From 25653b5dbb3dd56cde8d85321711269b46ea115c Mon Sep 17 00:00:00 2001 From: 0PrashantYadav0 Date: Fri, 16 Oct 2026 09:57:57 +0530 Subject: [PATCH] fix: return excess kurtosis in `stats/base/dists/kumaraswamy/kurtosis` MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit The implementation computed the kurtosis `μ₄/σ⁴` but never subtracted 3, so every value was off by exactly 3 from the documented excess kurtosis. This commit subtracts 3 in both the JavaScript and C implementations, fixes the README equation, updates the documented examples (including those for `kumaraswamy/ctor`), and replaces the placeholder tests with Julia fixtures. Closes: https://github.com/stdlib-js/stdlib/issues/15461 --- .../base/dists/kumaraswamy/ctor/README.md | 2 +- .../base/dists/kumaraswamy/ctor/docs/repl.txt | 2 +- .../base/dists/kumaraswamy/ctor/lib/main.js | 2 +- .../base/dists/kumaraswamy/kurtosis/README.md | 14 ++-- .../dists/kumaraswamy/kurtosis/docs/repl.txt | 6 +- .../kurtosis/docs/types/index.d.ts | 6 +- .../dists/kumaraswamy/kurtosis/lib/index.js | 6 +- .../dists/kumaraswamy/kurtosis/lib/main.js | 8 +- .../dists/kumaraswamy/kurtosis/lib/native.js | 6 +- .../dists/kumaraswamy/kurtosis/src/main.c | 4 +- .../kurtosis/test/fixtures/julia/REQUIRE | 3 + .../kurtosis/test/fixtures/julia/data.json | 1 + .../kurtosis/test/fixtures/julia/runner.jl | 73 +++++++++++++++++++ .../dists/kumaraswamy/kurtosis/test/test.js | 22 +++--- .../kumaraswamy/kurtosis/test/test.native.js | 22 +++--- 15 files changed, 131 insertions(+), 46 deletions(-) create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/REQUIRE create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/data.json create mode 100644 lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/runner.jl diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/README.md b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/README.md index b7e3d35d0134..8e0f8d630b27 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/README.md @@ -112,7 +112,7 @@ Returns the [excess kurtosis][kurtosis]. var kumaraswamy = new Kumaraswamy( 4.0, 12.0 ); var kurtosis = kumaraswamy.kurtosis; -// returns ~2.704 +// returns ~-0.296 ``` #### Kumaraswamy.prototype.mean diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/docs/repl.txt index dfa723e3aa45..d9d732849e68 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/docs/repl.txt +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/docs/repl.txt @@ -56,7 +56,7 @@ > kumaraswamy.b 5.0 > kumaraswamy.kurtosis - ~3.194 + ~0.194 > kumaraswamy.mean ~0.696 > kumaraswamy.mode diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/lib/main.js index d711a5365c21..0fc33e73f02a 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/ctor/lib/main.js @@ -182,7 +182,7 @@ function Kumaraswamy() { * var kumaraswamy = new Kumaraswamy( 4.0, 12.0 ); * * var v = kumaraswamy.kurtosis; -* // returns ~2.704 +* // returns ~-0.296 */ setReadOnlyAccessor( Kumaraswamy.prototype, 'kurtosis', function get() { return kurtosis( this.a, this.b ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/README.md b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/README.md index beb9fe352f24..c00bbce332ea 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/README.md +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/README.md @@ -28,13 +28,13 @@ limitations under the License. The [excess kurtosis][kurtosis] for a [Kumaraswamy's double bounded][kumaraswamy-distribution] random variable with first shape parameter `a` and second shape parameter `b` is - + ```math -\mathop{\mathrm{Kurt}}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) ) }{\left( m_2 - m_1^2 \right)^2} +\mathop{\mathrm{Kurt}}\left( X \right) = \frac{ m_4 - ( 4.0 \cdot m_3 \cdot m_1 ) + ( 6.0 \cdot m_2 \cdot m_1^2 ) - ( 3.0 \cdot m_1^4 ) }{\left( m_2 - m_1^2 \right)^2} - 3 ``` - @@ -78,13 +78,13 @@ Returns the [excess kurtosis][kurtosis] of a [Kumaraswamy's double bounded][kuma ```javascript var v = kurtosis( 1.0, 1.0 ); -// returns ~1.8 +// returns ~-1.2 v = kurtosis( 4.0, 12.0 ); -// returns ~2.704 +// returns ~-0.296 v = kurtosis( 2.0, 8.0 ); -// returns ~2.666 +// returns ~-0.334 ``` If provided `NaN` as any argument, the function returns `NaN`. @@ -187,7 +187,7 @@ Returns the [excess kurtosis][kurtosis] of a [Kumaraswamy's double bounded][kuma ```c double v = stdlib_base_dists_kumaraswamy_kurtosis( 0.5, 1.0 ); -// returns ~2.143 +// returns ~-0.857 ``` The function accepts the following arguments: diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/repl.txt index c05e811bf764..f3aa7020eb2b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/repl.txt +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/repl.txt @@ -22,11 +22,11 @@ Examples -------- > var v = {{alias}}( 1.0, 1.0 ) - ~1.8 + ~-1.2 > v = {{alias}}( 4.0, 12.0 ) - ~2.704 + ~-0.296 > v = {{alias}}( 16.0, 8.0 ) - ~4.311 + ~1.311 See Also -------- diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/types/index.d.ts index c6e60314e887..b3f3daf6f768 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/types/index.d.ts +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/docs/types/index.d.ts @@ -31,15 +31,15 @@ * * @example * var v = kurtosis( 0.5, 1.0 ); -* // returns ~2.143 +* // returns ~-0.857 * * @example * var v = kurtosis( 4.0, 12.0 ); -* // returns ~2.704 +* // returns ~-0.296 * * @example * var v = kurtosis( 12.0, 2.0 ); -* // returns ~4.817 +* // returns ~1.817 * * @example * var v = kurtosis( 1.0, -0.1 ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/index.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/index.js index 9d7f2efd67f3..55b1a690f87b 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/index.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/index.js @@ -27,13 +27,13 @@ * var kurtosis = require( '@stdlib/stats/base/dists/kumaraswamy/kurtosis' ); * * var v = kurtosis( 2.0, 1.0 ); -* // returns ~2.4 +* // returns ~-0.6 * * v = kurtosis( 4.0, 12.0 ); -* // returns ~2.704 +* // returns ~-0.296 * * v = kurtosis( 16.0, 8.0 ); -* // returns ~4.311 +* // returns ~1.311 */ // MODULES // diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/main.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/main.js index 286e10bb6987..c187712e62ea 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/main.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/main.js @@ -35,15 +35,15 @@ var beta = require( '@stdlib/math/base/special/beta' ); * * @example * var v = kurtosis( 0.5, 1.0 ); -* // returns ~2.143 +* // returns ~-0.857 * * @example * var v = kurtosis( 4.0, 12.0 ); -* // returns ~2.704 +* // returns ~-0.296 * * @example * var v = kurtosis( 12.0, 2.0 ); -* // returns ~4.817 +* // returns ~1.817 * * @example * var v = kurtosis( 1.0, -0.1 ); @@ -85,7 +85,7 @@ function kurtosis( a, b ) { mu2 = m1 * m1; out = ( m4 - ( 4.0*m3*m1 ) + ( 6.0*m2*mu2 ) - ( 3.0*mu2*mu2 ) ); out /= sigma2*sigma2; - return out; + return out - 3.0; } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/native.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/native.js index 0a85940b8c16..fc6f79e2c0a5 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/lib/native.js @@ -35,15 +35,15 @@ var addon = require( './../src/addon.node' ); * * @example * var v = kurtosis( 0.5, 1.0 ); -* // returns ~2.143 +* // returns ~-0.857 * * @example * var v = kurtosis( 4.0, 12.0 ); -* // returns ~2.704 +* // returns ~-0.296 * * @example * var v = kurtosis( 12.0, 2.0 ); -* // returns ~4.817 +* // returns ~1.817 * * @example * var v = kurtosis( 1.0, -0.1 ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/src/main.c b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/src/main.c index 00f822c68802..68f89dee24e7 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/src/main.c +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/src/main.c @@ -29,7 +29,7 @@ * * @example * double v = stdlib_base_dists_kumaraswamy_kurtosis( 0.5, 1.0 ); -* // returns ~2.143 +* // returns ~-0.857 */ double stdlib_base_dists_kumaraswamy_kurtosis( const double a, const double b ) { double sigma2; @@ -55,6 +55,6 @@ double stdlib_base_dists_kumaraswamy_kurtosis( const double a, const double b ) mu2 = m1 * m1; out = ( m4 - ( 4.0*m3*m1 ) + ( 6.0*m2*mu2 ) - ( 3.0*mu2*mu2 ) ); out /= sigma2*sigma2; - return out; + return out - 3.0; } diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/REQUIRE b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/REQUIRE new file mode 100644 index 000000000000..98be20b58ed3 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/REQUIRE @@ -0,0 +1,3 @@ +Distributions 0.23.8 +julia 1.5 +JSON 0.21 diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/data.json b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/data.json new file mode 100644 index 000000000000..1e89542ef2cc --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/data.json @@ -0,0 +1 @@ +{"a":[0.2001502022268642,0.33355992882462426,0.6334530782973938,0.7041339218776415,0.8341584473838619,0.06583917902474834,0.6972345653201768,0.5559796661218793,0.6920222779880452,0.15868479399788638,0.47143839228594075,0.6829258657755881,0.45045421857780654,0.0969906209628183,0.8763749683902511,0.46334617247252474,0.7386612835979373,0.9563953882289525,0.2980155288078171,0.8440559217554056,0.6159852646517043,0.568143323566892,0.7322522325609082,0.7930968116639806,0.6455976200481169,0.7870941380077195,0.7231548050248421,0.42172917201283366,0.783171485859583,0.6477770086368284,0.09656585756901137,0.4170766771868455,0.22503874091496479,0.9344681776055043,0.37117410955378827,0.8021090054427228,0.6461572868536484,0.4482529248072554,0.9676241879276999,0.5942007575239583,0.6614562704769759,0.870295359863449,0.18692304519235725,0.04469212231449249,0.45976775473267395,0.8908938224717408,0.1885816926075775,0.32077335299546783,0.828130506052566,0.36748011231199906,0.7279971531758042,0.18922987543448733,0.7321879926528417,0.6108824735192864,0.05563509535743849,0.40620837855285474,0.48483374048714467,0.2918800437749076,0.754322830536896,0.5294060062933189,0.8297774429468735,0.03908377568571442,0.10540324132699774,0.19075220815100447,0.6753455010783922,0.7959531123890463,0.9445322246089396,0.9135452866716255,0.005766928725828291,0.4475978568356953,0.7612917723892653,0.9390457153383672,0.538986837788841,0.702158091463387,0.5499860583680461,0.20015397028296444,0.05671986333515311,0.9913093039887928,0.40997057196073217,0.11947064626496984,0.6242265571672089,0.06867440652958412,0.058877636124814225,0.39861686664503804,0.2524908341137254,0.19140458823968232,0.5213629091959336,0.40767085462263086,0.14020537083550766,0.9066448103098468,0.641091878707441,0.7831473568289485,0.36779817028442463,0.25225054947430225,0.8383375170740678,0.8160831578459203,0.2170082499600856,0.8153675336852452,0.5692326649957827,0.43966794205432935,0.8982564943411736,0.18928635760112167,0.7517325282276848,0.44636784375793903,0.6209821977366788,0.5594567659185574,0.9057273348570803,0.957225379843758,0.3047338195080521,0.5290820465941309,0.049323105929703015,0.43171239346727797,0.1198786979637777,0.6494459510754603,0.3734189681606622,0.5739464050879837,0.3125832429224559,0.9287297743337097,0.9177954350307032,0.7005359357541201,0.26001629521292813,0.13091249394323534,0.32581965756080644,0.5795116050385339,0.6386085368926058,0.6507857255099555,0.7219731170531093,0.9710191544452955,0.09262371244647472,0.054295390116126385,0.9684838860163554,0.4249578526444753,0.736361602472602,0.2852410603725465,0.40251644382992513,0.10563760526883736,0.3323061944183553,0.712465538165387,0.060368035228293815,0.48283020342310223,0.8138246685349575,0.01391277297083493,0.7556395799236787,0.9011696907987042,0.3110114545462015,0.039618298100780325,0.35686953636687047,0.7516547875233047,0.7292663767641373,0.5922832948685902,0.0979386801517802,0.11923887398517985,0.3054201664877738,0.14036622069285154,0.1083780834492668,0.26828783209295304,0.44835080078771694,0.8912126447934291,0.5719005877254589,0.869553985458828,0.6824908392040386,0.9276177921557626,0.0714132195144368,0.8893219652733019,0.5266333913911772,0.10529212732293813,0.06654421849452119,0.21365349735630979,0.9231162030243375,0.2710723173012338,0.9178834541399539,0.6748845020535779,0.29335624807171434,0.9448768490486581,0.42869751248463417,0.6894064890903682,0.9794821036752951,0.8458454680500624,0.4081879557254169,0.54578734085494,0.4487259922384286,0.023320910176767295,0.8458296608832506,0.7307740328898,0.19111966221513055,0.9274789481545983,0.8557032056654957,0.9902447892946538,0.08921826285168277,0.1133033587318032,0.5444693664704577,0.4489316312376789,0.38929946904573365,0.6890751842187156,0.0005925944013900342,0.8630499454087479,0.6994297191272619,0.8469581644460584,0.32193629457320627,0.3944396807141466,0.7009642202773968,0.22434162628157384,0.15212100279933605,0.3034526188648299,0.07808960650131769,0.13969524127125987,0.8723661799213924,0.814719759967623,0.37368515785146805,0.33474538139014454,0.15521671493276012,0.27374332956750236,0.9503346161138709,0.41099195808894873,0.5532011420121371,0.8682162540257846,0.7812112023786879,0.029837497876384456,0.4610538652523396,0.8999891983435412,0.05130135307624473,0.8760976329329425,0.2721054125359369,0.442020811716753,0.8766731592547076,0.5287092166087498,0.8259382748317815,0.36922718434750357,0.4525743984405105,0.07066359183032356,0.3422521721455941,0.8093852266315309,0.5528949424161718,0.751692897410619,0.4868842413376092,0.02617524483605249,0.8481675462031385,0.26774260676569006,0.4565829676105988,0.5453454758237779,0.24711690976905776,0.5990942808818333,0.909041665024488,0.1549494174306456,0.3291456224327389,0.7450493224698326,0.5707226788420339,0.26239605888345063,0.2701649106703795,0.8168907300039568,0.7553877019639046,0.9753798779081375,0.6274645405489587,0.23681323746529137,0.698449980678088,0.5309966564133717,0.1657134768530132,0.25621227492734644,0.8213757896890085,0.5798883216060989,0.5709798602967213,0.9165315184442462,0.19111268877830112,0.13429383511475657,0.08597579610182737,0.7556302460788287,0.3072106528150047,0.17941268558552126,0.1463167136547674,0.8492112060995664,0.5901393934097887,0.37306096947221845,0.93695728896221,0.5130832328162628,0.023309588096167677,0.4270273240045266,0.5490570634716081,0.7422245282784607,0.03510271864236836,0.67996764285784,0.8917634987173209,0.5080370548432015,0.6022923798363042,0.2430588592091153,0.6137729541527281,0.5714763751735733,0.3274642524496173,0.25931106195877696,0.04987650830250734,0.7700581538496133,0.0958091622243663,0.6359892163478595,0.9298082661720038,0.7793692996277469,0.11281639226832607,0.2538681404142573,0.30474362906147634,0.36642672941268994,0.18501311514236118,0.21716627292183632,0.9769693887037477,0.502033314620258,0.0668609673060313,0.27124191088335503,0.8700176119470073,0.24747132306637998,0.6114118639683122,0.2516458753513956,0.3438282593930707,0.7864589918281498,0.6532990814184392,0.4796409433088087,0.3300136689137677,0.2698349859421795,0.5114887072917421,0.3659908177172334,0.3166599401834913,0.4896016158694526,0.5240468788773388,0.7804144051115008,0.3923825084645397,0.2032889636023265,0.3431417612885467,0.9673747267584974,0.33108572637619804,0.8771381958367763,0.1210291059318388,0.31040691966595135,0.3092087595619626,0.2838831935758479,0.35398678634863034,0.5093770016631289,0.9721999381405582,0.665273090077924,0.47668345115011357,0.4143671300809457,0.22786995587952108,0.5323265614639311,0.11718335570100824,0.19716906214740293,0.9029248677950827,0.21839263767541572,0.09125972318816555,0.44976571058350645,0.16587377872256215,0.30600218547432534,0.9856782845764162,0.6716053297764208,0.2853713378545678,0.734244499446015,0.4021859550987644,0.48946986426314054,0.21889220632464212,0.595238296467355,0.9948163356207184,0.2572731926675058,0.3766428693627799,0.011621957920485482,0.6337381921268112,0.28186489619362876,0.334297832524715,0.3366774154405415,0.5005408545130121,0.8761304314314939,0.22492895549190184,0.6746838189599335,0.1385327309026001,0.16529126311938824,0.8589106377272238,0.019012242811948132,0.19281460091310054,0.3436434011088222,0.14709345710621036,0.10310806038752085,0.4557906663958161,0.6643648022551484,0.23463776356016253,0.6645121191246627,0.4612198573750753,0.9012639609742726,0.2718594706509857,0.5614066491652202,0.6472827965490983,0.6298133037389712,0.8499192227826102,0.542712789544083,0.6634011633932517,0.42299370748529586,0.5868218128419478,0.891322660547705,0.0048086908760066605,0.32030119315876326,0.5247224778686269,0.25111871871208924,0.6065553597967316,0.3506253158845676,0.7087982622147141,0.5517264618604687,0.7831825962033663,0.2528699172086357,0.30828015747436166,0.9175550492881129,0.686286617975928,0.18821825988554775,0.43012617646879503,0.5902234385911158,0.9872389023976302,0.12838528062428334,0.1557483108294242,0.43436927009617887,0.462005405949552,0.04830509419041784,0.6039368096814982,0.018042771250703193,0.4063424053656244,0.3570772283831072,0.049096153329440395,0.896357398787928,0.7901642564704205,0.9717777088521055,0.7902666493574059,0.20511383609739842,0.005148693719719932,0.8421952135817133,0.594365623806687,0.4366226922264407,0.3434089438773166,0.8083545037117491,0.8105580312251099,0.2754626205946127,0.1893496558834996,0.939287748846525,0.4421187955500948,0.33954980973319837,0.2584857914949328,0.28298884538791735,0.5664538451820668,0.277969896678668,0.946472256583555,0.02185720613076858,0.8371361189282452,0.4747667614441916,0.45094337768196124,0.20610800463830747,0.04161774564484,0.6218877277206291,0.007333845785655213,0.9072635293852903,0.9530075369189563,0.10223903569809245,0.23901222436101022,0.23096874124432287,0.39406505479427445,0.8931616288992313,0.04240138616905165,0.5289434328062779,0.28294716046831037,0.7716086508131832,0.7857958790432688,0.9516040018573424,0.7049167058922545,0.9206708248019541,0.01807475664607472,0.9702778935739022,0.8411702795669506,0.7018023059690172,0.34798513137741