{"cases":[[{"__dict__":[["T",10],["x0",{"__nd__":[0.30471707975443135,-1.0399841062404955,0.7504511958064572,0.9405647163912139],"dtype":"float64","shape":[4]}],["noise",{"__nd__":[-1.9510351886538364,-1.302179506862318,0.12784040316728537,-0.3162425923435822],"dtype":"float64","shape":[4]}],["t",3]]},{"__dict__":[["betas",{"__nd__":[0.0001,0.002311111111111111,0.004522222222222223,0.006733333333333334,0.008944444444444444,0.011155555555555556,0.013366666666666667,0.015577777777777777,0.01778888888888889,0.02],"dtype":"float64","shape":[10]}],["alpha_bars",{"__nd__":[0.9999,0.99758912,0.993077800312889,0.9863910764574488,0.9775683562735794,0.9666630381658163,0.9537419755556666,0.9388847950031217,0.922183077705344,0.9037394161512371],"dtype":"float64","shape":[10]}],["x_t",{"__nd__":[0.07503406156773296,-1.1847920665809795,0.7602408020083951,0.8972507517769188],"dtype":"float64","shape":[4]}],["mean",{"__nd__":[0.18828066254864517,-1.113386398379153,0.7554094989989784,0.9186017835105784],"dtype":"float64","shape":[4]}],["variance",{"__nd__":0.0034249202552634,"dtype":"float64","shape":[]}]]}],[{"__dict__":[["T",50],["x0",{"__nd__":[[-0.016801157504288795,-0.85304392757358,0.8793979748628286],[0.7777919354289483,0.06603069756121605,1.1272412069680329]],"dtype":"float64","shape":[2,3]}],["noise",{"__nd__":[[0.4675093422520456,-0.8592924628832382,0.36875078408249884],[-0.9588826008289989,0.8784503013072725,-0.049925910986252896]],"dtype":"float64","shape":[2,3]}],["t",0]]},{"__dict__":[["betas",{"__nd__":[0.0001,0.0005061224489795919,0.0009122448979591838,0.0013183673469387756,0.0017244897959183675,0.002130612244897959,0.002536734693877551,0.002942857142857143,0.0033489795918367348,0.0037551020408163266,0.004161224489795919,0.00456734693877551,0.004973469387755103,0.005379591836734695,0.005785714285714286,0.006191836734693878,0.00659795918367347,0.007004081632653062,0.007410204081632654,0.007816326530612245,0.008222448979591837,0.008628571428571428,0.00903469387755102,0.009440816326530611,0.009846938775510204,0.010253061224489796,0.010659183673469389,0.011065306122448978,0.011471428571428572,0.011877551020408163,0.012283673469387755,0.012689795918367346,0.013095918367346939,0.01350204081632653,0.013908163265306124,0.014314285714285713,0.014720408163265307,0.015126530612244898,0.01553265306122449,0.015938775510204083,0.016344897959183674,0.016751020408163265,0.017157142857142857,0.01756326530612245,0.01796938775510204,0.018375510204081635,0.018781632653061223,0.019187755102040818,0.01959387755102041,0.02],"dtype":"float64","shape":[50]}],["alpha_bars",{"__nd__":[0.9999,0.9993939281632653,0.998482236151247,0.9971658697746068,0.9954462674073424,0.9933253574008664,0.9908055545044393,0.9878897553011834,0.9845813326716951,0.98088412930003,0.9768024502395345,0.9723410545586446,0.9675051460893397,0.9623003633034387,0.956732768344326,0.9508088352440062,0.9445354373575902,0.9379198340494039,0.9309696566668868,0.9236928938402864,0.9160978761478732,0.9081932601879686,0.8999880121005153,0.891491390582195,0.8827129294402376,0.8736624197310381,0.8643498915305172,0.8547855953838265,0.8449799834824948,0.8349436906174578,0.8246875149565874,0.8142223986953628,0.803559408629183,0.7927097166955285,0.7816845805337326,0.7704953241095212,0.7591533184507416,0.7476699625398092,0.7360566644073796,0.7243248224706008,0.712485807158015,0.7005509428617844,0.6885314902563987,0.6764386290214057,0.6642834410039905,0.6520768938554192,0.6398298251734775,0.6275529271810673,0.615256731969097,0.602951597329715],"dtype":"float64","shape":[50]}],["x_t",{"__nd__":[[-0.012125224002890886,-0.861594198939675,0.8830415117056079],[0.7681642188515989,0.07481189895686773,1.1266855843887]],"dtype":"float64","shape":[2,3]}],["mean",{"__nd__":[[-0.016801157504290645,-0.853043927573674,0.8793979748629254],[0.777791935429034,0.06603069756122332,1.127241206968157]],"dtype":"float64","shape":[2,3]}],["variance",{"__nd__":0.0,"dtype":"float64","shape":[]}]]}],[{"__dict__":[["T",50],["x0",{"__nd__":[[-0.18486236354526056,-0.6809295444039414,1.2225413386740