diff --git a/Manifest.toml b/Manifest.toml
index 903a9fe..673db2a 100644
--- a/Manifest.toml
+++ b/Manifest.toml
@@ -2,9 +2,9 @@
 
 [[AbstractFFTs]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "051c95d6836228d120f5f4b984dd5aba1624f716"
+git-tree-sha1 = "8ed9de2f1b1a9b1dee48582ad477c6e67b83eb2c"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
-version = "0.5.0"
+version = "1.0.0"
 
 [[AbstractTrees]]
 deps = ["Markdown"]
@@ -14,9 +14,9 @@ version = "0.3.3"
 
 [[Adapt]]
 deps = ["LinearAlgebra"]
-git-tree-sha1 = "42c42f2221906892ceb765dbcb1a51deeffd86d7"
+git-tree-sha1 = "87491f7d03ae1b423a353aff99cf61a45e3c993a"
 uuid = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
-version = "2.3.0"
+version = "3.1.0"
 
 [[Arpack]]
 deps = ["Arpack_jll", "Libdl", "LinearAlgebra"]
@@ -32,9 +32,9 @@ version = "3.5.0+3"
 
 [[ArrayInterface]]
 deps = ["LinearAlgebra", "Requires", "SparseArrays"]
-git-tree-sha1 = "3b5bd474a90bee86b50f26268bbb044bb4d9ef83"
+git-tree-sha1 = "91f95e873f0e53d8f5e6603516fa8ec3dc312859"
 uuid = "4fba245c-0d91-5ea0-9b3e-6abc04ee57a9"
-version = "2.14.9"
+version = "2.14.14"
 
 [[Artifacts]]
 deps = ["Pkg"]
@@ -230,9 +230,9 @@ version = "1.1.0"
 
 [[FFTW]]
 deps = ["AbstractFFTs", "FFTW_jll", "IntelOpenMP_jll", "Libdl", "LinearAlgebra", "MKL_jll", "Reexport"]
-git-tree-sha1 = "8b7c16b56936047ca41bf25effa137ae0b381ae8"
+git-tree-sha1 = "c31e446bf3b12aad2ec8fc500fe19528c148d811"
 uuid = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
-version = "1.2.4"
+version = "1.3.1"
 
 [[FFTW_jll]]
 deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
@@ -260,9 +260,9 @@ version = "0.4.2"
 
 [[ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "NaNMath", "Random", "SpecialFunctions", "StaticArrays"]
-git-tree-sha1 = "8de2519a83c6c1c2442c2f481dd9a8364855daf4"
+git-tree-sha1 = "c26b56e9b9f0687f7ca887f6b6ded03d269e0e35"
 uuid = "f6369f11-7733-5829-9624-2563aa707210"
-version = "0.10.14"
+version = "0.10.15"
 
 [[HDF5]]
 deps = ["Blosc", "Compat", "HDF5_jll", "Libdl", "Mmap", "Random", "Requires"]
@@ -289,10 +289,10 @@ uuid = "83e8ac13-25f8-5344-8a64-a9f2b223428f"
 version = "0.5.0"
 
 [[IntelOpenMP_jll]]
-deps = ["Libdl", "Pkg"]
-git-tree-sha1 = "fb8e1c7a5594ba56f9011310790e03b5384998d6"
+deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
+git-tree-sha1 = "d979e54b71da82f3a65b62553da4fc3d18c9004c"
 uuid = "1d5cc7b8-4909-519e-a0f8-d0f5ad9712d0"
-version = "2018.0.3+0"
+version = "2018.0.3+2"
 
 [[InteractiveUtils]]
 deps = ["Markdown"]
@@ -321,9 +321,9 @@ uuid = "82899510-4779-5014-852e-03e436cf321d"
 version = "1.0.0"
 