416,0.2862880895837804,0.5941288115862294,0.3897572587188697,0.5054541609755387,0.9157776217073916,0.07225575345865387,0.6750002476349427,0.05691663255717472,0.7243698420615841,0.9514730084935249,0.7499061458614324,0.8538131731555704,0.4635590420806215,0.4094242375669769,0.7014798577539473,0.5460183248076275,0.554714032397387,0.8581133162548196,0.7338848628139905,0.22594139429605153,0.9294484049674369,0.17247824896220576,0.6496427439363113,0.922321458130389,0.9644421792365945,0.9774984735644803,0.8573122761846438,0.38196751178944033,0.0539310498871155,0.5379402534284771,0.7413335441286775,0.045898409461434864,0.6241177858179577,0.9498394555111116,0.9508337153527198,0.8784965241223276,0.6504846160318354,0.8834215040104824,0.920351775399468,0.12724672168033468,0.4035431243380949,0.7535656717805443,0.4421245951400795,0.021387848224108996,0.6304930661640449,0.8158626880211658,0.14688091838426065,0.920924344818719,0.23391798423961097,0.562097084373533,0.01934918406536923,0.561141978756468,0.5541476852572504,0.4015646203842005,0.17324635679921718,0.6155269510952125,0.009364964103328877,0.5258127190726349,0.7759586881665842,0.03233259480331507,0.5698191077682281,0.13479912471046473,0.5027568042900955,0.7582900487540877,0.28959942789075044,0.752289610467829,0.4244622381575833,0.5010843815359655,0.35729948204931594,0.2856981225296561,0.5097386091255627,0.3974550333295538,0.8786553622865341,0.7776517796677345,0.9193430901815371,0.500878779672446,0.6392849435766177,0.6740906745305267,0.41014718506780024,0.8776575469028568,0.8470805444372709,0.13419740036603045,0.1589014428534955,0.40226837048110375,0.01775558703830471,0.9337585026987945,0.49453743996549815,0.907326053688709,0.0008106949050995516,0.7167225112983322,0.6947051739446074,0.4734575230127118,0.8544049043397582,0.34609887606563516,0.618954778067089,0.045629727923036656,0.7412446258667874,0.1856866902403822,0.5881200407282472,0.17663236599699372,0.07548911039129291,0.5363510960847704,0.049927120606039654,0.45383672303090583,0.10786985789317216,0.19400028094570398,0.6761061514749689,0.457367897737772,0.40448929633568276,0.19659264617391714,0.8356020092639095,0.30090843512510645,0.7372654891757245,0.6847073081604437,0.5914902849478878,0.0624353261830386,0.10802536565249587,0.12980861101668217,0.228085877504844,0.3201281504742779,0.6388485575836813,0.5091162323298632,0.02762532501060322,0.6396268905167272,0.26185218641219643,0.3680068442411304,0.9746450264688676,0.5345482461707819,0.24340966570498357,0.5793135341767617,0.5576334189859713,0.2876255729196502,0.5248510019694546,0.24957440795505037,0.8422053201341765,0.7119630950979461,0.4172552021541702,0.8969336529143982,0.3729393038097144,0.8812764073781928,0.6533190094492421,0.5403513479575673,0.034921244641025084,0.7455888208834319,0.8347011704245738,0.8036355156851933,0.023287903515941677,0.26266064564008496,0.18611464334142624,0.39246110062038486,0.6002235979076912,0.6768989297033723,0.24759226095629638,0.8022510685594336,0.42369963838125835,0.8202049273822901,0.27093887564128616,0.8009265642609655,0.6465237346261464,0.896009984404685,0.1881616795766894,0.039876649003911635,0.919313467316368,0.7476393038998366,0.43372024234894113,0.7282912761952245,0.9248462700407565,0.020680330794317414,0.19480444216055204,0.09957923807261382,0.8374362268692771,0.7937133274910649,0.010264162154603018,0.8214515138423413,0.49237491221915974,0.6541649345074441,0.07244439525472202,0.539042390593285,0.3505813562883284,0.5068585140278089,0.4578418405310756,0.6504188456169446,0.42065766360983325,0.5630780672736017,0.26836772933349573,0.6512265313973215,0.44960348430136976,0.7830531719949202,0.6932016583795736,0.19920916487609475,0.8966389437049483,0.7707708118046801,0.24372168652794246,0.7834138348633319,0.2944455700655697,0.6733470199836203,0.6585610346776737,0.1431145930770823,0.0011674837261852478,0.4832246492565373,0.5541060786095368,0.7518881711841865,0.7320690797580516,0.9220332036459925,0.9755953110095187,0.6743541026063773,0.6997049658300957,0.952255994474024,0.273367789447715,0.6224770738067247,0.12357621257265972,0.3360301332671448,0.4792248314310401,0.06544799611978758,0.3339743062895062,0.41600178458684867,0.19602902470655503,0.8230781447221318,0.717995415984141,0.9154566640512022,0.9959776313362955,0.17681886595691398,0.32421219320496797,0.8977414287712685,0.487063973759823,0.5230630890624508,0.8950460915346655,0.9421536607659805,0.49315312622742846,0.4495275677929804,0.2809984156266788,0.48032378460469527,0.5107915011975017,0.015106985582411636,0.3952823319092418,0.7732251227452567,0.5957465094670393,0.46954893570357936,0.7406943066762152,0.13773382488073294,0.6852175989527501,0.14553954395419166,0.4667401160333282,0.5740511555121193,0.485119131255316,0.006654970126789839,0.6337471963681252,0.7565215284691946,0.07570298347829829,0.9830507099022225,0.8037262578814357,0.354854748105189,0.7215299340317028,0.2640740054200502,0.3327620026236636,0.5721080314954924,0.971011016881487,0.43856985518834113,0.47709061249250484,0.2734644177834552,0.015151101475416873,0.0473601037261151,0.36004944674194506,0.6236592174975107,0.9450777369260478,0.2388669653540365,0.22969758196600898,0.6574328979321576,0.8461181036677234,0.06338882354869091,0.7092631698557396,0.4461859921671564,0.9043161493142745,0.7508679790480174,0.15396444889922045,0.886273972344332,0.2838002414255151,0.46731160751158296,0.10872664052731229,0.6078101727851886,0.7325433182079114,0.4268122822296492,0.9209528415841748,0.8604523186244595,0.9938473839663675,0.26610127854572574,0.28477516462133956,0.6288192938174161,0.4431788686419761,0.32360361440598484,0.9298307323934569,0.7775837960065456,0.3080898283469101,0.9526858452211633,0.38159712793618217,0.8047422933496641,0.48326219562445083,0.7806929844457072,0.3639319129302613,0.09482082065343089,0.016978827481365144,0.8812595680035765,0.4649663338865385,0.495404276289505,0.5834727997867524,0.8055479092031518,0.5492760397346141,0.4327310559040096,0.6264263317516263,0.45603304825925306,0.7635248790558622,0.004892536839482875,0.34527106174819877,0.6758930662729579,0.16308888813596845,0.3079932659953971,0.19240962353301805,0.3418059765621676,0.6346119872581856,0.7579390027238716,0.19082647884342896,0.2621146307277974,0.6116784857607376,0.4428383137986581,0.5371496044912918,0.08736808407914753,0.7276284556897147,0.7519930054672984,0.8932187904244802,0.2155891152134053,0.44938005780327406,0.8466791381286556,0.8099263516898411,0.018492138761545318,0.4900473812224344,0.11621846817140502,0.18357688749293322,0.22245814771562855,0.32300170663976224,0.3445629851347034,0.44532820658326033,0.11569745790115171,0.5930136880440454,0.14742815355290506,0.38109127659718445,0.5189834772645481,0.3886207577860117,0.547621686387574,0.6012393374093855,0.4600859910439453,0.4912562233572081,0.7732062608287782,0.9968824788415859,0.931054012578349,0.2804426316453237,0.6765428401147168,0.9219277845945185,0.504776774294939,0.9916053564005,0.3864372139867218,0.6489589155048243,0.8327475357040203,0.33134941108764615,0.7101981192424125,0.882653574758323,0.6738972765322196,0.5718291276225501,0.8471049053575428,0.3176718395822016,0.10921919309678285,0.7989455188996656,0.14169726459795307,0.6283276483105035,0.518113127370028,0.8540442539376655,0.07479133787454262,0.9221274874492492,0.6528652062335689,0.3709448481351275,0.8941438544327768,0.28001020680694866,0.3647744424775283,0.9485188974775801,0.18732942998199398,0.6853077264711721,0.9995082521069514,0.137119751608218,0.8817241300076001,0.4923676559612795,0.3041999034422237,0.8906737471060774,0.1447721884625377,0.14535559596835312,0.5895979669604071,0.3177456349647382,0.7647457622301168,0.23510285808500297,0.819858995845797,0.1696018721443623,0.5136272342817645,0.9831732558076796,0.6561366809721841,0.46097392662470404,0.5707070355475056,0.017513738522204392,0.4967499066507236,0.05489862125307177,0.39155220856521,0.4308876237288669,0.24255023046279967,0.6367133761602465,0.8939576952041474,0.6352599534316107,0.21792592731995508,0.9737062362980424,0.4878818919559038,0.23103065619704355,0.8038021741599809,0.02227449583901764,0.41222292753019374,0.6732804324604137,0.37657580202882035,0.31905685044854715,0.8747342509950884,0.41247773435890045,0.5633622672179415,0.5733692989747277,0.5157672888375214,0.007766779470334995,0.550997462841703,0.6231610462986232,0.305590467319534,0.5065191612306696,0.9735089855308858,0.8200914084512264,0.12104994854244522,0.9155428256662577,0.3822794302605965,0.4256069745880823,0.6203563734211665,0.24259088464475687,0.2916003820112181,0.17736616780527503,0.3475243558004474,0.8531400322000238,0.11007924308275441,0.0807826011043149,0.7192732286208462,0.26115233939956073,0.6639972337875878,0.7833949422874658,0.5623480915782942,0.19748260738965184,0.3385335082959383,0.005037855308196337,0.34355760476477926,0.8359550654246461,0.7288345924959704,0.8079362311492317,0.028951021142022637,0.04896861965649202,0.9738006660361181,0.080507651927327,0.4304008165376404,0.686