.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plotting/plot_vertex_embedding.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plotting_plot_vertex_embedding.py: .. _vertex_embedding_gallery: Vertex Embedding ======================================== This tutorial covers vertex embedding to visualize simplices and simplicial complexes. Most plotting functions assume that the user can provide x-y-z coordinates for each vertex. However, sometimes data doesn't come with x-y-z coordinates. For example, it might come from a a graph or hypergraph. In this case, we need to find a way to generate these coordinates. OAT provides several tools to help with this: - :func:`oat_python.simplex.networkx_graph_from_simplices` converts a collection of simplices into a NetworkX graph. NetworkX has many built-in graph layout algorithms that can be used to generate x-y or x-y-z coordinates for the vertices. - :func:`oat_python.dissimilarity.hop_distance_for_networkx_graph` computes the hop distance between vertices in a graph. The result is a distance matrix that can be used to generate a vertex embedding, e.g. using multidimensional scaling. - :func:`oat_python.dissimilarity.hop_distance_for_simplices` computes the hop distance between vertices in a collection of simplices. - :func:`oat.plot.vertex_embedding_for_simplices` Offers two methods, controlled by the keyword `method`: - ``spring``: this extracts the underlying graph (consisting of the vertices of the simplices, together with an edge (i,j) for every pair of vertices (i,j) that belong to one or more of the same simplices) - ``hop_mds``: this applies multidimensional scaling to the hop distance (i.e. shortest path distance) on the underlying graph. .. GENERATED FROM PYTHON SOURCE LINES 30-32 Setup ----------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 34-42 .. code-block:: Python import oat_python as oat import networkx as nx import numpy as np import plotly.graph_objects as go .. GENERATED FROM PYTHON SOURCE LINES 43-44 Define a collection of simplices, whose vertices are (i,j) pairs .. GENERATED FROM PYTHON SOURCE LINES 44-53 .. code-block:: Python N = 20 dowker_simplices = [] for i in range(N): for j in range(N): dowker_square = [(i,j), ( i+1,j), (i,j+1), ( i+1,j+1)] dowker_simplices.append(dowker_square) dowker_simplices.append( [ (0,j) for j in range(N) ] ) # Join all vertices in the bottom row dowker_simplices.append( [ (N,j) for j in range(N) ] ) # Join all vertices in the top row .. GENERATED FROM PYTHON SOURCE LINES 54-55 Relabel the (i,j) pairs as integers .. GENERATED FROM PYTHON SOURCE LINES 55-67 .. code-block:: Python xy_tuples = set() for simplex in dowker_simplices: for xy_tuple in simplex: xy_tuples.add(xy_tuple) xy_tuples = list(xy_tuples) vertex_labels = {xy_tuple: k for k, xy_tuple in enumerate(xy_tuples)} simplices = [ [vertex_labels[xy_tuple] for xy_tuple in simplex] for simplex in dowker_simplices ] .. GENERATED FROM PYTHON SOURCE LINES 68-70 Example 1 ----------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 73-76 Generate a vertex embedding ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 76-85 .. code-block:: Python points = oat.plot.vertex_embedding_for_simplices( simplices, dimension = 3, method = "hop_mds", random_state = 0, ) points .. rst-class:: sphx-glr-script-out .. code-block:: none {24: array([-0.94989218, 7.88253791, 5.17438999]), 155: array([-2.35159138, 7.94387987, 4.14283687]), 422: array([-0.97855559, 7.85599702, 5.10083593]), 435: array([-2.34370723, 7.7451072 , 4.16754306]), 249: array([-0.97283746, 7.78637941, 5.11189001]), 391: array([-2.29754181, 7.51792343, 4.28663582]), 210: array([-0.94178467, 7.68710889, 5.19459621]), 345: array([-2.19769575, 7.27648081, 4.46807505]), 167: array([-0.88660494, 7.60159958, 5.26261424]), 180: array([-2.04686365, 7.0025254 , 4.73481564]), 6: array([-0.8160753 , 7.50599697, 5.35724364]), 133: array([-1.83717731, 6.70955859, 5.04751161]), 402: array([-0.72623671, 7.41821122, 5.44862521]), 414: array([-1.56161028, 6.41294601, 5.37548237]), 232: array([-0.62065847, 7.3405257 , 5.53381784]), 369: array([-1.22519825, 6.1529121 , 5.66029528]), 190: array([-0.50064885, 7.28741439, 5.59262313]), 328: array([-0.84634136, 5.96133886, 5.86534499]), 26: array([-0.37322541, 7.23914015, 5.65349754]), 157: array([-0.44267102, 5.8425708 , 5.99258201]), 426: array([-0.24211593, 7.23466698, 5.66228439]), 115: array([-0.03840797, 5.82733267, 6.01276932]), 381: array([-0.12068574, 7.26813769, 5.62724581]), 394: array([0.34238354, 5.91944143, 5.92518927]), 213: array([-0.01618658, 7.33076026, 5.55971189]), 348: array([0.67764928, 6.1095228 , 5.73738699]), 170: array([0.07090428, 7.41182917, 5.4737813 ]), 182: array([0.95188664, 6.37649101, 5.46579322]), 10: array([0.13287272, 7.51250755, 5.36609917]), 136: array([1.15176073, 6.70149633, 5.12325835]), 406: array([0.17662587, 7.61791251, 5.25793568]), 100: array([1.27984705, 7.04192581, 4.75966526]), 234: array([0.2021699 , 7.72358316, 5.15603594]), 372: array([1.34139863, 7.37686291, 4.40371606]), 192: array([0.20986005, 7.82541761, 5.06710146]), 331: array([1.36281847, 7.6775886 , 4.10814131]), 146: array([0.20472481, 7.91479567, 5.00778907]), 160: array([1.34341285, 7.94975359, 3.88565657]), 428: array([0.18776684, 8.00014492, 4.96504841]), 118: array([1.30726902, 8.18509451, 3.75267187]), 383: array([0.81741103, 8.71972453, 4.54461293]), 396: array([1.25302943, 8.38938223, 3.7064776 ]), 307: array([-3.73103629, 7.60919776, 3.22737182]), 279: array([-3.63297222, 7.29612501, 3.34938843]), 97: array([-3.48768561, 6.97105808, 3.55177459]), 68: array([-3.29944582, 6.62108015, 3.83670211]), 326: array([-3.04964166, 6.22524496, 4.22624299]), 294: array([-2.71040205, 5.77439478, 4.71592914]), 266: array([-2.26100166, 5.3023532 , 5.23067311]), 81: array([-1.71638399, 4.90405979, 5.64040492]), 56: array([-1.11369678, 4.6216169 , 5.9134108 ]), 309: array([-0.48950558, 4.47516796, 6.04719152]), 281: array([0.12810204, 4.46840134, 6.05142793]), 98: array([0.71547374, 4.601654 , 5.93094469]), 70: array([1.24955625, 4.87129768, 5.68549255]), 43: array([1.70385711, 5.26534274, 5.31461672]), 296: array([2.04866414, 5.76163453, 4.82204973]), 268: array([2.26577211, 6.30854771, 4.24789206]), 82: array([2.37873297, 6.82629731, 3.69633676]), 57: array([2.41919309, 7.28598756, 3.23786066]), 311: array([2.44567546, 7.67455749, 