diff --git a/Manifest.toml b/Manifest.toml
index 2af964a..25d2784 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -1,827 +1,864 @@
 # This file is machine-generated - editing it directly is not advised
 
-[[AbstractTrees]]
+julia_version = "1.7.0"
+manifest_format = "2.0"
+
+[[deps.AbstractTrees]]
 git-tree-sha1 = "03e0550477d86222521d254b741d470ba17ea0b5"
 uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
 version = "0.3.4"
 
-[[Adapt]]
+[[deps.Adapt]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "84918055d15b3114ede17ac6a7182f68870c16f7"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
 version = "3.3.1"
 
-[[ArgTools]]
+[[deps.ArgTools]]
 uuid = "0dad84c5-d112-42e6-8d28-ef12dabb789f"
 
-[[ArnoldiMethod]]
+[[deps.ArnoldiMethod]]
 deps = ["LinearAlgebra", "Random", "StaticArrays"]
-git-tree-sha1 = "f87e559f87a45bece9c9ed97458d3afe98b1ebb9"
+git-tree-sha1 = "62e51b39331de8911e4a7ff6f5aaf38a5f4cc0ae"
 uuid = "ec485272-7323-5ecc-a04f-4719b315124d"
-version = "0.1.0"
+version = "0.2.0"
 
-[[ArrayInterface]]
+[[deps.ArrayInterface]]
 deps = ["Compat", "IfElse", "LinearAlgebra", "Requires", "SparseArrays", "Static"]
-git-tree-sha1 = "b8d49c34c3da35f220e7295659cd0bab8e739fed"
+git-tree-sha1 = "265b06e2b1f6a216e0e8f183d28e4d354eab3220"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "3.1.33"
+version = "3.2.1"
 
-[[Artifacts]]
+[[deps.Artifacts]]
 uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 
-[[BSON]]
-git-tree-sha1 = "92b8a8479128367aaab2620b8e73dff632f5ae69"
+[[deps.BSON]]
+git-tree-sha1 = "ebcd6e22d69f21249b7b8668351ebf42d6dc87a1"
 uuid = "fbb218c0-5317-5bc6-957e-2ee96dd4b1f0"
-version = "0.3.3"
+version = "0.3.4"
 
-[[Base64]]
+[[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
-[[Bijections]]
+[[deps.Bijections]]
 git-tree-sha1 = "705e7822597b432ebe152baa844b49f8026df090"
 uuid = "e2ed5e7c-b2de-5872-ae92-c73ca462fb04"
 version = "0.1.3"
 
-[[BitTwiddlingConvenienceFunctions]]
+[[deps.BitTwiddlingConvenienceFunctions]]
 deps = ["Static"]
-git-tree-sha1 = "652aab0fc0d6d4db4cc726425cadf700e9f473f1"
+git-tree-sha1 = "bc1317f71de8dce26ea67fcdf7eccc0d0693b75b"
 uuid = "62783981-4cbd-42fc-bca8-16325de8dc4b"
-version = "0.1.0"
+version = "0.1.1"
 
-[[CEnum]]
+[[deps.CEnum]]
 git-tree-sha1 = "215a9aa4a1f23fbd05b92769fdd62559488d70e9"
 uuid = "fa961155-64e5-5f13-b03f-caf6b980ea82"
 version = "0.4.1"
 
-[[CPUSummary]]
+[[deps.CPUSummary]]
 deps = ["Hwloc", "IfElse", "Static"]
-git-tree-sha1 = "38d0941d2ce6dd96427fd033d45471e1f26c3865"
+git-tree-sha1 = "87b0c9c6ee0124d6c1f4ce8cb035dcaf9f90b803"
 uuid = "2a0fbf3d-bb9c-48f3-b0a9-814d99fd7ab9"
-version = "0.1.5"
+version = "0.1.6"
 
-[[ChainRulesCore]]
+[[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "a325370b9dd0e6bf5656a6f1a7ae80755f8ccc46"
+git-tree-sha1 = "4c26b4e9e91ca528ea212927326ece5918a04b47"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.7.2"
+version = "1.11.2"
 
-[[CloseOpenIntervals]]
+[[deps.ChangesOfVariables]]
+deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
+git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
+uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
+version = "0.1.2"
+
+[[deps.CloseOpenIntervals]]
 deps = ["ArrayInterface", "Static"]
-git-tree-sha1 = "ce9c0d07ed6e1a4fecd2df6ace144cbd29ba6f37"
+git-tree-sha1 = "7b8f09d58294dc8aa13d91a8544b37c8a1dcbc06"
 uuid = "fb6a15b2-703c-40df-9091-08a04967cfa9"
-version = "0.1.2"
+version = "0.1.4"
 
-[[Combinatorics]]
+[[deps.Combinatorics]]
 git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
 uuid = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
 version = "1.0.2"
 
-[[CommonSolve]]
+[[deps.CommonSolve]]
 git-tree-sha1 = "68a0743f578349ada8bc911a5cbd5a2ef6ed6d1f"
 uuid = "38540f10-b2f7-11e9-35d8-d573e4eb0ff2"
 version = "0.2.0"
 
-[[CommonSubexpressions]]
+[[deps.CommonSubexpressions]]
 deps = ["MacroTools", "Test"]
 git-tree-sha1 = "7b8a93dba8af7e3b42fecabf646260105ac373f7"
 uuid = "bbf7d656-a473-5ed7-a52c-81e309532950"
 version = "0.3.0"
 
-[[Compat]]
+[[deps.Compat]]
 deps = ["Base64", "Dates", "DelimitedFiles", "Distributed", "InteractiveUtils", "LibGit2", "Libdl", "LinearAlgebra", "Markdown", "Mmap", "Pkg", "Printf", "REPL", "Random", "SHA", "Serialization", "SharedArrays", "Sockets", "SparseArrays", "Statistics", "Test", "UUIDs", "Unicode"]
-git-tree-sha1 = "31d0151f5716b655421d9d75b7fa74cc4e744df2"
+git-tree-sha1 = "44c37b4636bc54afac5c574d2d02b625349d6582"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.39.0"
+version = "3.41.0"
 
-[[CompilerSupportLibraries_jll]]
+[[deps.CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "e66e0078-7015-5450-92f7-15fbd957f2ae"
 
-[[CompositeTypes]]
+[[deps.CompositeTypes]]
 git-tree-sha1 = "d5b014b216dc891e81fea299638e4c10c657b582"
 uuid = "b152e2b5-7a66-4b01-a709-34e65c35f657"
 version = "0.1.2"
 
-[[ConstructionBase]]
+[[deps.ConstructionBase]]
 deps = ["LinearAlgebra"]
 git-tree-sha1 = "f74e9d5388b8620b4cee35d4c5a618dd4dc547f4"
 uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 version = "1.3.0"
 
-[[DEDataArrays]]
+[[deps.DEDataArrays]]
 deps = ["ArrayInterface", "DocStringExtensions", "LinearAlgebra", "RecursiveArrayTools", "SciMLBase", "StaticArrays"]
 git-tree-sha1 = "31186e61936fbbccb41d809ad4338c9f7addf7ae"
 uuid = "754358af-613d-5f8d-9788-280bf1605d4c"
 version = "0.2.0"
 
-[[DataAPI]]
+[[deps.DataAPI]]
 git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
 version = "1.9.0"
 
-[[DataStructures]]
+[[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "7d9d316f04214f7efdbb6398d545446e246eff02"
+git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.10"
+version = "0.18.11"
 
-[[DataValueInterfaces]]
+[[deps.DataValueInterfaces]]
 git-tree-sha1 = "bfc1187b79289637fa0ef6d4436ebdfe6905cbd6"
 uuid = "e2d170a0-9d28-54be-80f0-106bbe20a464"
 version = "1.0.0"
 
-[[Dates]]
+[[deps.Dates]]
 deps = ["Printf"]
 uuid = "ade2ca70-3891-5945-98fb-dc099432e06a"
 
-[[DelimitedFiles]]
+[[deps.DelimitedFiles]]
 deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
-[[Dierckx]]
+[[deps.DensityInterface]]
+deps = ["InverseFunctions", "Test"]
+git-tree-sha1 = "80c3e8639e3353e5d2912fb3a1916b8455e2494b"
+uuid = "b429d917-457f-4dbc-8f4c-0cc954292b1d"
+version = "0.4.0"
+
+[[deps.Dierckx]]
 deps = ["Dierckx_jll"]
 git-tree-sha1 = "5fefbe52e9a6e55b8f87cb89352d469bd3a3a090"
 uuid = "39dd38d3-220a-591b-8e3c-4c3a8c710a94"
 version = "0.5.1"
 
-[[Dierckx_jll]]
+[[deps.Dierckx_jll]]
 deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
 git-tree-sha1 = "a580560f526f6fc6973e8bad2b036514a4e3b013"
 uuid = "cd4c43a9-7502-52ba-aa6d-59fb2a88580b"
 version = "0.0.1+0"
 