129847011116,0.5714507342061808,0.19157086854104088,0.6345378794883431,0.47225798572161204,0.26075287178510476,0.7148273643535763,0.6612325114345877,0.70834178690735,0.48434297980344,0.5140976191413277,0.7215787846282381,0.8058727359270595,0.6912397373219027,0.3246699083406118,0.8908810359053411,0.9900291904076907,0.3005814086247137,0.7317952476176894,0.7308598963382569,0.4067496929227782,0.26783541954245726,0.22939704300541086,0.4120170850575645,0.2135720110330669,0.5368475418977705,0.049604906653614944,0.8343830355621531,0.6937116510251645,0.8299607920050919,0.5985148023574975,0.3364656481406634,0.9414287896052539,0.802733613502106,0.5063459981252738,0.5812517172099466,0.5321902191961401,0.9180097966415743,0.17399536167938234,0.396383000193155,0.33465754972974304,0.3024952601485458,0.3295945497469971,0.29534441717198334,0.9795037038179731,0.9652203039467128,0.4770172073461635,0.7045985800768534,0.35166615666013135,0.35681459374091573,0.9437135734057128,0.446691179012909,0.2563322336999754,0.42135888223476337,0.3218163093987343,0.8795953655011456,0.5166236390715335,0.02359438746074094,0.7097121158273163,0.9998602900214286,0.5291677022491097,0.009156237497148556,0.4601664240209252,0.6100369598311248,0.7637124204947947,0.026788473810891,0.13432353285906196,0.5689628361742499,0.39644339893122316],"b":[0.7084690682507957,0.12366082599781902,0.7839532486089075,0.4048502110552724,0.013522236973151136,0.14193880473305365,0.39880835085026933,0.7580204045986041,0.07278089394051546,0.5212719376621651,0.7430579810626937,0.024691191983734262,0.715116987074395,0.8874141079500735,0.0004749749406245396,0.29396494408343266,0.5299031875324018,0.3162831967341311,0.7543709950537814,0.35745763581701406,0.7640855854478186,0.11052037228290867,0.27466972691634617,0.43322913222387105,0.3642088554840196,0.011865033888482479,0.021376402759129554,0.938530227023835,0.47383250862264603,0.6111778057205351,0.9741203173696928,0.2502120391732987,0.658514840513492,0.48033004783277833,0.4684315890250256,0.02894296705310695,0.5094176832697354,0.23586077640972647,0.9423728809194236,0.5757225569723402,0.3177299475724298,0.4459774285076604,0.3483408755179255,0.4393147242896993,0.07635404466172868,0.07042859247628885,0.101210858580149,0.6614456532118905,0.04203852656014517,0.7398175666356582,0.0002938920295526559,0.6714493295664812,0.16007590764794344,0.8579451818617498,0.3316364173495764,0.007013279222562674,0.5324172806168517,0.944118599154984,0.7435815961148313,0.7886588500401126,0.197842434043348,0.925470070613971,0.8265702284749232,0.979805222456215,0.21489422267470626,0.715067440702168,0.37606061778137223,0.30866621163223895,0.9037122674805015,0.9077009689693438,0.6644480371906181,0.7658043262110311,0.2987710847025876,0.9026005741462562,0.8319218704931352,0.13731659745224478,0.34629898911794765,0.9790026888651883,0.07594079813664767,0.7751954830452192,0.5477284587606803,0.27626701768905837,0.7082115266583665,0.24026803120634443,0.7349004304221849,0.09482914282479826,0.3440591865787802,0.7715961138887175,0.05360110020585529,0.27608375960667775,0.9946034439558138,0.8128548152632151,0.814364382467675,0.5986072259617098,0.3684439987542115,0.07053759111455526,0.945410454453904,0.25900027052343844,0.21124778498448016,0.9778589908410569,0.6844490116095274,0.2521074608171251,0.18614472861467202,0.29220406441085023,0.6784637719489726,0.1793624477508574,0.4041043814912134,0.01980852508971731,0.2789513737317292,0.7495586771400508,0.8095926027296715,0.8413354713910017,0.4188204208653258,0.7645113646868004,0.3908859301069012,0.35120474406878477,0.6410857092755112,0.44706349091832887,0.4783453922916573,0.6205462109359292,0.971764871381728,0.6506340563073779,0.5787551443422364,0.8279597659426328,0.4776542854243222,0.19529538953505043,0.4351617589421187,0.16495589824858115,0.9716394763721975,0.7237732803232737,0.3943349355439889,0.38289504171916344,0.18766461039734195,0.25172200288697366,0.2579925914332071,0.8506017025610856,0.5481258447730532,0.8437583082190558,0.1943933112541083,0.06766135457860745,0.512425287680425,0.14109211304204206,0.36608591324413087,0.7397962251914371,0.18715948054425158,0.5417542423866581,0.8348516752925741,0.9031666537311822,0.6288047072981215,0.8399695812196082,0.12183584071283082,0.6843599343343219,0.5392840877228344,0.6252093928511971,0.221439921546413,0.8616043959023963,0.05338554318515354,0.31972104563546055,0.20385201287620203,0.6295029402576386,0.07037252171699249,0.5577379455415287,0.3469924267432215,0.8837955817496552,0.7596315804942826,0.3835708724955533,0.37079102693448407,0.09001471948699369,0.3672160403821546,0.8173882103866775,0.1613643869944128,0.5256788141250163,0.6469383278414951,0.4232937105980239,0.7717652279735665,0.9756956559961242,0.3404533608304855,0.4227754092092525,0.5235753070651927,0.6703272652059193,0.8628859009213562,0.6358386772753771,0.3146564247155187,0.6015258561773928,0.8426524461763221,0.28315416501597557,0.5095765501045589,0.7826262131289962,0.5959952565641194,0.7321916667140622,0.09100256549016184,0.5066115651688607,0.24799228832785025,0.4887022731580255,0.08905696738815871,0.849906150771742,0.5267771780998666,0.8127608475141813,0.347774830196639,0.777612970476397,0.34956331757850445,0.7099183130615464,0.7415091688451767,0.6434090766630272,0.6285167710425087,0.5027008128133786,0.48940876522033994,0.7903169531077717,0.48354821836790507,0.7997818940576924,0.19753930109747442,0.06991106078939091,0.9655988027185876,0.5234370349492549,0.13167124123553853,0.9530323148290255,0.2981307242561938,0.25836283031276674,0.03160364261184179,0.5052966815970582,0.8235063204079753,0.33979676011170945,0.07459229593421035,0.12343962896137173,0.11148197758309009,0.8684958749003613,0.1700068309235867,0.3518749974376353,0.6601646177062725,0.9603214885661452,0.5599631452235861,0.7167711789025484,0.11088914503160774,0.5659210106415842,0.6797523066504324,0.7554717919470135,0.7180755808971329,0.38824134488130635,0.5268344852796566,0.7719240628580343,0.49966348267218164,0.29821332373594145,0.21693184081327843,0.7215636797963942,0.06495298080565459,0.16535416051877572,0.7697993808399967,0.735032671959121,0.965994859569454,0.29781342218709606,0.37818183170559017,0.1442282802814001,0.07780024882911585,0.04497528385668503,0.73408670613595,0.03694167738458842,0.529737820925473,0.5057719848281751,0.7170532242702417,0.4713042324594916,0.32309854292615214,0.6653905947174541,0.4017534876786113,0.32553745158313585,0.16405981598499675,0.6843337144482698,0.8690133204890161,0.48262389073087564,0.99918958627326,0.5598047486312129,0.5978579335702257,0.5510404087055834,0.8323368689230032,0.8535804342700609,0.8930887027056128,0.6096104928687396,0.6140255831796889,0.727507820800142,0.3885744848448639,0.7692796560926055,0.5092593845730324,0.709119279373234,0.2665865600013556,0.5315048228381893,0.8796620922496159,0.12419324337257154,0.515098935356655,0.39269682565800323,0.5188732468843225,0.9662568184649744,0.2307709475956069,0.29862989249712324,0.3162829066563949,0.6197354473800165,0.27252506686399824,0.2520316826848884,0.8200638539464798,0.5119084721518923,0.7748737953818197,0.816688725951567,0.2392956496264974,0.2260974744552785,0.30501014128346415,0.7097020852232147,0.8697738955277818,0.13319729515282763,0.9037481118931054,0.12591450773474067,0.2701386094170828,0.22498789894390114,0.2869852647262904,0.24297273648931617,0.7623435871334778,0.3559782065463871,0.807773856336008,0.22851419106197757,0.3334567750585872,0.4429615809221402,0.13564574816538666,0.6755318462343851,0.2509100134393174,0.012041602277574559,0.8945823982356083,0.7130033531748202,0.598645195673165,0.30926306978943496,0.932129944425946,0.6312889046448239,0.4527118000048638,0.8959436306909656,0.4314081211638934,0.9859018269665764,0.9262260851874042,0.9072841539522315,0.014020622489653634,0.6394106186292392,0.4921709091864037,0.45121914804561947,0.300058117871672,0.9955424551912292,0.5631234214481882,0.22140257972118582,7.638481829508326e-5,0.1466671261850161,0.32117561281792284,0.15185505863300242,0.5116310513691179,0.12520560886824905,0.0822224448821045,0.23330260068599284,0.7487589297768039,0.8563192976189867,0.0026837549216371936,0.5680884402545532,0.8995665127757947,0.26355036975936263,0.5337076930707229,0.4392934650418362,0.41285071780965144,0.10592196457060421,0.7240879475851141,0.31224607225644807,0.19063467088752528,0.8712571677770065,0.010260368003088827,0.38337927753726175,0.22082373492449192,0.12132870526518547,0.2945104679442234,0.5110512141309645,0.2784836206953615,0.9092692535434138,0.3672441497083454,0.07477317953167406,0.029591489594030573,0.9678646800585852,0.053962329019284105,0.9649865549982416,0.8455915844089429,0.282865112953962,0.40819400311202536,0.37308732920207877,0.3509270290574682,0.19815685172827635,0.047020026474769994,0.46055166035242323,0.3875265325170153,0.36449536503201496,0.06656923960277461,0.9866619432492462,0.15467820234612062,0.5560851156941979,0.9546890699270502,0.22480383262178127,0.514438807034662,0.30