2.90892047]), 282: array([2.45155518, 8.02852725, 2.66843 ]), 252: array([2.43297812, 8.35722538, 2.51329603]), 58: array([-4.96147266, 6.96050247, 2.51554756]), 28: array([-4.76105759, 6.586833 , 2.72464339]), 283: array([-4.50412864, 6.20846496, 2.98240152]), 253: array([-4.19765868, 5.80632179, 3.32365381]), 71: array([-3.8330343 , 5.35000297, 3.77347763]), 44: array([-3.37204648, 4.81762267, 4.33954413]), 13: array([-2.77812675, 4.25650435, 4.92713839]), 269: array([-2.07340506, 3.78961213, 5.38019476]), 237: array([-1.31021191, 3.47285924, 5.66305615]), 60: array([-0.53091469, 3.31836159, 5.78913691]), 30: array([0.23642654, 3.32279919, 5.77723296]), 285: array([0.97064549, 3.48243185, 5.63630813]), 255: array([1.64970761, 3.79523149, 5.36444696]), 218: array([2.24441881, 4.25774906, 4.95108819]), 46: array([2.71707031, 4.84926478, 4.39269582]), 14: array([3.03993528, 5.50656676, 3.73243234]), 271: array([3.22428284, 6.14520662, 3.07132021]), 239: array([3.34752839, 6.69389736, 2.52011181]), 62: array([3.45059913, 7.16667149, 2.09803275]), 32: array([3.53880422, 7.59207598, 1.78321633]), 436: array([3.59551162, 7.99624148, 1.54553054]), 216: array([-6.0147551 , 6.09947736, 1.98353277]), 176: array([-5.70189022, 5.71981545, 2.2150379 ]), 12: array([-5.3384234 , 5.32779991, 2.51464017]), 411: array([-4.91650748, 4.91579142, 2.86864895]), 365: array([-4.43226007, 4.43204253, 3.35665568]), 198: array([-3.85207293, 3.88510628, 3.92576632]), 152: array([-3.14479109, 3.31982041, 4.49396921]), 433: array([-2.32724876, 2.83779916, 4.94172908]), 389: array([-1.45661586, 2.51902654, 5.21014917]), 217: array([-0.57270714, 2.36929832, 5.32188359]), 178: array([0.29759964, 2.38472019, 5.29623171]), 131: array([1.13385405, 2.56050129, 5.14294222]), 413: array([1.91478998, 2.89466219, 4.86012886]), 367: array([2.61204101, 3.38396482, 4.43721968]), 199: array([3.18868911, 4.00969903, 3.86751137]), 154: array([3.61042484, 4.71794968, 3.18178901]), 434: array([3.90480798, 5.39793838, 2.4869837 ]), 390: array([4.13881849, 5.98356132, 1.90208326]), 344: array([4.34116398, 6.49586802, 1.43075317]), 179: array([4.52255407, 6.95871167, 1.06216947]), 132: array([4.67914628, 7.3950039 , 0.77893693]), 352: array([-6.90670086, 5.04350964, 1.683717 ]), 315: array([-6.46501372, 4.74386116, 1.81432488]), 139: array([-6.00093412, 4.37105687, 2.11747821]), 103: array([-5.47744524, 3.98399811, 2.46701981]), 375: array([-4.88483741, 3.51865616, 2.93753023]), 334: array([-4.19617605, 3.00332064, 3.46870241]), 163: array([-3.39750018, 2.47557433, 3.98613661]), 121: array([-2.5061245 , 2.0303246 , 4.38494691]), 86: array([-1.56713123, 1.73355761, 4.62378214]), 354: array([-0.6160078, 1.5987515, 4.7163723]), 317: array([0.32209078, 1.62508214, 4.67871657]), 142: array([1.22710298, 1.80900985, 4.51918685]), 106: array([2.07819047, 2.14722155, 4.23720169]), 377: array([2.85000499, 2.63294783, 3.82592658]), 337: array([3.50826377, 3.25531568, 3.27539981]), 301: array([4.03916268, 3.93776579, 2.62664419]), 124: array([4.4573906 , 4.60038513, 1.96419682]), 89: array([4.79783972, 5.19822877, 1.3596386 ]), 357: array([5.11326879, 5.70684862, 0.88630157]), 320: array([5.39804236, 6.17282054, 0.49717274]), 288: array([5.64412629, 6.62196687, 0.16830671]), 92: array([-7.56634272, 4.00079334, 1.29045419]), 359: array([-7.06315486, 3.68332862, 1.51880063]), 322: array([-6.50637218, 3.37744647, 1.76371481]), 290: array([-5.89749107, 3.02143355, 2.11004227]), 110: array([-5.21596363, 2.62127567, 2.52319111]), 77: array([-4.44210586, 2.17295087, 2.97859889]), 340: array([-3.57058072, 1.71321455, 3.42514123]), 304: array([-2.6312029 , 1.33832919, 3.75117627]), 276: array([-1.65237482, 1.08676856, 3.94553923]), 93: array([-0.6620208 , 0.97798513, 4.01307494]), 65: array([0.31734208, 1.01651818, 3.96374731]), 323: array([1.26611249, 1.20147792, 3.80325828]), 291: array([2.16497242, 1.5280312 , 3.5324065 ]), 111: array([2.99036668, 1.99474782, 3.14383382]), 78: array([3.72544957, 2.56060229, 2.64632542]), 53: array([4.35537409, 3.18444608, 2.06166495]), 305: array([4.88294444, 3.80184055, 1.44776135]), 277: array([5.34056205, 4.35547947, 0.8903765 ]), 94: array([5.75236716, 4.84736269, 0.41391588]), 66: array([6.13414425, 5.29190154, 0.02311985]), 324: array([ 6.48430114, 5.71419843, -0.30230069]), 258: array([-8.07194652, 2.834653 , 1.07993167]), 221: array([-7.49901631, 2.56196564, 1.30746529]), 49: array([-6.8704625 , 2.34508402, 1.47335401]), 17: array([-6.19155153, 2.07155981, 1.74602348]), 274: array([-5.44279222, 1.74592667, 2.09589525]), 243: array([-4.61128736, 1.39219494, 2.46500245]), 202: array([-3.69496086, 1.03374883, 2.80673326]), 36: array([-2.72323824, 0.74514189, 3.05426236]), 440: array([-1.72324707, 0.55651301, 3.19398882]), 261: array([-0.71358511, 0.4849321 , 3.23017295]), 224: array([0.28732595, 0.53882713, 3.16765832]), 51: array([1.26207497, 0.71840941, 3.01075465]), 20: array([2.19214097, 1.02742554, 2.75642223]), 418: array([3.06452082, 1.4378736 , 2.41049546]), 246: array([3.86436451, 1.9308343 , 1.97764542]), 205: array([4.57478716, 2.47792393, 1.46275004]), 38: array([5.20174593, 3.00842602, 0.93659102]), 0: array([5.76041068, 3.49485361, 0.4422437 ]), 397: array([6.27691096, 3.9218613 , 0.02505646]), 226: array([ 6.75604293, 4.31423818, -0.33131009]), 184: array([ 7.20716007, 4.68209714, -0.62486839]), 2: array([-8.40173197, 1.61445439, 0.94162855]), 398: array([-7.77276848, 1.45283095, 1.07043066]), 228: array([-7.09916604, 1.28258154, 1.23558232]), 186: array([-6.37371323, 1.11706522, 1.40420979]), 22: array([-5.58277358, 0.90195952, 1.64642421]), 420: array([-4.71806716, 0.6610442 , 1.90854731]), 378: array([-3.78511385, 0.42898223, 2.13710688]), 207: array([-2.80103882, 0.24254501, 2.29100892]), 165: array([-1.79140624, 0.13037608, 2.36916821]), 4: array([-0.77661912, 0.10970415, 2.36445297]), 400: array([0.23240442, 0.18265801, 2.28651075]), 230: array([1.22030433, 0.36068063, 2.13224153]), 188: array([2.17591304, 0.62250292, 1.90973351]), 144: array([3.08719356, 0.96318079, 1.61882241]), 424: array([3.93879946, 1.36656263, 1.25905316]), 379: array([4.71784618, 1.80404638, 0.84318722]), 211: array([5.42823405, 2.22327508, 0.42548032]), 168: array([6.0773423 , 2.60969927, 0.03021401]), 8: array([ 6.68866715, 2.94062775, -0.29162904]), 404: array([ 7.25147399, 3.26146153, -0.59524427]), 360: array([ 7.77530286, 