在Python中拟合3D散点图数据

Question

我正试图顺利地适应3D中的一些不规则数据点。

我有z值的数据点不在网格上，但它们确实遵循某种模式。有一组有限的整数y值（比如10,14,30,41等），对于每一个，我都有一组~100 x个浮点值，范围从0以某种随机非均匀的方式得到1。

对于我的情况，重要的是让拟合通过所有初始数据点（或者如果不是这样的话，至少要有最大限度）。

因此，我首先尝试的数据是使用griddata中的scipy.interpolate。如果我使用线性拟合，我会得到一张我期望的图片：

然而，立方插值对我不起作用。首先，它显然是因为我有许多对齐点而永远挂起，但可以通过在我所做的每个y值上添加一些微小的随机数来修复（参见这个问题：Alternatives to scipy.interpolate.griddata that don't hang on aligned points）。但它会产生狂野振荡的结果：

所以，问题是如何调整数据和/或算法来处理它？如果不可能，我可以使用哪种其他插值方法来创建一个接近原始曲面的平滑曲面，并且Python是否有实现？

要试用的一些示例数据：

x = [0.95568, 0.94055, 0.91823, 0.88796, 0.84862, 0.79112, 0.7164900000000001,          0.6240399999999999, 0.5173399999999999, 0.40369, 0.29454, 0.20756, 0.14302, 0.09365, 0.06564, 0.04701, 0.95658, 0.95192, 0.94714, 0.94223, 0.93716, 0.93034, 0.92336, 0.91618, 0.90876, 0.89963, 0.89024, 0.87918, 0.86782, 0.85608, 0.84268, 0.82767, 0.81219, 0.79511, 0.77554, 0.75548, 0.73397, 0.71104, 0.68674, 0.66057, 0.6332599999999999, 0.6045, 0.57483, 0.5442199999999999, 0.51271, 0.48081999999999997, 0.44866999999999996, 0.41712, 0.38525, 0.35475, 0.32392, 0.29431999999999997, 0.26863000000000004, 0.24311, 0.22016999999999998, 0.19732, 0.17751, 0.15778, 0.14337, 0.1293, 0.11547, 0.10378, 0.09437000000000001, 0.08304, 0.0762, 0.06959, 0.06316000000000001, 0.056870000000000004, 0.05305, 0.04938, 0.04583, 0.04239, 0.04141, 0.95758, 0.95418, 0.9507099999999999, 0.94718, 0.9424, 0.93871, 0.93379, 0.92769, 0.9226, 0.91635, 0.91001, 0.90355, 0.89695, 0.88925, 0.8814, 0.8725, 0.86346, 0.85424, 0.844, 0.83358, 0.82218, 0.81057, 0.79801, 0.78522, 0.77151, 0.75695, 0.74212, 0.7259599999999999, 0.7095400000000001, 0.6928000000000001, 0.67492, 0.65671, 0.6375500000000001, 0.61807, 0.59798, 0.57735, 0.5562, 0.5346, 0.51262, 0.49051999999999996, 0.46813, 0.44582, 0.42352, 0.40166999999999997, 0.37961, 0.35773, 0.33666, 0.31537, 0.29589, 0.27712, 0.25829, 0.24111999999999997, 0.22393000000000002, 0.2087, 0.19242, 0.1783, 0.16417, 0.15253, 0.14231, 0.13223, 0.12222999999999999, 0.11374000000000001, 0.10535, 0.09702000000000001, 0.09031, 0.08367999999999999, 0.07057999999999999, 0.0658, 0.06283, 0.0582, 0.055389999999999995, 0.05265, 0.049980000000000004, 0.047369999999999995, 0.04481, 0.95916, 0.95644, 0.95368, 0.94994, 0.94709, 0.94328, 0.93942, 0.9355100000000001, 0.93155, 0.92752, 0.92258, 0.91841, 0.91333, 0.90739, 0.89607, 0.88363, 0.86937, 0.86207, 0.85465, 0.84645, 0.8375, 0.82845, 0.81925, 0.80935, 0.79878, 0.7885800000000001, 0.7772300000000001, 