-[[DiffEqBase]]
+[[deps.DiffEqBase]]
 deps = ["ArrayInterface", "ChainRulesCore", "DEDataArrays", "DataStructures", "Distributions", "DocStringExtensions", "FastBroadcast", "ForwardDiff", "FunctionWrappers", "IterativeSolvers", "LabelledArrays", "LinearAlgebra", "Logging", "MuladdMacro", "NonlinearSolve", "Parameters", "PreallocationTools", "Printf", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "Requires", "SciMLBase", "Setfield", "SparseArrays", "StaticArrays", "Statistics", "SuiteSparse", "ZygoteRules"]
-git-tree-sha1 = "420ad175d5e420e2c55a0ed8a9c18556e6735f80"
+git-tree-sha1 = "9e91342bac01b4028b6344b0bf6acdd5cb8856bd"
 uuid = "2b5f629d-d688-5b77-993f-72d75c75574e"
-version = "6.73.2"
+version = "6.79.0"
 
-[[DiffResults]]
+[[deps.DiffResults]]
 deps = ["StaticArrays"]
 git-tree-sha1 = "c18e98cba888c6c25d1c3b048e4b3380ca956805"
 uuid = "163ba53b-c6d8-5494-b064-1a9d43ac40c5"
 version = "1.0.3"
 
-[[DiffRules]]
-deps = ["NaNMath", "Random", "SpecialFunctions"]
-git-tree-sha1 = "7220bc21c33e990c14f4a9a319b1d242ebc5b269"
+[[deps.DiffRules]]
+deps = ["LogExpFunctions", "NaNMath", "Random", "SpecialFunctions"]
+git-tree-sha1 = "9bc5dac3c8b6706b58ad5ce24cffd9861f07c94f"
 uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
-version = "1.3.1"
+version = "1.9.0"
 
-[[Distributed]]
+[[deps.Distributed]]
 deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
-[[Distributions]]
-deps = ["ChainRulesCore", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns"]
-git-tree-sha1 = "ff7890c74e2eaffbc0b3741811e3816e64b6343d"
+[[deps.Distributions]]
+deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
+git-tree-sha1 = "6a8dc9f82e5ce28279b6e3e2cea9421154f5bd0d"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.18"
+version = "0.25.37"
 
-[[DocStringExtensions]]
+[[deps.DocStringExtensions]]
 deps = ["LibGit2"]
-git-tree-sha1 = "a32185f5428d3986f47c2ab78b1f216d5e6cc96f"
+git-tree-sha1 = "b19534d1895d702889b219c382a6e18010797f0b"
 uuid = "ffbed154-4ef7-542d-bbb7-c09d3a79fcae"
-version = "0.8.5"
+version = "0.8.6"
 
-[[DomainSets]]
+[[deps.DomainSets]]
 deps = ["CompositeTypes", "IntervalSets", "LinearAlgebra", "StaticArrays", "Statistics"]
-git-tree-sha1 = "627844a59d3970db8082b778e53f86741d17aaad"
+git-tree-sha1 = "5f5f0b750ac576bcf2ab1d7782959894b304923e"
 uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
-version = "0.5.7"
+version = "0.5.9"
 
-[[Downloads]]
+[[deps.Downloads]]
 deps = ["ArgTools", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 
-[[DynamicPolynomials]]
+[[deps.DynamicPolynomials]]
 deps = ["DataStructures", "Future", "LinearAlgebra", "MultivariatePolynomials", "MutableArithmetics", "Pkg", "Reexport", "Test"]
 git-tree-sha1 = "1b4665a7e303eaa7e03542cfaef0730cb056cb00"
 uuid = "7c1d4256-1411-5781-91ec-d7bc3513ac07"
 version = "0.3.21"
 
-[[EllipsisNotation]]
+[[deps.EllipsisNotation]]
 deps = ["ArrayInterface"]
-git-tree-sha1 = "8041575f021cba5a099a456b4163c9a08b566a02"
+git-tree-sha1 = "3fe985505b4b667e1ae303c9ca64d181f09d5c05"
 uuid = "da5c29d0-fa7d-589e-88eb-ea29b0a81949"
-version = "1.1.0"
+version = "1.1.3"
 
-[[ExprTools]]
+[[deps.ExprTools]]
 git-tree-sha1 = "b7e3d17636b348f005f11040025ae8c6f645fe92"
 uuid = "e2ba6199-217a-4e67-a87a-7c52f15ade04"
 version = "0.1.6"
 
-[[FastBroadcast]]
-deps = ["LinearAlgebra"]
-git-tree-sha1 = "26be48918640ce002f5833e8fc537b2ba7ed0234"
+[[deps.FastBroadcast]]
+deps = ["LinearAlgebra", "Polyester", "Static"]
+git-tree-sha1 = "e32a81c505ab234c992ca978f31ed8b0dabbc327"
 uuid = "7034ab61-46d4-4ed7-9d0f-46aef9175898"
-version = "0.1.8"
+version = "0.1.11"
 
-[[FillArrays]]
+[[deps.FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
-git-tree-sha1 = "29890dfbc427afa59598b8cfcc10034719bd7744"
+git-tree-sha1 = "8756f9935b7ccc9064c6eef0bff0ad643df733a3"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "0.12.6"
+version = "0.12.7"
 
-[[FiniteDiff]]
+[[deps.FiniteDiff]]
 deps = ["ArrayInterface", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays"]
 git-tree-sha1 = "8b3c09b56acaf3c0e581c66638b85c8650ee9dca"
 uuid = "6a86dc24-6348-571c-b903-95158fe2bd41"
 version = "2.8.1"
 
-[[Formatting]]
+[[deps.Formatting]]
 deps = ["Printf"]
 git-tree-sha1 = "8339d61043228fdd3eb658d86c926cb282ae72a8"
 uuid = "59287772-0a20-5a39-b81b-1366585eb4c0"
 version = "0.4.2"
 
-[[ForwardDiff]]
-deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "NaNMath", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "c4203b60d37059462af370c4f3108fb5d155ff13"
+[[deps.ForwardDiff]]
+deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "LinearAlgebra", "LogExpFunctions", "NaNMath", "Preferences", "Printf", "Random", "SpecialFunctions", "StaticArrays"]
+git-tree-sha1 = "2b72a5624e289ee18256111657663721d59c143e"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.20"
+version = "0.10.24"
 
-[[FunctionWrappers]]
+[[deps.FunctionWrappers]]
 git-tree-sha1 = "241552bc2209f0fa068b6415b1942cc0aa486bcc"
 uuid = "069b7b12-0de2-55c6-9aab-29f3d0a68a2e"
 version = "1.1.2"
 
-[[Future]]
+[[deps.Future]]
 deps = ["Random"]
 uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
 
-[[GeneralizedGenerated]]
+[[deps.GeneralizedGenerated]]
 deps = ["DataStructures", "JuliaVariables", "MLStyle", "Serialization"]
 git-tree-sha1 = "dd95197f27ebf3268dfe7401f982e0ede98cea51"
 uuid = "6b9d7cbe-bcb9-11e9-073f-15a7a543e2eb"
 version = "0.3.2"
 
-[[HostCPUFeatures]]
+[[deps.Graphs]]
+deps = ["ArnoldiMethod", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
+git-tree-sha1 = "92243c07e786ea3458532e199eb3feee0e7e08eb"
+uuid = "86223c79-3864-5bf0-83f7-82e725a168b6"
+version = "1.4.1"
+
+[[deps.HostCPUFeatures]]
 deps = ["BitTwiddlingConvenienceFunctions", "IfElse", "Libdl", "Static"]
-git-tree-sha1 = "3169c8b31863f9a409be1d17693751314241e3eb"
+git-tree-sha1 = "8f0dc80088981ab55702b04bba38097a44a1a3a9"
 uuid = "3e5b6fbb-0976-4d2c-9146-d79de83f2fb0"
-version = "0.1.4"
+version = "0.1.5"
 
-[[Hwloc]]
+[[deps.Hwloc]]
 deps = ["Hwloc_jll"]
 git-tree-sha1 = "92d99146066c5c6888d5a3abc871e6a214388b91"
 uuid = "0e44f5e4-bd66-52a0-8798-143a42290a1d"
 version = "2.0.0"
 
-[[Hwloc_jll]]
+[[deps.Hwloc_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "3395d4d4aeb3c9d31f5929d32760d8baeee88aaf"
 uuid = "e33a78d0-f292-5ffc-b300-72abe9b543c8"
 version = "2.5.0+0"
 
-[[IfElse]]
-git-tree-sha1 = "28e837ff3e7a6c3cdb252ce49fb412c8eb3caeef"
+[[deps.IfElse]]
+git-tree-sha1 = "debdd00ffef04665ccbb3e150747a77560e8fad1"
 uuid = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
-version = "0.1.0"
+version = "0.1.1"
 
-[[Inflate]]
+[[deps.Inflate]]
 git-tree-sha1 = "f5fc07d4e706b84f72d54eedcc1c13d92fb0871c"
 uuid = "d25df0c9-e2be-5dd7-82c8-3ad0b3e990b9"
 version = "0.1.2"
 
-[[InteractiveUtils]]
+[[deps.InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
-[[IntervalSets]]
+[[deps.IntervalSets]]
 deps = ["Dates", "EllipsisNotation", "Statistics"]
 git-tree-sha1 = "3cc368af3f110a767ac786560045dceddfc16758"
 uuid = "8197267c-284f-5f27-9208-e0e47529a953"
 version = "0.5.3"
 
-[[IrrationalConstants]]
-git-tree-sha1 = "f76424439413893a832026ca355fe273e93bce94"
+[[deps.InverseFunctions]]
+deps = ["Test"]
+git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
+uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
+version = "0.1.2"
+
+[[deps.IrrationalConstants]]
+git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
 uuid = "92d709cd-6900-40b7-9082-c6be49f344b6"
-version = "0.1.0"
+version = "0.1.1"
 