3.57293484, -0.8690489 ]), 141: array([-8.5488187 , 0.31854085, 0.91527534]), 105: array([-7.89222912, 0.26668016, 0.95689601]), 376: array([-7.19611669, 0.22244885, 0.99953539]), 336: array([-6.45113794, 0.16629321, 1.06837817]), 300: array([-5.64379671, 0.07089945, 1.19521073]), 123: array([-4.77706245, -0.01824184, 1.30241656]), 88: array([-3.84959474, -0.10777554, 1.39800056]), 356: array([-2.87521953, -0.17090709, 1.45268606]), 319: array([-1.87205336, -0.18606699, 1.44640572]), 143: array([-0.86083699, -0.14145815, 1.38988509]), 108: array([ 0.14568258, -0.0287691 , 1.28096442]), 75: array([1.14309613, 0.12416812, 1.14185066]), 339: array([2.11859298, 0.33505328, 0.95550194]), 303: array([3.06356701, 0.57878749, 0.74282774]), 125: array([3.9559383 , 0.87432633, 0.46898238]), 91: array([4.79452908, 1.16469553, 0.19143639]), 358: array([ 5.57135089, 1.45075891, -0.09695863]), 321: array([ 6.29319862, 1.71233525, -0.36641171]), 289: array([ 6.97934759, 1.92296377, -0.56600221]), 109: array([ 7.6041917 , 2.16179907, -0.81020706]), 76: array([ 8.21999614, 2.33598129, -0.94541831]), 292: array([-8.50500643, -0.96921582, 0.87539061]), 264: array([-7.85110496, -0.91395436, 0.83667662]), 79: array([-7.16055231, -0.85085197, 0.78935547]), 54: array([-6.42693532, -0.78065137, 0.73405179]), 306: array([-5.64205137, -0.70935491, 0.67934588]), 278: array([-4.79565259, -0.65533852, 0.6487055 ]), 96: array([-3.89717995, -0.58351647, 0.59051657]), 67: array([-2.95381358, -0.4894401 , 0.50303225]), 41: array([-1.97794783, -0.37107488, 0.38761183]), 293: array([-0.9815253 , -0.23123979, 0.2499069 ]), 265: array([ 0.02137349, -0.09448513, 0.11827206]), 80: array([ 1.0231436 , 0.04431041, -0.01417017]), 55: array([ 2.02147918, 0.16525327, -0.12504988]), 308: array([ 2.98903866, 0.31760427, -0.27357959]), 280: array([ 3.92410778, 0.4455646 , -0.39522409]), 251: array([ 4.81027787, 0.56606359, -0.51059008]), 69: array([ 5.64020469, 0.68355781, -0.62641651]), 42: array([ 6.4155363 , 0.79301222, -0.73560201]), 295: array([ 7.14422778, 0.88482583, -0.82201212]), 267: array([ 7.8304667 , 0.96730515, -0.89697385]), 236: array([ 8.46374683, 1.09385212, -1.0429478 ]), 25: array([-8.29308949, -2.19247382, 0.74351181]), 423: array([-7.65115511, -2.079261 , 0.70039227]), 250: array([-7.00133121, -1.8944805 , 0.53915772]), 209: array([-6.30269589, -1.71691617, 0.3882087 ]), 40: array([-5.56485825, -1.50272293, 0.18532653]), 7: array([-4.77129912, -1.27775946, -0.02419326]), 403: array([-3.92989294, -1.01142318, -0.27874749]), 233: array([-3.03027965, -0.75694997, -0.50979987]), 191: array([-2.08993467, -0.48894415, -0.75064717]), 27: array([-1.11434746, -0.2741048 , -0.94413574]), 427: array([-0.11414308, -0.12437028, -1.08526118]), 382: array([ 0.89269244, -0.01119272, -1.19830181]), 214: array([ 1.90084077, 0.04688586, -1.26655163]), 171: array([ 2.90012649, 0.04086606, -1.27247202]), 11: array([ 3.86570013, 0.00680736, -1.24863653]), 407: array([ 4.782374 , -0.04221323, -1.20261109]), 235: array([ 5.64389022, -0.10544822, -1.12946856]), 193: array([ 6.44297328, -0.15125477, -1.07519825]), 147: array([ 7.18656656, -0.18645839, -1.03759632]), 429: array([ 7.88181139, -0.21208661, -1.02220687]), 384: array([ 8.53480656, -0.22216389, -1.04353095]), 195: array([-7.87327786, -3.44314904, 0.6746017 ]), 149: array([-7.29125371, -3.21910013, 0.54066486]), 431: array([-6.70284 , -2.94100309, 0.30416095]), 386: array([-6.08284617, -2.6288351 , 0.0086303 ]), 215: array([-5.41091335, -2.29984382, -0.30547832]), 174: array([-4.69823348, -1.9026687 , -0.6999575 ]), 128: array([-3.91948178, -1.48562662, -1.09630128]), 410: array([-3.07235517, -1.07183602, -1.46666119]), 364: array([-2.16294512, -0.72924871, -1.76178109]), 197: array([-1.20926773, -0.45588214, -1.9971807 ]), 151: array([-0.22019145, -0.27701142, -2.15670155]), 432: array([ 0.7899295 , -0.1996017 , -2.24320852]), 388: array([ 1.80394997, -0.21130437, -2.25562569]), 343: array([ 2.80886142, -0.30870415, -2.19278932]), 177: array([ 3.78656448, -0.47857385, -2.05227081]), 130: array([ 4.71549582, -0.69383266, -1.84663191]), 412: array([ 5.57934813, -0.92388836, -1.60114697]), 366: array([ 6.3661537 , -1.08560481, -1.43994643]), 325: array([ 7.09518037, -1.252633 , -1.27033767]), 153: array([ 7.770338 , -1.33837492, -1.23871688]), 113: array([ 8.40458524, -1.51526476, -1.08568016]), 368: array([-7.27982262, -4.61743912, 0.51863808]), 327: array([-6.80330905, -4.27725306, 0.27204525]), 156: array([-6.29948201, -3.91587411, -0.03270595]), 114: array([-5.75213697, -3.53868238, -0.37114835]), 392: array([-5.18598118, -3.07625772, -0.83420831]), 346: array([-4.55398252, -2.57704362, -1.32299492]), 310: array([-3.85273481, -2.01837548, -1.85090612]), 134: array([-3.06004463, -1.51536012, -2.29689991]), 99: array([-2.19195991, -1.09742322, -2.65056846]), 370: array([-1.26224132, -0.78595139, -2.91150696]), 329: array([-0.28768281, -0.59525435, -3.07848093]), 158: array([ 0.71337067, -0.53148716, -3.14991599]), 116: array([ 1.72300308, -0.59997245, -3.12160133]), 83: array([ 2.7210283 , -0.7782643 , -2.99383209]), 349: array([ 3.68911365, -1.05406475, -2.76443051]), 312: array([ 4.60467619, -1.4100762 , -2.42452807]), 137: array([ 5.43708332, -1.75954058, -2.06570534]), 101: array([ 6.18643804, -2.03708416, -1.79211488]), 373: array([ 6.87112825, -2.29069376, -1.55468851]), 332: array([ 7.50382596, -2.50401279, -1.39619553]), 297: array([ 8.08737465, -2.74235778, -1.22668856]), 59: array([-6.57431405, -5.65024795, 0.17427327]), 29: array([-6.17453857, -5.2726252 , -0.06757863]), 284: array([-5.76235751, -4.86064087, -0.39964094]), 254: array([-5.32705075, -4.40315849, -0.81974398]), 72: array([-4.86614736, -3.86553539, -1.35586393]), 45: array([-4.33857833, -3.26162435, -1.9478355 ]), 298: array([-3.71946561, -2.63128786, -2.5423972 ]), 270: array([-2.99382456, -2.05325658, -3.05276033]), 238: array([-2.1715725 , -1.58339385, -3.44798133]), 61: array([-1.27513157, -1.24469502, -3.72929427]), 31: array([-0.32691243, -1.04848393, -3.89943599]), 286: array([ 0.65217039, -0.99881967, -3.95908271]), 256: array([ 1.64180107, -1.0972132 , -3.90268507]), 219: array([ 2.62036692, -1.34794744, -3.71721454]), 47: array([ 3.56069075, -1.7187812 , -3.4013871 ]), 15: array([ 4.43190918, -2.16879618, -2.97571844]), 272: array([ 5.20649717, -2.59840792, -2.54932758]), 240: array([ 