0.7540800000000001, 0.7418199999999999, 0.72936, 0.71632, 0.70275, 0.68897, 0.6744300000000001, 0.6597, 0.64455, 0.6290100000000001, 0.61327, 0.58075, 0.54713, 0.52998, 0.5126999999999999, 0.47773999999999994, 0.46008999999999994, 0.44242, 0.42504, 0.4075, 0.38974000000000003, 0.37248000000000003, 0.35545, 0.33824, 0.32234, 0.30695, 0.27663000000000004, 0.26236, 0.24877, 0.2223, 0.19730999999999999, 0.18517, 0.17392, 0.15335, 0.14518, 0.13709000000000002, 0.1222, 0.11542000000000001, 0.10869000000000001, 0.09658, 0.08592000000000001, 0.07537999999999999, 0.0677, 0.060160000000000005, 0.05566, 0.04986, 0.04565, 0.04155, 0.9578, 0.9522, 0.94897, 0.94571, 0.93909, 0.93572, 0.93157, 0.92387, 0.9146, 0.90512, 0.89475, 0.88291, 0.8708, 0.8572500000000001, 0.85036, 0.84285, 0.82759, 0.81933, 0.81098, 0.8025100000000001, 0.7935, 0.77511, 0.76534, 0.75507, 0.74468, 0.73414, 0.72314, 0.7117100000000001, 0.70014, 0.6883900000000001, 0.67624, 0.66372, 0.6508499999999999, 0.63783, 0.62449, 0.61087, 0.59709, 0.58306, 0.56881, 0.5543899999999999, 0.53978, 0.52502, 0.51024, 0.49533, 0.4804, 0.46531000000000006, 0.45023, 0.43518999999999997, 0.42025, 0.40544, 0.3905, 0.37573, 0.3608, 0.34648, 0.33249, 0.31934, 0.30618, 0.29296, 0.28021999999999997, 0.268, 0.25575, 0.24408000000000002, 0.23304, 0.22129000000000001, 0.21091, 0.20052, 0.19009, 0.18043, 0.17073, 0.16276, 0.14783, 0.13495, 0.12225, 0.11645, 0.11068, 0.10494, 0.10029, 0.09568, 0.0911, 0.08655, 0.08202000000000001, 0.07867, 0.07418, 0.07089, 0.06762, 0.06116, 0.056029999999999996, 0.05414, 0.05099, 0.047330000000000004, 0.04023, 0.95692, 0.94198, 0.92747, 0.9099, 0.9, 0.88993, 0.87805, 0.86599, 0.8532299999999999, 0.83973, 0.8251, 0.80977, 0.77629, 0.75789, 0.74871, 0.71942, 0.69878, 0.67726, 0.66622, 0.65489, 0.63163, 0.61971, 0.6075999999999999, 0.57047, 0.55782, 0.54503, 0.5321199999999999, 0.48023999999999994, 0.46718000000000004, 0.45416999999999996, 0.42828, 0.40247, 0.37711, 0.35202, 0.28007, 0.25742, 0.23735, 0.18382, 0.12552, 0.11413, 0.1047, 0.09735, 0.08913, 0.08307, 0.07607, 0.05196, 0.95684, 0.95154, 0.94005, 0.92637, 0.91001, 0.88141, 0.87061, 0.82046, 0.79141, 0.75937, 0.74222, 0.7059500000000001, 0.68668, 0.66683, 0.6566000000000001, 0.6462600000000001, 0.61404, 0.60303, 0.54618, 0.48743000000000003, 0.46386000000000005, 0.45203000000000004, 0.41678000000000004, 0.30339, 0.26345999999999997, 0.21106, 0.18027, 0.14079, 0.12022000000000001, 0.09763, 0.06905, 0.04882]