-[[IterativeSolvers]]
+[[deps.IterativeSolvers]]
 deps = ["LinearAlgebra", "Printf", "Random", "RecipesBase", "SparseArrays"]
-git-tree-sha1 = "1a8c6237e78b714e901e406c096fc8a65528af7d"
+git-tree-sha1 = "1169632f425f79429f245113b775a0e3d121457c"
 uuid = "42fd0dbc-a981-5370-80f2-aaf504508153"
-version = "0.9.1"
+version = "0.9.2"
 
-[[IteratorInterfaceExtensions]]
+[[deps.IteratorInterfaceExtensions]]
 git-tree-sha1 = "a3f24677c21f5bbe9d2a714f95dcd58337fb2856"
 uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"
 
-[[JLLWrappers]]
+[[deps.JLLWrappers]]
 deps = ["Preferences"]
 git-tree-sha1 = "642a199af8b68253517b80bd3bfd17eb4e84df6e"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
 version = "1.3.0"
 
-[[JuliaVariables]]
+[[deps.JuliaVariables]]
 deps = ["MLStyle", "NameResolution"]
 git-tree-sha1 = "49fb3cb53362ddadb4415e9b73926d6b40709e70"
 uuid = "b14d175d-62b4-44ba-8fb7-3064adc8c3ec"
 version = "0.2.4"
 
-[[LaTeXStrings]]
-git-tree-sha1 = "c7f1c695e06c01b95a67f0cd1d34994f3e7db104"
+[[deps.KLU]]
+deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse_jll"]
+git-tree-sha1 = "1ed18ccf6292d89abf85beba35b9399aeddff9b2"
+uuid = "ef3ab10e-7fda-4108-b977-705223b18434"
+version = "0.2.3"
+
+[[deps.LaTeXStrings]]
+git-tree-sha1 = "f2355693d6778a178ade15952b7ac47a4ff97996"
 uuid = "b964fa9f-0449-5b57-a5c2-d3ea65f4040f"
-version = "1.2.1"
+version = "1.3.0"
 
-[[LabelledArrays]]
-deps = ["ArrayInterface", "LinearAlgebra", "MacroTools", "StaticArrays"]
-git-tree-sha1 = "8f5fd068dfee92655b79e0859ecad8b492dfe8b1"
+[[deps.LabelledArrays]]
+deps = ["ArrayInterface", "ChainRulesCore", "LinearAlgebra", "MacroTools", "StaticArrays"]
+git-tree-sha1 = "3609bbf5feba7b22fb35fe7cb207c8c8d2e2fc5b"
 uuid = "2ee39098-c373-598a-b85f-a56591580800"
-version = "1.6.5"
+version = "1.6.7"
 
-[[Latexify]]
+[[deps.Latexify]]
 deps = ["Formatting", "InteractiveUtils", "LaTeXStrings", "MacroTools", "Markdown", "Printf", "Requires"]
-git-tree-sha1 = "a4b12a1bd2ebade87891ab7e36fdbce582301a92"
+git-tree-sha1 = "a8f4f279b6fa3c3c4f1adadd78a621b13a506bce"
 uuid = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
-version = "0.15.6"
+version = "0.15.9"
 
-[[LayoutPointers]]
+[[deps.LayoutPointers]]
 deps = ["ArrayInterface", "LinearAlgebra", "ManualMemory", "SIMDTypes", "Static"]
-git-tree-sha1 = "d2bda6aa0b03ce6f141a2dc73d0bcb7070131adc"
+git-tree-sha1 = "83b56449c39342a47f3fcdb3bc782bd6d66e1d97"
 uuid = "10f19ff3-798f-405d-979b-55457f8fc047"
-version = "0.1.3"
+version = "0.1.4"
 
-[[LibCURL]]
+[[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
 uuid = "b27032c2-a3e7-50c8-80cd-2d36dbcbfd21"
 
-[[LibCURL_jll]]
+[[deps.LibCURL_jll]]
 deps = ["Artifacts", "LibSSH2_jll", "Libdl", "MbedTLS_jll", "Zlib_jll", "nghttp2_jll"]
 uuid = "deac9b47-8bc7-5906-a0fe-35ac56dc84c0"
 
-[[LibGit2]]
+[[deps.LibGit2]]
 deps = ["Base64", "NetworkOptions", "Printf", "SHA"]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
 
-[[LibSSH2_jll]]
+[[deps.LibSSH2_jll]]
 deps = ["Artifacts", "Libdl", "MbedTLS_jll"]
 uuid = "29816b5a-b9ab-546f-933c-edad1886dfa8"
 
-[[Libdl]]
+[[deps.Libdl]]
 uuid = "8f399da3-3557-5675-b5ff-fb832c97cbdb"
 
-[[LightGraphs]]
-deps = ["ArnoldiMethod", "DataStructures", "Distributed", "Inflate", "LinearAlgebra", "Random", "SharedArrays", "SimpleTraits", "SparseArrays", "Statistics"]
-git-tree-sha1 = "432428df5f360964040ed60418dd5601ecd240b6"
-uuid = "093fc24a-ae57-5d10-9952-331d41423f4d"
-version = "1.3.5"
-
-[[LinearAlgebra]]
-deps = ["Libdl"]
+[[deps.LinearAlgebra]]
+deps = ["Libdl", "libblastrampoline_jll"]
 uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
-[[LogExpFunctions]]
-deps = ["ChainRulesCore", "DocStringExtensions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "34dc30f868e368f8a17b728a1238f3fcda43931a"
+[[deps.LogExpFunctions]]
+deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
+git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.3"
+version = "0.3.6"
 
-[[Logging]]
+[[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
-[[LoopVectorization]]
-deps = ["ArrayInterface", "CPUSummary", "CloseOpenIntervals", "DocStringExtensions", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "Requires", "SLEEFPirates", "Static", "ThreadingUtilities", "UnPack", "VectorizationBase"]
-git-tree-sha1 = "c2c1a765d943267ffc01fd6a127fcb482e80f63a"
+[[deps.LoopVectorization]]
+deps = ["ArrayInterface", "CPUSummary", "CloseOpenIntervals", "DocStringExtensions", "HostCPUFeatures", "IfElse", "LayoutPointers", "LinearAlgebra", "OffsetArrays", "PolyesterWeave", "Requires", "SIMDDualNumbers", "SLEEFPirates", "Static", "ThreadingUtilities", "UnPack", "VectorizationBase"]
+git-tree-sha1 = "9e10579c154f785b911d9ceb96c33fcc1a661171"
 uuid = "bdcacae8-1622-11e9-2a5c-532679323890"
-version = "0.12.82"
+version = "0.12.99"
 
-[[MLStyle]]
+[[deps.MLStyle]]
 git-tree-sha1 = "594e189325f66e23a8818e5beb11c43bb0141bcd"
 uuid = "d8e11817-5142-5d16-987a-aa16d5891078"
 version = "0.4.10"
 
-[[MacroTools]]
+[[deps.MacroTools]]
 deps = ["Markdown", "Random"]
-git-tree-sha1 = "5a5bc6bf062f0f95e62d0fe0a2d99699fed82dd9"
+git-tree-sha1 = "3d3e902b31198a27340d0bf00d6ac452866021cf"
 uuid = "1914dd2f-81c6-5fcd-8719-6d5c9610ff09"
-version = "0.5.8"
+version = "0.5.9"
 
-[[ManualMemory]]
+[[deps.ManualMemory]]
 git-tree-sha1 = "9cb207b18148b2199db259adfa923b45593fe08e"
 uuid = "d125e4d3-2237-4719-b19c-fa641b8a4667"
 version = "0.1.6"
 
-[[Markdown]]
+[[deps.Markdown]]
 deps = ["Base64"]
 uuid = "d6f4376e-aef5-505a-96c1-9c027394607a"
 
-[[MbedTLS_jll]]
+[[deps.MbedTLS_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "c8ffd9c3-330d-5841-b78e-0817d7145fa1"
 
-[[Missings]]
+[[deps.Missings]]
 deps = ["DataAPI"]
 git-tree-sha1 = "bf210ce90b6c9eed32d25dbcae1ebc565df2687f"
 uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
 version = "1.0.2"
 
-[[Mmap]]
+[[deps.Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 
-[[MozillaCACerts_jll]]
+[[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 
-[[MuladdMacro]]
+[[deps.MuladdMacro]]
 git-tree-sha1 = "c6190f9a7fc5d9d5915ab29f2134421b12d24a68"
 uuid = "46d2c3a1-f734-5fdb-9937-b9b9aeba4221"
 version = "0.2.2"
 
-[[MultivariatePolynomials]]
+[[deps.MultivariatePolynomials]]
 deps = ["DataStructures", "LinearAlgebra", "MutableArithmetics"]
 git-tree-sha1 = "45c9940cec79dedcdccc73cc6dd09ea8b8ab142c"
 uuid = "102ac46a-7ee4-5c85-9060-abc95bfdeaa3"
 version = "0.3.18"
 
-[[MutableArithmetics]]
+[[deps.MutableArithmetics]]
 deps = ["LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "3927848ccebcc165952dc0d9ac9aa274a87bfe01"
+git-tree-sha1 = "8d9496b2339095901106961f44718920732616bb"
 uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
-version = "0.2.20"
+version = "0.2.22"
 
