1"
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
+[[deps.SimpleTraits]]
+deps = ["InteractiveUtils", "MacroTools"]
+git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
+uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
+version = "0.9.4"
+
 [[deps.SimpleUnPack]]
 git-tree-sha1 = "58e6353e72cde29b90a69527e56df1b5c3d8c437"
 uuid = "ce78b400-467f-4804-87d8-8f486da07d0a"
 version = "1.1.0"
 
+[[deps.SimpleWeightedGraphs]]
+deps = ["Graphs", "LinearAlgebra", "Markdown", "SparseArrays"]
+git-tree-sha1 = "4b33e0e081a825dbfaf314decf58fa47e53d6acb"
+uuid = "47aef6b3-ad0c-573a-a1e2-d07658019622"
+version = "1.4.0"
+
 [[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
@@ -1028,6 +1753,58 @@ deps = ["Artifacts", "Libdl", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
 version = "7.2.1+1"
 
+[[deps.SymbolicAnalysis]]
+deps = ["DSP", "DataStructures", "Dictionaries", "Distributions", "DomainSets", "IfElse", "LinearAlgebra", "LogExpFunctions", "Manifolds", "PDMats", "RecursiveArrayTools", "StatsBase", "SymbolicUtils", "Symbolics"]
+git-tree-sha1 = "64f26bb4a666bb97baa16f063164ade83ca29ec9"
+uuid = "4297ee4d-0239-47d8-ba5d-195ecdf594fe"
+version = "0.3.0"
+
+[[deps.SymbolicIndexingInterface]]
+deps = ["Accessors", "ArrayInterface", "RuntimeGeneratedFunctions", "StaticArraysCore"]
+git-tree-sha1 = "988e04b34a4c3b824fb656f542473df99a4f610d"
+uuid = "2efcf032-c050-4f8e-a9bb-153293bab1f5"
+version = "0.3.30"
+
+[[deps.SymbolicLimits]]
+deps = ["SymbolicUtils"]
+git-tree-sha1 = "fabf4650afe966a2ba646cabd924c3fd43577fc3"
+uuid = "19f23fe9-fdab-4a78-91af-e7b7767979c3"
+version = "0.2.2"
+
+[[deps.SymbolicUtils]]
+deps = ["AbstractTrees", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicIndexingInterface", "TermInterface", "TimerOutputs", "Unityper"]
+git-tree-sha1 = "9983eabcbd6c7431e3bd0f34191ec6863b8f8084"
+uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
+version = "3.4.1"
+
+    [deps.SymbolicUtils.extensions]
+    SymbolicUtilsLabelledArraysExt = "LabelledArrays"
+
+    [deps.SymbolicUtils.weakdeps]
+    LabelledArrays = "2ee39098-c373-598a-b85f-a56591580800"
+
+[[deps.Symbolics]]
+deps = ["ADTypes", "ArrayInterface", "Bijections", "CommonWorldInvalidations", "ConstructionBase", "DataStructures", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "DynamicPolynomials", "IfElse", "LaTeXStrings", "LambertW", "Latexify", "Libdl", "LinearAlgebra", "LogExpFunctions", "MacroTools", "Markdown", "NaNMath", "PrecompileTools", "Primes", "RecipesBase", "Reexport", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArraysCore", "SymbolicIndexingInterface", "SymbolicLimits", "SymbolicUtils", "TermInterface"]
+git-tree-sha1 = "2226d810512c678d2ec9c2a9b2e227c2ebc43573"
+uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+version = "6.11.0"
+
+    [deps.Symbolics.extensions]
+    SymbolicsForwardDiffExt = "ForwardDiff"
+    SymbolicsGroebnerExt = "Groebner"
+    SymbolicsLuxExt = "Lux"
+    SymbolicsNemoExt = "Nemo"
+    SymbolicsPreallocationToolsExt = ["PreallocationTools", "ForwardDiff"]
+    SymbolicsSymPyExt = "SymPy"
+
+    [deps.Symbolics.weakdeps]
+    ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
+    Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
+    Lux = "b2108857-7c20-44ae-9111-449ecde12c47"
+    Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
+    PreallocationTools = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
+    SymPy = "24249f21-da20-56a4-8eb1-6a02cf4ae2e6"
+
 [[deps.TOML]]
 deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
@@ -1050,6 +1827,11 @@ deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 version = "1.10.0"
 
+[[deps.TermInterface]]
+git-tree-sha1 = "d673e0aca9e46a2f63720201f55cc7b3e7169b16"
+uuid = "8ea1fca8-c5ef-4a55-8b96-4e9afe9c9a3c"
+version = "2.0.0"
+
 [[deps.TerminalLoggers]]
 deps = ["LeftChildRightSiblingTrees", "Logging", "Markdown", "Printf", "ProgressLogging", "UUIDs"]
 git-tree-sha1 = "f133fab380933d042f6796eda4e130272ba520ca"
@@ -1060,6 +1842,22 @@ version = "0.1.7"
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
+[[deps.TimerOutputs]]
+deps = ["ExprTools", "Printf"]
+git-tree-sha1 = "5a13ae8a41237cff5ecf34f73eb1b8f42fff6531"
+uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
+version = "0.5.24"
+
+[[deps.Tracker]]
+deps = ["Adapt", "ChainRulesCore", "DiffRules", "ForwardDiff", "Functors", "LinearAlgebra", "LogExpFunctions", "MacroTools", "NNlib", "NaNMath", "Optimisers", "Printf", "Random", "Requires", "SpecialFunctions", "Statistics"]
+git-tree-sha1 = "da45269e1da051c2a13624194fcdc74d6483fad5"
+uuid = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
+version = "0.2.35"
+weakdeps = ["PDMats"]
+
+    [deps.Tracker.extensions]
+    TrackerPDMatsExt = "PDMats"
+
 [[deps.Transducers]]
 deps = ["Accessors", "Adapt", "ArgCheck", "BangBang", "Baselet", "CompositionsBase", "ConstructionBase", "DefineSingletons", "Distributed", "InitialValues", "Logging", "Markdown", "MicroCollections", "Requires", "SplittablesBase", "Tables"]
 git-tree-sha1 = "5215a069867476fc8e3469602006b9670e68da23"
@@ -1080,13 +1878,49 @@ version = "0.4.82"
     OnlineStatsBase = "925886fa-5bf2-5e8e-b522-a9147a512338"
     Referenceables = "42d2dcc6-99eb-4e98-b66c-637b7d73030e"
 
