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PJ7S@P3R R@Q pQZ! n Rf 2@`,PRj`k`l`m`n` p t 7`SZ! 2@`Sdo`STp`S`T$q`0TTr`TUs`TPU|ht` UUUpU.u`pUVV/ 2jSjUu`UV`>f`V@@X@0WNf`e`9Xf 6 0XX@2  `Xt`v`w`g`q`f`e`f.XXZ&`U.V@YY.f`YY2=x``Y?YY.d`Y0Zy`ZZz`PZZ{`Z [jc|`Zp[}`@[[~`[0\\[.`[\p\i %j0\`0\\zg:`P]@@ _@]N`e` _ p ^p^@l  ^g`h```~```e`f.`_`_ v0\p\__.`_``_p`P` `.` ``` %Qjp``p`0ac8`a@c0c@aN`e`0c   bb@  c``e`f.pcpcwKX`p`(.@e@cN`e`,eV & dd@  e  `    d``ee`e`D`i e  f. f f`p`(&`f*&f`fg2`fPg` gg`pggz2`g`h@hh.`hhh_ *}rj`h``h i˘&/$`i@k0k@iN`e`0k f jj@b  kh``g``e`f.pkpk `v`h@0m@kN`e`0m  ll@  m`e`f.pmpmkl/B``h.hmm.`mn `m``n0n.`0nnB`no_<`nPo` ooopo.`popp Nbjo`op`@up@ q  t r@t@prv0str4pr. @N``tpr  0tt@  `t``f.ttp`o.f. u u _avout@0s@0w@uN``0w  vv@  w``f.pwpwo#`o.pww.`w@x xw.`wxx Pj@x`@xyIN'``y@@{@yN``{  zz@  z```f.@{@{}`@x.x{`{.``{{{.`{N``P}  }|@  0}``f.}}A`..NP``@  ~~@  ~`P``0f.pp*aZT`Z! .NP`` V H @D  P``f.PP`Z..N&``Ђj ^ P@Z  D``f.!A@`]a3N$``~ r 0@n  `E``f.``\3N``0  @  F``f.ppx,`D$3N``  `@  D`F`E`G``+``p f.``;!(I 6 58z!p 6+.Pu;!p@I`Z! .Ns``  `@  F``f. &.`vwS3N``'  @@  p<````f.10 `g.N%``Z $ @  @   `'` `f.k!. 60 5p8z! 6+.Џu;!@I`Z! .N@``\ b @^  @`B`?`@``Ds`f.ББ3`!`qjL-V-V-NC``  @  @   :`  9`     3`C``Гf.'KJa@.]{4a 6 5 a! 6+.` k!@I`Z! V-NC``  p@  ЖC``f.PP7aV-V-.)Ba 6 5`@8z! 6+.u;!@I`Z! .NC``0  @  C``f.ppzu)K`5V-V- К 4F<5H+-^.f67>3.!M I-!R-  I-!P . O?-!Z 6+ I. L. L-.6+3+7= I.!P . O?-!Z6+37>++?/#9<59<5,/#9<59<5,/#9<59<5,/#9<59<5,/#9<59<5,/#9<59<5,?#self#fxsf1x5v E;8MdT"&.%Le \3bRXV9m)C-@oaJu/ :KSYOU[(#lIw_gc2p]>^G+!ixQ67q `t0BFPfjWy=Nn $1sHh?Z,4r'*k logrange(1, 4, length=5) 5-element Base.LogRange{Float64, Base.TwicePrecision{Float64}}: 1.0, 1.41421, 2.0, 2.82843, 4.0 julia> Base.LogRange{Float16}(1, 4, 5) 5-element Base.LogRange{Float16, Float64}: 1.0, 1.414, 2.0, 2.828, 4.0 julia> logrange(1e-310, 1e-300, 11)[1:2:end] 6-element Vector{Float64}: 1.0e-310 9.999999999999974e-309 9.999999999999981e-307 9.999999999999988e-305 9.999999999999994e-303 1.0e-300 julia> prevfloat(1e-308, 5) == ans[2] true ``` Note that integer eltype `T` is not allowed. Use for instance `round.(Int, xs)`, or explicit powers of some integer base: ``` julia> xs = logrange(1, 512, 4) 4-element Base.LogRange{Float64, Base.TwicePrecision{Float64}}: 1.0, 8.0, 64.0, 512.0 julia> 2 .^ (0:3:9) |> println [1, 8, 64, 512] ``` 3/opt/julia/packages/Compat/GTn3Z/src/compatmacro.jlڻQ _valid_macro(expr) Check if `expr` is a valid macro call with no arguments. ./opt/julia/packages/Compat/GTn3Z/src/Compat.jl/ڻ logrange(start, stop, length) logrange(start, stop; length) Construct a specialized array whose elements are spaced logarithmically between the given endpoints. That is, the ratio of successive elements is a constant, calculated from the length. This is similar to `geomspace` in Python. Unlike `PowerRange` in Mathematica, you specify the number of elements not the ratio. Unlike `logspace` in Python and Matlab, the `start` and `stop` arguments are always the first and last elements of the result, not powers applied to some base. # Examples ``` julia> logrange(10, 4000, length=3) 3-element Base.LogRange{Float64, Base.TwicePrecision{Float64}}: 10.0, 200.0, 4000.0 julia> ans[2] ≈ sqrt(10 * 4000) # middle element is the geometric mean true julia> range(10, 40, length=3)[2] ≈ (10 + 40)/2 # arithmetic mean true julia> logrange(1f0, 32f0, 11) 11-element Base.LogRange{Float32, Float64}: 1.0, 1.41421, 2.0, 2.82843, 4.0, 5.65685, 8.0, 11.3137, 16.0, 22.6274, 32.0 julia> logrange(1, 1000, length=4) ≈ 10 .