-[[NaNMath]]
-git-tree-sha1 = "bfe47e760d60b82b66b61d2d44128b62e3a369fb"
+[[deps.NaNMath]]
+git-tree-sha1 = "f755f36b19a5116bb580de457cda0c140153f283"
 uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
-version = "0.3.5"
+version = "0.3.6"
 
-[[NameResolution]]
+[[deps.NameResolution]]
 deps = ["PrettyPrint"]
 git-tree-sha1 = "1a0fa0e9613f46c9b8c11eee38ebb4f590013c5e"
 uuid = "71a1bf82-56d0-4bbc-8a3c-48b961074391"
 version = "0.1.5"
 
-[[NetworkOptions]]
+[[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
-[[NonlinearSolve]]
+[[deps.NonlinearSolve]]
 deps = ["ArrayInterface", "FiniteDiff", "ForwardDiff", "IterativeSolvers", "LinearAlgebra", "RecursiveArrayTools", "RecursiveFactorization", "Reexport", "SciMLBase", "Setfield", "StaticArrays", "UnPack"]
-git-tree-sha1 = "e9ffc92217b8709e0cf7b8808f6223a4a0936c95"
+git-tree-sha1 = "8dc3be3e9edf976a3e79363b3bd2ad776a627c31"
 uuid = "8913a72c-1f9b-4ce2-8d82-65094dcecaec"
-version = "0.3.11"
+version = "0.3.12"
 
-[[OffsetArrays]]
+[[deps.OffsetArrays]]
 deps = ["Adapt"]
-git-tree-sha1 = "c0e9e582987d36d5a61e650e6e543b9e44d9914b"
+git-tree-sha1 = "043017e0bdeff61cfbb7afeb558ab29536bbb5ed"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
-version = "1.10.7"
+version = "1.10.8"
 
-[[OpenBLAS_jll]]
+[[deps.OpenBLAS_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "Libdl"]
 uuid = "4536629a-c528-5b80-bd46-f80d51c5b363"
 
-[[OpenLibm_jll]]
+[[deps.OpenLibm_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "05823500-19ac-5b8b-9628-191a04bc5112"
 
-[[OpenSpecFun_jll]]
+[[deps.OpenSpecFun_jll]]
 deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "13652491f6856acfd2db29360e1bbcd4565d04f1"
 uuid = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 version = "0.5.5+0"
 
-[[OrderedCollections]]
+[[deps.OrderedCollections]]
 git-tree-sha1 = "85f8e6578bf1f9ee0d11e7bb1b1456435479d47c"
 uuid = "bac558e1-5e72-5ebc-8fee-abe8a469f55d"
 version = "1.4.1"
 
-[[PDMats]]
+[[deps.PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "4dd403333bcf0909341cfe57ec115152f937d7d8"
+git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.1"
+version = "0.11.5"
 
-[[Parameters]]
+[[deps.Parameters]]
 deps = ["OrderedCollections", "UnPack"]
 git-tree-sha1 = "34c0e9ad262e5f7fc75b10a9952ca7692cfc5fbe"
 uuid = "d96e819e-fc66-5662-9728-84c9c7592b0a"
 version = "0.12.3"
 
-[[Pkg]]
+[[deps.Pkg]]
 deps = ["Artifacts", "Dates", "Downloads", "LibGit2", "Libdl", "Logging", "Markdown", "Printf", "REPL", "Random", "SHA", "Serialization", "TOML", "Tar", "UUIDs", "p7zip_jll"]
 uuid = "44cfe95a-1eb2-52ea-b672-e2afdf69b78f"
 
-[[Polyester]]
+[[deps.Polyester]]
 deps = ["ArrayInterface", "BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "ManualMemory", "PolyesterWeave", "Requires", "Static", "StrideArraysCore", "ThreadingUtilities"]
-git-tree-sha1 = "97794179584fbb0336821d6c03c93682f19803bf"
+git-tree-sha1 = "a804f11a4da30c0561c824e09fc627531270d9a1"
 uuid = "f517fe37-dbe3-4b94-8317-1923a5111588"
-version = "0.5.3"
+version = "0.5.5"
 
-[[PolyesterWeave]]
+[[deps.PolyesterWeave]]
 deps = ["BitTwiddlingConvenienceFunctions", "CPUSummary", "IfElse", "Static", "ThreadingUtilities"]
-git-tree-sha1 = "371a19bb801c1b420b29141750f3a34d6c6634b9"
+git-tree-sha1 = "a3ff99bf561183ee20386aec98ab8f4a12dc724a"
 uuid = "1d0040c9-8b98-4ee7-8388-3f51789ca0ad"
-version = "0.1.0"
+version = "0.1.2"
 
-[[PreallocationTools]]
-deps = ["ArrayInterface", "ForwardDiff", "LabelledArrays"]
-git-tree-sha1 = "361c1f60ffdeeddf02f36b463ab8b138194e5f25"
+[[deps.PreallocationTools]]
+deps = ["Adapt", "ArrayInterface", "ForwardDiff", "LabelledArrays"]
+git-tree-sha1 = "435379f01c1e6f7ca65cf46fdd403226f1d36e37"
 uuid = "d236fae5-4411-538c-8e31-a6e3d9e00b46"
-version = "0.1.1"
+version = "0.2.1"
 
-[[Preferences]]
+[[deps.Preferences]]
 deps = ["TOML"]
-git-tree-sha1 = "00cfd92944ca9c760982747e9a1d0d5d86ab1e5a"
+git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
-version = "1.2.2"
+version = "1.2.3"
 
-[[PrettyPrint]]
+[[deps.PrettyPrint]]
 git-tree-sha1 = "632eb4abab3449ab30c5e1afaa874f0b98b586e4"
 uuid = "8162dcfd-2161-5ef2-ae6c-7681170c5f98"
 version = "0.2.0"
 
-[[Printf]]
+[[deps.Printf]]
 deps = ["Unicode"]
 uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
-[[QuadGK]]
+[[deps.QuadGK]]
 deps = ["DataStructures", "LinearAlgebra"]
 git-tree-sha1 = "78aadffb3efd2155af139781b8a8df1ef279ea39"
 uuid = "1fd47b50-473d-5c70-9696-f719f8f3bcdc"
 version = "2.4.2"
 
-[[REPL]]
+[[deps.REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets", "Unicode"]
 uuid = "3fa0cd96-eef1-5676-8a61-b3b8758bbffb"
 
-[[Random]]
-deps = ["Serialization"]
+[[deps.Random]]
+deps = ["SHA", "Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
-[[RecipesBase]]
-git-tree-sha1 = "44a75aa7a527910ee3d1751d1f0e4148698add9e"
+[[deps.RecipesBase]]
+git-tree-sha1 = "6bf3f380ff52ce0832ddd3a2a7b9538ed1bcca7d"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "1.1.2"
+version = "1.2.1"
 
-[[RecursiveArrayTools]]
+[[deps.RecursiveArrayTools]]
 deps = ["ArrayInterface", "ChainRulesCore", "DocStringExtensions", "FillArrays", "LinearAlgebra", "RecipesBase", "Requires", "StaticArrays", "Statistics", "ZygoteRules"]
-git-tree-sha1 = "ff7495c78a192ff7d59531d9f14db300c847a4bc"
+git-tree-sha1 = "827ae9e1dc9fc0170319c8e77e7934b123c9bbdf"
 uuid = "731186ca-8d62-57ce-b412-fbd966d074cd"
-version = "2.19.1"
+version = "2.21.1"
 
-[[RecursiveFactorization]]
+[[deps.RecursiveFactorization]]
 deps = ["LinearAlgebra", "LoopVectorization", "Polyester", "StrideArraysCore", "TriangularSolve"]
-git-tree-sha1 = "575c18c6b00ce409f75d96fefe33ebe01575457a"
+git-tree-sha1 = "b7edd69c796b30985ea6dfeda8504cdb7cf77e9f"
 uuid = "f2c3362d-daeb-58d1-803e-2bc74f2840b4"
-version = "0.2.4"
+version = "0.2.5"
 
-[[Reexport]]
+[[deps.Reexport]]
 git-tree-sha1 = "45e428421666073eab6f2da5c9d310d99bb12f9b"
 uuid = "189a3867-3050-52da-a836-e630ba90ab69"
 version = "1.2.2"
 
-[[Requires]]
+[[deps.Requires]]
 deps = ["UUIDs"]
-git-tree-sha1 = "4036a3bd08ac7e968e27c203d45f5fff15020621"
+git-tree-sha1 = "8f82019e525f4d5c669692772a6f4b0a58b06a6a"
 uuid = "ae029012-a4dd-5104-9daa-d747884805df"
-version = "1.1.3"
+version = "1.2.0"
 
-[[Rmath]]
+[[deps.Rmath]]
 deps = ["Random", "Rmath_jll"]
 git-tree-sha1 = "bf3188feca147ce108c76ad82c2792c57abe7b1f"
 uuid = "79098fc4-a85e-5d69-aa6a-4863f24498fa"
 version = "0.7.0"
 
-[[Rmath_jll]]
+[[deps.Rmath_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
 git-tree-sha1 = "68db32dff12bb6127bac73c209881191bf0efbb7"
 uuid = "f50d1b31-88e8-58de-be2c-1cc44531875f"
 version = "0.3.0+0"
 