5.89373602, -2.98745425, -2.16155103]), 63: array([ 6.51159774, -3.31869923, -1.86165342]), 33: array([ 7.07368374, -3.62600758, -1.61857266]), 437: array([ 7.61124425, -3.83946663, -1.56801493]), 241: array([-5.72445624, -6.5784344 , -0.28242673]), 200: array([-5.4291533 , -6.16613938, -0.53371452]), 34: array([-5.12647086, -5.71585733, -0.89009991]), 438: array([-4.7897425 , -5.23305009, -1.31650223]), 257: array([-4.43720391, -4.65707275, -1.87936985]), 220: array([-4.02299549, -4.00670836, -2.52622969]), 48: array([-3.50824712, -3.30836002, -3.19399778]), 16: array([-2.85643996, -2.68484954, -3.74829047]), 416: array([-2.0911575 , -2.18424829, -4.17215402]), 242: array([-1.24307192, -1.83288805, -4.46483481]), 201: array([-0.33929968, -1.63715824, -4.63431632]), 35: array([ 0.59808646, -1.59979397, -4.68241195]), 439: array([ 1.54804451, -1.72284875, -4.6032243 ]), 260: array([ 2.48708416, -2.01008923, -4.37912506]), 223: array([ 3.3755532 , -2.44173946, -4.01036496]), 183: array([ 4.17971452, -2.95959016, -3.5197435 ]), 19: array([ 4.87669134, -3.48030567, -2.99630659]), 417: array([ 5.47505342, -3.95082263, -2.52203327]), 245: array([ 6.00392724, -4.33834382, -2.17851221]), 204: array([ 6.47807767, -4.69443529, -1.90988429]), 162: array([ 6.90468015, -5.03660392, -1.70735082]), 393: array([-4.71148652, -7.38959056, -0.83381158]), 347: array([-4.54359237, -6.95989371, -1.09574518]), 181: array([-4.35658498, -6.5001725 , -1.4519405 ]), 135: array([-4.13256093, -6.00604432, -1.87736098]), 415: array([-3.89112013, -5.43546873, -2.43435619]), 371: array([-3.59495458, -4.77912674, -3.09351885]), 330: array([-3.18817957, -4.05644259, -3.80029662]), 159: array([-2.62246149, -3.42112766, -4.37660512]), 117: array([-1.93240174, -2.91530818, -4.81285156]), 395: array([-1.15524842, -2.56769958, -5.10614542]), 350: array([-0.32093628, -2.37990241, -5.26957817]), 313: array([ 0.54806141, -2.35340617, -5.30623515]), 138: array([ 1.43167862, -2.4936993 , -5.20668338]), 102: array([ 2.3011656 , -2.79788358, -4.95961315]), 374: array([ 3.11854606, -3.25592255, -4.55072047]), 333: array([ 3.83365099, -3.82603089, -3.99975502]), 161: array([ 4.42539026, -4.37654541, -3.44309088]), 119: array([ 4.9170323 , -4.87411006, -2.94739208]), 84: array([ 5.34105083, -5.29484233, -2.57994421]), 351: array([ 5.71272416, -5.67781828, -2.30430022]), 314: array([ 6.03342794, -6.05084141, -2.09273572]), 120: array([-3.62465711, -7.98864662, -1.61506601]), 85: array([-3.55240431, -7.59346449, -1.82286021]), 353: array([-3.45663466, -7.16980147, -2.11802438]), 316: array([-3.34456234, -6.70537682, -2.51766513]), 140: array([-3.21378673, -6.17157164, -3.03822612]), 104: array([-3.02521159, -5.55160259, -3.6727942 ]), 73: array([-2.71733322, -4.88610414, -4.33868421]), 335: array([-2.25801778, -4.27324389, -4.91596732]), 299: array([-1.67021824, -3.80085272, -5.33520957]), 122: array([-0.99556996, -3.47472555, -5.61731369]), 87: array([-0.26420034, -3.30336731, -5.76838159]), 355: array([ 0.50135614, -3.28790341, -5.79193007]), 318: array([ 1.27990508, -3.43154447, -5.68039542]), 287: array([ 2.04804391, -3.74821919, -5.40489364]), 107: array([ 2.75545407, -4.20040257, -4.97953712]), 74: array([ 3.35897437, -4.76216524, -4.40603188]), 338: array([ 3.82636892, -5.29035679, -3.86880033]), 302: array([ 4.195167 , -5.77437031, -3.38805408]), 273: array([ 4.50436933, -6.18084732, -3.04827438]), 90: array([ 4.76269512, -6.559272 , -2.78943651]), 64: array([ 5.00792207, -6.85945795, -2.73480679]), 259: array([-2.4492429 , -8.34683677, -2.58578588]), 222: array([-2.46661072, -8.01610018, -2.72772409]), 50: array([-2.44177522, -7.67634212, -2.9299621 ]), 18: array([-2.4133919 , -7.29325186, -3.24317899]), 275: array([-2.37244432, -6.83527239, -3.69728442]), 244: array([-2.2559944 , -6.33327829, -4.21656111]), 203: array([-2.055599 , -5.76741194, -4.80864418]), 37: array([-1.71940524, -5.26155758, -5.30546353]), 164: array([-1.27133982, -4.85831558, -5.68124409]), 262: array([-0.74094545, -4.58499302, -5.92783038]), 225: array([-0.1565622 , -4.44158272, -6.05774837]), 52: array([ 0.45727121, -4.43101526, -6.07197352]), 21: array([ 1.08119308, -4.56746616, -5.95299439]), 419: array([ 1.69001096, -4.85547623, -5.68142822]), 247: array([ 2.23505776, -5.22393315, -5.3186708 ]), 206: array([ 2.69654826, -5.71165259, -4.79761776]), 39: array([ 3.04653503, -6.15750441, -4.32914796]), 1: array([ 3.29828199, -6.56774298, -3.9362922 ]), 263: array([ 3.48768832, -6.93528948, -3.63065402]), 227: array([ 3.64530949, -7.24050706, -3.47521677]), 185: array([ 3.73357926, -7.57500087, -3.30761604]), 3: array([-1.29003466, -8.33890804, -3.84235022]), 399: array([-1.31402595, -8.16449308, -3.8132454 ]), 229: array([-1.34187355, -7.94280676, -3.91476888]), 187: array([-1.35358658, -7.67942344, -4.12243808]), 23: array([-1.33694737, -7.37925879, -4.41068094]), 421: array([-1.28859436, -7.03139987, -4.77895791]), 248: array([-1.16685415, -6.68273007, -5.14627667]), 208: array([-0.96486955, -6.3668689 , -5.470497 ]), 166: array([-0.69969604, -6.07968572, -5.76266612]), 5: array([-0.36732878, -5.88412017, -5.95389194]), 401: array([ 0.01470829, -5.80106927, -6.03075921]), 231: array([ 0.41685297, -5.80615951, -6.02326763]), 189: array([ 0.81639851, -5.8936993 , -5.93622717]), 145: array([ 1.20099911, -6.1083159 , -5.70910391]), 425: array([ 1.53887487, -6.35201295, -5.45296767]), 380: array([ 1.81913641, -6.64719367, -5.13559448]), 212: array([ 2.03720315, -6.93107235, -4.84484975]), 169: array([ 2.19117467, -7.22726212, -4.54791797]), 9: array([ 2.29301372, -7.46568766, -4.38563509]), 405: array([ 2.34209953, -7.70350987, -4.2531903 ]), 361: array([ 2.349353 , -7.90669489, -4.22155662]), 172: array([-0.17589778, -8.00013665, -5.07776817]), 126: array([-0.21111796, -7.9513642 , -5.04837184]), 408: array([-0.22045156, -7.88735044, -5.0499031 ]), 362: array([-0.22969335, -7.78889274, -5.12688978]), 194: array([-0.21808448, -7.68904011, -5.2104113 ]), 148: array([-0.1923931 , -7.58242888, -5.31163871]), 430: array([-0.15272084, -7.47183196, -5.42527764]), 385: array([-0.08775276, -7.37409882, -5.52600361]), 341: array([ 0.00772582, -7.30498403, -5.59301941]), 173: array([ 0.09722646, -7.21626741, -5.69593203]), 127: array([ 0.22337105, -7.18930539, -5.72126403]), 409: array([ 0.35552466, -7.21811393, -5.67966953]), 363: array([ 0.4828998 , -7.22985568, -5.67079162]), 196: array([ 0.60196508, -7.29604285, -5.59571056]), 150: array([ 0.70911458, -7.37106167, -5.51678457]), 112: array([ 0.79680471, -7.46741259, -5.41545048]), 387: array([ 0.86839519, -7.55793144, -5.33192625]), 342: array([ 0.92282418, -7.63976535, -5.27347984]), 175: array([ 0.94936158, -7.73360527, -5.20618271]), 129: array([ 0.96346477, -7.81531526, -5.17245677]), 95: array([ 1.82707344, -8.31793051, -5.00244309])} .. GENERATED FROM PYTHON SOURCE LINES 86-89 Plot the simplices using the vertex embedding ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 89-103 .. code-block:: Python fig = oat.plot.fig_3d_for_simplices( simplices = simplices, points = points, kwargs_points = {"marker": {"size": 3, "color": "white"}}, kwargs_edges = {"line": {"color": "white", "width": 3}}, ) fig.update_layout( height=700, ) fig .