fix a numeric bug cause acos domain error

Manifest.toml

@@ -1,6 +1,6 @@
 # This file is machine-generated - editing it directly is not advised
 
-julia_version = "1.7.1"
+julia_version = "1.7.2"
 manifest_format = "2.0"
 
 [[deps.ArgTools]]
@@ -12,17 +12,23 @@ uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
 [[deps.Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
 
+[[deps.Calculus]]
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "f641eb0a4f00c343bbc32346e1217b86f3ce9dad"
+uuid = "49dc2e85-a5d0-5ad3-a950-438e2897f1b9"
+version = "0.5.1"
+
 [[deps.ChainRulesCore]]
 deps = ["Compat", "LinearAlgebra", "SparseArrays"]
-git-tree-sha1 = "54fc4400de6e5c3e27be6047da2ef6ba355511f8"
+git-tree-sha1 = "9950387274246d08af38f6eef8cb5480862a435f"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.11.6"
+version = "1.14.0"
 
 [[deps.ChangesOfVariables]]
 deps = ["ChainRulesCore", "LinearAlgebra", "Test"]
-git-tree-sha1 = "bf98fa45a0a4cee295de98d4c1462be26345b9a1"
+git-tree-sha1 = "1e315e3f4b0b7ce40feded39c73049692126cf53"
 uuid = "9e997f8a-9a97-42d5-a9f1-ce6bfc15e2c0"
-version = "0.1.2"
+version = "0.1.3"
 
 [[deps.Combinatorics]]
 git-tree-sha1 = "08c8b6831dc00bfea825826be0bc8336fc369860"
@@ -36,9 +42,9 @@ version = "0.2.0"
 
 [[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 = "44c37b4636bc54afac5c574d2d02b625349d6582"
+git-tree-sha1 = "b153278a25dd42c65abbf4e62344f9d22e59191b"
 uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
-version = "3.41.0"
+version = "3.43.0"
 
 [[deps.CompilerSupportLibraries_jll]]
 deps = ["Artifacts", "Libdl"]
@@ -51,15 +57,15 @@ uuid = "187b0558-2788-49d3-abe0-74a17ed4e7c9"
 version = "1.3.0"
 
 [[deps.DataAPI]]
-git-tree-sha1 = "cc70b17275652eb47bc9e5f81635981f13cea5c8"
+git-tree-sha1 = "fb5f5316dd3fd4c5e7c30a24d50643b73e37cd40"
 uuid = "9a962f9c-6df0-11e9-0e5d-c546b8b5ee8a"
-version = "1.9.0"
+version = "1.10.0"
 
 [[deps.DataStructures]]
 deps = ["Compat", "InteractiveUtils", "OrderedCollections"]
-git-tree-sha1 = "3daef5523dd2e769dad2365274f760ff5f282c7d"
+git-tree-sha1 = "cc1a8e22627f33c789ab60b36a9132ac050bbf75"
 uuid = "864edb3b-99cc-5e75-8d2d-829cb0a9cfe8"
-version = "0.18.11"
+version = "0.18.12"
 
 [[deps.Dates]]
 deps = ["Printf"]
@@ -81,9 +87,9 @@ uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[deps.Distributions]]
 deps = ["ChainRulesCore", "DensityInterface", "FillArrays", "LinearAlgebra", "PDMats", "Printf", "QuadGK", "Random", "SparseArrays", "SpecialFunctions", "Statistics", "StatsBase", "StatsFuns", "Test"]
-git-tree-sha1 = "5863b0b10512ed4add2b5ec07e335dc6121065a5"
+git-tree-sha1 = "8a6b49396a4058771c5c072239b2e0a76e2e898c"
 uuid = "31c24e10-a181-5473-b8eb-7969acd0382f"
-version = "0.25.41"
+version = "0.25.58"
 
 [[deps.DocStringExtensions]]
 deps = ["LibGit2"]
@@ -95,31 +101,43 @@ version = "0.8.6"
 deps = ["ArgTools", "LibCURL", "NetworkOptions"]
 uuid = "f43a241f-c20a-4ad4-852c-f6b1247861c6"
 