-[[RuntimeGeneratedFunctions]]
+[[deps.RuntimeGeneratedFunctions]]
 deps = ["ExprTools", "SHA", "Serialization"]
 git-tree-sha1 = "cdc1e4278e91a6ad530770ebb327f9ed83cf10c4"
 uuid = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
 version = "0.5.3"
 
-[[SHA]]
+[[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
 
-[[SIMDTypes]]
+[[deps.SIMDDualNumbers]]
+deps = ["ForwardDiff", "IfElse", "SLEEFPirates", "VectorizationBase"]
+git-tree-sha1 = "62c2da6eb66de8bb88081d20528647140d4daa0e"
+uuid = "3cdde19b-5bb0-4aaf-8931-af3e248e098b"
+version = "0.1.0"
+
+[[deps.SIMDTypes]]
 git-tree-sha1 = "330289636fb8107c5f32088d2741e9fd7a061a5c"
 uuid = "94e857df-77ce-4151-89e5-788b33177be4"
 version = "0.1.0"
 
-[[SLEEFPirates]]
+[[deps.SLEEFPirates]]
 deps = ["IfElse", "Static", "VectorizationBase"]
-git-tree-sha1 = "2e8150c7d2a14ac68537c7aac25faa6577aff046"
+git-tree-sha1 = "1410aad1c6b35862573c01b96cd1f6dbe3979994"
 uuid = "476501e8-09a2-5ece-8869-fb82de89a1fa"
-version = "0.6.27"
+version = "0.6.28"
 
-[[SciMLBase]]
+[[deps.SciMLBase]]
 deps = ["ArrayInterface", "CommonSolve", "ConstructionBase", "Distributed", "DocStringExtensions", "IteratorInterfaceExtensions", "LinearAlgebra", "Logging", "RecipesBase", "RecursiveArrayTools", "StaticArrays", "Statistics", "Tables", "TreeViews"]
-git-tree-sha1 = "91e29a2bb257a4b992c48f35084064578b87d364"
+git-tree-sha1 = "c61870a745fb9a468649d9efdd05c18d30e6a6e2"
 uuid = "0bca4576-84f4-4d90-8ffe-ffa030f20462"
-version = "1.19.0"
+version = "1.24.0"
 
-[[Serialization]]
+[[deps.Serialization]]
 uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
-[[Setfield]]
+[[deps.Setfield]]
 deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
-git-tree-sha1 = "fca29e68c5062722b5b4435594c3d1ba557072a3"
+git-tree-sha1 = "0afd9e6c623e379f593da01f20590bacc26d1d14"
 uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
-version = "0.7.1"
+version = "0.8.1"
 
-[[SharedArrays]]
+[[deps.SharedArrays]]
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
 uuid = "1a1011a3-84de-559e-8e89-a11a2f7dc383"
 
-[[SimpleTraits]]
+[[deps.SimpleTraits]]
 deps = ["InteractiveUtils", "MacroTools"]
 git-tree-sha1 = "5d7e3f4e11935503d3ecaf7186eac40602e7d231"
 uuid = "699a6c99-e7fa-54fc-8d76-47d257e15c1d"
 version = "0.9.4"
 
-[[Sockets]]
+[[deps.Sockets]]
 uuid = "6462fe0b-24de-5631-8697-dd941f90decc"
 
-[[SortingAlgorithms]]
+[[deps.SortingAlgorithms]]
 deps = ["DataStructures"]
 git-tree-sha1 = "b3363d7460f7d098ca0912c69b082f75625d7508"
 uuid = "a2af1166-a08f-5f64-846c-94a0d3cef48c"
 version = "1.0.1"
 
-[[SparseArrays]]
+[[deps.SparseArrays]]
 deps = ["LinearAlgebra", "Random"]
 uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
-[[SparseDiffTools]]
-deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "LightGraphs", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays", "VertexSafeGraphs"]
-git-tree-sha1 = "36a4d27a02af48a1eafd2baff58b32deeeb68926"
+[[deps.SparseDiffTools]]
+deps = ["Adapt", "ArrayInterface", "Compat", "DataStructures", "FiniteDiff", "ForwardDiff", "Graphs", "LinearAlgebra", "Requires", "SparseArrays", "StaticArrays", "VertexSafeGraphs"]
+git-tree-sha1 = "f33a0f6721b270cdf417f0c986e93c973e5913c8"
 uuid = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
-version = "1.16.5"
+version = "1.19.1"
 
-[[SpecialFunctions]]
+[[deps.SpecialFunctions]]
 deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
-git-tree-sha1 = "793793f1df98e3d7d554b65a107e9c9a6399a6ed"
+git-tree-sha1 = "f0bccf98e16759818ffc5d97ac3ebf87eb950150"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "1.7.0"
+version = "1.8.1"
 
-[[Static]]
+[[deps.Static]]
 deps = ["IfElse"]
-git-tree-sha1 = "a8f30abc7c64a39d389680b74e749cf33f872a70"
+git-tree-sha1 = "7f5a513baec6f122401abfc8e9c074fdac54f6c1"
 uuid = "aedffcd0-7271-4cad-89d0-dc628f76c6d3"
-version = "0.3.3"
+version = "0.4.1"
 
-[[StaticArrays]]
+[[deps.StaticArrays]]
 deps = ["LinearAlgebra", "Random", "Statistics"]
 git-tree-sha1 = "3c76dde64d03699e074ac02eb2e8ba8254d428da"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
 version = "1.2.13"
 
-[[Statistics]]
+[[deps.Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
-[[StatsAPI]]
-git-tree-sha1 = "1958272568dc176a1d881acb797beb909c785510"
+[[deps.StatsAPI]]
+git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.0.0"
+version = "1.2.0"
 
-[[StatsBase]]
-deps = ["DataAPI", "DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "8cbbc098554648c84f79a463c9ff0fd277144b6c"
+[[deps.StatsBase]]
+deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
+git-tree-sha1 = "2bb0cb32026a66037360606510fca5984ccc6b75"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.10"
+version = "0.33.13"
 
-[[StatsFuns]]
-deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "95072ef1a22b057b1e80f73c2a89ad238ae4cfff"
+[[deps.StatsFuns]]
+deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.12"
+version = "0.9.14"
 
-[[StrideArraysCore]]
+[[deps.StrideArraysCore]]
 deps = ["ArrayInterface", "CloseOpenIntervals", "IfElse", "LayoutPointers", "ManualMemory", "Requires", "SIMDTypes", "Static", "ThreadingUtilities"]
-git-tree-sha1 = "1258e25e171aec339866f283a11e7d75867e77d7"
+git-tree-sha1 = "12cf3253ebd8e2a3214ae171fbfe51e7e8d8ad28"
 uuid = "7792a7ef-975c-4747-a70f-980b88e8d1da"
-version = "0.2.4"
+version = "0.2.9"
 
-[[SuiteSparse]]
+[[deps.SuiteSparse]]
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]
 uuid = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 
-[[SuiteSparse_jll]]
-deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
+[[deps.SuiteSparse_jll]]
+deps = ["Artifacts", "Libdl", "Pkg", "libblastrampoline_jll"]
 uuid = "bea87d4a-7f5b-5778-9afe-8cc45184846c"
 
-[[Sundials]]
+[[deps.Sundials]]
 deps = ["CEnum", "DataStructures", "DiffEqBase", "Libdl", "LinearAlgebra", "Logging", "Reexport", "SparseArrays", "Sundials_jll"]
-git-tree-sha1 = "12d529a67c232bd27e9868fbcfad4997435786a5"
+git-tree-sha1 = "012f7a35993d791889844d32483ac1198f477a1c"
 uuid = "c3572dad-4567-51f8-b174-8c6c989267f4"
-version = "4.6.0"
+version = "4.7.1"
 
-[[Sundials_jll]]
-deps = ["CompilerSupportLibraries_jll", "Libdl", "OpenBLAS_jll", "Pkg", "SuiteSparse_jll"]
-git-tree-sha1 = "013ff4504fc1d475aa80c63b455b6b3a58767db2"
+[[deps.Sundials_jll]]
+deps = ["Artifacts", "CompilerSupportLibraries_jll", "JLLWrappers", "Libdl", "OpenBLAS_jll", "Pkg", "SuiteSparse_jll"]
+git-tree-sha1 = "04777432d74ec5bc91ca047c9e0e0fd7f81acdb6"
 uuid = "fb77eaff-e24c-56d4-86b1-d163f2edb164"
-version = "5.2.0+1"
+version = "5.2.1+0"
 
-[[SymbolicUtils]]
+[[deps.SymbolicUtils]]
 deps = ["AbstractTrees", "Bijections", "ChainRulesCore", "Combinatorics", "ConstructionBase", "DataStructures", "DocStringExtensions", "DynamicPolynomials", "IfElse", "LabelledArrays", "LinearAlgebra", "MultivariatePolynomials", "NaNMath", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "TermInterface", "TimerOutputs"]
-git-tree-sha1 = "b747ed621b12281f9bc69e7a6e5337334b1d0c7f"
+git-tree-sha1 = "3bbb35b0316ddae1234199ae9393d9a7356abb57"
 uuid = "d1185830-fcd6-423d-90d6-eec64667417b"
-version = "0.16.0"
+version = "0.17.0"
 