303],[-0.15452948206880215,-0.4283278221631072,-0.3521335504882296]],"dtype":"float64","shape":[2,3]}],["noise",{"__nd__":[[0.5323091855533487,0.36544406436407834,0.4127326115959884],[0.43082100300788273,2.1416476008704612,-0.4064150163846156]],"dtype":"float64","shape":[2,3]}],["t",49]]},{"__dict__":[["betas",{"__nd__":[0.0001,0.0005061224489795919,0.0009122448979591838,0.0013183673469387756,0.0017244897959183675,0.002130612244897959,0.002536734693877551,0.002942857142857143,0.0033489795918367348,0.0037551020408163266,0.004161224489795919,0.00456734693877551,0.004973469387755103,0.005379591836734695,0.005785714285714286,0.006191836734693878,0.00659795918367347,0.007004081632653062,0.007410204081632654,0.007816326530612245,0.008222448979591837,0.008628571428571428,0.00903469387755102,0.009440816326530611,0.009846938775510204,0.010253061224489796,0.010659183673469389,0.011065306122448978,0.011471428571428572,0.011877551020408163,0.012283673469387755,0.012689795918367346,0.013095918367346939,0.01350204081632653,0.013908163265306124,0.014314285714285713,0.014720408163265307,0.015126530612244898,0.01553265306122449,0.015938775510204083,0.016344897959183674,0.016751020408163265,0.017157142857142857,0.01756326530612245,0.01796938775510204,0.018375510204081635,0.018781632653061223,0.019187755102040818,0.01959387755102041,0.02],"dtype":"float64","shape":[50]}],["alpha_bars",{"__nd__":[0.9999,0.9993939281632653,0.998482236151247,0.9971658697746068,0.9954462674073424,0.9933253574008664,0.9908055545044393,0.9878897553011834,0.9845813326716951,0.98088412930003,0.9768024502395345,0.9723410545586446,0.9675051460893397,0.9623003633034387,0.956732768344326,0.9508088352440062,0.9445354373575902,0.9379198340494039,0.9309696566668868,0.9236928938402864,0.9160978761478732,0.9081932601879686,0.8999880121005153,0.891491390582195,0.8827129294402376,0.8736624197310381,0.8643498915305172,0.8547855953838265,0.8449799834824948,0.8349436906174578,0.8246875149565874,0.8142223986953628,0.803559408629183,0.7927097166955285,0.7816845805337326,0.7704953241095212,0.7591533184507416,0.7476699625398092,0.7360566644073796,0.7243248224706008,0.712485807158015,0.7005509428617844,0.6885314902563987,0.6764386290214057,0.6642834410039905,0.6520768938554192,0.6398298251734775,0.6275529271810673,0.615256731969097,0.602951597329715],"dtype":"float64","shape":[50]}],["x_t",{"__nd__":[[0.1918719287584219,-0.2984687065682756,1.2093729880567037],[0.151475891322865,1.0168938341092921,-0.529520877332414]],"dtype":"float64","shape":[2,3]}],["mean",{"__nd__":[[0.1767528383418786,-0.3132159156837682,1.2084180273882161],[0.13920062707124928,0.9585516579940022,-0.5218662447140013]],"dtype":"float64","shape":[2,3]}],["variance",{"__nd__":0.01938016954322819,"dtype":"float64","shape":[]}]]}],[{"__dict__":[["T",100],["x0",{"__nd__":[[-0.5122427290715373,-0.8137727282478777],[0.6159794225754956,1.1289722927208916],[-0.11394745765487507,-0.840156476962528],[-0.8244812156912396,0.6505927878247011],[0.7432541712034423,0.543154268305195]],"dtype":"float64","shape":[5,2]}],["noise",{"__nd__":[[-0.6655097072886943,0.23216132306671977],[0.11668580914072822,0.21868859672901295],[0.8714287779481898,0.22359554877468227],[0.6789135630718949,0.06757906948889146],[0.28911939868998415,0.6312882258385404]],"dtype":"float64","shape":[5,2]}],["t",{"__nd__":[0,10,50,99,1],"dtype":"int64","shape":[5]}]]},{"__dict__":[["betas",{"__nd__":[0.0001,0.00030101010101010105,0.000502020202020202,0.0007030303030303031,0.0009040404040404042,0.001105050505050505,0.0013060606060606062,0.0015070707070707072,0.0017080808080808083,0.0019090909090909093,0.00211010101010101,0.002311111111111111,0.002512121212121212,0.0027131313131313135,0.002914141414141414,0.003115151515151515,0.0033161616161616163,0.0035171717171717173,0.0037181818181818184,0.0039191919191919194,0.0041202020202020205,0.0043212121212121216,0.004522222222222223,0.004723232323232324,0.004924242424242425,0.005125252525252526,0.005326262626262628,0.005527272727272728,0.005728282828282829,0.00592929292929293,0.00613030303030