+[[deps.DualNumbers]]
+deps = ["Calculus", "NaNMath", "SpecialFunctions"]
+git-tree-sha1 = "5837a837389fccf076445fce071c8ddaea35a566"
+uuid = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
+version = "0.6.8"
+
 [[deps.FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Statistics"]
-git-tree-sha1 = "8756f9935b7ccc9064c6eef0bff0ad643df733a3"
+git-tree-sha1 = "246621d23d1f43e3b9c368bf3b72b2331a27c286"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "0.12.7"
+version = "0.13.2"
 
 [[deps.Future]]
 deps = ["Random"]
 uuid = "9fa8497b-333b-5362-9e8d-4d0656e87820"
 
+[[deps.HypergeometricFunctions]]
+deps = ["DualNumbers", "LinearAlgebra", "SpecialFunctions", "Test"]
+git-tree-sha1 = "cb7099a0109939f16a4d3b572ba8396b1f6c7c31"
+uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
+version = "0.3.10"
+
 [[deps.HypothesisTests]]
 deps = ["Combinatorics", "Distributions", "LinearAlgebra", "Random", "Rmath", "Roots", "Statistics", "StatsBase"]
-git-tree-sha1 = "dc9bb7abfa265e0cf030635315184a476a2dd5f3"
+git-tree-sha1 = "10b23fc711999d34f6888ab6df4c510def193fd9"
 uuid = "09f84164-cd44-5f33-b23f-e6b0d136a0d5"
-version = "0.10.6"
+version = "0.10.10"
 
 [[deps.InteractiveUtils]]
 deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[deps.InverseFunctions]]
 deps = ["Test"]
-git-tree-sha1 = "a7254c0acd8e62f1ac75ad24d5db43f5f19f3c65"
+git-tree-sha1 = "336cc738f03e069ef2cac55a104eb823455dca75"
 uuid = "3587e190-3f89-42d0-90ee-14403ec27112"
-version = "0.1.2"
+version = "0.1.4"
 
 [[deps.IrrationalConstants]]
 git-tree-sha1 = "7fd44fd4ff43fc60815f8e764c0f352b83c49151"
@@ -128,9 +146,9 @@ version = "0.1.1"
 
 [[deps.JLLWrappers]]
 deps = ["Preferences"]
-git-tree-sha1 = "22df5b96feef82434b07327e2d3c770a9b21e023"
+git-tree-sha1 = "abc9885a7ca2052a736a600f7fa66209f96506e1"
 uuid = "692b3bcd-3c85-4b1f-b108-f13ce0eb3210"
-version = "1.4.0"
+version = "1.4.1"
 
 [[deps.LibCURL]]
 deps = ["LibCURL_jll", "MozillaCACerts_jll"]
@@ -157,9 +175,9 @@ uuid = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [[deps.LogExpFunctions]]
 deps = ["ChainRulesCore", "ChangesOfVariables", "DocStringExtensions", "InverseFunctions", "IrrationalConstants", "LinearAlgebra"]
-git-tree-sha1 = "e5718a00af0ab9756305a0392832c8952c7426c1"
+git-tree-sha1 = "09e4b894ce6a976c354a69041a04748180d43637"
 uuid = "2ab3a3ac-af41-5b50-aa03-7779005ae688"
-version = "0.3.6"
+version = "0.3.15"
 
 [[deps.Logging]]
 uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
@@ -190,6 +208,11 @@ uuid = "a63ad114-7e13-5084-954f-fe012c677804"
 [[deps.MozillaCACerts_jll]]
 uuid = "14a3606d-f60d-562e-9121-12d972cd8159"
 
+[[deps.NaNMath]]
+git-tree-sha1 = "737a5957f387b17e74d4ad2f440eb330b39a62c5"
+uuid = "77ba4419-2d1f-58cd-9bb1-8ffee604a2e3"
+version = "1.0.0"
+
 [[deps.NetworkOptions]]
 uuid = "ca575930-c2e3-43a9-ace4-1e988b2c1908"
 
@@ -214,19 +237,19 @@ version = "1.4.1"
 
 [[deps.PDMats]]
 deps = ["LinearAlgebra", "SparseArrays", "SuiteSparse"]
-git-tree-sha1 = "ee26b350276c51697c9c2d88a072b339f9f03d73"
+git-tree-sha1 = "027185efff6be268abbaf30cfd53ca9b59e3c857"
 uuid = "90014a1f-27ba-587c-ab20-58faa44d9150"
-version = "0.11.5"
+version = "0.11.10"
 