353822363565075,0.6797240476790042,0.30174364650946583,0.5647841714313436,0.859342055469793,0.3598619402619012,0.6917262312176732,0.27625078166350514,0.2880293800028313,0.8209901480015543,0.0034224021708821883,0.8586065980832877,0.09027429604823745,0.47145977851771526,0.712920642870766,0.011449750053622476,0.8655769738486087,0.7190432733955756,0.5525668293200515,0.4846517373229471,0.9895316387053954,0.865389994761303,0.36278962771557244,0.9770890747018586,0.36081655529836965,0.8608821398532867,0.7382732189722622,0.7102397147967676,0.6703726639391059,0.2212129347913655,0.8142221983115231,0.8504602878896217,0.3201660825439989,0.8758407075036136,0.6905892218962926,0.42607670766426986,0.8826102849720348,0.5357179162082996,0.26695540643349247,0.8061906839312794,0.5058527113718897,0.6008274390339079,0.4766080215979629,0.6416417024583506,0.08067008782443874,0.8827749065451178,0.28257698700020073,0.4353938350595973,0.37460594939129943,0.46748958294661214,0.29764829574931173,0.4423816175703922,0.6741991264007772,0.6895685593708645,0.434947161898801,0.563234107962385,0.38452584656361266,0.10933508358446942,0.2102782638597952,0.9235471298431216,0.7455538320756433,0.5209731520057922,0.22572259917617854,0.9243214272260212,0.8212204703310177,0.7828906980997552,0.0019103418751406087,0.026551723972305985,0.41117954466788953,0.9577079446911816,0.743807870740258,0.07947282552730683,0.3677184794553554,0.6845287727403562,0.4877412684452074,0.08193147248452282,0.16875542638874896,0.6789707531138109,0.9501336949842503,0.5291005368949651,0.5980854641261182,0.07983175759042527,0.6476695767018638,0.5869617416728179,0.7250070239846925,0.5115859013679566,0.26667095287787723,0.9421234545765438,0.07960924041366635,0.446997656387499,0.3709823768795414,0.7040530039383128,0.7666834010586632,0.2555168847578534,0.045094696464505035,0.10305279984886961,0.0967963605234673,0.2635405243071892,0.9719112768691824,0.8987779174915345,0.7107457956217393,0.20254861324617346,0.9030095524084594,0.6212187085524777,0.9260484627121812,0.08639105070987507,0.49040968467557655,0.5248846122525244,0.8799091367928941,0.9850551415829856,0.054662640667718754,0.1634306197336547,0.3192338171795208,0.5056906801057948,0.8590324004726172,0.47105854608842135,0.6316923553704249,0.9019052606330461,0.7529465397637085,0.9042033662340094,0.06619691160206986,0.10856493394158262,0.11870614865644491,0.4096075710805642,0.2872374478451277,0.2991993868684504,0.22440622374512198,0.2670768035756452,0.6223868227261834,0.09487991853960653,0.16698884150258153,0.5664814035923763,0.36675222142582153,0.5878164462956939,0.29250315732251475,0.07055849969654682,0.5742120045793303,0.9879944691547817,0.969266242968115,0.6708172127529459,0.1773150001037609,0.2415491987081213,0.8782544876753244,0.6661277034086233,0.5844109886247808,0.9105437849062186,0.3837036404903237,0.1852692062520035,0.19191553234426106,0.24865036890547998,0.2561505701951595,0.844113339684723,0.4884718025857505,0.3446969664283447,0.47987338740351626,0.43114625935056605,0.6734046981941872,0.7126187088923213,0.2983525422624803,0.44627206168803846,0.7270196193182054,0.3367405110243199,0.5658051100446244,0.7230172303387448,0.9821975636953193,0.275237524734814,0.21199239307943052,0.6605988042585357,0.167697163448298,0.27100677193413825,0.2865347583934461,0.5257356273308573,0.6946103724285291,0.11648974190891137,0.5467133857521588,0.5445065336171352,0.7829931294638846,0.046472524924799474,0.8471209110062613,0.3776581704029969,0.4031232111133315,0.9269850906788917,0.25682919991596875,0.3398097965699647,0.2492526809444383,0.518379627322983,0.7972500056572565,0.034537503368730404,0.5220370849137493,0.7264752479105554,0.760280447884165,0.1278524371168115,0.5584788012056853,0.4772224687722316,0.7400659400034201,0.5962095202185258,0.008328963550613078,0.2220818338607351,0.9070619845198902,0.5440035089967894,0.5059720107438045,0.6968094238485687,0.4041276449468092,0.18363722007234162,0.9120739671819245,0.874711719805957,0.9390563870007814,0.6763893857214867,0.9161076986428955,0.6625345417357622,0.24380005267437344,0.9463935395351406,0.02412592466192709,0.18451503059701246,0.9874130140551065,0.8945556206474115,0.39511048082568523,0.9111934248486137,0.7145728390372019,0.6090344785747479,0.28702863765504805,0.5389037458956576,0.9815226744043345,0.8017041406266102,0.7149000354916445,0.7725489816272707,0.4466290043803526,0.07362543752942496,0.7105577315095284,0.6713713017992581,0.21407379575745455,0.10552822600199607,0.923524612292197,0.12138269774594823,0.5974973186650556,0.040282578789139545,0.3491206888940874,0.7016484457245686,0.7540088111700886,0.14844558979807398,0.10506811409551575,0.3453848425510283,0.19066126365602087,0.00015282739755728691,0.4481273737550474,0.6053789731634909,0.48565344671937016,0.14292566240563387,0.32315481039843585,0.656141345887009,0.5393496466386158,0.34455539817775593,0.1756454140224234,0.4745134788415246,0.20560680476909066,0.6065735268572204,0.9388279446734785,0.06805099935233883,0.16792581768163795,0.9503189563717525,0.9375075535015747,0.08120532418215065,0.25318935440119883,0.7916500102476448,0.6674096995647908,0.8808132150438874,0.755604065192203,0.35272621339809695,0.024429452055910073,0.9652765904645925,0.03582049167788404,0.0037045890590325925,0.33733604414070306,0.8992720528524106,0.3318944715771469,0.3300472059727203,0.667478967381747,0.1737901976447067,0.11078482936879863,0.6201783031648344,0.11226602872574065,0.9615165629801836,0.09184221754581834,0.6716345703752192,0.27761634842981064,0.7976112095401571,0.5224972075119894,0.5989014190960027,0.2875645639687253,0.7856110420389023,0.1446766566769666,0.8698282413564955,0.7948445745901236,0.14424950903025446,0.21581936870390894,0.31545165510241224,0.9330657819467951,0.5781772432336857,0.8702397029261626,0.6928850701324949,0.24997519209673846,0.5513586389337319,0.886713799410775,0.25168408580713486,0.7153979143567222,0.8732033009273049,0.6805050751318396,0.1345223260339986,0.3284972361335198,0.5658870259467668,0.3788942987702607,0.46111866531054646,0.6542561569966814,0.5452341902227684,0.6601125086277436,0.5632372449001186,0.9522927028450819,0.5595167080517084,0.7334088435754398,0.044027489446249124,0.9596686476712278,0.3768343149685528,0.8726159618802765,0.7980781710944513,0.7284471556813983,0.6017096487161722,0.5134163166191705,0.00221653570175373,0.5446885215367641,0.44521935075610486,0.6704262643765851,0.9158165299196845,0.47209245916966436,0.30758426500148184,0.04086827838058715,0.117788422108695,0.49880470321186565,0.8618938556767919,0.34060419967876787,0.5913972170960672,0.15849510952181745,0.4439366436460579,0.9024926270651328,0.11728590129339223,0.5350147827104926,0.5526024184786301,0.4157866232263312,0.856801434105118,0.6979289479714382,0.823524014415886,0.11688007035480819,0.5970760251561859,0.7348206286656436,0.2935779136118304,0.3222488102906067,0.33866425179700355,0.7341243901821336,0.7937610784870552,0.32962290809833905,0.6694970331484806,0.11822663538687217,0.8649448726366801,0.8942327515404808,0.7124817768505441,0.8453157094724557,0.9438969506770927,0.34690843720010067,0.3533634511791103,0.9987618951809808,0.1876044908297444,0.4723961787398422,0.3312473458364431,0.32592327942737276,0.18059566094660406,0.4955816684109784,0.1756977853509678,0.8263062695836836,0.17588931464524116,0.6359713711065274,0.34584722607329765,0.27876793324042715,0.6463900540212745,0.3138256833839024,0.9668050241975715,0.1308616740793782,0.05975517676678943,0.3072199506619847,0.5853096387578345,0.1487402007747326,0.8445668217904636,0.33309749990441695,0.8292283592345572,0.7408198954256985,0.1063791905251299,0.7991250719591091,0.11572710765620542,0.36389407349675074,0.17265611361820943,0.5097666273535377,0.41165321456975357,0.17544499739076191,0.3066467726392239,0.849815713391365,0.8779857987620887,0.9364292445869372,0.1720596322013923,0.8514801817573449,0.2825637386349008,0.20312837328194489,0.6340714340397949,0.19553045264742286,0.47556948323082315,0.660890750228579,0.9659620636935189,0.741641653255296,0.9354202317456226,0.9982481103988552,0.875674572469598,0.8379796689666869,0.8879428905779045,0.1455091925934393,0.8617074641216556,0.45201521602506567,0.43176907502029893,0.6647203665894493,0.48952583018795903,0.933870527461388,0.1362930438370067,0.7540457802322401,0.21651228772583553,0.3738105632984642,0.20533329529970634,0.658429839123616,0.28096164126270684,0.721971689783022,0.5857222036908182,0.7960505704090279,0.37430066470942003,0.3641050402680297,0.07256174429685625,0.6939508294257716,0.13181548474295313,0.1986359877361331,0.2863000041560252,0.9291464740193217,0.39057505632749145,0.2744689501102592,0.6265164056972831,0.7665320893525437,0.1275965105058795,0.7301472273126423,0.15601863018593298,0.1071101744306171,0.581878229901717,0.15046419097108488,0.09671278860477739,0.140569832222888,0.25122133092052634,0.2062061748090358,0.2442639288276588,0.25498716538532984,0.7628858564931121,0.447722475717365,0.9116468542306246,0.7403839