diff --git a/graphics/background/bach/instability/frame_1.png b/graphics/background/bach/instability/frame_1.png deleted file mode 100644 index f4f17e9..0000000 Binary files a/graphics/background/bach/instability/frame_1.png and /dev/null differ diff --git a/graphics/background/bach/instability/frame_18.png b/graphics/background/bach/instability/frame_18.png deleted file mode 100644 index 367d979..0000000 Binary files a/graphics/background/bach/instability/frame_18.png and /dev/null differ diff --git a/graphics/background/bach/instability/frame_25.png b/graphics/background/bach/instability/frame_25.png deleted file mode 100644 index 2e64dee..0000000 Binary files a/graphics/background/bach/instability/frame_25.png and /dev/null differ diff --git a/graphics/background/bach/instability/frame_7.png b/graphics/background/bach/instability/frame_7.png deleted file mode 100644 index 8128b19..0000000 Binary files a/graphics/background/bach/instability/frame_7.png and /dev/null differ diff --git a/graphics/background/sign-based-overlay.typ b/graphics/background/sign-based-overlay.typ deleted file mode 100644 index 1de5ff3..0000000 --- a/graphics/background/sign-based-overlay.typ +++ /dev/null @@ -1,34 +0,0 @@ -#import "@preview/cetz:0.3.4": canvas -#import "@preview/cetz-plot:0.1.1": plot, chart - -#let ymax = 1/calc.sqrt(2*calc.pi) - -#let line_style = (stroke: (paint: black, thickness: 3pt)) -#let dashed = (stroke: (dash: "dashed")) -#canvas({ - - plot.plot(size: (11,6), - legend: "north", - legend-style: (orientation: ltr, item: (spacing: 0.5)), - x-tick-step: none, - x-ticks: ((0, [0]), (100, [0])), - y-label: $cal(Q)(1, x)$, - x-label: $x$, - y-tick-step: none, - y-ticks: ((0, [0]), (ymax, [1])), - axis-style: "left", - x-min: -3, - x-max: 3, - y-min: 0, - y-max: ymax,{ - plot.add( - plot.sample-fn( - (x) => 1/calc.sqrt(2*calc.pi)*calc.exp(-(calc.pow(x,2)/2)), - (-3, 3), - 300), - style: (stroke: (paint: red, thickness: 3pt)), - // label: [PDF einer Normalverteilung] - ) - plot.add(((-3,0), (0,0), (0,ymax), (3,ymax)), style: line_style, /*label: [$cal(Q)(1,x)$]*/) - }) -}) diff --git a/graphics/background/two-bit-enroll.typ b/graphics/background/two-bit-enroll.typ deleted file mode 100644 index c8e8191..0000000 --- a/graphics/background/two-bit-enroll.typ +++ /dev/null @@ -1,26 +0,0 @@ -#import "@preview/cetz:0.3.4": canvas, draw, palette -#import "@preview/cetz-plot:0.1.1": plot, chart - -#let line_style = (stroke: (paint: black, thickness: 3pt)) -#let dashed = (stroke: (dash: "dashed")) -#canvas({ - import draw: * - set-style(axes: (shared-zero: false)) - plot.plot(size: (8,6), - x-tick-step: none, - x-ticks: ((0.25, [$g_1$]), (0.5, [0]), (0.75, [$g_2$])), - y-label: $cal(Q)(2, 1, tilde(x))$, - x-label: $tilde(x)$, - y-tick-step: none, - y-ticks: ((0.25, [00]), (0.5, [01]), (0.75, [10]), (1, [11])), - axis-style: "left", - //x-min: 0, - x-max: 1, - y-min: 0, - y-max: 1,{ - plot.add(((0,0.25), (0.25,0.25), (0.5,0.5), (0.75,0.75), (1, 1)), line: "vh", style: line_style) - //plot.add(((0,0), (0,0)), style: (stroke: none)) - plot.add-hline(0.25, 0.5, 0.75, 1, style: dashed) - plot.add-vline(0.25, 0.5, 0.75, 1, style: dashed) - }) -}) diff --git a/graphics/background/z_distribution.csv b/graphics/background/z_distribution.csv deleted file mode 100644 index 8f17016..0000000 --- a/graphics/background/z_distribution.csv +++ /dev/null @@ -1,1000 +0,0 @@ --10.0,1.5670866530993244e-11 --9.97997997997998,1.731898421572835e-11 --9.95995995995996,1.913660039744377e-11 --9.93993993993994,2.1140737179795716e-11 --9.91991991991992,2.3350083243845715e-11 --9.8998998998999,2.57851526231251e-11 --9.87987987987988,2.8468458165120247e-11 --9.85985985985986,3.142470099460374e-11 --9.83983983983984,3.4680977407952604e-11 --9.81981981981982,3.826700475075735e-11 --9.7997997997998,4.2215367964389906e-11 --9.77977977977978,4.656178863156737e-11 --9.75975975975976,5.134541850719675e-11 --9.73973973973974,5.6609159689839135e-11 --9.71971971971972,6.240001377199487e-11 --9.6996996996997,6.876946250516688e-11 --9.67967967967968,7.577388272945277e-11 --9.65965965965966,8.347499854850021e-11 --9.63963963963964,9.194037398035494e-11 --9.61961961961962,1.012439495844808e-10 --9.5995995995996,1.114666268565524e-10 --9.57957957957958,1.226969044971726e-10 --9.55955955955956,1.3503157100019476e-10 --9.53953953953954,1.4857645837274253e-10 --9.51951951951952,1.6344726219431744e-10 --9.4994994994995,1.7977043364875085e-10 --9.47947947947948,1.9768414962249373e-10 --9.45945945945946,2.1733936745835158e-10 --9.43943943943944,2.3890097148788503e-10 --9.41941941941942,2.6254901904118343e-10 --9.3993993993994,2.884800942525761e-10 --9.37937937937938,3.1690877864837094e-10 --9.35935935935936,3.480692482213214e-10 --9.33933933933934,3.8221700746994e-10 --9.31931931931932,4.1963077171299245e-10 --9.2992992992993,4.6061450988468017e-10 --9.27927927927928,5.054996609787182e-10 --9.25925925925926,5.546475383444925e-10 --9.23923923923924,6.084519371509368e-10 --9.21921921921922,6.673419615290896e-10 --9.1991991991992,7.317850891883775e-10 --9.17917917917918,8.022904926806516e-10 --9.15915915915916,8.794126379666174e-10 --9.13913913913914,9.637551825284225e-10 --9.11911911911912,1.0559751969774664e-09 --9.0990990990991,1.1567877359357649e-09 --9.07907907907908,1.266970785931154e-09 --9.05905905905906,1.38737062015004e-09 --9.03903903903904,1.5189075921459597e-09 --9.01901901901902,1.6625824030183372e-09 --8.998998998999,1.8194828791637996e-09 --8.97897897897898,1.9907913004742718e-09 --8.95895895895896,2.1777923218238912e-09 --8.93893893893894,2.3818815338630113e-09 --8.91891891891892,2.604574712536835e-09 --8.8988988988989,2.847517810382273e-09 --8.87887887887888,3.1124977465452213e-09 --8.85885885885886,3.401454056618205e-09 --8.83883883883884,3.716491467841983e-09 --8.81881881881882,4.059893469963204e-09 --8.7987987987988,4.434136957112363e-09 --8.77877877877878,4.841908021483401e-09 --8.75875875875876,5.28611898537923e-09 --8.73873873873874,5.7699267643599956e-09 --8.71871871871872,6.296752660816444e-09 --8.6986986986987,6.870303694316149e-09 --8.67867867867868,7.494595582561493e-09 --8.65865865865866,8.173977494784034e-09 --8.63863863863864,8.913158707911974e-09 --8.618618618618619,9.717237304914516e-09 --8.598598598598599,1.0591731064385666e-08 --8.578578578578579,1.1542610700715167e-08 --8.558558558558559,1.2576335625140197e-08 --8.538538538538539,1.3699892409622672e-08 --8.518518518518519,1.4920836147889933e-08 --8.498498498498499,1.6247334921157145e-08 --8.478478478478479,1.768821759006418e-08 --8.458458458458459,1.925302514925403e-08 --8.438438438438439,2.0952065896847053e-08 --8.418418418418419,2.279647468787558e-08 --8.398398398398399,2.4798276558596732e-08 --8.378378378378379,2.697045502755155e-08 --8.358358358358359,2.9327025399350928e-08 --8.338338338338339,3.188311341850448e-08 --8.318318318318319,3.465503964323947e-08 --8.298298298298299,3.766040993324921e-08 --8.278278278278279,4.0918212470738604e-08 --8.258258258258259,4.444892176108461e-08 --8.238238238238239,4.8274610087966266e-08 --8.218218218218219,5.2419066928043386e-08 --8.198198198198199,5.6907926862259885e-08 --8.178178178178179,6.176880655469655e-08 --8.158158158158159,6.703145140571939e-08 --8.138138138138139,7.272789252404431e-08 --8.118118118118119,7.889261470237839e-08 --8.098098098098099,8.556273612362166e-08 --8.078078078078079,9.277820056931877e-08 --8.058058058058059,1.005819829492733e-07 --8.038038038038039,1.090203090210869e-07 --8.018018018018019,1.1814289022100969e-07 --7.997997997997998,1.280031745830038e-07 --7.977977977977978,1.3865861478146744e-07 --7.957957957957958,1.5017095439483e-07 --7.937937937937938,1.6260653355226902e-07 --7.917917917917918,1.760366151943899e-07 --7.897897897897898,1.9053773325091437e-07 --7.877877877877878,2.0619206411446424e-07 --7.857857857857858,2.2308782286955728e-07 --7.837837837837838,2.4131968582014157e-07 --7.817817817817818,2.60989240947569e-07 --7.797797797797798,2.8220546802402006e-07 --7.777777777777778,3.0508525020428403e-07 --7.757757757757758,3.297539190216215e-07 --7.737737737737738,3.5634583482144844e-07 --7.717717717717718,3.850050047799669e-07 --7.697697697697698,4.1588574077388583e-07 --7.677677677677678,4.491533594922085e-07 --7.657657657657658,4.849849273120141e-07 --7.637637637637638,5.235700525974041e-07 --7.617617617617618,5.651117282246177e-07 --7.597597597597598,6.098272272870181e-07 --7.5775775775775776,6.57949055091367e-07 --7.5575575575575575,7.09725960721983e-07 --7.5375375375375375,7.65424011622138e-07 --7.5175175175175175,8.253277348227375e-07 --7.4974974974974975,8.897413286372491e-07 --7.4774774774774775,9.589899488392686e-07 --7.4574574574574575,1.0334210735453198e-06 --7.4374374374374375,1.1134059512408164e-06 --7.4174174174174174,1.199341136611844e-06 --7.397397397397397,1.2916501190799208e-06 --7.377377377377377,1.3907850491813618e-06 --7.357357357357357,1.4972285681878009e-06 --7.337337337337337,1.611495746629939e-06 --7.317317317317317,1.7341361376632257e-06 --7.297297297297297,1.8657359515020452e-06 --7.277277277277277,2.006920357448644e-06 --7.257257257257257,2.1583559203545643e-06 --7.237237237237237,2.320753178676383e-06 --7.217217217217217,2.494869371624047e-06 --7.197197197197197,2.6815113232498275e-06 --7.177177177177177,2.88153849168874e-06 --7.157157157157157,3.0958661921378957e-06 --7.137137137137137,3.325469002552811e-06 --7.117117117117117,3.5713843614435337e-06 --7.097097097097097,3.834716367572821e-06 --7.077077077077077,4.116639791792958e-06 --7.057057057057057,4.418404311707384e-06 --7.037037037037037,4.7413389803081e-06 --7.017017017017017,5.0868569402207576e-06 --6.996996996996997,5.4564603956860075e-06 --6.976976976976977,5.851745854918396e-06 --6.956956956956957,6.27440965601412e-06 --6.936936936936937,6.726253790124496e-06 --6.916916916916917,7.209192036175427e-06 --6.896896896896897,7.725256421992914e-06 --6.876876876876877,8.276604027292446e-06 --6.856856856856857,8.865524144603897e-06 --6.836836836836837,9.494445814836332e-06 --6.816816816816817,1.0165945754836244e-05 --6.796796796796797,1.0882756694959566e-05 --6.776776776776776,1.164777614536284e-05 --6.756756756756756,1.2464075610420089e-05 --6.736736736736736,1.333491027139234e-05 --6.716716716716716,1.4263729158212225e-05 --6.696696696696696,1.5254185832000592e-05 --6.676676676676676,1.631014960070239e-05 --6.656656656656656,1.7435717291016563e-05 --6.636636636636636,1.863522560059733e-05 --6.616616616616616,1.9913264055325213e-05 --6.596596596596596,2.127468859727959e-05 --6.576576576576576,2.2724635829895226e-05 --6.556556556556556,2.426853794764979e-05 --6.536536536536536,2.5912138378506833e-05 --6.516516516516516,2.7661508168229998e-05 --6.496496496496496,2.9523063136588983e-05 --6.476476476476476,3.150358183639016e-05 --6.456456456456456,3.361022434719256e-05 --6.436436436436436,3.5850551936503606e-05 --6.416416416416416,3.8232547622191276e-05 --6.396396396396396,4.0764637670801285e-05 --6.376376376376376,4.345571406742176e-05 --6.356356356356356,4.63151579936988e-05 --6.336336336336336,4.935286435156909e-05 --6.316316316316316,5.257926737124008e-05 --6.296296296296296,5.600536734290842e-05 --6.276276276276276,5.964275851267281e-05 --6.256256256256256,6.350365818404851e-05 --6.236236236236236,6.760093706744167e-05 --6.216216216216216,7.194815092088287e-05 --6.196196196196196,7.655957352624463e-05 --6.176176176176176,8.145023104608553e-05 --6.156156156156156,8.663593780715748e-05 --6.136136136136136,9.213333355749476e-05 --6.116116116116116,9.795992224485415e-05 --6.096096096096096,0.00010413411236510995 --6.076076076076076,0.00011067525893000403 --6.056056056056056,0.00011760370710442046 --6.036036036036036,0.0001249408375640866 --6.016016016016016,0.0001327091136252933 --5.995995995995996,0.00014093213019887355 --5.975975975975976,0.00014963466462127818 --5.955955955955956,0.00015884272941613561 --5.935935935935936,0.0001685836270401698 --5.915915915915916,0.00017888600666777975 --5.895895895895896,0.00018977992306894084 --5.875875875875876,0.00020129689763538565 --5.8558558558558556,0.00021346998161022183 --5.8358358358358355,0.00022633382157628671 --5.8158158158158155,0.00023992472725856636 --5.7957957957957955,0.0002542807416959667 --5.7757757757757755,0.0002694417138375578 --5.7557557557557555,0.0002854493736181665 --5.7357357357357355,0.0003023474095678058 --5.7157157157157155,0.00032018154900895126 --5.6956956956956954,0.0003389996408950473 --5.675675675675675,0.00035885174134287574 --5.655655655655655,0.0003797902019105335 --5.635635635635635,0.0004018697606717221 --5.615615615615615,0.0004251476361358544 --5.595595595595595,0.0004496836240621328 --5.575575575575575,0.00047554019721421945 --5.555555555555555,0.0005027826081004157 --5.535535535535535,0.0005314789947423646 --5.515515515515515,0.0005617004895132139 --5.495495495495495,0.0005935213310838689 --5.475475475475475,0.0006270189795134673 --5.455455455455455,0.0006622742345174681 --5.435435435435435,0.0006993713569438073 --5.415415415415415,0.0007383981934843471 --5.395395395395395,0.000779446304645428 --5.375375375375375,0.0008226110959976018 --5.355355355355355,0.000867991952720666 --5.335335335335335,0.0009156923774558751 --5.315315315315315,0.0009658201314726541 --5.295295295295295,0.001018487379152321 --5.275275275275275,0.0010738108357861902 --5.255255255255255,0.0011319119186799756 --5.235235235235235,0.001192916901550638 --5.215215215215215,0.0012569570721957229 --5.195195195195195,0.0013241688934087711 --5.175175175175175,0.001394694167107605 --5.155155155155155,0.0014686802016351133 --5.135135135135135,0.0015462799821846208 --5.115115115115115,0.0016276523442940464 --5.095095095095095,0.0017129621503447277 --5.075075075075075,0.0018023804689920857 --5.055055055055055,0.0018960847574462532 --5.035035035035035,0.001994259046511198 --5.015015015015015,0.0020970941282810306 --4.994994994994995,0.0022047877463817387 --4.974974974974975,0.0023175447886358397 --4.954954954954955,0.002435577482016225 --4.934934934934935,0.002559105589743716 --4.914914914914915,0.0026883566103707754 --4.894894894894895,0.0028235659786812048 --4.874874874874875,0.002964977268222571 --4.854854854854855,0.003112842395274624 --4.834834834834835,0.0032674218240429324 --4.814814814814815,0.003428984772852527 --4.794794794794795,0.0035978094211013725 --4.774774774774775,0.00377418311671811 --4.754754754754755,0.003958402583852563 --4.734734734734735,0.004150774130511219 --4.714714714714715,0.004351613855833014 --4.694694694694695,0.004561247856683402 --4.674674674674675,0.004780012433227109 --4.654654654654655,0.005008254293121478 --4.634634634634635,0.005246330753953948 --4.614614614614615,0.0054946099435278575 --4.594594594594595,0.00575347099758133 --4.574574574574575,0.006023304254504144 --4.554554554554555,0.006304511446596883 --4.534534534534535,0.006597505887396182 --4.514514514514515,0.006902712654568585 --4.494494494494495,0.007220568767854154 --4.474474474474475,0.007551523361519132 --4.454454454454455,0.007896037850754864 --4.434434434434435,0.008254586091437772 --4.414414414414415,0.008627654532642649 --4.394394394394395,0.009015742361278398 --4.374374374374375,0.009419361638192679 --4.354354354354355,0.00983903742506844 --4.334334334334335,0.010275307901411965 --4.314314314314315,0.01072872447090897 --4.2942942942942945,0.011199851856401556 --4.2742742742742745,0.01168926818271556 --4.2542542542542545,0.012197565046544496 --4.2342342342342345,0.012725347572573213 --4.2142142142142145,0.013273234455001096 --4.1941941941941945,0.013841857983602079 --4.1741741741741745,0.014431864053436409 --4.1541541541541545,0.015043912157306556 --4.134134134134134,0.015678675360028607 --4.114114114114114,0.016336840253568966 --4.094094094094094,0.017019106892075923 --4.074074074074074,0.017726188705815753 --4.054054054054054,0.018458812393004165 --4.034034034034034,0.019217717788505423 --4.014014014014014,0.020003657708354907 --3.9939939939939944,0.02081739776904414 --3.9739739739739743,0.02165971618049301 --3.9539539539539543,0.022531403511619683 --3.9339339339339343,0.023433262427407193 --3.9139139139139143,0.024366107396354447 --3.8938938938938943,0.02533076436719051 --3.8738738738738743,0.026328070413723918 --3.8538538538538543,0.027358873346693253 --3.8338338338338342,0.02842403129148174 --3.8138138138138142,0.029524412230557802 --3.7937937937937942,0.030660893509504135 --3.773773773773774,0.03183436130550208 --3.753753753753754,0.03304571005714362 --3.733733733733734,0.0342958418544526 --3.713713713713714,0.03558566578800867 --3.693693693693694,0.03691609725608191 --3.673673673673674,0.03828805722870484 --3.653653653653654,0.039702471467628966 --3.633633633633634,0.04116026970113942 --3.613613613613614,0.042662384752728134 --3.593593593593594,0.044209751622660116 --3.573573573573573,0.0458033065215029 --3.553553553553553,0.047443985854729656 --3.533533533533533,0.04913272515755299 --3.513513513513513,0.050870457979193213 --3.493493493493493,0.05265811471584135 --3.473473473473473,0.05449662139163453 --3.453453453453453,0.05638689838702504 --3.433433433433433,0.05832985911399387 --3.413413413413413,0.0603264086376319 --3.393393393393393,0.062377442243692585 --3.373373373373373,0.064483843951803 --3.353353353353353,0.06664648497411085 --3.333333333333333,0.06886622211924037 --3.313313313313313,0.07114389614153088 --3.293293293293293,0.07348033003563922 --3.273273273273273,0.07587632727669916 --3.253253253253253,0.07833267000635018 --3.233233233233233,0.08085011716507168 --3.213213213213213,0.08342940257138931 --3.193193193193193,0.08607123294865582 --3.173173173173173,0.08877628590025081 --3.153153153153153,0.09154520783419165 --3.133133133133133,0.0943786118383004 --3.113113113113113,0.09727707550723183 --3.093093093093093,0.10024113872283032 --3.073073073073073,0.10327130138945494 --3.053053053053053,0.10636802112608579 --3.033033033033033,0.10953171091720558 --3.013013013013013,0.11276273672463424 --2.992992992992993,0.11606141506268455 --2.972972972972973,0.11942801053920006 --2.952952952952953,0.1228627333652338 --2.932932932932933,0.12636573683632818 --2.9129129129129128,0.1299371147885596 --2.8928928928928928,0.1335768990327204 --2.8728728728728727,0.1372850567702184 --2.8528528528528527,0.14106148799448787 --2.8328328328328327,0.1449060228819167 --2.8128128128128127,0.14881841917651079 --2.7927927927927927,0.15279835957272928 --2.7727727727727727,0.15684544910113893 --2.7527527527527527,0.16095921252174966 --2.7327327327327327,0.16513909173010413 --2.7127127127127126,0.16938444318140403 --2.6926926926926926,0.17369453533816254 --2.6726726726726726,0.17806854614707487 --2.6526526526526526,0.18250556055099768 --2.6326326326326326,0.18700456804211996 --2.6126126126126126,0.19156446026259658 --2.5925925925925926,0.19618402865909465 --2.5725725725725725,0.2008619621978751 --2.5525525525525525,0.20559684514719556 --2.5325325325325325,0.2103871549339737 --2.5125125125125125,0.2152312600817946 --2.4924924924924925,0.22012741823747614 --2.4724724724724725,0.22507377429352604 --2.4524524524524525,0.23006835861392994 --2.4324324324324325,0.23510908537080208 --2.4124124124124124,0.24019375099950463 --2.3923923923923924,0.24532003277990322 --2.3723723723723724,0.2504854875514676 --2.3523523523523524,0.25568755056995285 --2.3323323323323324,0.2609235345133989 --2.3123123123123124,0.26619062864517573 --2.2922922922922924,0.27148589814176244 --2.2722722722722724,0.27680628359289655 --2.2522522522522523,0.28214860068164466 --2.2322322322322323,0.28750954005185 --2.2122122122122123,0.29288566737028165 --2.1921921921921923,0.2982734235906623 --2.1721721721721723,0.3036691254265737 --2.1521521521521523,0.3090689660400416 --2.1321321321321323,0.31446901595237053 --2.1121121121121122,0.3198652241835473 --2.0920920920920922,0.3252534196262526 --2.0720720720720722,0.330629312660209 --2.052052052052052,0.33598849701226363 --2.032032032032032,0.3413264518672368 --2.012012012012012,0.3466385442341817 --1.9919919919919913,0.3519200315722841 --1.9719719719719713,0.3571660646801803 --1.9519519519519513,0.3623716908520156 --1.9319319319319312,0.3675318573030495 --1.9119119119119112,0.37264141486710983 --1.8918918918918912,0.3776951219676369 --1.8718718718718712,0.3826876488634936 --1.8518518518518512,0.3876135821701197 --1.8318318318318312,0.39246742965598913 --1.8118118118118112,0.3972436253136903 --1.7917917917917912,0.401936534704289 --1.7717717717717711,0.40654046057295334 --1.7517517517517511,0.41104964873312405 --1.7317317317317311,0.41545829421579805 --1.711711711711711,0.41976054767977017 --1.691691691691691,0.423950522077931 --1.671671671671671,0.4280222995739732 --1.651651651651651,0.4319699387030971 --1.631631631631631,0.43578748176953475 --1.611611611611611,0.43946896247294936 --1.591591591591591,0.4430084137549828 --1.571571571571571,0.4463998758564555 --1.551551551551551,0.44963740457495227 --1.531531531531531,0.4527150797117528 --1.511511511511511,0.4556270136963157 --1.491491491491491,0.4583673603757667 --1.471471471471471,0.4609303239561081 --1.451451451451451,0.4633101680811427 --1.431431431431431,0.46550122503440133 --1.411411411411411,0.46749790504867855 --1.391391391391391,0.4692947057071206 --1.3713713713713709,0.4708862214191754 --1.3513513513513509,0.47226715295410504 --1.3313313313313309,0.4734323170141925 --1.3113113113113108,0.474376655829227 --1.2912912912912908,0.47509524675335163 --1.2712712712712708,0.4755833118448928 --1.2512512512512508,0.47583622740936404 --1.2312312312312308,0.47584953348546066 --1.2112112112112108,0.47561894325352555 --1.1911911911911908,0.4751403523456854 --1.1711711711711708,0.4744098480366173 --1.1511511511511507,0.4734237182937297 --1.1311311311311307,0.47217846066540864 --1.1111111111111107,0.4706707909859138 --1.0910910910910907,0.46889765187548965 --1.0710710710710707,0.4668562210143071 --1.0510510510510507,0.46454391916895027 --1.0310310310310307,0.4619584179503327 --1.0110110110110107,0.45909764728215247 --0.9909909909909906,0.4559598025592853 --0.9709709709709706,0.45254335147586633 --0.9509509509509506,0.4488470405032282 --0.9309309309309306,0.44486990099833645 --0.9109109109109106,0.4406112549239086 --0.8908908908908906,0.43607072016199944 --0.8708708708708706,0.43124821540350194 --0.8508508508508505,0.4261439645967348 --0.8308308308308305,0.4207585009390703 --0.8108108108108105,0.41509267039639447 --0.7907907907907905,0.4091476347360894 --0.7707707707707705,0.40292487406017524 --0.7507507507507505,0.3964261888262516 --0.7307307307307305,0.3896537013449287 --0.7107107107107105,0.38260985674353837 --0.6906906906906904,0.3752974233870535 --0.6706706706706704,0.3677194927483342 --0.6506506506506504,0.359879478721034 --0.6306306306306304,0.3517811163697624 --0.6106106106106104,0.3434284601133834 --0.5905905905905904,0.33482588133865004 --0.5705705705705704,0.3259780654427104 --0.5505505505505504,0.3168900083043852 --0.5305305305305303,0.3075670121854888 --0.5105105105105103,0.29801468106485723 --0.4904904904904903,0.2882389154091395 --0.4704704704704703,0.27824590638580954 --0.4504504504504503,0.2680421295252516 --0.4304304304304303,0.2576343378401671 --0.41041041041041026,0.24702955441193125 --0.39039039039039025,0.23623506445489637 --0.37037037037037024,0.22525840687098933 --0.3503503503503502,0.21410736530827468 --0.3303303303303302,0.20278995873845546 --0.3103103103103102,0.19131443156954947 --0.2902902902902902,0.17968924331120906 --0.2702702702702702,0.16792305781134376 --0.25025025025025016,0.15602473208385073 --0.23023023023023015,0.14400330474835524 --0.21021021021021014,0.1318679841039111 --0.19019019019019012,0.11962813585960007 --0.1701701701701701,0.10729327054590174 --0.1501501501501501,0.09487303063157487 --0.13013013013013008,0.08237717737159582 --0.11011011011011007,0.06981557741243653 --0.09009009009009006,0.05719818918163008 --0.07007007007007005,0.04453504908916654 --0.05005005005005003,0.03183625756877909 --0.03003003003003002,0.01911196498762333 --0.010010010010010006,0.006372357453216047 -0.010010010010010006,0.006372357453216047 -0.03003003003003002,0.01911196498762333 -0.05005005005005003,0.03183625756877909 -0.07007007007007005,0.04453504908916654 -0.09009009009009006,0.05719818918163008 -0.11011011011011007,0.06981557741243653 -0.13013013013013008,0.08237717737159582 -0.1501501501501501,0.09487303063157487 -0.1701701701701701,0.10729327054590174 -0.19019019019019012,0.11962813585960007 -0.21021021021021014,0.1318679841039111 -0.23023023023023015,0.14400330474835524 -0.25025025025025016,0.15602473208385073 -0.2702702702702702,0.16792305781134376 -0.2902902902902902,0.17968924331120906 -0.3103103103103102,0.19131443156954947 -0.3303303303303302,0.20278995873845546 -0.3503503503503502,0.21410736530827468 -0.37037037037037024,0.22525840687098933 -0.39039039039039025,0.23623506445489637 -0.41041041041041026,0.24702955441193125 -0.4304304304304303,0.2576343378401671 -0.4504504504504503,0.2680421295252516 -0.4704704704704703,0.27824590638580954 -0.4904904904904903,0.2882389154091395 -0.5105105105105103,0.29801468106485723 -0.5305305305305303,0.3075670121854888 -0.5505505505505504,0.3168900083043852 -0.5705705705705704,0.3259780654427104 -0.5905905905905904,0.33482588133865004 -0.6106106106106104,0.3434284601133834 -0.6306306306306304,0.3517811163697624 -0.6506506506506504,0.359879478721034 -0.6706706706706704,0.3677194927483342 -0.6906906906906904,0.3752974233870535 -0.7107107107107105,0.38260985674353837 -0.7307307307307305,0.3896537013449287 -0.7507507507507505,0.3964261888262516 -0.7707707707707705,0.40292487406017524 -0.7907907907907905,0.4091476347360894 -0.8108108108108105,0.41509267039639447 -0.8308308308308305,0.4207585009390703 -0.8508508508508505,0.4261439645967348 -0.8708708708708706,0.43124821540350194 -0.8908908908908906,0.43607072016199944 -0.9109109109109106,0.4406112549239086 -0.9309309309309306,0.44486990099833645 -0.9509509509509506,0.4488470405032282 -0.9709709709709706,0.45254335147586633 -0.9909909909909906,0.4559598025592853 -1.0110110110110107,0.45909764728215247 -1.0310310310310307,0.4619584179503327 -1.0510510510510507,0.46454391916895027 -1.0710710710710707,0.4668562210143071 -1.0910910910910907,0.46889765187548965 -1.1111111111111107,0.4706707909859138 -1.1311311311311307,0.47217846066540864 -1.1511511511511507,0.4734237182937297 -1.1711711711711708,0.4744098480366173 -1.1911911911911908,0.4751403523456854 -1.2112112112112108,0.47561894325352555 -1.2312312312312308,0.47584953348546066 -1.2512512512512508,0.47583622740936404 -1.2712712712712708,0.4755833118448928 -1.2912912912912908,0.47509524675335163 -1.3113113113113108,0.474376655829227 -1.3313313313313309,0.4734323170141925 -1.3513513513513509,0.47226715295410504 -1.3713713713713709,0.4708862214191754 -1.391391391391391,0.4692947057071206 -1.411411411411411,0.46749790504867855 -1.431431431431431,0.46550122503440133 -1.451451451451451,0.4633101680811427 -1.471471471471471,0.4609303239561081 -1.491491491491491,0.4583673603757667 -1.511511511511511,0.4556270136963157 -1.531531531531531,0.4527150797117528 -1.551551551551551,0.44963740457495227 -1.571571571571571,0.4463998758564555 -1.591591591591591,0.4430084137549828 -1.611611611611611,0.43946896247294936 -1.631631631631631,0.43578748176953475 -1.651651651651651,0.4319699387030971 -1.671671671671671,0.4280222995739732 -1.691691691691691,0.423950522077931 -1.711711711711711,0.41976054767977017 -1.7317317317317311,0.41545829421579805 -1.7517517517517511,0.41104964873312405 -1.7717717717717711,0.40654046057295334 -1.7917917917917912,0.401936534704289 -1.8118118118118112,0.3972436253136903 -1.8318318318318312,0.39246742965598913 -1.8518518518518512,0.3876135821701197 -1.8718718718718712,0.3826876488634936 -1.8918918918918912,0.3776951219676369 -1.9119119119119112,0.37264141486710983 -1.9319319319319312,0.3675318573030495 -1.9519519519519513,0.3623716908520156 -1.9719719719719713,0.3571660646801803 -1.9919919919919913,0.3519200315722841 -2.0120120120120113,0.34663854423418194 -2.0320320320320313,0.3413264518672369 -2.0520520520520513,0.3359884970122639 -2.0720720720720713,0.3306293126602093 -2.0920920920920913,0.32525341962625287 -2.1121121121121114,0.31986522418354757 -2.1321321321321314,0.31446901595237076 -2.1521521521521514,0.30906896604004186 -2.1721721721721714,0.30366912542657387 -2.1921921921921914,0.29827342359066256 -2.2122122122122114,0.29288566737028193 -2.2322322322322314,0.2875095400518502 -2.2522522522522515,0.28214860068164493 -2.2722722722722715,0.27680628359289683 -2.2922922922922915,0.27148589814176277 -2.3123123123123115,0.2661906286451759 -2.3323323323323315,0.2609235345133992 -2.3523523523523515,0.2556875505699531 -2.3723723723723715,0.2504854875514678 -2.3923923923923915,0.24532003277990344 -2.4124124124124116,0.2401937509995049 -2.4324324324324316,0.2351090853708023 -2.4524524524524516,0.23006835861393016 -2.4724724724724716,0.22507377429352624 -2.4924924924924916,0.2201274182374764 -2.5125125125125116,0.21523126008179483 -2.5325325325325316,0.21038715493397392 -2.5525525525525516,0.20559684514719578 -2.5725725725725717,0.20086196219787533 -2.5925925925925917,0.19618402865909484 -2.6126126126126117,0.19156446026259677 -2.6326326326326317,0.18700456804212012 -2.6526526526526517,0.18250556055099787 -2.6726726726726717,0.17806854614707507 -2.6926926926926917,0.1736945353381627 -2.7127127127127117,0.16938444318140422 -2.7327327327327318,0.1651390917301043 -2.7527527527527518,0.16095921252174983 -2.772772772772772,0.1568454491011391 -2.792792792792792,0.15279835957272947 -2.812812812812812,0.14881841917651098 -2.8328328328328336,0.1449060228819165 -2.8528528528528536,0.1410614879944877 -2.8728728728728736,0.13728505677021827 -2.8928928928928936,0.13357689903272021 -2.9129129129129137,0.12993711478855943 -2.9329329329329337,0.12636573683632804 -2.9529529529529537,0.12286273336523365 -2.9729729729729737,0.11942801053919991 -2.9929929929929937,0.11606141506268441 -3.0130130130130137,0.11276273672463409 -3.0330330330330337,0.10953171091720544 -3.0530530530530537,0.10636802112608565 -3.0730730730730738,0.10327130138945477 -3.0930930930930938,0.10024113872283019 -3.113113113113114,0.09727707550723172 -3.133133133133134,0.09437861183830025 -3.153153153153154,0.09154520783419148 -3.173173173173174,0.0887762859002507 -3.193193193193194,0.08607123294865572 -3.213213213213214,0.0834294025713892 -3.233233233233234,0.08085011716507157 -3.253253253253254,0.07833267000635004 -3.273273273273274,0.07587632727669905 -3.293293293293294,0.07348033003563913 -3.313313313313314,0.07114389614153079 -3.333333333333334,0.06886622211924029 -3.353353353353354,0.06664648497411077 -3.373373373373374,0.06448384395180291 -3.393393393393394,0.0623774422436925 -3.413413413413414,0.06032640863763181 -3.433433433433434,0.058329859113993784 -3.453453453453454,0.05638689838702498 -3.473473473473474,0.05449662139163443 -3.493493493493494,0.052658114715841274 -3.513513513513514,0.050870457979193116 -3.533533533533534,0.0491327251575529 -3.553553553553554,0.047443985854729594 -3.573573573573574,0.045803306521502836 -3.593593593593594,0.044209751622660116 -3.613613613613614,0.042662384752728134 -3.633633633633634,0.04116026970113942 -3.653653653653654,0.039702471467628966 -3.673673673673674,0.03828805722870484 -3.693693693693694,0.03691609725608191 -3.713713713713714,0.03558566578800867 -3.733733733733734,0.0342958418544526 -3.753753753753754,0.03304571005714362 -3.773773773773774,0.03183436130550208 -3.7937937937937942,0.030660893509504135 -3.8138138138138142,0.029524412230557802 -3.8338338338338342,0.02842403129148174 -3.8538538538538543,0.027358873346693253 -3.8738738738738743,0.026328070413723918 -3.8938938938938943,0.02533076436719051 -3.9139139139139143,0.024366107396354447 -3.9339339339339343,0.023433262427407193 -3.9539539539539543,0.022531403511619683 -3.9739739739739743,0.02165971618049301 -3.9939939939939944,0.02081739776904414 -4.014014014014014,0.020003657708354907 -4.034034034034034,0.019217717788505423 -4.054054054054054,0.018458812393004165 -4.074074074074074,0.017726188705815753 -4.094094094094094,0.017019106892075923 -4.114114114114114,0.016336840253568966 -4.134134134134134,0.015678675360028607 -4.1541541541541545,0.015043912157306556 -4.1741741741741745,0.014431864053436409 -4.1941941941941945,0.013841857983602079 -4.2142142142142145,0.013273234455001096 -4.2342342342342345,0.012725347572573213 -4.2542542542542545,0.012197565046544496 -4.2742742742742745,0.01168926818271556 -4.2942942942942945,0.011199851856401556 -4.314314314314315,0.01072872447090897 -4.334334334334335,0.010275307901411965 -4.354354354354355,0.00983903742506844 -4.374374374374375,0.009419361638192679 -4.394394394394395,0.009015742361278398 -4.414414414414415,0.008627654532642649 -4.434434434434435,0.008254586091437772 -4.454454454454455,0.007896037850754864 -4.474474474474475,0.007551523361519132 -4.494494494494495,0.007220568767854154 -4.514514514514515,0.006902712654568585 -4.534534534534535,0.006597505887396182 -4.554554554554555,0.006304511446596883 -4.574574574574575,0.006023304254504144 -4.594594594594595,0.00575347099758133 -4.614614614614615,0.0054946099435278575 -4.634634634634635,0.005246330753953948 -4.654654654654655,0.005008254293121478 -4.674674674674675,0.004780012433227109 -4.694694694694695,0.004561247856683402 -4.714714714714715,0.004351613855833014 -4.734734734734735,0.004150774130511219 -4.754754754754755,0.003958402583852563 -4.774774774774775,0.00377418311671811 -4.794794794794795,0.0035978094211013725 -4.814814814814815,0.003428984772852527 -4.834834834834835,0.0032674218240429324 -4.854854854854855,0.003112842395274624 -4.874874874874875,0.002964977268222571 -4.894894894894895,0.0028235659786812048 -4.914914914914915,0.0026883566103707754 -4.934934934934935,0.002559105589743716 -4.954954954954955,0.002435577482016225 -4.974974974974975,0.0023175447886358397 -4.994994994994995,0.0022047877463817387 -5.015015015015015,0.0020970941282810306 -5.035035035035035,0.001994259046511198 -5.055055055055055,0.0018960847574462532 -5.075075075075075,0.0018023804689920857 -5.095095095095095,0.0017129621503447277 -5.115115115115115,0.0016276523442940464 -5.135135135135135,0.0015462799821846208 -5.155155155155155,0.0014686802016351133 -5.175175175175175,0.001394694167107605 -5.195195195195195,0.0013241688934087711 -5.215215215215215,0.0012569570721957229 -5.235235235235235,0.001192916901550638 -5.255255255255255,0.0011319119186799756 -5.275275275275275,0.0010738108357861902 -5.295295295295295,0.001018487379152321 -5.315315315315315,0.0009658201314726541 -5.335335335335335,0.0009156923774558751 -5.355355355355355,0.000867991952720666 -5.375375375375375,0.0008226110959976018 -5.395395395395395,0.000779446304645428 -5.415415415415415,0.0007383981934843471 -5.435435435435435,0.0006993713569438073 -5.455455455455455,0.0006622742345174681 -5.475475475475475,0.0006270189795134673 -5.495495495495495,0.0005935213310838689 -5.515515515515515,0.0005617004895132139 -5.535535535535535,0.0005314789947423646 -5.555555555555555,0.0005027826081004157 -5.575575575575575,0.00047554019721421945 -5.595595595595595,0.0004496836240621328 -5.615615615615615,0.0004251476361358544 -5.635635635635635,0.0004018697606717221 -5.655655655655655,0.0003797902019105335 -5.675675675675675,0.00035885174134287574 -5.6956956956956954,0.0003389996408950473 -5.7157157157157155,0.00032018154900895126 -5.7357357357357355,0.0003023474095678058 -5.7557557557557555,0.0002854493736181665 -5.7757757757757755,0.0002694417138375578 -5.7957957957957955,0.0002542807416959667 -5.8158158158158155,0.00023992472725856636 -5.8358358358358355,0.00022633382157628671 -5.8558558558558556,0.00021346998161022183 -5.875875875875876,0.00020129689763538565 -5.895895895895896,0.00018977992306894084 -5.915915915915916,0.00017888600666777975 -5.935935935935936,0.0001685836270401698 -5.955955955955956,0.00015884272941613561 -5.975975975975976,0.00014963466462127818 -5.995995995995996,0.00014093213019887355 -6.016016016016017,0.00013270911362529258 -6.0360360360360374,0.0001249408375640859 -6.0560560560560575,0.00011760370710441984 -6.0760760760760775,0.00011067525893000344 -6.0960960960960975,0.00010413411236510938 -6.1161161161161175,9.795992224485362e-05 -6.1361361361361375,9.213333355749412e-05 -6.1561561561561575,8.663593780715703e-05 -6.1761761761761775,8.145023104608508e-05 -6.1961961961961975,7.65595735262442e-05 -6.216216216216218,7.194815092088248e-05 -6.236236236236238,6.76009370674413e-05 -6.256256256256258,6.350365818404818e-05 -6.276276276276278,5.9642758512672495e-05 -6.296296296296298,5.6005367342908116e-05 -6.316316316316318,5.25792673712398e-05 -6.336336336336338,4.9352864351568826e-05 -6.356356356356358,4.6315157993698466e-05 -6.376376376376378,4.3455714067421535e-05 -6.396396396396398,4.076463767080106e-05 -6.416416416416418,3.8232547622191e-05 -6.436436436436438,3.585055193650334e-05 -6.456456456456458,3.361022434719238e-05 -6.476476476476478,3.150358183638999e-05 -6.496496496496498,2.9523063136588824e-05 -6.516516516516518,2.766150816822985e-05 -6.536536536536538,2.5912138378506647e-05 -6.556556556556558,2.426853794764966e-05 -6.576576576576578,2.2724635829895104e-05 -6.596596596596598,2.1274688597279437e-05 -6.616616616616618,1.9913264055325105e-05 -6.636636636636638,1.8635225600597198e-05 -6.656656656656658,1.7435717291016437e-05 -6.676676676676678,1.63101496007023e-05 -6.696696696696698,1.5254185832000485e-05 -6.716716716716718,1.426372915821215e-05 -6.736736736736738,1.3334910271392269e-05 -6.756756756756758,1.246407561042e-05 -6.776776776776778,1.1647776145362758e-05 -6.796796796796798,1.0882756694959527e-05 -6.816816816816818,1.0165945754836208e-05 -6.836836836836838,9.4944458148363e-06 -6.856856856856858,8.865524144603866e-06 -6.876876876876878,8.276604027292432e-06 -6.896896896896898,7.7252564219929e-06 -6.916916916916918,7.209192036175401e-06 -6.936936936936938,6.726253790124483e-06 -6.956956956956958,6.274409656014098e-06 -6.976976976976978,5.851745854918375e-06 -6.996996996996998,5.456460395685988e-06 -7.017017017017018,5.086856940220749e-06 -7.037037037037038,4.741338980308082e-06 -7.057057057057058,4.418404311707375e-06 -7.077077077077078,4.116639791792951e-06 -7.097097097097098,3.834716367572807e-06 -7.117117117117118,3.571384361443521e-06 -7.137137137137138,3.3254690025527993e-06 -7.157157157157158,3.0958661921378847e-06 -7.177177177177178,2.8815384916887304e-06 -7.197197197197198,2.6815113232498177e-06 -7.217217217217218,2.4948693716240375e-06 -7.237237237237238,2.320753178676375e-06 -7.257257257257258,2.1583559203545567e-06 -7.277277277277278,2.0069203574486368e-06 -7.297297297297298,1.8657359515020388e-06 -7.317317317317318,1.7341361376632196e-06 -7.337337337337338,1.6114957466299333e-06 -7.357357357357358,1.4972285681877958e-06 -7.377377377377378,1.390785049181357e-06 -7.397397397397398,1.2916501190799161e-06 -7.417417417417418,1.1993411366118397e-06 -7.437437437437438,1.1134059512408126e-06 -7.457457457457458,1.0334210735453162e-06 -7.477477477477478,9.589899488392652e-07 -7.497497497497498,8.89741328637246e-07 -7.517517517517518,8.253277348227345e-07 -7.537537537537538,7.654240116221353e-07 -7.557557557557558,7.097259607219805e-07 -7.577577577577578,6.579490550913645e-07 -7.5975975975975985,6.098272272870159e-07 -7.6176176176176185,5.651117282246155e-07 -7.6376376376376385,5.235700525974022e-07 -7.6576576576576585,4.849849273120124e-07 -7.6776776776776785,4.4915335949220685e-07 -7.6976976976976985,4.1588574077388435e-07 -7.7177177177177185,3.8500500477996553e-07 -7.7377377377377385,3.563458348214471e-07 -7.7577577577577586,3.2975391902162033e-07 -7.777777777777779,3.050852502042829e-07 -7.797797797797799,2.8220546802401906e-07 -7.817817817817819,2.60989240947568e-07 -7.837837837837839,2.4131968582014115e-07 -7.857857857857859,2.2308782286955646e-07 -7.877877877877879,2.061920641144635e-07 -7.897897897897899,1.905377332509137e-07 -7.917917917917919,1.7603661519438925e-07 -7.937937937937939,1.6260653355226847e-07 -7.957957957957959,1.5017095439482947e-07 -7.977977977977979,1.3865861478146696e-07 -7.997997997997999,1.2800317458300336e-07 -8.018018018018019,1.1814289022100969e-07 -8.038038038038039,1.090203090210869e-07 -8.058058058058059,1.005819829492733e-07 -8.078078078078079,9.277820056931877e-08 -8.098098098098099,8.556273612362166e-08 -8.118118118118119,7.889261470237839e-08 -8.138138138138139,7.272789252404431e-08 -8.158158158158159,6.703145140571939e-08 -8.178178178178179,6.176880655469655e-08 -8.198198198198199,5.6907926862259885e-08 -8.218218218218219,5.2419066928043386e-08 -8.238238238238239,4.8274610087966266e-08 -8.258258258258259,4.444892176108461e-08 -8.278278278278279,4.0918212470738604e-08 -8.298298298298299,3.766040993324921e-08 -8.318318318318319,3.465503964323947e-08 -8.338338338338339,3.188311341850448e-08 -8.358358358358359,2.9327025399350928e-08 -8.378378378378379,2.697045502755155e-08 -8.398398398398399,2.4798276558596732e-08 -8.418418418418419,2.279647468787558e-08 -8.438438438438439,2.0952065896847053e-08 -8.458458458458459,1.925302514925403e-08 -8.478478478478479,1.768821759006418e-08 -8.498498498498499,1.6247334921157145e-08 -8.518518518518519,1.4920836147889933e-08 -8.538538538538539,1.3699892409622672e-08 -8.558558558558559,1.2576335625140197e-08 -8.578578578578579,1.1542610700715167e-08 -8.598598598598599,1.0591731064385666e-08 -8.618618618618619,9.717237304914516e-09 -8.63863863863864,8.913158707911974e-09 -8.65865865865866,8.173977494784034e-09 -8.67867867867868,7.494595582561493e-09 -8.6986986986987,6.870303694316149e-09 -8.71871871871872,6.296752660816444e-09 -8.73873873873874,5.7699267643599956e-09 -8.75875875875876,5.28611898537923e-09 -8.77877877877878,4.841908021483401e-09 -8.7987987987988,4.434136957112363e-09 -8.81881881881882,4.059893469963204e-09 -8.83883883883884,3.716491467841983e-09 -8.85885885885886,3.401454056618205e-09 -8.87887887887888,3.1124977465452213e-09 -8.8988988988989,2.847517810382273e-09 -8.91891891891892,2.604574712536835e-09 -8.93893893893894,2.3818815338630113e-09 -8.95895895895896,2.1777923218238912e-09 -8.97897897897898,1.9907913004742718e-09 -8.998998998999,1.8194828791637996e-09 -9.01901901901902,1.6625824030183372e-09 -9.03903903903904,1.5189075921459597e-09 -9.05905905905906,1.38737062015004e-09 -9.07907907907908,1.266970785931154e-09 -9.0990990990991,1.1567877359357649e-09 -9.11911911911912,1.0559751969774664e-09 -9.13913913913914,9.637551825284225e-10 -9.15915915915916,8.794126379666174e-10 -9.17917917917918,8.022904926806516e-10 -9.1991991991992,7.317850891883775e-10 -9.21921921921922,6.673419615290896e-10 -9.23923923923924,6.084519371509368e-10 -9.25925925925926,5.546475383444925e-10 -9.27927927927928,5.054996609787182e-10 -9.2992992992993,4.6061450988468017e-10 -9.31931931931932,4.1963077171299245e-10 -9.33933933933934,3.8221700746994e-10 -9.35935935935936,3.480692482213214e-10 -9.37937937937938,3.1690877864837094e-10 -9.3993993993994,2.884800942525761e-10 -9.41941941941942,2.6254901904118343e-10 -9.43943943943944,2.3890097148788503e-10 -9.45945945945946,2.1733936745835158e-10 -9.47947947947948,1.9768414962249373e-10 -9.4994994994995,1.7977043364875085e-10 -9.51951951951952,1.6344726219431744e-10 -9.53953953953954,1.4857645837274253e-10 -9.55955955955956,1.3503157100019476e-10 -9.57957957957958,1.226969044971726e-10 -9.5995995995996,1.114666268565524e-10 -9.61961961961962,1.012439495844808e-10 -9.63963963963964,9.194037398035494e-11 -9.65965965965966,8.347499854850021e-11 -9.67967967967968,7.577388272945277e-11 -9.6996996996997,6.876946250516688e-11 -9.71971971971972,6.240001377199487e-11 -9.73973973973974,5.6609159689839135e-11 -9.75975975975976,5.134541850719675e-11 -9.77977977977978,4.656178863156737e-11 -9.7997997997998,4.2215367964389906e-11 -9.81981981981982,3.826700475075735e-11 -9.83983983983984,3.4680977407952604e-11 -9.85985985985986,3.142470099460374e-11 -9.87987987987988,2.8468458165120247e-11 -9.8998998998999,2.57851526231251e-11 -9.91991991991992,2.3350083243845715e-11 -9.93993993993994,2.1140737179795716e-11 -9.95995995995996,1.913660039744377e-11 -9.97997997997998,1.731898421572835e-11 -10.0,1.5670866530993244e-11 diff --git a/graphics/background/z_distribution.typ b/graphics/background/z_distribution.typ deleted file mode 100644 index f0ead54..0000000 --- a/graphics/background/z_distribution.typ +++ /dev/null @@ -1,27 +0,0 @@ -#import "@preview/cetz:0.3.4": canvas -#import "@preview/cetz-plot:0.1.1": plot, chart - -#let data = csv("./z_distribution.csv") -#let data = data.map(value => value.map(v => float(v))) - -#let line_style = (stroke: (paint: black, thickness: 3pt)) -#let dashed = (stroke: (dash: "dashed")) -#canvas({ - plot.plot(size: (11,5), - legend : "south", - legend-style: (orientation: ltr, item: (spacing: 0.5)), - x-tick-step: none, - x-ticks: ((0, [0]), (100, [0])), - y-label: $cal(Q)(1, z), abs(f_"Z" (z))$, - x-label: $z$, - y-tick-step: none, - y-ticks: ((0, [0]), (0.6, [1])), - axis-style: "left", - x-min: -5, - x-max: 5, - y-min: 0, - y-max: 0.6,{ - plot.add((data), style: (stroke: (paint: red, thickness: 3pt)), /*label: [Optimierte PDF]*/) - plot.add(((-5, 0), (0, 0), (0, 0.6), (5, 0.6)), style: line_style, /*label: [Quantisierer]*/) - }) -}) diff --git a/graphics/bruteforce_dist.svg b/graphics/bruteforce_dist.svg deleted file mode 100644 index 194d14a..0000000 --- a/graphics/bruteforce_dist.svg +++ /dev/null @@ -1,3145 +0,0 @@ - - - - - - - - - - - - x - - - - - - - -10 - - - - - -5 - - - - - 0 - - - - - 5 - - - - - 10 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 1000 - - - - - 2000 - - - - - 3000 - - - - - 4000 - - - - - - - Sensible Apprpach - - - - - - - - - - diff --git a/graphics/bruteforce_dist2.svg b/graphics/bruteforce_dist2.svg deleted file mode 100644 index b427359..0000000 --- a/graphics/bruteforce_dist2.svg +++ /dev/null @@ -1,3145 +0,0 @@ - - - - - - - - - - - - x - - - - - - - -10 - - - - - -5 - - - - - 0 - - - - - 5 - - - - - 10 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 1000 - - - - - 2000 - - - - - 3000 - - - - - 4000 - - - - - - - Brute-Force results - - - - - - - - - - diff --git a/graphics/bruteforce_helperdata1.svg b/graphics/bruteforce_helperdata1.svg deleted file mode 100644 index 71cada8..0000000 --- a/graphics/bruteforce_helperdata1.svg +++ /dev/null @@ -1,242 +0,0 @@ - - - - - - - - - - - - Bool Vector - - - - - - - Vector{Bool}[[0], [0], [1]] - - - - - Vector{Bool}[[0], [0], [0]] - - - - - Vector{Bool}[[0], [1], [1]] - - - - - Vector{Bool}[[0], [1], [0]] - - - - - - - - Symbol 1 - - - - - Symbol 2 - - - - - Symbol 3 - - - - - Symbol 4 - - - - - - - - - - - - - - - - - - - - - Source - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 2.0×10⁴ - - - - - 4.0×10⁴ - - - - - 6.0×10⁴ - - - - - 8.0×10⁴ - - - - - 1.0×10⁵ - - - - - - - Count - - - - - - - Helper Data occurrences by quantized bits - - - - - - - - - - diff --git a/graphics/bruteforce_helperdata2.svg b/graphics/bruteforce_helperdata2.svg deleted file mode 100644 index 32a366d..0000000 --- a/graphics/bruteforce_helperdata2.svg +++ /dev/null @@ -1,298 +0,0 @@ - - - - - - - - - - - - Bool Vector - - - - - - - Vector{Bool}[[0], [0], [1]] - - - - - Vector{Bool}[[0], [0], [0]] - - - - - Vector{Bool}[[0], [1], [1]] - - - - - Vector{Bool}[[0], [1], [0]] - - - - - - - - Symbol 1 - - - - - Symbol 2 - - - - - Symbol 3 - - - - - Symbol 4 - - - - - Symbol 5 - - - - - Symbol 6 - - - - - Symbol 7 - - - - - Symbol 8 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Source - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 5.0×10⁴ - - - - - 1.0×10⁵ - - - - - - - Count - - - - - - - Helper Data occurrences by quantized bits - - - - - - - - - - diff --git a/graphics/execution/brute-force-occurs.png b/graphics/execution/brute-force-occurs.png deleted file mode 100644 index ec84674..0000000 Binary files a/graphics/execution/brute-force-occurs.png and /dev/null differ diff --git a/graphics/execution/brute-force.png b/graphics/execution/brute-force.png deleted file mode 100644 index 7a2219a..0000000 Binary files a/graphics/execution/brute-force.png and /dev/null differ diff --git a/graphics/execution/given_codeword.png b/graphics/execution/given_codeword.png deleted file mode 100644 index e12d965..0000000 Binary files a/graphics/execution/given_codeword.png and /dev/null differ diff --git a/graphics/execution/helperdata_occurs.png b/graphics/execution/helperdata_occurs.png deleted file mode 100644 index efbe1f7..0000000 Binary files a/graphics/execution/helperdata_occurs.png and /dev/null differ diff --git a/graphics/execution/recursive.typ b/graphics/execution/recursive.typ deleted file mode 100644 index c86cec4..0000000 --- a/graphics/execution/recursive.typ +++ /dev/null @@ -1,65 +0,0 @@ -#import "@preview/fletcher:0.5.8" as fletcher: diagram, node, edge -#import fletcher.shapes: pill -#import "@preview/touying:0.6.1": * - -#let fletcher-diagram = touying-reducer.with(reduce: fletcher.diagram, cover: fletcher.hide) - -#fletcher-diagram( - spacing: (-3mm, 8mm), // wide columns, narrow rows - node-stroke: 1pt, // outline node shapes - edge-stroke: 1pt, // make lines thicker - mark-scale: 60%, // make arrowheads smaller - node((0,0), [Start], name: ), - pause, - - node((-4, 1), [u1], name: ), - node((4, 1), [u2], name: ), - node(enclose: (, ), stroke: aqua, fill: aqua.lighten(90%), name: ), - edge(, , "->"), - edge(, , "->"), - node((-20mm, 39mm), [n1], shape: pill, name: ), - edge(, , "->"), - pause, - - node((-6, 2), [u11], name: ), - node((-2, 2), [u12], name: ), - node((2, 2), [u21], name: ), - node((6, 