 [[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"
 
 [[deps.Preferences]]
 deps = ["TOML"]
-git-tree-sha1 = "2cf929d64681236a2e074ffafb8d568733d2e6af"
+git-tree-sha1 = "47e5f437cc0e7ef2ce8406ce1e7e24d44915f88d"
 uuid = "21216c6a-2e73-6563-6e65-726566657250"
-version = "1.2.3"
+version = "1.3.0"
 
 [[deps.Printf]]
 deps = ["Unicode"]
@@ -271,9 +294,9 @@ version = "0.3.0+0"
 
 [[deps.Roots]]
 deps = ["CommonSolve", "Printf", "Setfield"]
-git-tree-sha1 = "0abe7fc220977da88ad86d339335a4517944fea2"
+git-tree-sha1 = "30e3981751855e2340e9b524ab58c1ec85c36f33"
 uuid = "f2b01f46-fcfa-551c-844a-d8ac1e96c665"
-version = "1.3.14"
+version = "2.0.1"
 
 [[deps.SHA]]
 uuid = "ea8e919c-243c-51af-8825-aaa63cd721ce"
@@ -283,9 +306,9 @@ uuid = "9e88b42a-f829-5b0c-bbe9-9e923198166b"
 
 [[deps.Setfield]]
 deps = ["ConstructionBase", "Future", "MacroTools", "Requires"]
-git-tree-sha1 = "0afd9e6c623e379f593da01f20590bacc26d1d14"
+git-tree-sha1 = "38d88503f695eb0301479bc9b0d4320b378bafe5"
 uuid = "efcf1570-3423-57d1-acb7-fd33fddbac46"
-version = "0.8.1"
+version = "0.8.2"
 
 [[deps.SharedArrays]]
 deps = ["Distributed", "Mmap", "Random", "Serialization"]
@@ -306,30 +329,31 @@ uuid = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [[deps.SpecialFunctions]]
 deps = ["ChainRulesCore", "IrrationalConstants", "LogExpFunctions", "OpenLibm_jll", "OpenSpecFun_jll"]
-git-tree-sha1 = "e08890d19787ec25029113e88c34ec20cac1c91e"
+git-tree-sha1 = "5ba658aeecaaf96923dce0da9e703bd1fe7666f9"
 uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
-version = "2.0.0"
+version = "2.1.4"
 
 [[deps.Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[deps.StatsAPI]]
-git-tree-sha1 = "d88665adc9bcf45903013af0982e2fd05ae3d0a6"
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "c82aaa13b44ea00134f8c9c89819477bd3986ecd"
 uuid = "82ae8749-77ed-4fe6-ae5f-f523153014b0"
-version = "1.2.0"
+version = "1.3.0"
 
 [[deps.StatsBase]]
 deps = ["DataAPI", "DataStructures", "LinearAlgebra", "LogExpFunctions", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "StatsAPI"]
-git-tree-sha1 = "51383f2d367eb3b444c961d485c565e4c0cf4ba0"
+git-tree-sha1 = "8977b17906b0a1cc74ab2e3a05faa16cf08a8291"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.33.14"
+version = "0.33.16"
 
 [[deps.StatsFuns]]
-deps = ["ChainRulesCore", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
-git-tree-sha1 = "bedb3e17cc1d94ce0e6e66d3afa47157978ba404"
+deps = ["ChainRulesCore", "HypergeometricFunctions", "InverseFunctions", "IrrationalConstants", "LogExpFunctions", "Reexport", "Rmath", "SpecialFunctions"]
+git-tree-sha1 = "5783b877201a82fc0014cbf381e7e6eb130473a4"
 uuid = "4c63d2b9-4356-54db-8cca-17b64c39e42c"
-version = "0.9.14"
+version = "1.0.1"
 
 [[deps.SuiteSparse]]
 deps = ["Libdl", "LinearAlgebra", "Serialization", "SparseArrays"]

src/src.jl

@@ -163,7 +163,7 @@ function circ_confmean(α; xi = 0.05, w = ones(size(α)), d = 0, dims = 1)
   end
 
   # apply final transform
-  t = acos.(t ./ R)
+  t = acos.(clamp.(t ./ R, -1, 1))
   t = length(t) == 1 ? t[1] : t
 end