#!usr/bin/env python """Unit tests for fast metric scaling functions""" from cogent.util.unit_test import TestCase, main from cogent.cluster import goodness_of_fit from cogent.cluster.approximate_mds \ import nystrom from cogent.cluster.approximate_mds \ import calc_matrix_a, calc_matrix_b, build_seed_matrix from cogent.cluster.approximate_mds import rowmeans, \ affine_mapping, adjust_mds_to_ref, recenter, combine_mds, \ cmds_tzeng, CombineMds from numpy import array, matrix, random, argsort __author__ = "Andreas Wilm" __copyright__ = "Copyright 2007-2012, The Cogent Project" __credits__ = ["Andreas Wilm"] __license__ = "GPL" __version__ = "1.5.3" __maintainer__ = "Andreas Wilm" __email__ = "andreas.wilm@ucd.ie" __status__ = "FIXME" PRINT_STRESS = False # Bigish symmetrical matrix for testing: The following is a distance # matrix of 100 points making up a 16-dimensional spiral. Idea was # copied from Tzeng et al. 2008 (PMID 18394154). # # Note: the objects are ordered, i.e. permuting the distances will # give better MDS approximations # FULL_SYM_MATRIX = array([ [ 0. , 9.94319, 7.11402, 7.30016, 9.1998 , 7.52661, 10.1122 , 11.71544, 11.72171, 12.23729, 16.55706, 15.07764, 17.41182, 19.23286, 22.03428, 20.37969, 21.79021, 23.31804, 25.27884, 25.33384, 25.51721, 25.23346, 27.13757, 27.77099, 31.89744, 30.12906, 30.853 , 31.25053, 32.01368, 32.92915, 34.80687, 34.67094, 34.61157, 33.95445, 36.09099, 34.39821, 35.29278, 33.43954, 35.50327, 34.96861, 34.61776, 31.52205, 31.5479 , 31.86234, 30.85453, 29.69611, 29.41756, 28.83014, 30.11403, 28.76504, 23.7291 , 25.6983 , 25.97412, 25.13513, 24.45972, 21.55045, 21.69278, 19.95303, 16.26348, 17.11013, 14.32254, 17.62265, 15.44168, 17.37134, 13.90914, 11.73735, 12.23879, 12.84236, 16.11693, 14.78883, 14.85241, 16.81082, 15.84987, 19.49531, 19.10495, 20.82333, 22.2353 , 24.10629, 25.58022, 26.94421, 29.15922, 29.35633, 30.44926, 33.44155, 33.20634, 35.10944, 37.58041, 36.97612, 37.4974 , 39.19126, 41.96371, 39.49224, 44.24451, 44.49713, 46.20998, 45.17665, 43.34276, 45.20143, 42.75318, 46.74111], [ 9.94319, 0. , 9.15502, 9.50864, 4.67066, 8.73786, 10.65396, 7.07033, 7.65245, 11.7303 , 13.97535, 14.44678, 14.4366 , 17.67632, 17.78924, 17.34483, 20.92378, 19.64563, 22.37953, 22.50652, 22.59182, 23.16428, 25.36422, 24.53657, 28.53754, 28.8102 , 28.67001, 29.99149, 29.0992 , 30.78134, 32.60362, 33.06432, 32.35053, 31.31204, 33.96212, 32.70361, 34.0075 , 31.79899, 34.1394 , 34.08447, 34.40636, 32.09843, 31.55098, 32.21933, 29.68935, 30.64989, 29.84656, 30.31266, 30.95073, 29.50086, 25.13342, 26.92125, 26.77764, 25.45479, 26.64139, 24.28835, 23.54393, 21.14658, 19.0042 , 19.69926, 17.01569, 17.70308, 16.76036, 18.85088, 15.67933, 13.11373, 14.57384, 14.49709, 13.93834, 13.97627, 15.28133, 15.43603, 15.38908, 19.14731, 18.0164 , 19.25691, 20.79821, 21.17772, 23.34925, 24.69467, 25.91663, 26.0043 , 27.48027, 31.09767, 29.88905, 31.87226, 35.07482, 34.08161, 34.96767, 36.59085, 39.56174, 37.35437, 42.00158, 42.65467, 44.21824, 42.7808 , 41.49634, 42.89946, 41.51576, 45.2993 ], [ 7.11402, 9.15502, 0. , 6.86568, 9.13056, 6.40397, 9.71158, 8.69917, 8.75907, 9.94964, 12.60852, 10.83371, 13.24922, 15.56278, 18.00935, 17.28358, 18.64376, 18.74751, 21.30424, 20.79329, 22.52019, 21.17382, 24.35227, 24.04257, 27.79547, 27.14583, 27.9384 , 28.31876, 29.19352, 30.31387, 32.49497, 