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 104-106 Example 2 ----------------------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 108-109 Modify the set of simplices .. GENERATED FROM PYTHON SOURCE LINES 109-114 .. code-block:: Python for j in range(N): dowker_square = [(0,j), ( N,j), (0,j+1), ( N,j+1)] dowker_square = [ vertex_labels[xy_tuple] for xy_tuple in dowker_square ] simplices.append(dowker_square) .. GENERATED FROM PYTHON SOURCE LINES 115-118 Generate a vertex embedding ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 118-127 .. code-block:: Python points = oat.plot.vertex_embedding_for_simplices( simplices, dimension = 3, method = "hop_mds", random_state = 0, ) points .. rst-class:: sphx-glr-script-out .. code-block:: none {24: array([-2.8457751 , 0.18721218, -2.30055021]), 155: array([-3.15442875, -0.31548649, -3.33226595]), 422: array([-2.7802923 , 0.12370099, -2.27007687]), 435: array([-2.93388005, -0.39558264, -3.32191102]), 249: array([-2.70118372, 0.08006172, -2.23588834]), 391: array([-2.69938373, -0.44352127, -3.29817571]), 210: array([-2.61265357, 0.05909537, -2.19449475]), 345: array([-2.44846285, -0.44821223, -3.26008244]), 167: array([-2.52018345, 0.06303967, -2.14543916]), 180: array([-2.19238322, -0.40133863, -3.20125032]), 6: array([-2.42994246, 0.09274857, -2.08918106]), 133: array([-1.94353313, -0.29930266, -3.12102307]), 402: array([-2.34788989, 0.14809078, -2.02726121]), 414: array([-1.71493739, -0.14089739, -3.0213484 ]), 232: array([-2.27927603, 0.22802686, -1.96181298]), 369: array([-1.52180401, 0.07037808, -2.90369806]), 190: array([-2.2288499 , 0.33023073, -1.89483754]), 328: array([-1.37684566, 0.32995821, -2.77224482]), 26: array([-2.20023514, 0.4516558 , -1.82859526]), 157: array([-1.29234958, 0.62897 , -2.62929677]), 426: array([-2.19531846, 0.58893524, -1.76511001]), 115: array([-1.27705071, 0.94925703, -2.48762679]), 381: array([-2.21764427, 0.72929295, -1.71353612]), 394: array([-1.33347683, 1.27166838, -2.36247158]), 213: array([-2.2620811 , 0.8575859 , -1.67582495]), 348: array([-1.45617061, 1.57224897, -2.25654817]), 170: array([-2.32603636, 0.97041232, -1.65340019]), 182: array([-1.6336646 , 1.83048499, -2.17318649]), 10: array([-2.40534069, 1.06453546, -1.64666968]), 136: array([-1.85375054, 2.04000024, -2.11559063]), 406: array([-2.49543575, 1.13737456, -1.65567265]), 100: array([-2.10113573, 2.19649497, -2.08546805]), 234: array([-2.59000587, 1.18744043, -1.68026917]), 372: array([-2.36176238, 2.29787486, -2.08226704]), 192: array([-2.68382604, 1.21377551, -1.71833349]), 331: array([-2.62198228, 2.34508142, -2.10470826]), 146: array([-2.77057406, 1.21740718, -1.76889626]), 160: array([-2.87838768, 2.33753677, -2.14425556]), 428: array([-2.85389035, 1.20517847, -1.82531141]), 118: array([-3.11001805, 2.29665275, -2.20264169]), 383: array([-3.608873 , 1.42775169, -1.43992634]), 396: array([-3.31880808, 2.22382677, -2.27947598]), 307: array([-3.05347281, -1.03337988, -4.3735174 ]), 279: array([-2.66085471, -1.09642942, -4.35336815]), 97: array([-2.26095215, -1.10224803, -4.30775296]), 68: array([-1.84912446, -1.04866311, -4.23966657]), 326: array([-1.42803216, -0.92716243, -4.14666521]), 294: array([-1.0144129 , -0.7297123 , -4.02212741]), 266: array([-0.63301605, -0.45475017, -3.86387218]), 81: array([-0.31100108, -0.10689346, -3.67408968]), 56: array([-0.06896085, 0.30849227, -3.45993703]), 309: array([ 0.07057032, 0.77151166, -3.23623056]), 281: array([ 0.09688906, 1.26011387, -3.01897346]), 98: array([ 0.00778117, 1.75235152, -2.82855198]), 70: array([-0.19135502, 2.21886205, -2.66737329]), 43: array([-0.48632512, 2.63389418, -2.53689737]), 296: array([-0.85453033, 2.9759107 , -2.43901482]), 268: array([-1.27086493, 3.23830194, -2.37363844]), 82: array([-1.70830452, 3.41936287, -2.3413252 ]), 57: array([-2.15173115, 3.51988697, -2.33790237]), 311: array([-2.57151643, 3.56093792, -2.36351943]), 282: array([-2.96304077, 3.54615171, -2.42467172]), 252: array([-3.34195548, 3.47422636, -2.50638467]), 58: array([-2.54963974, -1.93253254, -5.27790538]), 28: array([-2.03034608, -1.96663835, -5.18131183]), 283: array([-1.45880284, -1.88777192, -5.08722335]), 253: array([-0.93174229, -1.75393466, -4.9377731 ]), 71: array([-0.38164137, -1.53065065, -4.76454667]), 44: array([ 0.14043872, -1.23125351, -4.54908005]), 13: array([ 0.61553351, -0.84687243, -4.29360124]), 269: array([ 1.01754505, -0.37667802, -4.00206047]), 237: array([ 1.31030252, 0.16446662, -3.69231627]), 60: array([ 1.47627198, 0.75881987, -3.38400102]), 30: array([ 1.50301111, 1.386407 , -3.10051507]), 285: array([ 1.39377211, 2.02268885, -2.85943405]), 255: array([ 1.15030656, 2.63750012, -2.66453298]), 218: array([ 0.7855182 , 3.20242733, -2.5153663 ]), 46: array([ 0.32312993, 3.69251157, -2.40776446]), 14: array([-0.20514645, 4.08970104, -2.33796878]), 271: array([-0.77586945, 4.39077243, -2.30120584]), 239: array([-1.34258789, 4.60878109, -2.29771592]), 62: array([-1.90596166, 4.74801669, -2.32167817]), 32: array([-2.44774782, 4.81219775, -2.38501889]), 436: array([-2.98944062, 4.79543125, -2.48085928]), 216: array([-1.75789711, -2.98995245, -5.8930139 ]), 176: array([-1.13548312, -2.95147349, -5.70276991]), 12: array([-0.43818236, -2.77978321, -5.51403401]), 411: array([ 0.18526012, -2.53282127, -5.2718761 ]), 365: array([ 0.77981453, -2.21238599, -4.9824333 ]), 198: array([ 1.34098331, -1.80006812, -4.65720276]), 152: array([ 1.83503075, -1.30706331, -4.29298742]), 433: array([ 2.23851113, -0.7339533 , -3.9056001 ]), 389: array([ 