-[[Symbolics]]
+[[deps.Symbolics]]
 deps = ["ConstructionBase", "DiffRules", "Distributions", "DocStringExtensions", "DomainSets", "IfElse", "Latexify", "Libdl", "LinearAlgebra", "MacroTools", "NaNMath", "RecipesBase", "Reexport", "Requires", "RuntimeGeneratedFunctions", "SciMLBase", "Setfield", "SparseArrays", "SpecialFunctions", "StaticArrays", "SymbolicUtils", "TreeViews"]
-git-tree-sha1 = "e17bd63d88ae90df2ef3c0505a687a534f86f263"
+git-tree-sha1 = "f7111115caa28991f3f019c572866af8abdbfae8"
 uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
-version = "3.4.1"
+version = "3.5.1"
 
-[[TOML]]
+[[deps.TOML]]
 deps = ["Dates"]
 uuid = "fa267f1f-6049-4f14-aa54-33bafae1ed76"
 
-[[TableTraits]]
+[[deps.TableTraits]]
 deps = ["IteratorInterfaceExtensions"]
 git-tree-sha1 = "c06b2f539df1c6efa794486abfb6ed2022561a39"
 uuid = "3783bdb8-4a98-5b6b-af9a-565f29a5fe9c"
 version = "1.0.1"
 
-[[Tables]]
+[[deps.Tables]]
 deps = ["DataAPI", "DataValueInterfaces", "IteratorInterfaceExtensions", "LinearAlgebra", "TableTraits", "Test"]
-git-tree-sha1 = "fed34d0e71b91734bf0a7e10eb1bb05296ddbcd0"
+git-tree-sha1 = "bb1064c9a84c52e277f1096cf41434b675cd368b"
 uuid = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
-version = "1.6.0"
+version = "1.6.1"
 
-[[Tar]]
+[[deps.Tar]]
 deps = ["ArgTools", "SHA"]
 uuid = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 
-[[TermInterface]]
+[[deps.TermInterface]]
 git-tree-sha1 = "02a620218eaaa1c1914d228d0e75da122224a502"
 uuid = "8ea1fca8-c5ef-4a55-8b96-4e9afe9c9a3c"
 version = "0.1.8"
 
-[[Test]]
+[[deps.Test]]
 deps = ["InteractiveUtils", "Logging", "Random", "Serialization"]
 uuid = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
-[[ThreadingUtilities]]
+[[deps.ThreadingUtilities]]
 deps = ["ManualMemory"]
 git-tree-sha1 = "03013c6ae7f1824131b2ae2fc1d49793b51e8394"
 uuid = "8290d209-cae3-49c0-8002-c8c24d57dab5"
 version = "0.4.6"
 
-[[TimerOutputs]]
+[[deps.TimerOutputs]]
 deps = ["ExprTools", "Printf"]
 git-tree-sha1 = "7cb456f358e8f9d102a8b25e8dfedf58fa5689bc"
 uuid = "a759f4b9-e2f1-59dc-863e-4aeb61b1ea8f"
 version = "0.5.13"
 
-[[TreeViews]]
+[[deps.TreeViews]]
 deps = ["Test"]
 git-tree-sha1 = "8d0d7a3fe2f30d6a7f833a5f19f7c7a5b396eae6"
 uuid = "a2a6695c-b41b-5b7d-aed9-dbfdeacea5d7"
 version = "0.3.0"
 
-[[TriangularSolve]]
+[[deps.TriangularSolve]]
 deps = ["CloseOpenIntervals", "IfElse", "LayoutPointers", "LinearAlgebra", "LoopVectorization", "Polyester", "Static", "VectorizationBase"]
-git-tree-sha1 = "ed55426a514db35f58d36c3812aae89cfc057401"
+git-tree-sha1 = "ec9a310324dd2c546c07f33a599ded9c1d00a420"
 uuid = "d5829a12-d9aa-46ab-831f-fb7c9ab06edf"
-version = "0.1.6"
+version = "0.1.8"
 
-[[UUIDs]]
+[[deps.UUIDs]]
 deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
-[[UnPack]]
+[[deps.UnPack]]
 git-tree-sha1 = "387c1f73762231e86e0c9c5443ce3b4a0a9a0c2b"
 uuid = "3a884ed6-31ef-47d7-9d2a-63182c4928ed"
 version = "1.0.2"
 
-[[Unicode]]
+[[deps.Unicode]]
 uuid = "4ec0a83e-493e-50e2-b9ac-8f72acf5a8f5"
 
-[[VectorizationBase]]
+[[deps.VectorizationBase]]
 deps = ["ArrayInterface", "CPUSummary", "HostCPUFeatures", "Hwloc", "IfElse", "LayoutPointers", "Libdl", "LinearAlgebra", "SIMDTypes", "Static"]
-git-tree-sha1 = "a6ca373834ec22aa850c09392399add8f13d476a"
+git-tree-sha1 = "6e261bff5c9f2537776165dea3067df9de4440cf"
 uuid = "3d5dd08c-fd9d-11e8-17fa-ed2836048c2f"
-version = "0.21.13"
+version = "0.21.23"
 
-[[VertexSafeGraphs]]
-deps = ["LightGraphs"]
-git-tree-sha1 = "b9b450c99a3ca1cc1c6836f560d8d887bcbe356e"
+[[deps.VertexSafeGraphs]]
+deps = ["Graphs"]
+git-tree-sha1 = "8351f8d73d7e880bfc042a8b6922684ebeafb35c"
 uuid = "19fa3120-7c27-5ec5-8db8-b0b0aa330d6f"
-version = "0.1.2"
+version = "0.2.0"
 
-[[Zlib_jll]]
+[[deps.Zlib_jll]]
 deps = ["Libdl"]
 uuid = "83775a58-1f1d-513f-b197-d71354ab007a"
 
-[[ZygoteRules]]
+[[deps.ZygoteRules]]
 deps = ["MacroTools"]
 git-tree-sha1 = "8c1a8e4dfacb1fd631745552c8db35d0deb09ea0"
 uuid = "700de1a5-db45-46bc-99cf-38207098b444"
 version = "0.2.2"
 
-[[nghttp2_jll]]
+[[deps.libblastrampoline_jll]]
+deps = ["Artifacts", "Libdl", "OpenBLAS_jll"]
+uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
+
+[[deps.nghttp2_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
 
-[[p7zip_jll]]
+[[deps.p7zip_jll]]
 deps = ["Artifacts", "Libdl"]
 uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
diff --git a/Project.toml b/Project.toml
index a203687..80681a8 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "PETLION"
 uuid = "5e0a28e4-193c-47fa-bbb8-9c901cc1ac2c"
 authors = ["Marc D. Berliner", "Richard D. Braatz"]
-version = "0.1.6"
+version = "0.2.0"
 
 [deps]
 BSON = "fbb218c0-5317-5bc6-957e-2ee96dd4b1f0"
@@ -9,6 +9,7 @@ Dierckx = "39dd38d3-220a-591b-8e3c-4c3a8c710a94"
 GeneralizedGenerated = "6b9d7cbe-bcb9-11e9-073f-15a7a543e2eb"
 IfElse = "615f187c-cbe4-4ef1-ba3b-2fcf58d6d173"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+KLU = "ef3ab10e-7fda-4108-b977-705223b18434"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 RecursiveArrayTools = "731186ca-8d62-57ce-b412-fbd966d074cd"
 SHA = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -17,7 +18,6 @@ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
 StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-SuiteSparse = "4607b0f0-06f3-5cda-b6b1-a6196a1729e9"
 Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 
@@ -26,6 +26,7 @@ BSON = "0.3"
 Dierckx = "0.5"
 GeneralizedGenerated = "0.3"
 IfElse = "0.1.0"
+KLU = "0.2"
 RecipesBase = "1"
 RecursiveArrayTools = "2"
 SciMLBase = "1"
@@ -34,7 +35,7 @@ SpecialFunctions = "1"
 StatsBase = "0.3 - 0.33"
 Sundials = "4"
 Symbolics = "0.1, 1, 2, 3"
-julia = "1, 1.5, 1.6"
+julia = "1, 1.5, 1.6, 1.7"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
diff --git a/src/PETLION.jl b/src/PETLION.jl
index 3854bd0..d2e0a1d 100644
--- a/src/PETLION.jl
+++ b/src/PETLION.jl
@@ -5,7 +5,8 @@ using SciMLBase: DAEFunction, DAEProblem, step!, init
 using Dierckx: Spline1D
 using GeneralizedGenerated: mk_function, RuntimeFn
 using LinearAlgebra: diagind, Tridiagonal, norm
-using SparseArrays: sparse, findnz, SparseMatrixCSC, spzeros
+using KLU: klu, klu!, KLUFactorization
+using SparseArrays: sparse, findnz, SparseMatrixCSC, spzeros, spdiagm
 using SparseDiffTools: matrix_colors, ForwardColorJacCache, forwarddiff_color_jacobian!
 using RecursiveArrayTools: VectorOfArray
 using Symbolics: @variables, Num, gradient, jacobian_sparsity, expand_derivatives, Differential, get_variables, sparsejacobian, substitute, simplify, build_function, IfElse
@@ -15,7 +16,6 @@ using SHA: sha1
 
 import Sundials
 import LinearAlgebra
-import SuiteSparse
 
 # Must be loaded last
 using BSON: @load, @save
diff --git a/src/generate_functions.jl b/src/generate_functions.jl
index 7cd8835..9bf6558 100644
--- a/src/generate_functions.jl
+++ b/src/generate_functions.jl
@@ -1,4 +1,4 @@
-const PETLION_VERSION = (0,1,6)
+const PETLION_VERSION = (0,2,0)
 const options = Dict{Symbol,Any}(
     :SAVE_SYMBOLIC_FUNCTIONS => true,
     :FILE_DIRECTORY => pwd(),
@@ -24,11 +24,49 @@ function load_functions(p::AbstractParam)
     return funcs
 end
 