32.53298, 32.54342, 31.6677 , 34.4333 , 33.06171, 33.8104 , 32.32825, 34.54666, 33.66703, 34.21985, 31.60984, 31.44096, 32.23245, 30.68488, 30.737 , 30.20034, 30.13288, 31.62192, 30.13293, 25.84322, 27.91135, 28.12311, 27.30813, 27.01853, 24.69093, 24.94734, 23.21836, 20.37644, 20.92257, 17.85377, 20.91217, 19.36837, 20.86528, 17.38101, 14.14065, 15.49992, 14.33989, 17.43602, 15.89444, 14.88863, 15.37154, 15.57648, 18.73803, 17.66276, 19.14902, 19.51857, 21.56308, 22.21288, 23.47894, 25.86362, 25.36028, 26.33286, 29.98075, 29.33639, 31.30981, 33.73965, 33.6759 , 34.04663, 35.63369, 38.24726, 36.06871, 40.78921, 41.34813, 43.00012, 42.36618, 40.24461, 42.30763, 40.55066, 44.09355], [ 7.30016, 9.50864, 6.86568, 0. , 7.99096, 7.60197, 10.10639, 9.22165, 8.8801 , 9.49238, 13.66406, 12.57744, 13.13858, 15.46775, 17.73952, 16.56614, 18.40617, 19.64056, 21.45177, 22.03097, 21.88416, 22.61383, 24.92398, 25.28642, 29.08492, 27.8259 , 29.18638, 29.3961 , 30.42798, 31.81182, 33.20848, 33.36339, 34.03547, 33.03364, 35.82444, 34.7116 , 35.8487 , 33.89059, 36.02136, 35.60052, 36.08047, 33.37669, 33.34017, 33.79942, 32.42774, 31.97527, 31.72587, 31.85386, 33.66607, 32.0357 , 26.92882, 29.3656 , 29.6113 , 28.77098, 27.98344, 25.49869, 26.08835, 24.3511 , 21.22304, 21.25266, 18.87943, 21.25316, 19.09945, 20.88305, 16.98734, 14.43121, 14.87293, 12.60412, 16.25858, 14.52592, 14.10743, 13.84321, 13.02127, 16.58691, 15.13994, 17.45726, 18.68005, 20.17601, 21.41715, 23.0355 , 25.07801, 24.73817, 26.67714, 29.31584, 29.02044, 31.28387, 33.55744, 33.39091, 34.49413, 36.29427, 39.09789, 36.46602, 41.84873, 41.95262, 44.21519, 43.15904, 41.86844, 43.70448, 41.85398, 45.9426 ], [ 9.1998 , 4.67066, 9.13056, 7.99096, 0. , 8.10903, 8.12191, 6.68991, 6.01745, 8.81851, 12.76517, 13.05449, 13.25358, 16.08166, 16.85701, 14.96082, 18.58137, 18.78881, 21.03104, 21.37792, 20.97864, 22.24007, 23.27987, 23.47925, 27.51623, 27.08492, 27.63842, 28.49791, 28.08892, 29.94971, 31.60411, 32.35099, 31.64065, 30.7586 , 33.58783, 32.51966, 33.71852, 31.59205, 34.09468, 34.22325, 34.16007, 32.3283 , 31.89116, 32.43132, 30.52192, 31.02961, 30.1106 , 31.0687 , 31.53677, 30.2114 , 25.7518 , 27.6139 , 28.20037, 27.20175, 27.57982, 25.10337, 25.22312, 22.84998, 20.28434, 20.93006, 18.50018, 19.27925, 17.75401, 20.49716, 16.24356, 13.95706, 14.68697, 14.86848, 14.61363, 14.13096, 14.51717, 15.68778, 14.51018, 17.43174, 16.76305, 18.13449, 19.68793, 19.75357, 21.78947, 23.32496, 24.54554, 24.18059, 26.19812, 29.52194, 28.20267, 30.01717, 33.36934, 32.26088, 33.40864, 34.83176, 38.18059, 35.81903, 40.65885, 41.40321, 43.17206, 41.53149, 40.71829, 42.49124, 40.79031, 44.66045], [ 7.52661, 8.73786, 6.40397, 7.60197, 8.10903, 0. , 6.16569, 7.32563, 7.75387, 7.69682, 10.69552, 9.88725, 11.3961 , 14.00163, 16.23874, 15.6289 , 16.73334, 17.44048, 19.99725, 19.9533 , 20.46002, 19.84823, 22.72976, 23.22363, 27.33355, 26.83688, 27.09796, 28.27618, 28.3494 , 29.75656, 31.77772, 32.50386, 32.5482 , 31.99727, 34.67355, 33.19062, 34.46902, 33.13995, 35.80184, 35.25591, 35.33808, 33.38177, 33.04059, 33.91149, 32.75336, 32.5993 , 32.43664, 32.23116, 33.38874, 32.62237, 28.36209, 30.55605, 30.3347 , 29.56765, 29.58556, 27.53405, 26.86667, 25.00712, 21.74171, 23.02809, 19.62897, 22.0497 , 20.71073, 20.89719, 18.9401 , 14.67542, 15.87359, 14.84921, 15.9765 , 14.6316 , 