362254672,0.2751376659742416,0.125694005457188,0.4747011413572084,0.41449796658553617,0.42813329671976386,0.31838224412990535,0.5287873747440377,0.7455932602677288,0.7878837565820072,0.5547861940990688,0.08429549836915484,0.5331023661330954,0.5640996786480968,0.4520483445138943,0.6150946958011736,0.6240268926951036,0.7224550146886819,0.13587132646999045,0.1620885514210677,0.05111695347909939,0.2637407197250422,0.642154460254683,0.33207516947326854,0.33621978485682713,0.3639300590132962,0.09611017482463902,0.7243536413539956,0.3508760652421056,0.9097045780499656,0.4954661869868189,0.6302335554948468,0.6777298869818853,0.31512754809894206,0.5428836209008768,0.23323369678992256,0.6625363453197933,0.8878569973652659,0.04084915870784134,0.7523848402631323,0.8314207111850549,0.033870241497201414,0.13671677868724919,0.5885706926537708,0.18405041558792834,0.8259252223253446,0.6750196594997493,0.6248969780386637,0.24906188085898728,0.8866738923291502,0.027160430649302847,0.28524206018645726,0.9276014132959386,0.21771833131922758,0.5582542168154354,0.32571838743058124,0.23886458553178247,0.41499554324857735,0.30727136011708456,0.18636083942151282,0.5825569872228025,0.7300733507542685,0.8269887232737105,0.8821451439619066,0.466279557892616,0.7915499033025093,0.019660657400271342,0.4086296011568201,0.47452470429492044,0.4592921939933112,0.05024280424649186,0.5513076536121918,0.33980864428500723,0.5537399782605741,0.7964978216682381,0.5319898511428182,0.8279611969526003,0.9773423939061383,0.035845626583996926,0.7202000376034761,0.009982408305027612,0.5540688337054099,0.2524883435992622,0.3993660015140169,0.5731623010671687,0.3456664930058937,0.0957118924805942,0.1298199907903559,0.8855084399140083,0.21752087964640132,0.9346771212636029,0.47215374719627157,0.6358141629512142,0.42267939481290917,0.5197732568537146,0.07675378913497699,0.8670399318824686,0.04089583932936469,0.5587306916016915,0.17216002024528199,0.6933960334083067,0.15342844901308028,0.40051606453631505,0.670276454218632,0.022867724962192026,0.5776284432273417,0.8994923540495579,0.5617047316555537,0.7372213595428434,0.6786367326201325,0.45880171790797397,0.27534476220525006,0.15711526662060116,0.3796431356208936,0.8570571471309039,0.30048131864064564,0.22371669158145624,0.9304497059960654,0.7105044005935452,0.2596238078791283,0.17614911423745883,0.21564367176173194,0.7431997384124276,0.9368960493774102,0.2721950036618893,0.9937967722546683,0.12427158991810261,0.4684771682836193,0.9052438110729437,0.6589933617528437,0.3490800707320455,0.47059580152396663,0.2127795414277217,0.3765246438828397,0.6741002276506624,0.3910867185690312,0.021490583108311756,0.5403934269457846,0.8660175018852933,0.40880831875767776,0.9031148209938197],"expected":[-0.36052352304655244,0.8416887559115462,-1.3249182796531016,-1.0340400772736726,63.252147674757424,-1.4577778073716392,-1.0260251010824029,-1.3230326119677354,7.572882109332326,-1.0391735865687912,-1.2780869841394538,29.15858999287758,-1.29897875907728,4.521206894442644,1953.8418741271598,-1.0612321990138935,-1.2497911242189308,-0.05181567305837831,-0.8168794106432675,-0.569961808714305,-1.337112851305645,3.0010786032484944,-0.22723346911304176,-0.9765294485861538,-0.9932156275429134,70.19999059289631,35.4596505406266,-0.7606457468156758,-1.0971894901128192,-1.385223981856789,6.330869488479092,-0.9057977106401225,-0.8076447633868096,-0.8974728199386792,-1.5389985838304756,26.936885305930243,-1.3284144837815735,-0.6860686050311102,-1.221249406547708,-1.4135755762171185,-0.7291280832414904,-0.8939969669115184,-1.6525356231674646,0.027187068929309,4.885620396497857,9.77270897985041,0.5448676038288061,-1.1869576679050906,17.80850071822398,-1.1050691971920226,2857.8149863271137,-0.46858622083180945,1.7715881662030917,-1.2462275107182692,-1.2998706084064326,85.29661736945907,-1.4750464795670983,0.00661819031853339,-1.3289816539340913,-1.2688073594429012,1.1797969255945304,16.897892694773816,2.9722420590282477,1.7617549794920722,0.3306057871333854,-1.310488698243152,-0.47649508150066167,-0.08492998751619396,105.57930892594291,-0.9168722046710389,-1.323108720467945,-1.2336741817400168,-0.9036870162839445,-1.248087539104145,-1.2297606917771151,-0.4260168471343597,-1.2079105030141095,-1.2070178587032319,4.430187113003788,1.6916952191086283,-1.3810221275183858,-1.6717896067379552,3.9592360436076577,-0.883787189711422,-0.6421712780840472,0.8519226863426836,-1.1582289556400418,-1.124863145718939,3.434216033228064,0.21146480107309662,-1.1111117268695803,-1.303103744249028,-0.9081935343759167,-1.1686142011189882,-0.6394661452319537,9.081505463685337,0.9463208357487631,0.1622269851537963,0.01701100421574342,-0.7234549736147731,-1.2308227930057296,-1.5687712585494162,1.1534745069276235,-1.0935323340547027,-1.387845058255188,0.5346487860632436,-0.6818882030707494,45.692014453314876,-1.3799232385728823,-1.3175982080110993,8.168051165596319,-1.0254081230427479,-1.3064924125503992,-1.340377574187797,-1.513181928207839,-1.0812101629555035,-1.220097359819843,-0.8061207559170693,-0.9161706634163194,-1.3524274251503332,0.48547471609276105,0.1396092308291461,-1.3890248063528885,-1.2589551785152384,-1.296814931676461,0.5804991915240589,-1.093690657309323,2.6101186031915455,6.6743423770765435,4.815595840509087,-0.5259329713104948,-1.432627989886303,1.0605929963526943,-1.30599343467122,-1.0050620264578751,3.3335652996360112,-1.4515615634353174,-1.293673761840709,-1.764585789095445,6.239772871746533,-1.1330886881009397,-1.8474233241662392,-0.7883213701837128,-1.2511450760040816,-0.6579672413014537,2.0479514338463307,-0.8077114779060692,-1.2597097690282324,-1.3346294553549574,-1.2539556686085953,-0.8937974882289899,0.6958048930822325,-1.4394902532436546,-0.21275095114014064,-1.6906806074352776,-0.17704250786775066,8.42374383534363,-0.224275492065229,0.13897133829382202,-1.2183036257673991,7.86229968959627,-1.0711537676145924,-1.3565915550144323,-1.2563434115360037,-1.303796903947497,-1.3926637027124285,-1.1508001035097057,1.324789525564924,-0.46889831284322137,-0.4043099801097094,2.520092307326757,-1.314757793483224,-1.1509575546724753,-0.6938736772070175,-1.1662152893857265,-1.1741346265054171,-0.18726198451890097,-0.8566195896495397,-1.5034108359584955,-1.39946604081113,-1.0186747241582361,7.702013124161917,-0.2877343854426728,-1.3210954846236942,0.6366130683324029,0.1884360612748721,-1.0739350214002115,-1.2052845054895351,0.5281253901549534,1.3835835770839386,4.20836265727213,-1.4958069624317083,-0.9730340934022186,-1.2506753295435624,-1.9125640787346903,-1.2716144312340079,-1.2895615981011634,-1.2836493529519846,-1.5271867727884108,-1.0808247653934475,-0.8178263049194578,-0.5607801328307258,0.5244127682093547,-1.1901710949319624,1.3177956061254443,-1.0032390821764778,-1.0082038897193852,-1.2989628150269552,-1.5321166735353662,-0.8265311264292374,-1.424879648941743,3.543229166712316,-1.2202365925132328,-1.5030952471620624,1.8846023658980142,-1.2366424558114142,-0.30910342608867003,-1.4897634881103914,17.149594555785114,-1.0064728459258794,8.270134300849273,-0.398386972403038,3.0662874517335625,1.5543662123340258,4.84892259572503,-1.1522942249774142,1.8659487824161403,-1.4608876501186148,-1.3796014954187745,9.334259017477375,-1.441153874354055,-1.3030660559475713,2.878841614566122,-1.275442563817167,-1.375167273023775,12.761723549059687,-1.2797671279412977,-1.6071321180196554,-1.4887802992521897,-1.3015506981751341,-1.4396385430476661,-0.7535719161141583,1.0635612250504973,0.30939583102665447,4.818550751334681,1.6673789585767977,-1.317728204018211,-0.7029064886408514,0.3337095618487824,-0.22034227119227,-0.8429189248634876,3.455722338768699,6.286668242675404,6.917463100530892,-1.349170767138331,15.474482447225018,-1.0422328678825028,-1.4407171006358446,-1.296078599702278,-1.3593135302781183,-0.9621487648604354,-1.203748826494658,-1.5756124281144324,-1.6638426268853777,-1.5179953204082142,-1.3301742216945542,-0.43436008583478536,-1.3124938911989532,3.45904961141917,-1.1645859587037797,-1.4172521509293947,-1.4736927077501412,-1.2437133680098902,-1.1544556571767235,25.95920775207283,-1.4278837767343484,-1.4303360409840453,-1.3361236494992612,-0.2791394718783953,-1.3371301341744517,-1.025942123218719,-1.35248379479694,-0.5055919632821233,-1.3481649650723195,-1.2239911519037552,2.311509516760135,-1.4975241617850306,-1.6088538344821872,0.9612829426492668,-1.2198561444414056,-1.7340253825972558,-0.6661871644316486,-0.11113973165862268,-1.2909688256396041,-1.7228872151340129,-1.396542031996023,-0.6097976574407196,-1.5131249141271206,0.24105580276619332,0.09531137275475698,0.8850455450485142,-0.4072090334286762,-1.5484897850669515,-0.8516640382520375,-1.2650563979675633,-0.016165131120238208,-1.1939447645166903,0.20949577829784438,-1.2403490253125617,0.5370239011268678,-0.537977485577525,-0.6531125782888831,-0.9254755232703045,-1.6015557881562323,-1.224062276991183,-0.8904144837783652,-1.5110520332986632,-1.4317523991923569,1.569543843