^ (0:3) true ``` See the [`Compat.LogRange`](@ref Compat.LogRange) type for further details. !!! compat "Julia 1.9" The version of this struct in Compat.jl does not use `Base.TwicePrecision{Float64}` before Julia 1.9, so it sometimes has larger floating-point errors on intermediate points. !!! compat "Julia 1.11" The printing of Compat.jl's version of the struct is also different, less like `LinRange` and more like `Vector`. <5f+.!J9<549<5.49<56+.!J49<5-^.Q6+.!J49<5.!M.w g6 +.!J49<5.!M -y .!M.Q9<5@6+.!J49<5.!M.w9<577=7=7=7=++?/#9<59<5,9? #self#expr<5+0 I.!J49<5.!M.!J49<5.!M.wZ6 .!J49<5.!M .!J 49<5.!M .!J49<5.O49<53.!J49<5 I.!M.!J49<5.!M.!J49<5.!M I.!J49<5 I-Z49<5 I-!P. O?-!Z6+. I. L. L-9<5 AZ49<5#$ I AZ4I"%.!J49<5.' I.!P!. O?-!Z*6++.3+.!J49<5..7+0+0?/#9<59<5,/#9<59<5, /#9<59<5,!/#9<59<5,"/#9<59<5,#/#9<59<5,$/#9<59<5,%/#9<59<5,&/#9<59<5,'/#9<59<5,(? '#self#exparametersvaluespasgnex<5Z?-9<5-7?/#9<59<5,? #self#__source____module__ex<5DEV` Invalid Syntax: `@compat e.Q49<563 A!y9<59<59<5--U I-9<5.9<59<56 Z9<5 A }!P  - 77??/#9<59<5 ,-/#9<59<5 ,./#9<59<5 ,//#9<59<5 ,0?9#self#__source____module__publicsymbols_exprsymbols<5J.!J49<5.O49<56.!J49<5.!M.wg67Z.!J49<5- F 9<5.!J49<5.  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A9<57++?/#9<59<5,\?#unused#startstoplength<5&): endpoints differ, while length is 1): can't have negative length, LogRange(0LogRange is only defined for finite start & stop)LogRange does not accept negative numbers%LogRange cannot start or stop at zero*LogRange{T} does not support integer typesY +S. d>6-9<5-U-F63-F6 . F.9<5 9<5-U 3+0._63._6+. F.9<59<5-U3+0-9<5-k6+3+-9<5-k6+#. F.9<59<5-U 3+0._6#+) Ay9<59<59<59<5-%-U&3+0.Q6)+0.v6++0 Ay9<59<59<59<5 ---U. I A9<5 9<5 d.!M-3 A K124. 5 I . w 668+;3+< I .!N6  . 5 I. w=6?+B3+C I.!N=. 5 I. wD6F+I3+J I.!ND. 5 I. wK6M+P3+Q I.!NK R5<CJQ7R+S+S?/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,/#9<5 9<5 ,? "#ctor-self#startstoplenex<5. K9<5 d.N d.N d.N A7?/#9<59<5,?#self#startstoplen<5--. I-. K9<5.N.N.N A7 ?/#9<59<5,/#9<59<5,?#self#startstoplenTJallequal./opt/julia/packages/Compat/GTn3Z/src/Compat.jlCompat__init___dep_message_uuid5uuid5UUIDsparseall_dep_message_parseall parseatom_dep_message_parseatom#get_num_threadsget_num_threads#set_num_threadsset_num_threads&~<<UInt64 reinterpret#_log_twice64_unchecked_log_twice64_unchecked sign_maskTwicePrecisionMath_log_extValFloat64expNumber#_exp_allowing_twice64_exp_allowing_twice64exp_implhiloℯlastshowfirst IOContext=>printIOcopysign+ checkbounds/-log*#_logrange_extra_logrange_extrafloat promote_typeconverttypeof!=isfinite DomainErroriszero<: AbstractArray ##logrange#32 #logrange#32logrange #lograngeUndefKeywordErrorLogRangestartstoplenextraXTIntReal @boundscheckInteger Iteratorsisequal allunique<=@inline@eval @inbounds@doc @constprop @nospecialize @MIME_str@assume_effects isdefined! hasmethodModulegetfieldBase enumerateundefVector #_get_symbols _get_symbols3/opt/julia/packages/Compat/GTn3Z/src/compatmacro.jl _valid_macroargshead ##meta#58typesigmodule linenumberbindingpathAnyTupleLineNumberNodestringlengthMeta #_valid_macroisexpr macrocall>=throw ArgumentError==Unionpush! 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