13.43337, 14.09887, 13.393 , 15.35339, 15.15473, 15.57783, 16.38066, 18.12999, 19.33544, 20.47957, 22.53012, 23.41117, 23.94749, 27.14785, 27.12172, 29.01223, 32.1432 , 31.53822, 31.97442, 34.20046, 36.96213, 35.11644, 39.86917, 40.59916, 42.25278, 42.35218, 40.45489, 42.53407, 40.64863, 44.57547], [ 10.1122 , 10.65396, 9.71158, 10.10639, 8.12191, 6.16569, 0. , 8.95464, 7.95483, 6.96854, 10.2321 , 9.1072 , 11.40191, 13.88653, 16.49484, 12.77356, 14.76539, 17.37815, 19.05223, 19.09134, 19.48543, 19.25793, 20.07018, 21.44923, 26.16354, 24.71872, 25.7368 , 26.60446, 26.8787 , 27.97926, 30.01728, 31.59176, 31.2204 , 30.74726, 33.36662, 32.19782, 33.24557, 32.26498, 35.20755, 35.27066, 34.3224 , 33.45572, 33.21501, 33.77282, 32.98931, 33.29691, 32.48639, 32.89237, 33.31269, 33.17576, 29.06571, 31.25932, 31.50259, 31.19405, 31.33608, 28.94501, 28.98748, 26.83509, 23.67883, 25.4293 , 22.19619, 23.92894, 22.48331, 23.70778, 20.61034, 16.80414, 17.54135, 17.64634, 18.13698, 16.73796, 15.0992 , 16.73965, 15.39915, 15.3146 , 16.21818, 15.90665, 16.80116, 17.15962, 18.1004 , 20.22697, 21.04317, 22.01882, 23.10616, 25.70386, 25.33855, 26.90823, 30.27089, 29.34631, 29.92087, 31.66778, 35.17056, 33.31352, 37.56416, 39.27059, 40.62456, 40.2062 , 39.40489, 41.81369, 39.33236, 43.20546], [ 11.71544, 7.07033, 8.69917, 9.22165, 6.68991, 7.32563, 8.95464, 0. , 3.7505 , 6.85568, 7.69523, 9.7299 , 8.8292 , 12.08808, 12.84075, 12.41397, 15.7665 , 13.80821, 17.10528, 17.0151 , 18.03523, 18.49492, 21.4005 , 20.91953, 24.56468, 24.98275, 25.20224, 26.47583, 26.01966, 28.37676, 30.43507, 31.12544, 31.08021, 29.96861, 33.06401, 32.57304, 33.997 , 32.11079, 34.68809, 34.12659, 35.42161, 33.62916, 33.16394, 34.14988, 31.96731, 33.13473, 32.68089, 33.34788, 34.37908, 32.97516, 29.38917, 31.30679, 31.86587, 30.67301, 31.14565, 29.06828, 29.04268, 27.11562, 24.63125, 25.08637, 22.31814, 23.71491, 22.41495, 23.87865, 20.79483, 17.13811, 18.05839, 16.67094, 16.67337, 15.59013, 15.29917, 14.46026, 14.31921, 16.68845, 14.41634, 16.10611, 16.76691, 16.68857, 18.02822, 19.23566, 20.91886, 19.93191, 21.22647, 25.60087, 24.01222, 26.23519, 29.55426, 29.01695, 29.67471, 31.85062, 34.7836 , 32.77038, 38.06911, 38.63774, 40.78472, 39.75408, 38.43139, 40.51321, 39.43324, 43.19846], [ 11.72171, 7.65245, 8.75907, 8.8801 , 6.01745, 7.75387, 7.95483, 3.7505 , 0. , 6.25554, 7.94184, 9.40809, 9.37058, 12.64537, 13.25671, 11.69312, 15.73247, 14.29708, 17.17558, 17.07269, 18.18613, 18.66698, 20.99351, 20.83302, 24.42795, 24.65435, 25.16361, 26.40833, 26.00333, 28.48816, 30.39505, 31.12778, 31.04052, 30.02038, 33.06101, 32.51077, 33.91746, 32.16109, 34.72522, 34.26106, 35.29431, 33.7662 , 33.40285, 34.11146, 32.13639, 33.33042, 32.66608, 33.38514, 34.29769, 32.89254, 29.26526, 31.06269, 32.01605, 30.75263, 31.17672, 28.89607, 29.20958, 27.32181, 24.53975, 25.21252, 22.16274, 23.60181, 22.19147, 23.8951 , 20.57865, 17.20223, 17.67657, 16.61788, 17.05001, 15.68349, 15.30447, 14.95815, 14.4235 , 16.70277, 14.6234 , 16.24885, 16.87216, 16.49137, 17.85663, 19.18505, 20.91421, 19.70914, 21.64589, 25.6927 , 24.18448, 26.08005, 29.35354, 29.00965, 29.70327, 31.74665, 34.68077, 32.64932, 37.91062, 38.78521, 40.83826, 39.61926, 38.5705 , 40.69567, 39.56802, 43.04025], [ 12.23729, 11.7303 , 9.94964, 9.49238, 8.81851, 7.69682, 6.96854, 6.85568, 6.25554, 0. , 7.3016 , 8.07212, 8.2089 , 9.98656, 12.42781, 10.62705, 12.28722, 13.48977, 16.04661, 16.19534, 16.3577 , 17.32154, 19.0178 , 20.5046 , 23.95953, 23.43756, 24.50878, 25.26128, 25.60517, 28.0269 , 30.02525, 31.11886, 31.15891, 30.49865, 33.86459, 33.37975, 34.65544, 33.14589, 36.03802, 35.51766, 36.24468, 35.04257, 34.67094, 35.65553, 34.59658, 34.79422, 34.36677, 35.45895, 36.3779 , 35.3327 , 31.54706, 33.65312, 34.74652, 33.95725, 33.40518, 31.44167, 31.93944, 30.05815, 26.96615, 27.64338, 24.84473, 26.74278, 24.89471, 26.39705, 22.80323, 19.30856, 19.43576, 18.22819, 18.64491, 17.05169, 14.82973, 15.51568, 14.01205, 14.33961, 13.3435 , 14.52817, 14.70497, 14.77414, 15.56051, 16.74031, 18.93591, 17.75143, 19.27456, 22.94456, 21.91537, 23.84675, 27.42168, 26.76934, 27.66108, 29.75946, 33.0935 , 30.98471, 36.65424, 37.30058, 39.65202, 39.12975, 38.02632, 40.69416, 39.21815, 43.02089], [ 16.55706, 13.97535, 12.60852, 13.66406, 12.76517, 10.69552, 10.2321 , 7.69523, 7.94184, 7.3016 , 0. , 6.34024, 6.29442, 9.31874, 10.60831, 9.48152, 11.679 , 9.86008, 12.78319, 12.47705, 15.20036, 14.79868, 18.06249, 17.95878, 21.80304, 21.94482, 22.94088, 24.29869, 24.32754, 26.55776, 29.0597 , 30.47032, 31.03937, 29.92437, 33.13454, 33.19895, 34.69406, 33.79095, 36.57048, 36.01451, 37.16413, 36.42303, 36.18591, 37.09342, 35.61312, 37.27428, 36.78719, 37.18274, 38.417 , 37.62287, 34.72634, 36.87088, 37.5226 , 36.63014, 37.07125, 35.13839, 35.36933, 33.57977, 30.77296, 31.75893, 28.54674, 30.22502, 28.99081, 29.49656, 27.01958, 22.64011, 23.11653, 21.4745 , 21.88627, 19.79573, 18.19257, 16.9958 , 16.94848, 16.33478, 14.10467, 14.58976, 14.07395, 12.99207, 12.74353, 13.92433, 15.69868, 14.25548, 15.27649, 19.74988, 18.25877, 20.80091, 23.91183, 24.08524, 24.27307, 27.16596, 30.02343, 28.55089, 33.83448, 35.47091, 37.51809, 37.42083, 36.17692, 39.05643, 38.09928, 41.43184], [ 15.07764, 14.44678, 10.83371, 12.57744, 13.05449, 9.88725, 9.1072 , 9.7299 , 9.40809, 8.07212, 6.34024, 0. , 6.9511 , 8.1817 , 12.01962, 9.83166, 10.03616, 10.82597, 12.22157, 12.42638, 14.81562, 13.24075, 15.91179, 16.17176, 20.81994, 19.82228, 21.65753, 22.19242, 23.10866, 24.91478, 26.51025, 27.84524, 28.94428, 28.23706, 31.0608 , 30.49635, 31.58452, 31.13131, 34.00834, 33.61703, 34.00148, 33.33828, 33.20841, 33.84176, 33.36215, 34.29352, 34.00194, 34.24137, 35.53305, 35.23732, 32.32311, 34.68689, 34.89579, 34.4585 , 34.33839, 33.07445, 33.23999, 31.99141, 28.83607, 30.27728, 27.08538, 29.42086, 28.13654, 28.78396, 26.43445, 22.12388, 23.17097, 21.90119, 23.31711, 21.43302, 19.21266, 18.09438, 18.37291, 17.67573, 16.69031, 16.42476, 15.74665, 15.65608, 14.72969, 16.18704, 17.54084, 16.84414, 17.82539, 20.46911, 20.57828, 21.7296 , 24.02904, 24.20871, 24.33682, 26.71437, 29.08875, 27.8246 , 32.39523, 33.86684, 35.84499, 36.03478, 34.76023, 37.39742, 35.57779, 39.06011], [ 17.41182, 14.4366 , 13.24922, 13.13858, 13.25358, 11.3961 , 11.40191, 8.8292 , 9.37058, 8.2089 , 6.29442, 6.9511 , 0. , 5.80269, 7.34823, 7.61967, 8.88048, 8.03171, 10.84203, 11.15163, 12.21275, 12.34706, 16.11929, 16.0975 , 19.45663, 20.33958, 21.24043, 22.37157, 22.50594, 24.89152, 26.47231, 28.19409, 29.03612, 28.11855, 31.78424, 31.68759, 33.16023, 32.00993, 35.12134, 34.61314, 36.07251, 35.37259, 34.85009, 36.19004, 34.77939, 36.03767, 35.84771, 37.05029, 38.33912, 37.71305, 