930325,-1.3132838382998635,-0.9850843889675951,34.32002201877197,-0.549842590347962,-1.1919095359353995,-1.356352976909317,-0.1735690001687309,3.761492607908748,-1.2403957279225242,-1.5612231530023202,-0.14749893990293161,-1.5530132544425947,-0.9088266592047329,-1.2225930216102219,-1.2275486971326595,44.322127543559176,-1.3803174576983201,-1.4214954678502754,-1.3909768092663446,-1.6938297391583186,1.7433596036213928,-1.1083106934336808,-1.3420072779422962,4550.0871759217935,0.8107952939429639,-1.6763189010752801,-0.0945574067235091,-0.9058030340374206,2.841065564745537,2.5757716417778402,0.2512413513453686,-1.163141508054771,-1.1130108636095994,173.67600550298164,-1.4114130232651108,-1.2166021010142503,-1.4369866990280413,-1.49404422426682,3.3770396799930236,-1.1737609292741382,1.1588395934342763,-1.0534044473035151,-1.423428538841657,0.08125054258168385,-1.2629938104815601,42.89075108332018,-1.0122137116216683,-1.6026487654671713,-0.3100269444485835,-0.09001378125155224,3.996271210652278,-1.6244102148241977,-0.501290670076552,-1.590461123318385,0.8282822425433096,18.448235059936188,-1.163968740146598,5.0807146301242625,-1.1672400836142398,-1.0811976579760927,0.1261950094501918,-1.5970706266753476,-1.1821813384916116,-0.9332985368947715,0.4493887111603554,15.832587375458544,-1.389942746318353,-1.0471277013706684,-1.3994651942415657,7.527727186512461,-1.220622811593266,-1.7405215079524174,-1.42548769771511,-1.0005246278243325,-1.251977053365332,-1.374464495917211,-1.3662456650834247,-1.3550834371427527,-0.8904263252778013,-1.242156529048465,-0.04753101265940263,-1.5609675953773785,-1.2194987970696312,-0.3632363198652939,-1.6463256306617575,-1.0663977037732735,216.27270701449547,-1.220043796909036,0.3716355504966722,-1.255413672173868,-1.2839165777465757,54.24270128870066,10.547734903704317,-1.3683451435946976,5.801290015114251,-1.5198586275665207,-0.29548319490856656,10.340282980332915,-0.49619435859008254,-1.2173244168835915,-0.336732887255613,-1.2835781312582346,-0.23801546480474123,41.84572419093755,-1.2674167475256792,-0.03565784214019896,-1.0948760041303354,-0.7002690670009915,-0.41270911511410135,-1.274915424310845,-0.9419681257521928,-1.5175047296046558,-1.2401392604649044,-1.4904122932166606,-1.2352812021326192,-0.3603216714012212,-1.476664660009976,-1.4279692776567265,-1.5223304632654884,-1.1569599181095083,-0.996131694907973,-1.2684144933034738,-0.9670458802928712,-1.4676723317795475,-1.6278655708778436,0.5715680918022628,-0.6939896777646486,5.274492727963086,-1.2174877146395666,-1.189271994514403,-1.0906186139019793,-1.2402694740626108,-1.619695666285247,1.8602690333880236,1.1397307379753823,15.295094756689384,-1.3222172891315613,-1.4472652278163218,0.4785949271841399,-1.250554501324558,-1.23574169645744,-1.3282013732951294,496.4312649841314,4.266361152217273,-0.6005463697832476,-1.2351047434911744,-1.3450775624618165,3.449820500774961,-1.591228168927921,-1.389468085496464,-1.5255937999518454,4.721763406037523,2.264277230036636,2.3871302660840756,-1.1905332346629225,0.785898890324475,-1.3245081751126215,8.691113341578726,-1.3261900914425808,-1.1929681497967863,-1.2974348108263904,-1.5097034870049533,-0.2330859389055746,-1.0600658355270598,5.415883933449463,-0.9160796632517876,-0.8524015719266171,-0.6014520859762205,-1.2399361922885852,-1.6179743243721627,13.806919980958629,5.80170435842987,6.665006603515854,0.5426601103872741,-1.2281560462760661,-0.7185615660774771,4.527274851587877,0.03347679902700662,-1.2580971448117126,3.217736663116886,-1.1782563881515011,7.764177628910462,-0.9009048958466352,-1.0739843884888038,-1.2464162081330759,-1.221630563829325,13.919336823673515,-1.2771264002594087,-1.3084629216387789,-1.1972883992981043,-1.0114301898986102,2.368874449697646,-1.3954081267243459,-1.2629366629430676,0.7287847585307854,-1.2427456724546015,3.423268932645229,3.077023120655415,-1.6951501315014554,-1.2799971249115416,-0.792963281571093,-1.2343891125765183,-1.5085899793315163,-0.4732723001292105,15.868294239144856,3.746983452601624,1.7495428241620576,3.3982207277412364,-1.1460747668508338,-0.4128451297042144,-0.9557496504209104,8.54686601207669,-1.3388738105828915,-1.1969545824504764,-0.6897591786911121,-1.3905503915935864,-0.30864429455600195,-1.2469478243468102,-1.1081469622088698,-1.3190002103278806,-1.1639160535203632,-1.2580514250332855,-0.5630826949188612,0.17642618906599106,0.6017562694200884,-0.12188751881713733,-0.9700980830117127,-1.26781871102095,-1.041018154888735,-1.624077440852175,-1.2344066481236926,-1.5140770190071027,12.263991166449435,-1.2177850023814745,-1.0091060680843715,-0.8370490049996304,188.8189255481612,-0.7176459741621395,-1.329971276138463,-1.309937669172535,-1.2228411563748378,-1.2598342913853655,0.1810980495725767,4.208377305091612,1.583460045318943,-1.6240371364301551,-0.7011996156991329,-1.1237930925299566,2.466139884602822,2.4689115334860023,1.4189290624838566,-1.483539038263883,2.2281785381073718,5.720990684427903,-1.2850470576588087,-1.3724693403754666,-1.4887773068328025,1.1865534031625415,0.24396575496674267,-1.546350528614987,0.05609515445055058,-1.2961143498783145,-1.2994420259224793,4.775569539565158,-0.5482871698720864,0.8628833921610113,-0.33520190109981884,0.6134120401537957,-1.3744701936761967,-1.4414480877484486,11.241948887111649,-1.3877660570127375,57.6095942262469,-0.8246766271360548,-1.2241511251388784,-1.447055978261131,-1.4173232758601737,-1.382443356949626,-1.272978319546297,-0.7154383792820127,-1.0752488464516516,0.06719466612504155,-1.244284891327574,-1.3535410546233066,-0.8033238352820091,-1.218589649419126,-0.9920215113119819,-1.238207573534653,29.131336291481595,0.3528503344693612,24.01297387424131,-1.2644944020642317,-0.7694993233093017,-1.2587321498952746,11.75618364585716,-1.1700586656954852,-1.6483566999857078,-1.491833130445576,-1.0798535343352393,-1.3179312859493728,-0.6984602127719244,-1.306244306803085,-1.502630661376347,8.590772101454483,-0.8469009870306738,-1.2981467606795347,0.24479002171319664,5.428305245882287,1.3346828195278517,-1.4692310838743814,-1.1367066538684683,17.483194655653932,-1.3427598443223092,-1.3447827164445028,-1.2396573355318379,-1.8250694423708174,0.45057005491195623,-1.531074426014516,1.3678270740087637,5760.6955624021875,4.161644087242162,-1.2430064634860258,-1.4616941049079306,1.9878021442270484,-1.494097800957752,-1.4092310879787713,-1.477563771009683,-1.1888545374966062,0.17190809165859422,-1.2771745148902178,-0.4510087761938264,-1.4280845377700928,0.20986435888250865,7.940446827602962,0.2900451168631961,-1.233838864957469,-1.213574644052194,1.7010358940363455,0.4588627435811299,-1.3126536684298957,-0.8766156381045827,-1.274598399571945,-0.7953074451229765,-0.8889519860933488,28.8631422167933,3.158401428861426,-0.20441503634626157,179.9239070197744,-1.064485335390811,-1.2622856803158065,-0.656840985725097,-0.233793655477589,-1.1529904935617366,1.1412118472162032,3.8294034850221017,-1.1291298144047417,0.8275789063415213,-1.1330126439960138,0.24694450548628977,-1.198228054205552,-0.9239947548288256,5.4135245103055105,-1.491071424388959,-1.4354813658095353,-1.6332766531803622,-1.2963716574231647,2.237108375115989,-1.2505269068929274,-1.205116617532964,-0.7128197698892662,-0.9218258865039313,-0.17644093636303326,-0.9617396272678111,-1.4500352803987273,-1.257458954523789,-1.2003437939929507,-0.6748844342019922,-1.4811078046908355,-0.1660788265952835,-0.7280575601802766,-1.3467658401675517,36.7659316835075,-1.2896059588848652,2.938887268341033,-0.934868751131158,-1.4698684999430969,-0.8733549422868809,-1.2059134923692219,-1.3672104443045736,-0.8075150301450051,-1.3877667283406925,-1.4245458033566205,-0.9178052513162318,13.942858397265933,-1.359331261042977,15.817482236636579,8.496014060965583,-0.40827935393017123,-1.277054237829916,-0.9094105540403614,-1.3436930843826824,-1.197767074244656,-1.502411689214351,330.6341462332846,-0.9955781907695518,-1.4880216210568968,-1.3809939595867171,0.040941696855283816,3.5769516007235183,-1.3699857124568016,10.518580084946763,2.944176568241355,-0.9301050783989471,0.11162449678214426,-1.6336307942322477,-1.374018156232007,2.3185455763972556,-0.46358944887869535,-1.2505190021175543,1.8455019507000818,-1.0602699723825932,-1.2629161384542298,-1.4633734351520669,-1.2627593586180859,-0.9521088916377094,-1.1349566578888508,-0.6897579655914194,-1.4076249125089144,-1.3385271215425725,-1.1482752547833825,-0.17785139880276413,-0.42397682323115893,-1.1827728868026,-0.47403256879884914,-1.555309711811713,-1.3888444898653711,1.7833814253096678,-0.5485877918731363,-1.2418319249461323,-1.3202868859207133,-0.5326372578527363,-1.225136574793692,-1.4296338803584392,-0.6264846907637129,-0.8138487339829767,1.2293017269162263,-1.5399704578164923,-1.5670469074532203,-0.2691057368275769,1.7829917052932478,-1.4858835445089218,0.3359563554169571,-1.2635801863751264,1.6181616751315673,-1.420608877277563,-1.3353726909017551,-0.5426187423139681,-1.398495663173322,-0.46984