+function get_saved_model_version(p::AbstractParam)
+    """
+    Gets the version of PETLION used to generate the saved model
+    """
+    str = strings_directory_func(p)
+    str *= "/info.txt"
+    
+    out = readline(str)
+    out = replace(out, "PETLION version: v" => "")
+    # convert this to a tuple
+    out = (Meta.parse.(split(out,"."))...,)
+end
+
+function remove_model_files(p::AbstractParam)
+    """
+    Removes symbolic files for the model
+    """
+    str = strings_directory_func(p) * "/"
+    for x in readdir(str)
+        rm(str*x)
+    end
+end
+
 function load_functions_symbolic(p::AbstractParam)
     dir = strings_directory_func(p) * "/"
     files_exist = isdir(dir)
 
-    if files_exist && options[:SAVE_SYMBOLIC_FUNCTIONS]
+    if files_exist
+        file_version = get_saved_model_version(p)
+        
+        # have there been any breaking changes since creating the functions?
+        no_breaking_changes = (file_version[1] == PETLION_VERSION[1]) && (file_version[2] == PETLION_VERSION[2])
+
+        if !no_breaking_changes
+            @warn "Breaking updates encountered: re-evaluating model..."
+            remove_model_files(p)
+        end
+
+    else
+        no_breaking_changes = false
+    end
+
+    if files_exist && no_breaking_changes && options[:SAVE_SYMBOLIC_FUNCTIONS]
         ## residuals
         initial_guess! = include(dir * "initial_guess.jl")
         f_alg!         = include(dir * "f_alg.jl")
diff --git a/src/model_evaluation.jl b/src/model_evaluation.jl
index 42c475f..fee616f 100644
--- a/src/model_evaluation.jl
+++ b/src/model_evaluation.jl
@@ -367,14 +367,14 @@ end
     YP   .= 0.0
     J     = J_alg.sp
     γ     = 0.0
-    L     = J_alg.L
+    L     = J_alg.L # KLU factorization
     
     # starting loop for Newton's method
     @inbounds for iter in 1:itermax
         # updating res, Y, and J
         R_alg(res,t,Y,YP,p,run)
         J_alg(t,Y,YP,γ,p,run)
-        LinearAlgebra.lu!(L, J)
+        klu!(L, J)
         
         Y_old .= Y_new
         Y_new .-= L\res
diff --git a/src/params.jl b/src/params.jl
index 5007dcc..1607ca1 100644
--- a/src/params.jl
+++ b/src/params.jl
@@ -404,7 +404,7 @@ function system_NMC_LiC6(θ, funcs, cathode, anode;
     # Effective electrolyte conductivity function
     K_eff = K_eff,
     # Thermodynamic factor, ∂ln(f)/∂ln(c_e)
-    thermodynamic_factor = thermodynamic_factor,
+    thermodynamic_factor = thermodynamic_factor_linear,
     # By default, this
     ## Custon functions
     # Reaction rate equation will use the reaction defined by the cathode
diff --git a/src/physics_equations/numerical_tools.jl b/src/physics_equations/numerical_tools.jl
index 806c9aa..139ca84 100644
--- a/src/physics_equations/numerical_tools.jl
+++ b/src/physics_equations/numerical_tools.jl
@@ -199,21 +199,21 @@ function interpolate_electrolyte_concetration_fluxes(c_e, p::AbstractParam)
     Δx = Δx_values(p.N)
 
     # Fluxes within the positive electrode
-    @inbounds @views c_e_flux_p = (c_e[2:p.N.p] .- c_e[1:p.N.p-1])/(Δx.p*p.θ[:l_p])
+    @inbounds @views ∂ₓc_e_p = (c_e[2:p.N.p] .- c_e[1:p.N.p-1])/(Δx.p*p.θ[:l_p])
 
     # Fluxes at the separator-positive interface
-    @inbounds @views c_e_flux_ps = (c_e[p.N.p+1] .- c_e[p.N.p]) / ((Δx.p*p.θ[:l_p]/2+Δx.s*p.θ[:l_s]/2))
+    @inbounds @views ∂ₓc_e_ps = (c_e[p.N.p+1] .- c_e[p.N.p]) / ((Δx.p*p.θ[:l_p]/2+Δx.s*p.θ[:l_s]/2))
 
     # Fluxes within the separator
-    @inbounds @views c_e_flux_s = (c_e[p.N.p+2:p.N.p+p.N.s] .- c_e[p.N.p+1:p.N.p+p.N.s-1])/(Δx.s*p.θ[:l_s])
+    @inbounds @views ∂ₓc_e_s = (c_e[p.N.p+2:p.N.p+p.N.s] .- c_e[p.N.p+1:p.N.p+p.N.s-1])/(Δx.s*p.θ[:l_s])
 
     # Fluxes at the separator-negative interface
-    @inbounds @views c_e_flux_sn = (c_e[p.N.p+p.N.s+1] .- c_e[p.N.p+p.N.s]) / ((Δx.n*p.θ[:l_n]/2+Δx.s*p.θ[:l_s]/2))
+    @inbounds @views ∂ₓc_e_sn = (c_e[p.N.p+p.N.s+1] .- c_e[p.N.p+p.N.s]) / ((Δx.n*p.θ[:l_n]/2+Δx.s*p.θ[:l_s]/2))
 
     # Fluxes within the negative electrode
-    @inbounds @views c_e_flux_n = (c_e[p.N.p+p.N.s+2:end] .- c_e[p.N.p+p.N.s+1:end-1])/(Δx.n*p.θ[:l_n])
+    @inbounds @views ∂ₓc_e_n = (c_e[p.N.p+p.N.s+2:end] .- c_e[p.N.p+p.N.s+1:end-1])/(Δx.n*p.θ[:l_n])
 
-    return [c_e_flux_p; c_e_flux_ps], [c_e_flux_s; c_e_flux_sn], c_e_flux_n
+    return [∂ₓc_e_p; ∂ₓc_e_ps], [∂ₓc_e_s; ∂ₓc_e_sn], ∂ₓc_e_n
 end
 
 Δx_values(N) = (p=1/N.p, s=1/N.s, n=1/N.n, a=1/N.a, z=1/N.z)
\ No newline at end of file
diff --git a/src/physics_equations/residuals.jl b/src/physics_equations/residuals.jl
index a806dfd..5bf0e7e 100644
--- a/src/physics_equations/residuals.jl
+++ b/src/physics_equations/residuals.jl
@@ -249,24 +249,24 @@ function residuals_c_s_avg!(res, states, ∂states, p::T) where {jac,temp,T<:Abs
             c_s = @inbounds @views c_s_avg[ind]
             
             # First order derivatives matrix multiplication
-            ∂ₓc_s_avg = deriv[1](c_s)
+            ∂ᵣc_s = deriv[1](c_s)
     
             # Boundary condition at r = 1
-            ∂ₓc_s_avg[N_r] = -j[i]/D_s_eff[i]*Rp
+            ∂ᵣc_s[N_r] = -j[i]/D_s_eff[i]*Rp
     
             # Boundary condition at r = 0
-            ∂ₓc_s_avg[1] = 0
+            ∂ᵣc_s[1] = 0
     
             # Second order derivatives matrix multiplication
-            ∂ₓₓc_s_avg = deriv[2](c_s)
+            ∂ᵣᵣc_s = deriv[2](c_s)
     
             # Neumann BC at r = 1
-            ∂ₓₓc_s_avg[end] += 50deriv[2].Δx*∂ₓc_s_avg[N_r]*(deriv[2].coeff)
+            ∂ᵣᵣc_s[end] += 50deriv[2].Δx*∂ᵣc_s[N_r]*(deriv[2].coeff)
     
             # Make the RHS vector for this particle
             @inbounds rhsCs[ind] .= (D_s_eff[i]./Rp^2) .* [
-                3∂ₓₓc_s_avg[1]
-                ∂ₓₓc_s_avg[2:end]+2.0./range(1/(N_r-1), 1, length=N_r-1).*∂ₓc_s_avg[2:end]
+                3∂ᵣᵣc_s[1]
+                ∂ᵣᵣc_s[2:end]+2.0./range(1/(N_r-1), 1, length=N_r-1).*∂ᵣc_s[2:end]
                 ]
 
         end
@@ -314,13 +314,13 @@ function residuals_c_s_avg!(res, states, ∂states, p::T) where {jac,temp,T<:Abs
             ind = ind = (1:N_r) .+ N_r*(i-1)
             c_s = c_s_avg[ind]
             
-            ∂ₓc_s_avg = diffusion_matrix*reverse(c_s)
-            ∂ₓc_s_avg[1] = -j[i]*Rp*0.5/D_s_eff[i] # modified BC value due to cheb scheme
-            ∂ₓc_s_avg[end] = 0 # no flux BC
+            ∂ᵣc_s = diffusion_matrix*reverse(c_s)
+            ∂ᵣc_s[1] = -j[i]*Rp*0.5/D_s_eff[i] # modified BC value due to cheb scheme
+            ∂ᵣc_s[end] = 0 # no flux BC
             