34.34605, 36.90215, 37.11372, 36.56462, 36.48557, 35.26936, 35.32999, 33.72941, 31.33676, 32.09544, 29.33582, 31.07569, 29.78355, 30.69899, 27.88792, 23.6909 , 24.95077, 22.44497, 22.73515, 21.53386, 19.39791, 17.15086, 17.26961, 16.50911, 14.97885, 14.84698, 14.0348 , 13.16584, 12.28025, 14.13143, 14.59832, 13.82806, 14.44424, 17.8433 , 16.98162, 19.04357, 22.24141, 22.05366, 22.98183, 25.33998, 28.35413, 26.6982 , 32.11611, 32.88203, 35.32819, 35.61998, 34.74136, 37.0847 , 36.06984, 40.03816], [ 19.23286, 17.67632, 15.56278, 15.46775, 16.08166, 14.00163, 13.88653, 12.08808, 12.64537, 9.98656, 9.31874, 8.1817 , 5.80269, 0. , 7.38877, 8.41906, 6.8504 , 7.29774, 9.2088 , 10.31162, 9.70575, 10.45564, 13.73927, 14.84133, 17.61261, 18.12427, 19.27123, 19.82935, 20.31297, 23.84286, 24.56468, 25.91998, 27.59428, 26.89288, 30.55842, 30.76624, 32.23747, 30.8686 , 34.10976, 33.50914, 35.42056, 34.64547, 34.19767, 35.53408, 35.0925 , 35.58014, 35.82126, 37.49003, 38.6495 , 38.10808, 35.42106, 37.82413, 38.53678, 38.03388, 37.13566, 36.62481, 36.8622 , 35.93997, 33.1206 , 33.81829, 31.46152, 33.72103, 32.12859, 33.34453, 30.4796 , 26.68134, 27.47971, 25.54979, 25.74229, 24.75989, 22.16485, 20.06477, 20.06272, 19.02226, 17.40359, 17.54345, 16.56831, 15.07742, 13.83543, 14.50581, 15.50799, 13.55086, 13.77702, 16.34443, 16.4955 , 17.40327, 20.09447, 19.53993, 20.64083, 23.14301, 25.73473, 23.91935, 30.1514 , 29.62866, 33.12758, 33.46496, 32.47884, 35.00942, 33.91675, 38.06303], [ 22.03428, 17.78924, 18.00935, 17.73952, 16.85701, 16.23874, 16.49484, 12.84075, 13.25671, 12.42781, 10.60831, 12.01962, 7.34823, 7.38877, 0. , 9.98466, 10.45042, 7.01399, 9.5126 , 10.22698, 8.29332, 10.75866, 15.09764, 14.55 , 16.07545, 19.17678, 18.69286, 20.74564, 19.36248, 23.2144 , 24.62428, 26.05861, 27.01352, 25.91131, 30.18725, 30.6706 , 32.78994, 31.0901 , 34.2731 , 33.85408, 36.35145, 35.76726, 35.06246, 36.69763, 35.34281, 36.84744, 36.8362 , 38.82735, 39.99487, 39.19622, 36.6623 , 39.10442, 39.88191, 38.95773, 38.89602, 38.43435, 38.31651, 37.10258, 34.93565, 35.54241, 33.22748, 34.83971, 33.64244, 34.72378, 32.11209, 28.69735, 29.37637, 27.27617, 26.28932, 25.69016, 23.88593, 21.52732, 21.55272, 20.82185, 18.79088, 18.59526, 17.84671, 15.16618, 14.82818, 14.49505, 15.15638, 12.82821, 12.71296, 15.97897, 14.73869, 16.7043 , 19.42872, 18.50832, 20.11721, 22.55747, 25.22857, 23.0396 , 29.71055, 29.41731, 32.39176, 32.91178, 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17.6646 , 19.57784, 19.94906, 20.85881, 20.58748, 25.22437, 28.10747, 27.61326, 29.72708, 30.50207, 33.76313, 34.57233, 37.70556, 38.86882, 39.8812 , 42.53511, 44.98107, 47.05231, 47.06461, 46.87143, 49.64106, 50.61611, 51.99425, 52.1621 , 53.32 , 53.08869, 55.50578, 54.94413, 58.22332, 55.4712 , 53.92575, 55.78262, 55.43629, 55.76022, 55.54874, 54.48838, 53.03856, 53.18936, 52.69689, 51.31535, 50.97824, 49.8669 , 47.23448, 45.16766, 45.17244, 43.95332, 40.15198, 37.67062, 38.15204, 36.03614, 34.37541, 29.3083 , 28.64282, 27.20938, 24.13398, 21.68822, 19.6484 , 18.41451, 14.74353, 12.86819, 11.78426, 6.63421, 0. , 8.83043, 8.80103], [ 42.75318, 41.51576, 40.55066, 41.85398, 40.79031, 40.64863, 39.33236, 39.43324, 39.56802, 39.21815, 38.09928, 35.57779, 36.06984, 33.91675, 34.18837, 33.47656, 31.31277, 33.5043 , 29.47687, 28.60458, 28.39343, 26.15777, 