y = [5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 63, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 96, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 125, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 157, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187, 187]

z = [0.22435679999999997, 0.2142728, 0.2057014, 0.1968387, 0.1865643, 0.1796222, 0.17312629999999998, 0.16746, 0.16087820000000003, 0.15840410000000002, 0.1555075, 0.15833699999999998, 0.162905, 0.1655981, 0.1740023, 0.1830651, 0.3173607, 0.3141693, 0.3103343, 0.3059325, 0.3010236, 0.29817009999999994, 0.2945795, 0.2903363, 0.2855052, 0.28205630000000004, 0.27788779999999996, 0.2747509, 0.27082059999999997, 0.2661676, 0.26225640000000006, 0.2589043, 0.254695, 0.25088649999999996, 0.2484922, 0.24507220000000002, 0.24173200000000003, 0.23839229999999997, 0.23498379999999996, 0.2323808, 0.2295386, 0.227307, 0.22472129999999998, 0.22174899999999997, 0.21921300000000002, 0.2179324, 0.21616149999999998, 0.2156397, 0.2137493, 0.2131757, 0.21121109999999998, 0.2097163, 0.21087199999999998, 0.210788, 0.2116495, 0.21128049999999998, 0.21214299999999997, 0.211811, 0.2146356, 0.2166123, 0.2176525, 0.21949929999999998, 0.2224562, 0.22256820000000002, 0.22624740000000002, 0.2294154, 0.23202870000000003, 0.2340288, 0.23844570000000004, 0.24255429999999997, 0.2463399, 0.2497837, 0.256654, 0.3265555, 0.3239183, 0.32090609999999997, 0.3175562, 0.3160885, 0.3120466, 0.30971770000000004, 0.3087986, 0.30556690000000003, 0.303637, 0.30122990000000005, 0.2983908, 0.295156, 0.2928952, 0.2901738, 0.2882425, 0.28581090000000003, 0.2829183, 0.2806566, 0.2779074, 0.2756775, 0.2729446, 0.27064109999999997, 0.2678258, 0.2653658, 0.26320079999999996, 0.260491, 0.2587889, 0.25649970000000005, 0.2536468, 0.2516623, 0.2490801, 0.2472737, 0.2448443, 0.24246020000000004, 0.2400991, 0.2377411, 0.2360094, 0.2336024, 0.23242979999999996, 0.2305617, 0.22927460000000002, 0.2279277, 0.22717960000000004, 0.22572289999999998, 0.2242105, 0.2233436, 0.22174970000000002, 0.22159279999999998, 0.22150509999999998, 0.22073520000000002, 0.2208658, 0.2203379, 0.22086889999999998, 0.21986309999999998, 0.2200442, 0.2195909, 0.22059220000000002, 0.2221877, 0.2233259, 0.22397229999999999, 0.22539499999999998, 0.22638089999999997, 0.2268911, 0.2284279, 0.22957579999999997, 0.23055279999999997, 0.232251, 0.2356695, 0.23681100000000002, 0.23983890000000002, 0.24270160000000002, 0.2453939, 0.2479096, 0.250241, 0.3320691, 0.32972009999999996, 0.327113, 0.32625570000000004, 0.3231124, 0.3215746, 0.3196973, 0.3175134, 0.3150502, 0.31233059999999996, 0.3107871, 0.3075553, 0.3054195, 0.3042283, 0.299627, 0.2949814, 0.2911661, 0.28878190000000004, 0.286107, 0.2840244, 0.2824596, 0.2805393, 0.2782853, 0.276471, 0.2750419, 0.2725318, 0.2710885, 0.26709390000000005, 0.2652112, 0.262967, 0.260981, 0.25922399999999995, 0.2570881, 0.25572670000000003, 