2), [u22], name: ), - node(enclose: (, ), stroke: teal, fill: teal.lighten(90%), name: ), - node((-20mm, 21.9mm), [n2], shape: pill, name: ), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - pause, - - node((-7, 3), [u111], name: ), - node((-5, 3), [u112], name: ), - node((-3, 3), [u121], name: ), - node((-1, 3), [u122], name: ), - node((1, 3), [u211], name: ), - node((3, 3), [u212], name: ), - node((5, 3), [u221], name: ), - node((7, 3), [u222], name: ), - - node((-20mm, 4.6mm), [n3], shape: pill, name: ), - - - edge(, , "->"), - - - - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - edge(, , "->"), - - - node(enclose: (, ), stroke: eastern, fill: eastern.lighten(90%), name: ) - -) diff --git a/graphics/execution/recursive_distribution .png b/graphics/execution/recursive_distribution .png deleted file mode 100644 index b9ad89b..0000000 Binary files a/graphics/execution/recursive_distribution .png and /dev/null differ diff --git a/graphics/given_codeword_dist.svg b/graphics/given_codeword_dist.svg deleted file mode 100644 index 2a39f3d..0000000 --- a/graphics/given_codeword_dist.svg +++ /dev/null @@ -1,3153 +0,0 @@ - - - - - - - - - - - - x - - - - - - - -6 - - - - - -4 - - - - - -2 - - - - - 0 - - - - - 2 - - - - - 4 - - - - - 6 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 100 - - - - - 200 - - - - - 300 - - - - - - - Final result of input value optimizaition - - - - - - - - - - diff --git a/graphics/recursive_distribution.svg b/graphics/recursive_distribution.svg deleted file mode 100644 index 432a1ef..0000000 --- a/graphics/recursive_distribution.svg +++ /dev/null @@ -1,3145 +0,0 @@ - - - - - - - - - - - - x - - - - - - - -20 - - - - - -10 - - - - - 0 - - - - - 10 - - - - - 20 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 500 - - - - - 1000 - - - - - 1500 - - - - - 2000 - - - - - - - Final result of recursive method - - - - - - - - - - diff --git a/graphics/recursive_helperdata_dist.svg b/graphics/recursive_helperdata_dist.svg deleted file mode 100644 index a19a882..0000000 --- a/graphics/recursive_helperdata_dist.svg +++ /dev/null @@ -1,274 +0,0 @@ - - - - - - - - - - - - Bool Vector - - - - - - - Vector{Bool}[[0, 0], [0, 0], [0, 0]] - - - - - Vector{Bool}[[0, 0], [0, 0], [1, 1]] - - - - - Vector{Bool}[[0, 0], [1, 1], [0, 0]] - - - - - Vector{Bool}[[0, 0], [1, 1], [1, 1]] - - - - - Vector{Bool}[[0, 1], [1, 0], [1, 0]] - - - - - Vector{Bool}[[0, 1], [1, 0], [0, 1]] - - - - - Vector{Bool}[[0, 1], [0, 1], [1, 0]] - - - - - Vector{Bool}[[0, 1], [0, 1], [0, 1]] - - - - - - - - Symbol 1 - - - - - Symbol 2 - - - - - Symbol 3 - - - - - Symbol 4 - - - - - - - - - - - - - - - - - - - - - Source - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 0 - - - - - 1.0×10⁴ - - - - - 2.0×10⁴ - - - - - 3.0×10⁴ - - - - - 4.0×10⁴ - - - - - 5.0×10⁴ - - - - - - - Count - - - - - - - Helper Data occurrences by quantized bits - - - - - - - - - - diff --git a/main.typ b/main.typ index 849d214..789a589 100644 --- a/main.typ +++ b/main.typ @@ -14,164 +14,12 @@ ), ) -= Ausgangslage += Einführung -== 1-Bit Quantisierung +== Ausgangslage -#figure( - include("./graphics/background/sign-based-overlay.typ"), - // caption: [] -) +== Planung -- Stufe des Quantisiererfunktion nahe des Erwartungswertes der Wahrscheinlichkeitsverteilung += Ergebnisse -== Optimierung der 1-Bit Quantisierung - -- Eingangswerte als Gewichtete Summen - -#v(1em) - -$ f(bold(x), bold(h)) = h_1 x_1 + h_2 x_2 + h_3 x_3 $ - -- $h_i$ als Helperdaten - -#v(1em) - -- Betragsmäßige Maximierung von $f(bold(x), bold(h))$ für möglichst wenige Werte nahe der $0$ - -#v(1em) - -$ max_(h_1, h_2, h_3) |f(bold(x), bold(h))| $ - -== Optimierung der 1-Bit Quantisierung (2) - -#align(horizon)[ -#figure( - include("./graphics/background/z_distribution.typ"), - caption: [Optimierte Sign-Based Quantisierung] -)] - -== Verallgemeinerung auf n-Bit - -- Definition der Quantisierung höherer Ordnung als mehrstufige Funktion - -#v(1em) - -#figure( - include("./graphics/background/two-bit-enroll.typ") -) - -- Problem: Optimale Position der Quantisierergrenzen $g_1$ und $g_2$ - -== Verallgemeinerung auf n-Bit --- Optimierungsbedingung - -- Zwei Möglichkeiten zur optimalen Positionierung der Linearkombinationen: - 1. Beste Approximation zur Mitte einer Quantisiererstufe - 2. Maximierung des Abstandes zur nächstgelegenen Grenze der Linearkombination - -== Verallgemeinerung auf n-Bit --- Algorithmus - -1. Naives Raten der Grenzen $g_(1,2)$ und erste Optimierung -2. Über eCDF der resultierenden Verteilung neue Grenzen definieren, sodass jedes Symbol gleich wahrscheinlich ist - - - -== Verallgemeinerung auf n-Bit --- Probleme - -- Approximation zur Mitte konvergiert, allerdings keine Verbesserung der Fehlerrate -- Maximierung des Abstandes konvergiert nicht - -#figure( -grid( - columns: (1fr, 1fr), - rows: (2), - [//#figure( - #image("./graphics/background/bach/instability/frame_1.png", width: 80%) - #v(-0.5em) - //) - Iteration 1], - [//#figure( - #image("./graphics/background/bach/instability/frame_18.png", width: 80%) - #v(-0.5em) - //) - Iteration 18], -), -) - -= Implementierung - -== Mögliche Lösungen - -- Rekursiver Ansatz - -- Vorgabe des Codeworts - -- Brute-Force Ansatz - -== Rekursiver Ansatz - -1. Teile Verteilung am Erwartungswert auf -2. Addiere weitere Weights ($0.25, 0.125, ...$) -3. Maximiere Abstand zur nächstgelegenen Grenze -4. Teile neue Verteilungen wieder am Erwartungswert auf - -== Rekursiver Ansatz -#align(horizon)[ -#include("./graphics/execution/recursive.typ") -] - -== Rekursiver Ansatz --- Resultierende Verteilung - -#align(horizon)[ -#figure( - image("./graphics/recursive_distribution.svg", width: 60%) -)] - -== Rekursiver Ansatz --- Helperdaten - -#align(horizon)[ - #figure( - image("./graphics/recursive_helperdata_dist.svg", width: 60%) - ) -] - -== Vorgabe des Codeworts - -- Generierung eines zufälligen Schlüssels -- Nutze Quantile der Normalverteilung als vorgegebene Grenzen -- Wähle jeweilige Linearkombination, die am besten das Quantil des Vorgegebenen Bits annähert - -== Vorgabe des Codeworts --- Verteilung - -#figure( - image("./graphics/given_codeword_dist.svg") -) - -== Brute-Force Ansatz - -- Großer Datensatz mit Grenzen -- Führe Optimierung und Quantisierung mit jedem Satz Grenzen durch -- Pearson's Chi-Square Test der Quantisierten Symbole auf Gleichverteilung -- Maximales Resultat des Chi-Square Tests gibt optimale Grenzen zurück - -== Brute-Force Ansatz --- Verteilung - -#figure( - image("./graphics/bruteforce_dist.svg") -) - -== Brute-Force Ansatz --- Helperdaten - -#figure( - image("./graphics/bruteforce_helperdata1.svg") -) - -= Fazit - -- Rekursiver Ansatz generiert gleichverteilte Ausgansverteilungen - - Helperdaten geben Informationen über das Codewort bekannt -- Vorgabe des Codeworts als Bedingung nicht stark genug -- Brute-Force Ansatz findet Gleichverteilungen - - Helperdaten geben keine Informationen bekannt - - Verbesserung der Bitfehlerrate um einen Faktor $10$ - - Vorberechnete Grenzen können auf beliebige Normalverteilungen angewendet werden +== Hier dann