24.09575, 22.23873, 20.9814 , 18.30611, 17.0517 , 15.52057, 16.96968, 13.96013, 11.80224, 10.23459, 12.12231, 12.80535, 10.96839, 13.95903, 14.73243, 16.52504, 17.8264 , 18.68724, 20.37247, 24.43796, 24.23459, 25.83973, 27.94986, 30.48797, 31.19456, 34.12645, 34.90814, 36.95114, 39.36061, 42.0262 , 43.63606, 44.40938, 43.90372, 46.62981, 47.78862, 49.21381, 49.27814, 50.79307, 50.68305, 53.14199, 52.52346, 56.01087, 53.09032, 51.51095, 53.64081, 53.67147, 54.37677, 54.10548, 52.87226, 51.85091, 51.82288, 50.98398, 50.31884, 49.73738, 48.80525, 46.50554, 44.28871, 45.04898, 43.33299, 40.34494, 38.17835, 38.01118, 36.48471, 34.48999, 29.80644, 28.83705, 27.40981, 23.94398, 22.49918, 20.7999 , 17.69405, 15.81852, 13.30844, 11.47244, 10.22093, 8.83043, 0. , 7.46263], [ 46.74111, 45.2993 , 44.09355, 45.9426 , 44.66045, 44.57547, 43.20546, 43.19846, 43.04025, 43.02089, 41.43184, 39.06011, 40.03816, 38.06303, 37.85652, 37.35049, 35.47796, 36.83706, 32.87905, 31.58328, 32.42605, 29.63547, 27.8713 , 25.49112, 23.64271, 21.75684, 20.42138, 19.39125, 20.31666, 17.63429, 16.78251, 14.84621, 15.73701, 16.20137, 13.95765, 16.88417, 17.36648, 20.00963, 20.38759, 20.88898, 22.75393, 27.26505, 27.25467, 28.4507 , 30.43803, 33.78487, 34.11927, 36.59337, 37.3594 , 39.24277, 42.55081, 44.83658, 46.86818, 47.37281, 47.26843, 49.95592, 51.26349, 52.79329, 52.86302, 54.50537, 54.16762, 56.6705 , 56.22352, 59.61459, 56.86156, 55.33784, 57.31579, 57.5573 , 58.38252, 57.89195, 56.74007, 55.85643, 55.93366, 55.16405, 54.28067, 53.71283, 52.57763, 50.1937 , 47.87966, 48.29225, 46.9185 , 43.38612, 41.31302, 41.47549, 39.63076, 37.48156, 32.34705, 32.02712, 30.03519, 26.50431, 24.09327, 23.08624, 18.89004, 18.51871, 14.52224, 12.76638, 9.98474, 8.80103, 7.46263, 0. ]]) class FastMetricScmdsScalingTests(TestCase): """test the functions to do metric scaling""" def setUp(self): """creates inputs""" self.dist_func = lambda x, y: (FULL_SYM_MATRIX[x, y]) self.num_objects = FULL_SYM_MATRIX.shape[0] def test_scmds_cmds_tzeng(self): """cmds_tzeng() should return eigenvectors and eigenvalues, sorted by the eigenvalues """ dim = 3 (eigvec, eigval) = cmds_tzeng(FULL_SYM_MATRIX, dim) self.assertTrue(len(eigval) == dim) self.assertTrue(eigvec.shape == (FULL_SYM_MATRIX.shape[0], dim)) self.assertTrue(sorted(eigval, reverse=True) == eigval.tolist()) self.assertFloatEqual(eigval[0], 27336.883436) self.assertFloatEqual(eigval[-1], 536.736247) self.assertFloatEqual(eigvec[0, 0], -14.978621) self.assertFloatEqual(eigvec[-1, -1], 0.673001) # full pcoa dim = FULL_SYM_MATRIX.shape[0] (eigvec, eigval) = cmds_tzeng(FULL_SYM_MATRIX, dim) self.assertTrue(len(eigval) == dim) self.assertTrue(eigvec.shape == (FULL_SYM_MATRIX.shape[0], dim)) self.assertTrue(sorted(eigval, reverse=True) == eigval.tolist()) self.assertFloatEqual(eigval[0], 27336.883436043929) self.assertFloatEqual(eigval[-1], 0.000000) self.assertFloatEqual(eigvec[0, 0], -14.978621) self.assertFloatEqual(eigvec[-1, -1], 0.000000) def test_scmds_rowmeans(self): """rowmeans() should return a vector of row-means for a 2d matrix. """ rm = rowmeans(FULL_SYM_MATRIX[:10]) self.assertTrue(rm.shape[0] == 10) self.assertFloatEqual(float(rm[0]), 25.983320) self.assertFloatEqual(float(rm[-1]), 23.967050) def test_scmds_recenter(self): """recenter() should recenter an mds solution """ mds_coords = matrix([ [-3.78333558, -2.90925004, 2.75333034], [ 5.18887751, -1.2130882 , -0.86476508], [-3.10404298, -0.6620052 , -3.91668873], [-2.53758526, 3.99102424, 0.86289149], [ 4.23608631, 0.7933192 , 1.16523198]]) centered_coords = recenter(mds_coords) self.assertTrue(centered_coords.shape == mds_coords.shape) center_of_gravity = sum([centered_coords[:, x].sum() \ for x in range(centered_coords.shape[1])]) self.assertFloatEqual(center_of_gravity, 0.0) def test_scmds_affine_mapping(self): """affine_mapping() should return a touple of two matrices of certain shape """ matrix_x = matrix([ [-24.03457111, 10.10355666, -23.17039728, 28.48438894, 22.57322482], [ 0.62716392, 20.84502664, 6.42317521, -7.66901011, 14.37923852], [ -2.60793417, 2.83532649, 2.91024821, 1.37414959, -4.22916659]]) matrix_y = matrix([ [-29.81089477, -2.01312927, -30.5925487 , 23.05985801, 11.68581751], [ -4.68879117, 23.62633294, 1.07934315, 0.57461989, 20.52800221], [ -0.51503505, 1.18377044, 0.83671471, 1.81751358, -3.28812925]]) dim = matrix_x.shape[0] (tu, tb) = affine_mapping(matrix_x, matrix_y) self.assertTrue(tu.shape[0] == dim and tb.shape[0] == dim) self.assertTrue(tu.shape[0] == tu.shape[1]) self.assertFloatEqual(tu[0, 0], 0.966653) self.assertFloatEqual(tu[-1, -1], 0.994816) self.assertFloatEqual(tb[0, 0], -6.480975) self.assertFloatEqual(tb[-1, -1], 0.686521) def test_scmds_adjust_mds_to_ref(self): """adjust_mds_to_ref() should return an adjusted mds solutions""" overlap = 5 dim = 3 size = 10 fake_mds_coords_ref = FULL_SYM_MATRIX[:size, :dim] fake_mds_coords_add = FULL_SYM_MATRIX[overlap:size+overlap, :dim] mds_adj = adjust_mds_to_ref(fake_mds_coords_ref, fake_mds_coords_add, overlap) self.assertTrue(mds_adj.shape == fake_mds_coords_add.shape) self.assertFloatEqual(mds_adj[0, 0], 7.526609) self.assertFloatEqual(mds_adj[-1, -1], 18.009350) def test_scmds_combine_mds(self): """combine_mds() should merge two mds solutions """ overlap = 3 dim = 3 mds_coords_1 = matrix([ [-3.78333558, -2.90925004, 2.75333034], [ 5.18887751, -1.2130882 , -0.86476508], [-3.10404298, -0.6620052 , -3.91668873], [-2.53758526, 3.99102424, 0.86289149], [ 4.23608631, 0.7933192 , 1.16523198]]) mds_coords_2 = matrix([ [-3.78333558, -2.90925004, 2.75333034], [ 5.18887751, -1.2130882 , -0.86476508], [-3.10404298, -0.6620052 , -3.91668873], [-2.53758526, 3.99102424, 0.86289149], [ 4.23608631, 0.7933192 , 1.16523198]]) comb_mds = combine_mds(mds_coords_1, mds_coords_2, overlap) self.assertTrue(comb_mds.shape == ( mds_coords_1.shape[0]*2-overlap, dim)) self.assertFloatEqual(comb_mds[0, 0], -3.783335) #self.assertFloatEqual(comb_mds[-1, -1], 0.349951) def test_scmds_class_combinemds(self): """class CombineMds() should be able to join MDS solutions """ # tmp note # tile1 = FULL_SYM_MATRIX[0:5, 0:5] # tile2 = FULL_SYM_MATRIX[2:7, 2:7] # mds_coords_1 = cmds_tzeng(tile1, 3) # mds_coords_2 = cmds_tzeng(tile2, 3) overlap = 3 mds_coords_1 = matrix([ [-3.78333558, -2.90925004, 2.75333034], [ 5.18887751, -1.2130882 , -0.86476508], [-3.10404298, -0.6620052 , -3.91668873], [-2.53758526, 3.99102424, 0.86289149], [ 4.23608631, 0.7933192 , 1.16523198]]) mds_coords_2 = matrix([ [-3.78333558, -2.90925004, 2.75333034], [ 5.18887751, -1.2130882 , -0.86476508], [-3.10404298, -0.6620052 , -3.91668873], [-2.53758526, 3.99102424, 0.86289149], [ 4.23608631, 0.7933192 , 1.16523198]]) comb_mds = CombineMds() comb_mds.add(mds_coords_1, overlap) comb_mds.add(mds_coords_2, overlap) final_mds = comb_mds.getFinalMDS() self.assertTrue(final_mds.shape == (mds_coords_1.shape[0]*2-overlap, mds_coords_1.shape[1])) #self.assertFloatEqual(final_mds[0, 0], 0.0393279) #self.assertFloatEqual(final_mds[-1, -1], -5.322599) class FastMetricNystromScalingTests(TestCase): """test the functions to do metric scaling""" def setUp(self): """creates inputs""" self.big_seed_matrix = FULL_SYM_MATRIX[:49] self.small_seed_matrix = FULL_SYM_MATRIX[:25] def test_calc_matrix_a(self): """calc_matrix_a should calculate a k x k matrix of (predefined) association matrix K of certain (predefined) value""" nseeds = self.small_seed_matrix.shape[0] matrix_e = self.small_seed_matrix[:, 0:nseeds] matrix_a = calc_matrix_a(matrix_e) self.assertFloatEqual(matrix_a[0, 0], 250.032270) self.assertFloatEqual(matrix_a[-1][-1], 316.875461) def test_nystrom_build_seed_matrix(self): """build_seed_matrix() should return a seedmatrix and an order """ seedmat_dim = 10 dist_func = lambda x, y: (FULL_SYM_MATRIX[x, y]) (seedmat, order) = build_seed_matrix( FULL_SYM_MATRIX.shape[0], seedmat_dim, dist_func) self.assertTrue(len(order) == FULL_SYM_MATRIX.shape[0]) self.assertTrue(sorted(order) == range(FULL_SYM_MATRIX.shape[0])) self.assertTrue(seedmat.shape == ( seedmat_dim, FULL_SYM_MATRIX.shape[0])) # build_seed_matrix randomises order ind = argsort(order) i = random.randint(0, seedmat.shape[0]) j = random.randint(0, seedmat.shape[1]) self.assertFloatEqual(seedmat[i, j], FULL_SYM_MATRIX[ind[i], ind[j]]) def test_nystrom(self): """nystrom() should return an MDS approximation""" dim = 3 mds_coords = nystrom(self.big_seed_matrix, dim) self.assertTrue(len(mds_coords.shape) == 2) self.assertTrue(mds_coords.shape[0] == self.big_seed_matrix.shape[1]) self.assertTrue(mds_coords.shape[1] == dim) self.assertFloatEqual(mds_coords[0, 0], -10.709626) self.assertFloatEqual(mds_coords[-1, -1], -1.778160) def test_nystrom_seed_number(self): """nystrom() should give better MDS approximations the more seeds were used""" dim = 3 mds_coords = nystrom(self.big_seed_matrix, dim) stress = goodness_of_fit.Stress(FULL_SYM_MATRIX, mds_coords) kruskal_stress_big_mat = stress.calcKruskalStress() if PRINT_STRESS: print("INFO: Kruskal stress for Nystrom MDS (big_seed_matrix, dim=%d) = %f" % \ (dim, kruskal_stress_big_mat)) self.assertTrue(kruskal_stress_big_mat < 0.04) mds_coords = nystrom(self.small_seed_matrix, dim) stress = goodness_of_fit.Stress(FULL_SYM_MATRIX, mds_coords) kruskal_stress_small_mat = stress.calcKruskalStress() if PRINT_STRESS: print("INFO: Kruskal stress for Nystrom MDS (small_seed_matrix, dim=%d) = %f" % \ (dim, kruskal_stress_small_mat)) self.assertTrue(kruskal_stress_small_mat < 0.06) self.assertTrue(kruskal_stress_small_mat > kruskal_stress_big_mat) def test_calc_matrix_b(self): """calc_matrix_b should calculate a k x n-k matrix of association matrix K """ nseeds = self.small_seed_matrix.shape[0] matrix_e = self.small_seed_matrix[:, 0:nseeds] matrix_f = self.small_seed_matrix[:, nseeds:] matrix_b = calc_matrix_b(matrix_e, matrix_f) self.assertTrue(matrix_b.shape == matrix_f.shape) self.assertFloatEqual(matrix_b[0, 0], -272.711227) self.assertFloatEqual(matrix_b[-1, -1], -64.898372) #run if called from the command line if __name__ == '__main__': main()