2.52715664, -0.09080605, -3.51416751]), 217: array([ 2.6835622 , 0.60798781, -3.14139081]), 178: array([ 2.70453377, 1.34190215, -2.80325416]), 131: array([ 2.58770617, 2.09122462, -2.5237693 ]), 413: array([ 2.33679373, 2.82631358, -2.30225721]), 367: array([ 1.96072121, 3.5205992 , -2.13838131]), 199: array([ 1.47890878, 4.15029688, -2.02600411]), 154: array([ 0.90905859, 4.69621486, -1.95814087]), 434: array([ 0.29736579, 5.15032871, -1.92729408]), 390: array([-0.34334762, 5.51348739, -1.92810062]), 344: array([-1.00370983, 5.78631782, -1.9588522 ]), 179: array([-1.68397815, 5.96715057, -2.01867435]), 132: array([-2.34100265, 6.0603888 , -2.12792888]), 352: array([-0.81723396, -4.14530583, -6.1293384 ]), 315: array([-0.07423531, -3.98069314, -5.86004263]), 139: array([ 0.65869556, -3.7221223 , -5.54516328]), 103: array([ 1.31012083, -3.36607356, -5.1996857 ]), 375: array([ 1.91351407, -2.93295616, -4.80669546]), 334: array([ 2.44195756, -2.41385784, -4.38488418]), 163: array([ 2.89428755, -1.81908516, -3.93903398]), 121: array([ 3.25361051, -1.15255042, -3.48657842]), 86: array([ 3.50467683, -0.42283842, -3.04260035]), 354: array([ 3.63545292, 0.35826302, -2.62594793]), 317: array([ 3.64252774, 1.17435548, -2.25211687]), 142: array([ 3.52762238, 2.00830098, -1.94028489]), 106: array([ 3.29194037, 2.83425345, -1.68889214]), 377: array([ 2.94108256, 3.63036134, -1.49892464]), 337: array([ 2.47999242, 4.3771542 , -1.36823113]), 301: array([ 1.94310329, 5.0575562 , -1.28340586]), 124: array([ 1.33923351, 5.65916568, -1.24022527]), 89: array([ 0.67108203, 6.17171317, -1.23884947]), 357: array([-0.04916264, 6.59075799, -1.2653686 ]), 320: array([-0.81576629, 6.91186801, -1.31642553]), 288: array([-1.63796049, 7.12203626, -1.41920785]), 92: array([ 0.07114059, -5.29688695, -5.99114342]), 359: array([ 0.83471602, -5.06728884, -5.59203909]), 322: array([ 1.62660423, -4.66272446, -5.21074586]), 290: array([ 2.28801978, -4.21503052, -4.75628172]), 110: array([ 2.85546956, -3.66938947, -4.29232644]), 77: array([ 3.33228943, -3.04856604, -3.81334309]), 340: array([ 3.72325609, -2.36132447, -3.32222301]), 304: array([ 4.02281162, -1.61206677, -2.83600524]), 276: array([ 4.22471082, -0.80757199, -2.36933542]), 93: array([ 4.3249545 , 0.03895231, -1.92634805]), 65: array([ 4.31698089, 0.91909308, -1.53215042]), 323: array([ 4.20830905, 1.8146664 , -1.1907952 ]), 291: array([ 3.99579455, 2.70675205, -0.9063795 ]), 111: array([ 3.67620615, 3.57948588, -0.68350173]), 78: array([ 3.27138481, 4.41407541, -0.51194605]), 53: array([ 2.78295516, 5.19770241, -0.39125744]), 305: array([ 2.2117246 , 5.91888542, -0.32106882]), 277: array([ 1.56617186, 6.56328462, -0.29264202]), 94: array([ 0.83251163, 7.12222796, -0.31489288]), 66: array([ 0.02359799, 7.58354017, -0.37411295]), 324: array([-0.85083796, 7.93629992, -0.48367169]), 258: array([ 0.80641744, -6.38673313, -5.53509799]), 221: array([ 1.65000112, -6.02903051, -5.06159632]), 49: array([ 2.37437423, -5.56193806, -4.57758286]), 17: array([ 2.99849433, -5.00836462, -4.06984123]), 274: array([ 3.5242498 , -4.38202183, -3.54340287]), 243: array([ 3.94984461, -3.67999545, -3.02907844]), 202: array([ 4.2845596 , -2.9132127 , -2.52398028]), 36: array([ 4.52847106, -2.09313534, -2.0323067 ]), 440: array([ 4.68617328, -1.22969369, -1.55407449]), 261: array([ 4.75516029, -0.32776741, -1.10858897]), 224: array([ 4.73583977, 0.59920759, -0.69767279]), 51: array([ 4.63329465, 1.53972565, -0.33229111]), 20: array([ 4.43834878, 2.48060147, -0.01898435]), 418: array([4.16292595, 3.40485113, 0.24653596]), 246: array([3.80464608, 4.30040811, 0.46283298]), 205: array([3.36151592, 5.15786523, 0.62496872]), 38: array([2.83370615, 5.9650736 , 0.73633213]), 0: array([2.21734716, 6.71305294, 0.79192491]), 397: array([1.51094546, 7.38770521, 0.79767537]), 226: array([0.69795613, 7.97618739, 0.74842472]), 184: array([-0.21057412, 8.45961207, 0.65863178]), 2: array([ 1.29329639, -7.35454253, -4.87270901]), 398: array([ 2.12435819, -6.91339536, -4.32245497]), 228: array([ 2.82524636, -6.38414668, -3.73983866]), 186: array([ 3.40997837, -5.73411444, -3.2238722 ]), 22: array([ 3.88696241, -5.03392333, -2.67835672]), 420: array([ 4.26821058, -4.27043911, -2.14396238]), 378: array([ 4.55904728, -3.44948143, -1.62900154]), 207: array([ 4.76411024, -2.57720997, -1.13953006]), 165: array([ 4.88654794, -1.66882726, -0.66110823]), 4: array([ 4.93123145, -0.72737669, -0.21407165]), 400: array([4.90217314, 0.23396512, 0.20547827]), 230: array([4.80093761, 1.20740805, 0.58736084]), 188: array([4.63134569, 2.17867697, 0.93061734]), 144: array([4.3863779 , 3.13693247, 1.23162291]), 424: array([4.06247098, 4.07316727, 1.48512101]), 379: array([3.65745171, 4.97881649, 1.68738389]), 211: array([3.16862222, 5.8453974 , 1.83667118]), 168: array([2.58988535, 6.66611972, 1.92730619]), 8: array([1.91003731, 7.43386987, 1.94686419]), 404: array([1.12788095, 8.12270213, 1.92361826]), 360: array([0.20851245, 8.72383969, 1.82090379]), 141: array([ 1.52869992, -8.19557843, -4.0552628 ]), 105: array([ 2.33210668, -7.67231987, -3.45944052]), 376: array([ 2.9863494 , -7.05229481, -2.88944473]), 336: array([ 3.5251241 , -6.36194242, -2.32035616]), 300: array([ 3.95661054, -5.61221862, -1.76154662]), 123: array([ 4.29740983, -4.80414429, -1.22554187]), 88: array([ 4.55245244, -3.94807197, -0.70410733]), 356: array([ 4.72862414, -3.04556578, -0.20988784]), 319: array([ 4.82830058, -2.10626968, 0.26024032]), 143: array([ 4.85522016, -1.1406946 , 0.70883278]), 108: array([ 4.81512685, -0.15495522, 1.1277126 ]), 75: array([4.72342529, 0.83557876, 1.52528413]), 339: array([4.56944448, 1.82531465, 1.8877274 ]), 303: array([4.3450176 , 2.8039822 , 2.21268318]), 125: array([4.04763272, 3.76608783, 2.48970449]), 91: array([3.67313672, 4.70125066, 2.72223188]), 358: array([3.21956691, 5.60709292, 2.89883616]), 321: array([2.68017555, 6.47772795, 3.01541232]), 289: array([2.04460558, 7.30229011, 3.07405307]), 109: array([1.29337486, 8.07453487, 3.05833234]), 76: array([0.43853087, 8.76643702, 2.97638877]), 292: array([ 1.36563254, -8.77648428, -3.16977605]), 264: array([ 2.14511482, -8.20309314, -2.60707499]), 79: array([ 2.77178056, -7.56797577, -1.99180289]), 54: array([ 3.28558533, -6.85227033, -1.42689034]), 306: array([ 3.7005643 , -6.08003535, -0.86095902]), 278: array([ 4.02003383, -5.25748423, -0.31714315]), 96: array([ 4.26470115, -4.38146916, 0.19213886]), 67: array([ 4.42870282, -3.46702961, 0.68566189]), 41: array([ 4.51838421, -2.51867354, 1.15751532]), 293: array([ 4.53317735, -1.54042672, 1.5995762 ]), 265: array([ 4.49292997, -0.54901585, 2.02333114]), 80: array([4.40456787, 0.44791799, 2.42491754]), 55: array([4.25528032, 1.44276597, 2.79719779]), 308: array([4.0398895 , 2.42921798, 3.12961707]), 280: array([3.75203525, 3.39789551, 3.42185786]), 251: array([3.3914681 , 4.34511462, 3.66455542]), 69: array([2.95288581, 5.26464892, 3.85648295]), 42: array([2.43030662, 6.15190267, 3.99220405]), 295: array([1.81680434, 7.00179072, 4.06205274]), 267: array([1.09617917, 7.79712185, 4.07329711]), 236: array([0.25903846, 8.55050249, 3.95710854]), 25: array([ 0.6723612 , -8.90479493, -2.49130113]), 423: array([ 1.4668789 , -8.41838739, -1.80363801]), 250: array([ 2.12776192, -7.811687 , -1.20408143]), 209: array([ 2.65739922, -7.13007198, -0.61838559]), 40: array([ 3.09069153, -6.37941536, -0.0607413 ]), 7: array([ 3.42725718, -5.57413789, 0.48351675]), 403: array([ 3.68820324, -4.71342535, 0.99568028]), 233: array([ 3.8675639 , -3.80942976, 1.48753154]), 191: array([ 3.96920248, -2.86963816, 1.9571056 ]), 27: array([ 3.99852705, -1.90253972, 2.40253803]), 427: array([ 3.95822156, -0.91780011, 2.82384662]), 382: array([3.86589126, 0.07196073, 3.22304394]), 214: array([3.71086155, 1.05998018, 3.58931872]), 171: array([3.48543494, 2.03764375, 3.91652642]), 11: array([3.18607216, 2.99718722, 4.19907619]), 407: array([2.81131513, 3.93272558, 4.43114223]), 235: array([2.35561202, 4.83726071, 4.61092612]), 193: array([1.81960466, 5.70787454, 4.72707235]), 147: array([1.1865448 , 6.53289999, 4.78199147]), 429: array([0.44695435, 7.31347429, 4.7474236 ]), 384: array([-0.39196988, 8.0257643 , 4.61917104]), 195: array([-0.25976749, -8.71052671, -1.8874563 ]), 149: array([ 0.52138658, -8.32261891, -1.20437617]), 431: array([ 1.17987966, -7.81241908, -0.5613003 ]), 386: array([ 1.75462879, -7.19858188, 0.02388759]), 215: array([ 2.21748755, -6.50814475, 0.59398298]), 174: array([ 2.6012102 , -5.74537535, 1.130893 ]), 128: array([ 2.89311114, -4.92496624, 1.64848791]), 410: array([ 3.10354425, -4.05287088, 2.14075404]), 364: array([ 3.22997524, -3.14033666, 2.60999715]), 197: array([ 3.27994123, -2.19636716, 3.05209025]), 151: array([ 3.2546481 , -1.23292257, 3.46705754]), 432: array([ 3.15288118, -0.26137265, 3.85316876]), 388: array([2.97869231, 0.70522661, 4.20666059]), 343: array([2.73081514, 1.66003393, 4.51524326]), 177: array([2.40275717, 2.59332573, 4.77538598]), 130: array([1.99792379, 3.49928972, 4.97770384]), 412: array([1.51247322, 4.36906613, 5.11929144]), 366: array([0.94322785, 5.20027799, 5.18900593]), 325: array([0.28680765, 5.98156076, 5.18021011]), 153: array([-0.46809528, 6.71443836, 5.06412865]), 113: array([-1.30909308, 7.37112861, 4.83885467]), 368: array([-1.34268431, -8.2717739 , -1.36231867]), 327: array([-0.60450852, -7.98871016, -0.71997701]), 156: array([ 0.06436229, -7.58395807, -0.10474274]), 114: array([ 0.6580542 , -7.06839424, 0.503013 ]), 392: array([ 1.16806774, -6.45712069, 1.06427636]), 346: array([ 1.58864935, -5.76503369, 1.60407751]), 310: array([ 1.92646805, -5.00247309, 2.11813977]), 134: array([ 2.17727172, -4.18090739, 2.60846733]), 99: array([ 2.34319501, -3.3109668 , 3.0728897 ]), 370: array([ 2.42325802, -2.40361978, 3.50764057]), 329: array([ 2.40872628, -1.47385157, 3.91217246]), 158: array([ 2.30134179, -0.53741763, 4.28611112]), 116: array([2.10259989, 0.39741082, 4.61284914]), 83: array([1.81967816, 1.31470466, 4.89371222]), 349: array([1.4557302 , 2.20651805, 5.1185807 ]), 312: array([1.01464808, 3.06483039, 5.27952524]), 137: array([0.49433185, 3.88163176, 5.37071436]), 101: array([-0.10042382, 4.65169733, 5.3812542 ]), 373: array([-0.7685364 , 5.37166906, 5.29566882]), 332: array([-1.51278274, 6.02822746, 5.10179751]), 297: array([-2.28921884, 6.56840706, 4.86353921]), 59: array([-2.49585762, -7.52144951, -1.07896907]), 29: array([-1.78614535, -7.36951939, -0.42834298]), 284: array([-1.13491109, -7.08771068, 0.17422844]), 254: array([-0.54025135, -6.69286142, 0.75396071]), 72: array([-0.00780159, -6.1921332 , 1.31144575]), 45: array([ 0.45442322, -5.59678489, 1.84934644]), 298: array([ 0.83939315, -4.91898838, 2.36296774]), 270: array([ 1.14098911, -4.17073318, 2.85232907]), 238: array([ 1.35232437, -3.36308678, 3.31348288]), 61: array([ 1.45978583, -2.5097283 , 3.74112339]), 31: array([ 1.45569235, -1.62787602, 4.13136929]), 286: array([ 1.34490298, -0.7361222 , 4.48089102]), 256: array([1.12711993, 0.15016132, 4.77799443]), 219: array([0.80390667, 1.01813649, 5.01169907]), 47: array([0.40022276, 1.85343739, 5.18230441]), 15: array([-0.07910902, 2.64674413, 5.28252459]), 272: array([-0.62637213, 3.39174137, 5.30368154]), 240: array([-1.23553329, 4.07840777, 5.2397144 ]), 63: array([-1.89700988, 4.69821736, 5.08350881]), 33: array([-2.60583651, 5.26245758, 4.81176486]), 437: array([-3.35681402, 5.71406657, 4.47384653]), 241: array([-3.53781747, -6.48659295, -0.92827559]), 200: array([-2.89941843, -6.45538602, -0.3668094 ]), 34: array([-2.29669726, -6.30541834, 0.19666633]), 438: array([-1.72882469, -6.0452074 , 0.75723554]), 257: array([-1.19930668, -5.68001999, 1.30024626]), 220: array([-0.71709157, -5.21109449, 1.83437645]), 48: array([-0.29540756, -4.64800474, 2.35021816]), 16: array([ 0.04856628, -3.99923133, 2.84318373]), 416: array([ 0.29770676, -3.27591499, 3.30200035]), 242: array([ 0.42988892, -2.49514958, 3.719578 ]), 201: array([ 0.43989131, -1.67724169, 4.0890502 ]), 35: array([ 0.32486817, -0.8463122 , 4.40752683]), 439: array([ 0.08848633, -0.02123648, 4.66057484]), 260: array([-0.25463804, 0.78068694, 4.83801294]), 223: array([-0.6949402 , 1.54524721, 4.93062793]), 183: array([-1.19778849, 2.25756659, 4.94633529]), 19: array([-1.75156761, 2.91031405, 4.87972384]), 417: array([-2.33766435, 3.48767846, 4.73644215]), 245: array([-2.94443065, 3.99089359, 4.51988511]), 204: array([-3.58243761, 4.41972525, 4.21878268]), 162: array([-4.23184874, 4.74866962, 3.86560441]), 393: array([-4.3134331 , -5.23279866, -0.89223952]), 347: array([-3.77903779, -5.29653557, -0.4618986 ]), 181: array([-3.26505285, -5.26246119, 0.01101853]), 135: array([-2.75968782, -5.13589717, 0.52119269]), 415: array([-2.27252115, -4.91211646, 1.0326182 ]), 371: array([-1.80865359, -4.590632 , 1.54985093]), 330: array([-1.38755208, -4.16483513, 2.061874 ]), 159: array([-1.03224672, -3.63800765, 2.55279242]), 117: array([-0.76981974, -3.02211688, 3.00454665]), 395: array([-0.62180818, -2.335862 , 3.4056689 ]), 350: array([-0.60647284, -1.60398149, 3.74757453]), 313: array([-0.71753936, -0.85356105, 4.02517209]), 138: array([-0.95426437, -0.10752304, 4.22262468]), 102: array([-1.29931864, 0.61265298, 4.32978342]), 374: array([-1.73090861, 1.28758821, 4.34257742]), 333: array([-2.22706192, 1.90384879, 4.25692911]), 161: array([-2.74404813, 2.4416571 , 4.10196744]), 119: array([-3.27409941, 2.90371769, 3.88215017]), 84: array([-3.80917899, 3.28886639, 3.60387814]), 351: array([-4.34131302, 3.5856432 , 3.2864792 ]), 314: array([-4.89879584, 3.81866086, 2.85654547]), 120: array([-4.72141169, -3.84191614, -1.03024767]), 85: array([-4.30758217, -3.98044612, -0.68267944]), 353: array([-3.89891448, -4.03743861, -0.30446693]), 316: array([-3.49136221, -4.01852745, 0.10893135]), 140: array([-3.08513338, -3.92191861, 0.55511661]), 104: array([-2.68850553, -3.73720841, 1.02601914]), 73: array([-2.31941738, -3.45146084, 1.50154741]), 335: array([-2.00220047, -3.05796885, 1.96167092]), 299: array([-1.76277133, -2.5676704 , 2.38492722]), 122: array([-1.6267421 , -1.99993927, 2.75217659]), 87: array([-1.60474229, -1.38008689, 3.05308449]), 355: array([-1.70482626, -0.73754853, 3.28065077]), 318: array([-1.91803003, -0.09700219, 3.41915916]), 287: array([-2.22697731, 0.5172216 , 3.45951585]), 107: array([-2.60549784, 1.0822414 , 3.40135492]), 74: array([-3.02527833, 1.57722622, 3.25386222]), 338: array([-3.46513436, 1.99629036, 3.02948703]), 302: array([-3.89869545, 2.33352683, 2.7695969 ]), 273: array([-4.32276972, 2.58962727, 2.48334135]), 90: array([-4.74082915, 2.77208346, 2.16068313]), 64: array([-5.15341818, 2.89068606, 1.77731846]), 259: array([-4.69837978, -2.48818607, -1.12844526]), 222: array([-4.40952584, -2.64240661, -0.90944932]), 50: array([-4.11701986, -2.74341825, -0.65293421]), 18: array([-3.81956898, -2.79160309, -0.35984073]), 275: array([-3.51957329, -2.7783571 , -0.02888519]), 244: array([-3.22587546, -2.68922524, 0.33813436]), 203: array([-2.95343491, -2.51284409, 0.71560897]), 37: array([-2.71967696, -2.24590566, 1.08677315]), 164: array([-2.54191318, -1.88982368, 1.43237959]), 262: array([-2.43840513, -1.46107339, 1.73160886]), 225: array([-2.42251895, -0.9822329 , 1.97061753]), 52: array([-2.50046239, -0.48104267, 2.14171617]), 21: array([-2.66305266, 0.01799742, 2.23131627]), 419: array([-2.89330071, 0.49063876, 2.234394 ]), 247: array([-3.17135985, 0.91309682, 2.15368154]), 206: array([-3.4781013 , 1.27205223, 2.00389865]), 39: array([-3.79650384, 1.55948612, 1.80020573]), 1: array([-4.11354908, 1.77371351, 1.55224389]), 263: array([-4.41770786, 1.91418736, 1.30143868]), 227: array([-4.70853661, 1.99720782, 1.03132259]), 185: array([-4.98992911, 2.00865794, 0.76076604]), 3: array([-4.26290725, -1.29719113, -1.14461329]), 399: array([-4.08771126, -1.4173082 , -1.0454405 ]), 229: array([-3.90421214, -1.5104082 , -0.92153373]), 187: array([-3.71309021, -1.56857172, -0.76589032]), 23: array([-3.52053975, -1.57849394, -0.58130945]), 421: array([-3.33501578, -1.53324753, -0.37496247]), 248: array([-3.1668619 , -1.42912019, -0.1539142 ]), 208: array([-3.02575704, -1.26490906, 0.06979043]), 166: array([-2.92056474, -1.04177513, 0.28178088]), 5: array([-2.85912193, -0.76429434, 0.47244735]), 401: array([-2.8501434 , -0.45036155, 0.62840805]), 231: array([-2.90024639, -0.1222404 , 0.74090899]), 189: array([-2.99990571, 0.19911564, 0.80096782]), 145: array([-3.13809197, 0.49241894, 0.80624077]), 425: array([-3.30609307, 0.74735027, 0.76262631]), 380: array([-3.49475271, 0.95570453, 0.67692607]), 212: array([-3.69355384, 1.11207361, 0.55757124]), 169: array([-3.89301116, 1.21377124, 0.4140462 ]), 9: array([-4.08427974, 1.2651992 , 0.24492992]), 405: array([-4.26242468, 1.27237694, 0.08032449]), 361: array([-4.42868398, 1.23775236, -0.08105806]), 172: array([-3.50216079, -0.39548902, -1.0022329 ]), 126: array([-3.41868243, -0.4429558 , -1.00768412]), 408: array([-3.32990111, -0.4780421 , -0.99290154]), 362: array([-3.237128 , -0.49527713, -0.95994135]), 194: array([-3.14424126, -0.49104178, -0.91159432]), 148: array([-3.05590242, -0.4630991 , -0.85151149]), 430: array([-2.97701987, -0.41058971, -0.78303055]), 385: array([-2.91209718, -0.33397544, -0.71003726]), 341: array([-2.86494643, -0.23470251, -0.63665786]), 173: array([-2.8383362 , -0.11510187, -0.56636435]), 127: array([-2.83382304, 0.02162928, -0.50178673]), 409: array([-2.85624414, 0.16204885, -0.45043418]), 363: array([-2.89907811, 0.29195983, -0.41641292]), 196: array([-2.96015785, 0.40725148, -0.39947854]), 150: array([-3.03661732, 0.50398939, -0.3987191 ]), 112: array([-3.12396346, 0.5789042 , -0.4124251 ]), 387: array([-3.21790877, 0.62954355, -0.43839864]), 342: array([-3.31337518, 0.6545613 , -0.47328277]), 175: array([-3.40584912, 0.65318724, -0.51248618]), 129: array([-3.4952651 , 0.63555203, -0.55676794]), 95: array([-3.7872515 , 1.26918173, -1.08584908])} .. GENERATED FROM PYTHON SOURCE LINES 128-131 Plot the simplices using the vertex embedding ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 131-143 .. code-block:: Python fig = oat.plot.fig_3d_for_simplices( simplices = simplices, points = points, kwargs_points = {"marker": {"size": 3, "color": "white"}}, kwargs_edges = {"line": {"color": "white", "width": 3}}, ) fig.update_layout( height=700, ) fig .. raw:: html


.. GENERATED FROM PYTHON SOURCE LINES 144-146 Adjust the plot ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 146-156 .. code-block:: Python oat.plot.set_background_color(fig, "black") fig.update_layout( scene=dict( camera=dict( eye=dict(x=-0.3, y=-1.0, z=1.25), # Adjust x, y, z for position and zoom up=dict(x=1, y=1, z=0), # Z-axis points up center=dict(x=0, y=0, z=0) # Camera looks at the origin ) ) ) .. raw:: html


.. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.725 seconds) .. _sphx_glr_download_auto_examples_plotting_plot_vertex_embedding.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_vertex_embedding.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_vertex_embedding.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_vertex_embedding.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_