-            rhs_numerator = reverse(diffusion_matrix*(4*D_s_eff[i]*((radial_position .+ 1).^2).*∂ₓc_s_avg/(Rp^2)))
+            rhs_numerator = reverse(diffusion_matrix*(4*D_s_eff[i]*((radial_position .+ 1).^2).*∂ᵣc_s/(Rp^2)))
             
-            rhs_limit_vector = (4*D_s_eff[i]/Rp^2)*3*(diffusion_matrix*∂ₓc_s_avg) # limit at r_tilde tends to -1 (at center)
+            rhs_limit_vector = (4*D_s_eff[i]/Rp^2)*3*(diffusion_matrix*∂ᵣc_s) # limit at r_tilde tends to -1 (at center)
             
             @inbounds rhsCs[ind] .= [
                 rhs_limit_vector[end] # L'hopital's rule at the center of the particle
@@ -422,7 +422,11 @@ function residuals_T!(res, states, ∂states, p)
     T_BC_sx =  p.θ[:h_cell]*(p.θ[:T_amb]-T[1])/(Δx.a*p.θ[:l_a])
     T_BC_dx = -p.θ[:h_cell]*(T[end]-p.θ[:T_amb])/(Δx.z*p.θ[:l_z])
 
-    block_tridiag(N) = sparse(Matrix(Tridiagonal{eltype(I_density)}(ones(N-1),-[1;2ones(N-1)],ones(N-1))))
+    block_tridiag(N) = block_tridiag(N) = spdiagm(
+        -1 => ones(eltype(I_density),N-1),
+        0 => -[1;2ones(eltype(I_density),N-2);1],
+        +1 => ones(eltype(I_density),N-1),
+        )
 
     # Positive current collector
     A_a = p.θ[:λ_a].*block_tridiag(p.N.a)
@@ -649,7 +653,7 @@ function residuals_j_s!(res, states, p::AbstractParam)
     η_s = Φ_s.n .- Φ_e.n .- p.θ[:Uref_s] .- F.*j_s.*R_film
     α = 0.5
 
-    j_s_calc = (p.θ[:i_0_jside].*(I_density/I1C)^p.θ[:w]./F).*(exp.((1-α).*F./(R.*T.n).*η_s)-exp.(-α.*F./(R.*T.n).*η_s))
+    j_s_calc = -abs.((p.θ[:i_0_jside].*(I_density/I1C)^p.θ[:w]./F).*(-exp.(-α.*F./(R.*T.n).*η_s)))
 
     # Only activate the side reaction during charge
     j_s_calc .= [IfElse.ifelse(I_density > 0, x, 0) for x in j_s_calc]
@@ -730,7 +734,7 @@ function residuals_Φ_e!(res, states, p::AbstractParam)
     ## Electrolyte fluxes
     # Evaluate the interpolation of the electrolyte concentration fluxes at the
     # edges of the control volumes.
-    c_e_flux_p, c_e_flux_s, c_e_flux_n = PETLION.interpolate_electrolyte_concetration_fluxes(c_e, p)
+    ∂ₓc_e_p, ∂ₓc_e_s, ∂ₓc_e_n = PETLION.interpolate_electrolyte_concetration_fluxes(c_e, p)
     
     ## RHS arrays
     ν_p,ν_s,ν_n = p.numerics.thermodynamic_factor(c_e.p, c_e.s, c_e.n, T.p, T.s, T.n, p)
@@ -739,9 +743,9 @@ function residuals_Φ_e!(res, states, p::AbstractParam)
     K = 2R.*(1-p.θ[:t₊]).*ν[1:end-1]/F
 
     prod_tot = [
-        K̂_eff_p.*T̄_p.*c_e_flux_p./c̄_e_p # p
-        K̂_eff_s.*T̄_s.*c_e_flux_s./c̄_e_s # s
-        K̂_eff_n[1:end-1].*T̄_n.*c_e_flux_n./c̄_e_n # n
+        K̂_eff_p.*T̄_p.*∂ₓc_e_p./c̄_e_p # p
+        K̂_eff_s.*T̄_s.*∂ₓc_e_s./c̄_e_s # s
+        K̂_eff_n[1:end-1].*T̄_n.*∂ₓc_e_n./c̄_e_n # n
     ]
     
     prod_tot[2:end] .-= prod_tot[1:end-1]
@@ -791,7 +795,11 @@ function residuals_Φ_s!(res, states, p::AbstractParam)
     f_p[1]   += -I_density*(Δx.p*p.θ[:l_p]/σ_eff_p)
     f_n[end] += +I_density*(Δx.n*p.θ[:l_n]/σ_eff_n)
 
-    block_tridiag(N) = sparse(Matrix(Tridiagonal{eltype(j.p)}(ones(N-1),-[1;2ones(N-2);1],ones(N-1))))
+    block_tridiag(N) = spdiagm(
+        -1 => ones(eltype(j.p),N-1),
+        0 => -[1;2ones(eltype(j.p),N-2);1],
+        +1 => ones(eltype(j.p),N-1),
+        )
     
     A_p = block_tridiag(p.N.p)
     A_n = block_tridiag(p.N.n)
diff --git a/src/physics_equations/scalar_residual.jl b/src/physics_equations/scalar_residual.jl
index 69bff7f..dd41daf 100644
--- a/src/physics_equations/scalar_residual.jl
+++ b/src/physics_equations/scalar_residual.jl
@@ -13,6 +13,8 @@
 
 @inline calc_T(Y::Vector{<:Number}, p::AbstractParamTemp{true}) = @inbounds @views Y[p.ind.T]
 @inline calc_T(::Vector{<:Number}, p::AbstractParamTemp{false}) = repeat([p.θ[:T₀]], p.N.a+p.N.p+p.N.s+p.N.n+p.N.z)
+@inline calc_K_eff(Y::Vector{<:Number}, p::AbstractParamTemp{true})  = @inbounds @views p.numerics.K_eff(Y[p.ind.c_e.p], Y[p.ind.c_e.s], Y[p.ind.c_e.n], Y[p.ind.T.p], Y[p.ind.T.s], Y[p.ind.T.n], p)
+@inline calc_K_eff(Y::Vector{<:Number}, p::AbstractParamTemp{false}) = @inbounds @views p.numerics.K_eff(Y[p.ind.c_e.p], Y[p.ind.c_e.s], Y[p.ind.c_e.n], repeat([p.θ[:T₀]], p.N.p), repeat([p.θ[:T₀]], p.N.s), repeat([p.θ[:T₀]], p.N.n), p)
 
 @inline method_I(Y, p)   = calc_I(Y,p)
 @inline method_V(Y, p)   = calc_V(Y,p)
@@ -316,9 +318,9 @@ function _get_jacobian_combined(J_sp_base,J_base_func,J_sp_scalar,J_scalar_func,
     J_sp = [J_sp_base; J_sp_scalar']
 
     if lu_decomposition
-        L = LinearAlgebra.lu(J_sp)
+        L = klu(J_sp)
     else
-        L = LinearAlgebra.lu(sparse([1],[1],[1.0]))
+        L = klu(sparse([1],[1],[1.0]))
     end
 
     ind_base   = findall(J_sp.rowval .< size(J_sp,1))
diff --git a/src/structures.jl b/src/structures.jl
index 649e8cc..2b7e9a7 100644
--- a/src/structures.jl
+++ b/src/structures.jl
@@ -115,7 +115,7 @@ struct jacobian_combined{
     J_scalar::SubArray{Float64, 1, Vector{Float64}, Tuple{Vector{Int64}}, false}
     θ_tot::Vector{Float64}
     θ_keys::Vector{Symbol}
-    L::SuiteSparse.UMFPACK.UmfpackLU{Float64, Int64}
+    L::KLUFactorization{Float64, Int64}
 end
 Base.getindex(J::jacobian_combined,i...) = getindex(J.sp,i...)
 Base.axes(J::jacobian_combined,i...) = axes(J.sp,i...)
@@ -576,6 +576,7 @@ function Base.show(io::IO, run::T) where {T<:AbstractRun}
     
     print(io, str)
 end
+(funcs::model_funcs)(model::model_output) = (@assert !isempty(model); (@inbounds funcs(model.results[end].run)))
 Base.show(io::IO, funcs::model_funcs) = println(io,"PETLION model functions")
 function Base.show(io::IO, model::model_output)
     results = model.results
@@ -650,6 +651,7 @@ end
     print(io, str[1:end-1])
 end
 
+#=
 function _MTK_MatVecProd(A, x; simple::Bool = true)
     """
     Change matrix-vector multiplication in Symbolics to ignore 0s in the matrix.
@@ -682,6 +684,7 @@ end
 # overloads of * to use _MTK_MatVecProd when appropriate
 Base.:*(A::AbstractMatrix, x::AbstractVector{Num}; simple::Bool = true) = _MTK_MatVecProd(A, x; simple=simple)
 Base.:*(A::Union{Array{T,2}, Array{T,2}, Array{T,2}, Array{T,2}}, x::StridedArray{Num, 1}; simple::Bool = true) where {T<:Union{Float32, Float64}} = _MTK_MatVecProd(A, x; simple=simple)
+=#
 
 Base.deleteat!(a::VectorOfArray, i::Integer) = (Base._deleteat!(a.u, i, 1); a.u)