303,0.006331313131313131,0.006532323232323233,0.006733333333333334,0.006934343434343435,0.0071353535353535355,0.007336363636363637,0.0075373737373737384,0.007738383838383839,0.007939393939393939,0.00814040404040404,0.008341414141414141,0.008542424242424242,0.008743434343434343,0.008944444444444444,0.009145454545454545,0.009346464646464646,0.009547474747474747,0.009748484848484848,0.00994949494949495,0.01015050505050505,0.010351515151515151,0.010552525252525254,0.010753535353535352,0.010954545454545455,0.011155555555555556,0.011356565656565657,0.011557575757575758,0.011758585858585859,0.01195959595959596,0.01216060606060606,0.01236161616161616,0.012562626262626261,0.012763636363636364,0.012964646464646465,0.013165656565656566,0.013366666666666667,0.013567676767676768,0.01376868686868687,0.013969696969696969,0.01417070707070707,0.01437171717171717,0.014572727272727274,0.014773737373737375,0.014974747474747476,0.015175757575757577,0.015376767676767676,0.015577777777777777,0.015778787878787878,0.01597979797979798,0.01618080808080808,0.01638181818181818,0.016582828282828282,0.016783838383838384,0.016984848484848485,0.017185858585858586,0.017386868686868687,0.017587878787878788,0.01778888888888889,0.01798989898989899,0.01819090909090909,0.018391919191919192,0.018592929292929293,0.018793939393939394,0.018994949494949495,0.019195959595959596,0.019396969696969697,0.0195979797979798,0.0197989898989899,0.02],"dtype":"float64","shape":[100]}],["alpha_bars",{"__nd__":[0.9999,0.99959902,0.9990972010980405,0.9983948054899957,0.9974922162466487,0.9963899369693014,0.9950885913243506,0.9935889224574254,0.9918917922878542,0.9899981806843956,0.9879091845233353,0.9856260166302147,0.9831500046066194,0.980482589543616,0.9776253246235824,0.9745798736123308,0.9713480092435739,0.9679316114979314,0.9643326657788164,0.9605532609876832,0.9565955875012502,0.9524619350534417,0.9481546905249223,0.9436763356432106,0.9390294445964827,0.9342166815642782,0.9292407981684312,0.9241046308476457,0.9188110981592245,0.9133631980115531,0.9077640048310156,0.9020166666670957,0.8961244022394834,0.8900904979310709,0.883918304730771,0.8776112351301466,0.8711727599778737,0.8646064052961011,0.8579157490627946,0.8511044179641748,0.8441760841213735,0.8371344617954398,0.8299833040748297,0.8227263995495047,0.8153675689757564,0.8079106619358508,0.8003595534965656,0.792718140870657,0.7849903400852603,0.7771800826611797,0.7692913123069754,0.7613279816317009,0.7532940488800783,0.7451934746938386,0.7370302189028742,0.72880823734978,0.7205314787512713,0.7122038815998855,0.703829371109275,0.6954118562063115,0.6869552265731117,0.6784633497419988,0.6699400682463006,0.6613891968297752,0.6528145197173406,0.644219787949668,0.6356087167840742,0.6269849831640301,0.6183522232594757,0.6097140300800025,0.6010739511628385,0.5924354863374396,0.5838020855683586,0.5751771468779315,0.5665640143501888,0.5579659762172623,0.5493862630294286,0.5408280459097924,0.5322944348944825,0.523788477359098,0.5153131565320117,0.5068713900950055,0.49846602887158153,0.4900998556031672,0.48177558381330127,0.4734958567597664,0.46526324647450795,0.4570802528910593,0.44894930305907504,0.4408727504454567,0.4328528743214443,0.4248918792349344,0.4169918945671794,0.40915497417291985,0.40138309610289785,0.3936781624076055,0.3860419990210265,0.37847635572304067,0.3709829061790737,0.3635632480554922],"dtype":"float64","shape":[100]}],["x_t",{"__nd__":[[-0.5188722133676349,-0.8114104253635315],[0.6250748178563382,1.146173053099646],[0.31862346294851557,-0.629497236485142],[0.0444858854067941,0.4461953136926428],[0.7488946082994267,0.5556865820039955]],"dtype":"float64","shape":[5,2]}],["mean",{"__nd__":[[-0.5122427290715937,-0.8137727282479673],[0.6234937795438206,1.1431831672547044],[0.3017431193369916,-0.6374659743534578],[0.027744445057210163,0.44901393144494145],[0.744660619630239,0.5462792169769195]],"dtype":"float64","shape":[5,2]}],["variance",{"__nd__":[[0.0],[0.001745527345234659],[0.009803422311127805],[0.01976683753410179],[7.506860716496371e-05]],"dtype":"float64","shape":[5,1]}]]}]]}