841612461414,169.9055692304396,0.6795959015568993,9.82145201001834,-1.683493026833135,-1.3473129882728774,-0.6926006761814181,-0.7122310496040067,-0.8740930755001908,-1.3010793571760746,-0.06399226112189327,0.9770268543663363,-1.3060749982091424,1.8948697111167245,-1.1970592777136166,-1.5698567083210777,-1.2352630660254522,-0.9753816688460426,1.9726905522370632,-1.627423427328523,-1.0478055907145598,-1.2682966317625255,-1.2453492425936568,-1.8212741731795563,-1.122633582690297,-1.71484081015528,-1.3495288771302094,-0.8999459783443764,-0.7118021947740782,-1.5420037042662218,-1.373807583573221,4.632058500506881,-1.3506322064361125,2.6159669190370884,-0.4058080742148227,-1.126891208563172,-0.9130631378918075,-1.1474477613615026,1.6298792443560792,-1.0464597447811057,-1.4390779092673054,-1.0038032101377696,-1.1309884636878136,-0.9264826192886209,0.06322464739936429,2.363224356875408,-1.2415517856970182,-0.28248186605161285,-0.3751980750288735,-0.5779304375874363,-1.3841467512289523,-0.02730832235891567,-1.0502048587812527,-1.3293194223890572,-1.2694041105984022,-0.9795260201370648,-1.1331968001564965,9.004192464725568,-1.088046119268208,-0.979287927065978,1.054143645060961,-1.701288718632572,-1.1782369717690422,-1.3041047599171927,0.09360236950512801,1.4288747676190585,-1.2444296041250529,2.6205450792917695,-1.137217312051219,2.6130866445721663,1.0915549842627472,-1.4258887333368764,3.0653156270854307,0.7246289543493658,2.23461472625622,0.7683222938480245,-1.5446615569693853,0.5381830348476386,-0.7201308517676925,-0.8157047330459539,-0.8677033960161107,2.431811465279945,0.6477086669038901,-0.6114561370945886,0.667291755737784,-1.1247751960262415,-1.5880513638451115,-0.9174345311305849,-1.6764404862511273,-1.4585155756407664,-1.1963218008550187,-1.325347355383188,-1.4771167939475787,5.051835958969832,5.178794769802662,-1.4634044314763435,-0.15604038357541183,-1.39752357810292,-1.4124344502932216,-0.6320718110180747,2.1714372623171077,2.3961602167694585,11.55890649064224,-1.5353269378159875,-1.131273274952806,-1.180495580173175,-1.6309077481179604,-0.6838310702533028,-1.3516055297173477,-1.2314384684340203,-0.8804718065730954,-0.662869069974009,-1.5190221336490213,-1.2141361088292675,-1.3172537556718047,-0.9380657271215149,-1.4199607607922797,-0.4410305433976074,23.179248880504506,-1.151874006648109,15.18961654617247,-0.8583483968996259,-1.1812178330348957,25.537810307934006,3.0722398641794033,-0.21249188695147936,1.8179325882593114,-0.9247462278310468,-1.336238733237236,-1.400754969119213,-1.4145082688106103,-0.25086244964149085,12.039396702590418,-1.3021217661466178,-1.2487300650051492,-1.6767110799423437,0.3347221790072057,-0.6478284632832869,-1.3068732834115326,-1.1308799434217787,-0.37575821638508033,0.4069197178646764,-0.9849794543884038,-1.0496412344518107,80.38733475728179,-0.5948021227962914,-1.003422526777176,-1.3213241713854054,41.55534716301095,0.32335528209131725,0.3407148484970026,-0.7766059190715207,2.5373457328273874,-1.4833326548753953,-0.7991010135218923,-1.424442257263251,0.29788508574793715,-1.3611977513713451,-1.1352434980922963,0.5079217410254868,19.510561559287577,-1.3626929238544903,79.25610105079534,-1.4707727436781768,-0.6344766394584869,-0.9857130914640804,-1.2275715140588477,-0.8184174036444181,2.0441825711710075,3.771591064755211,-1.219122650099965,-1.0226184646068166,-1.2322105430728945,-1.1662516111202121,-1.3791802701373008,-1.5864370854166425,-1.3473340702049137,4.364980762479716,0.4613756383502774,13.714364444647114,1.649911968721618,1.8369779271517803,-1.3605558395336754,2.428962387295611,-1.1981594447591641,-1.2026445370183898,38.70334226848989,-1.2354678178289638,-1.0650879435566145,-1.4195077733006671,-1.3335562666665874,-1.2113622025924666,-1.3793918834749668,-1.129328322854264,-0.05032438639762038,-1.58135568206133,-0.609523892613629,-1.4736395191981,1.1569694411052334,-1.2241845822967599,-1.3304529110011363,-0.15304779412752234,-0.3154533797142025,-0.8016674047820032,-1.223528518960104,-0.8465865295201445,-1.4715197524814378,-0.6110032380837085,0.7419043570548349,-0.9452196020882191,-1.0730377209246313,8.680178699520631,-0.7975392403178017,-0.773313473350429,-0.14706334946963961,1.9659842339743339,-1.3665565035995537,-1.151993240338716,36.43621456395037,3.4697732886227373,2.265033713669559,-1.2661013550749474,-0.7632802350520564]} diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/runner.jl b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/runner.jl new file mode 100644 index 000000000000..9b237d5d9e41 --- /dev/null +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/fixtures/julia/runner.jl @@ -0,0 +1,73 @@ +#!/usr/bin/env julia +# +# @license Apache-2.0 +# +# Copyright (c) 2026 The Stdlib Authors. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +import Distributions: kurtosis, Kumaraswamy +import JSON + +""" + gen( a, b, name ) + +Generate fixture data and write to file. + +# Arguments + +* `a`: shape parameter a (must be positive) +* `b`: shape parameter b (must be positive) +* `name::AbstractString`: output filename + +# Examples + +``` julia +julia> a = rand( 1000 ); +julia> b = rand( 1000 ); +julia> gen( a, b, \"data.json\" ); +``` +""" +function gen( a, b, name ) + z = Array{Float64}( undef, length(a) ); + for i in eachindex(a) + z[ i ] = kurtosis( Kumaraswamy( a[ i ], b[ i ] ) ); + end + + # Store data to be written to file as a collection: + data = Dict([ + ("a", a), + ("b", b), + ("expected", z) + ]); + + # Based on the script directory, create an output filepath: + filepath = joinpath( dir, name ); + + # Write the data to the output filepath as JSON: + outfile = open( filepath, "w" ); + write( outfile, JSON.json(data) ); + write( outfile, "\n" ); + close( outfile ); +end + +# Get the filename: +file = @__FILE__; + +# Extract the directory in which this file resides: +dir = dirname( file ); + +# Generate fixtures: +a = rand( 1000 ); +b = rand( 1000 ); +gen( a, b, "data.json" ); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.js index 45aadd3a243a..e14be4b365e7 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.js @@ -21,15 +21,18 @@ // MODULES // var tape = require( 'tape' ); -var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive; +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var randu = require( '@stdlib/random/base/randu' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); var kurtosis = require( './../lib' ); +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); + + // TESTS // tape( 'main export is a function', function test( t ) { @@ -100,17 +103,18 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', function test }); tape( 'the function returns the excess kurtosis of a Kumaraswamy\'s double bounded distribution', function test( t ) { + var expected; var a; var b; var i; var y; - // TODO: Add fixtures - for ( i = 0; i < 100; i++ ) { - a = ( randu()*5.0 ) + EPS; - b = ( randu()*5.0 ) + EPS; - y = kurtosis( a, b ); - t.strictEqual( isNumber( y ), true, 'returns expected value' ); + expected = data.expected; + a = data.a; + b = data.b; + for ( i = 0; i < expected.length; i++ ) { + y = kurtosis( a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1043762 ), true, 'returns expected value' ); } t.end(); }); diff --git a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.native.js b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.native.js index 8c08d54f26cc..d101e7b8df10 100644 --- a/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.native.js +++ b/lib/node_modules/@stdlib/stats/base/dists/kumaraswamy/kurtosis/test/test.native.js @@ -23,12 +23,15 @@ var resolve = require( 'path' ).resolve; var tape = require( 'tape' ); var tryRequire = require( '@stdlib/utils/try-require' ); -var isNumber = require( '@stdlib/assert/is-number' ).isPrimitive; +var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' ); var isnan = require( '@stdlib/math/base/assert/is-nan' ); -var randu = require( '@stdlib/random/base/randu' ); var PINF = require( '@stdlib/constants/float64/pinf' ); var NINF = require( '@stdlib/constants/float64/ninf' ); -var EPS = require( '@stdlib/constants/float64/eps' ); + + +// FIXTURES // + +var data = require( './fixtures/julia/data.json' ); // VARIABLES // @@ -112,17 +115,18 @@ tape( 'if provided a nonpositive `b`, the function returns `NaN`', opts, functio }); tape( 'the function returns the excess kurtosis of a Kumaraswamy\'s double bounded distribution', opts, function test( t ) { + var expected; var a; var b; var i; var y; - // TODO: Add fixtures - for ( i = 0; i < 100; i++ ) { - a = ( randu()*5.0 ) + EPS; - b = ( randu()*5.0 ) + EPS; - y = kurtosis( a, b ); - t.strictEqual( isNumber( y ), true, 'returns expected value' ); + expected = data.expected; + a = data.a; + b = data.b; + for ( i = 0; i < expected.length; i++ ) { + y = kurtosis( a[i], b[i] ); + t.strictEqual( isAlmostSameValue( y, expected[ i ], 1043762 ), true, 'returns expected value' ); } t.end(); });