 [[JLLWrappers]]
-git-tree-sha1 = "04b49c556240b62d5a799e94c63d5fc14d3c07cd"
+git-tree-sha1 = "a431f5f2ca3f4feef3bd7a5e94b8b8d4f2f647a0"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
-version = "1.1.4"
+version = "1.2.0"
 
 [[JSON]]
 deps = ["Dates", "Mmap", "Parsers", "Unicode"]
@@ -467,9 +467,9 @@ version = "0.7.1"
 
 [[MutableArithmetics]]
 deps = ["LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "90c8d17c4120915732fd2c4c2e80078206a1296e"
+git-tree-sha1 = "6b6bb8f550dc38310afd4a0af0786dc3222459e2"
 uuid = "d8a4904e-b15c-11e9-3269-09a3773c0cb0"
-version = "0.2.13"
+version = "0.2.14"
 
 [[NLSolversBase]]
 deps = ["Calculus", "DiffEqDiffTools", "DiffResults", "Distributed", "ForwardDiff"]
@@ -484,9 +484,9 @@ version = "0.3.5"
 
 [[OffsetArrays]]
 deps = ["Adapt"]
-git-tree-sha1 = "b0cc1c42b63e30b759f4e1cf045ad8a51069d6cc"
+git-tree-sha1 = "6247fe4b373b354b9b7fc155ae9c137267c9a07f"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
-version = "1.4.2"
+version = "1.5.1"
 
 [[OpenBLAS_jll]]
 deps = ["CompilerSupportLibraries_jll", "Libdl", "Pkg"]
@@ -575,9 +575,9 @@ uuid = "de0858da-6303-5e67-8744-51eddeeeb8d7"
 
 [[PyCall]]
 deps = ["Conda", "Dates", "Libdl", "LinearAlgebra", "MacroTools", "Serialization", "VersionParsing"]
-git-tree-sha1 = "b6dff5fa725eff4f775f472acd86756d6e31fb02"
+git-tree-sha1 = "dd1a970b543bd02efce2984582e996af28cab27f"
 uuid = "438e738f-606a-5dbb-bf0a-cddfbfd45ab0"
-version = "1.92.1"
+version = "1.92.2"
 
 [[PyPlot]]
 deps = ["Colors", "LaTeXStrings", "PyCall", "Sockets", "Test", "VersionParsing"]
@@ -765,9 +765,9 @@ uuid = "3bb67fe8-82b1-5028-8e26-92a6c54297fa"
 version = "0.9.5"
 
 [[URIs]]
-git-tree-sha1 = "bc331715463c41d601cf8bfd38ca70a490af5c5b"
+git-tree-sha1 = "7855809b88d7b16e9b029afd17880930626f54a2"
 uuid = "5c2747f8-b7ea-4ff2-ba2e-563bfd36b1d4"
-version = "1.1.0"
+version = "1.2.0"
 
 [[UUIDs]]
 deps = ["Random", "SHA"]
@@ -800,9 +800,9 @@ version = "2.9.10+3"
 
 [[YAML]]
 deps = ["Base64", "Dates", "Printf"]
-git-tree-sha1 = "eb846197b193d3eaa3474798a572c3ebf8a1862d"
+git-tree-sha1 = "78c02bd295bbd0ca330f95e07ccdfcb69f6cbcd4"
 uuid = "ddb6d928-2868-570f-bddf-ab3f9cf99eb6"
-version = "0.4.5"
+version = "0.4.6"
 
 [[ZipFile]]
 deps = ["Libdl", "Printf", "Zlib_jll"]
diff --git a/Project.toml b/Project.toml
index 3a940da..03ea43d 100644
--- a/Project.toml
+++ b/Project.toml
@@ -46,6 +46,7 @@ LsqFit = "0.12"
 MicroLogging = "0.4"
 Optim = "^0.18.0, ^0.21.0, 0.22"
 QuantumTomography = "0.1.1"
+Roots = "1.0"
 Seaborn = "0.4"
 YAML = "0.4"
 julia = "1.3"