+[[deps.Turing]]
+deps = ["ADTypes", "AbstractMCMC", "Accessors", "AdvancedHMC", "AdvancedMH", "AdvancedPS", "AdvancedVI", "BangBang", "Bijectors", "Compat", "DataStructures", "Distributions", "DistributionsAD", "DocStringExtensions", "DynamicPPL", "EllipticalSliceSampling", "ForwardDiff", "Libtask", "LinearAlgebra", "LogDensityProblems", "LogDensityProblemsAD", "MCMCChains", "NamedArrays", "Optimization", "OptimizationOptimJL", "OrderedCollections", "Printf", "Random", "Reexport", "Requires", "SciMLBase", "SpecialFunctions", "Statistics", "StatsAPI", "StatsBase", "StatsFuns"]
+git-tree-sha1 = "f69f33f7862a66674c279fe9b86b457a96767e35"
+uuid = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
+version = "0.34.1"
+
+    [deps.Turing.extensions]
+    TuringDynamicHMCExt = "DynamicHMC"
+    TuringOptimExt = "Optim"
+
+    [deps.Turing.weakdeps]
+    DynamicHMC = "bbc10e6e-7c05-544b-b16e-64fede858acb"
+    Optim = "429524aa-4258-5aef-a3af-852621145aeb"
+
 [[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
+[[deps.UnPack]]
+git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
+uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
+version = "1.0.2"
+
 [[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
+[[deps.Unityper]]
+deps = ["ConstructionBase"]
+git-tree-sha1 = "25008b734a03736c41e2a7dc314ecb95bd6bbdb0"
+uuid = "a7c27f48-0311-42f6-a7f8-2c11e75eb415"
+version = "0.1.6"
+
+[[deps.UnsafeAtomics]]
+git-tree-sha1 = "6331ac3440856ea1988316b46045303bef658278"
+uuid = "013be700-e6cd-48c3-b4a1-df204f14c38f"
+version = "0.2.1"
+
+[[deps.UnsafeAtomicsLLVM]]
+deps = ["LLVM", "UnsafeAtomics"]
+git-tree-sha1 = "2d17fabcd17e67d7625ce9c531fb9f40b7c42ce4"
+uuid = "d80eeb9a-aca5-4d75-85e5-170c8b632249"
+version = "0.2.1"
+
 [[deps.WoodburyMatrices]]
 deps = ["LinearAlgebra", "SparseArrays"]
 git-tree-sha1 = "c1a7aa6219628fcd757dede0ca95e245c5cd9511"
@@ -1098,6 +1932,12 @@ deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 version = "1.2.13+1"
 
+[[deps.ZygoteRules]]
+deps = ["ChainRulesCore", "MacroTools"]
+git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00"
+uuid = "700de1a5-db45-46bc-99cf-38207098b444"
+version = "0.2.5"
+
 [[deps.libaec_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl"]
 git-tree-sha1 = "46bf7be2917b59b761247be3f317ddf75e50e997"
diff --git a/Project.toml b/Project.toml
index 3c21120..a2d6d7b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -19,6 +19,7 @@ Markdown = "d6f4376e-aef5-505a-96c1-9c027394607a"
 ProgressMeter = "92933f4c-e287-5a05-a399-4b506db050ca"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
+Turing = "fce5fe82-541a-59a6-adf8-730c64b5f9a0"
 
 [compat]
 AbstractMCMC = "4.4, 5"
diff --git a/src/MicroCanonicalHMC.jl b/src/MicroCanonicalHMC.jl
index f64329a..5f41a40 100644
--- a/src/MicroCanonicalHMC.jl
+++ b/src/MicroCanonicalHMC.jl
@@ -3,7 +3,7 @@ module MicroCanonicalHMC
 using LinearAlgebra, Statistics, Adapt, Random, HDF5,
     LogDensityProblemsAD, LogDensityProblems, ForwardDiff,
     AbstractMCMC, MCMCChains, MCMCDiagnosticTools,
-    Distributions, ProgressMeter, Markdown, DynamicPPL
+    Distributions, ProgressMeter, Markdown, DynamicPPL, Turing
 
 export Settings, MCHMC, Sample, Step, Summarize,
     TuringTarget, RosenbrockTarget, CustomTarget
diff --git a/test/turing.jl b/test/turing.jl
index a648cf6..ba98d75 100644
--- a/test/turing.jl
+++ b/test/turing.jl
@@ -39,7 +39,7 @@
 
         # Sample
         target = TuringTarget(model)
-        samples = Sample(mchmc, target, 100_000)
+        samples = Sample(mchmc, target, 100)
         # Just check if it ran
         @test true
     end