0.2539644, 0.25236420000000004, 0.2509092, 0.24904690000000002, 0.24570100000000003, 0.2422638, 0.2409471, 0.2397154, 0.2369755, 0.23546060000000002, 0.2340183, 0.2331739, 0.2318828, 0.2301334, 0.22899679999999997, 0.2279498, 0.2264395, 0.2261656, 0.22604139999999998, 0.22510679999999997, 0.2249176, 0.22495259999999997, 0.22446420000000003, 0.22370749999999998, 0.2230614, 0.2227643, 0.22260990000000003, 0.22373089999999998, 0.22456220000000002, 0.2262969, 0.22724429999999998, 0.22791370000000002, 0.22953600000000002, 0.23131880000000002, 0.23203249999999997, 0.2346393, 0.23642559999999999, 0.24096170000000003, 0.2431212, 0.24664070000000002, 0.2496571, 0.33568990000000004, 0.3323899, 0.3312173, 0.3297465, 0.3260212, 0.3238114, 0.3227546, 0.31851399999999996, 0.3157475, 0.31193000000000004, 0.3081958, 0.30537109999999995, 0.3015, 0.2983052, 0.29632179999999997, 0.2948481, 0.29110759999999997, 0.2895523, 0.2877298, 0.2856533, 0.28396409999999994, 0.2798044, 0.27794009999999997, 0.2763865, 0.2745558, 0.2724577, 0.270638, 0.2690729, 0.2672236, 0.2650978, 0.2632022, 0.261519, 0.2600321, 0.2582472, 0.256644, 0.25521020000000005, 0.2534704, 0.2518887, 0.2504563, 0.24871, 0.24710429999999997, 0.24563320000000002, 0.2447436, 0.243529, 0.24243969999999998, 0.24102220000000002, 0.2397272, 0.23855549999999998, 0.2375092, 0.23659229999999998, 0.235341, 0.23422110000000002, 0.23275860000000004, 0.23191660000000003, 0.23123139999999998, 0.2312197, 0.2308987, 0.2302589, 0.22982170000000002, 0.22960830000000002, 0.2290843, 0.22880830000000002, 0.228809, 0.22791129999999998, 0.2279124, 0.2276229, 0.2270263, 0.2267863, 0.2262448, 0.22684320000000002, 0.2280863, 0.2300344, 0.2311638, 0.23185279999999997, 0.2323363, 0.23260229999999996, 0.23365740000000002, 0.2345442, 0.2352545, 0.23577889999999999, 0.23610570000000003, 0.23744459999999998, 0.237389, 0.2384175, 0.23930059999999997, 0.2405984, 0.24279650000000003, 0.24451889999999998, 0.24447689999999997, 0.24740340000000002, 0.2521253, 0.3245058, 0.3180594, 0.3126934, 0.3080352, 0.3057295, 0.3025071, 0.3008695, 0.2982377, 0.2954341, 0.2924375, 0.28985259999999996, 0.28697940000000005, 0.2814263, 0.2791592, 0.2774252, 0.2728833, 0.2698403, 0.26680290000000007, 0.2651647, 0.2637353, 0.2610313, 0.2597459, 0.25863800000000003, 0.2546754, 0.25341060000000004, 0.2518993, 0.2505452, 0.247048, 0.2460449, 0.24519210000000002, 0.24353870000000002, 0.24168850000000003, 0.2400663, 0.23827089999999998, 0.23288040000000002, 0.231019, 0.2306532, 0.2300663, 0.2283889, 0.22863720000000004, 0.22986700000000002, 0.2323381, 0.23337829999999998, 0.23591220000000002, 0.23694320000000002, 0.24616210000000002, 0.3323315, 0.33019509999999996, 0.3247211, 0.31962840000000003, 0.315317, 0.30788730000000003, 0.3053588, 0.29530209999999996, 0.2897451, 0.2842533, 0.2815665, 0.2757268, 0.27296190000000004, 0.2698501, 0.2684138, 0.2667857, 0.2630827, 0.26183429999999996, 0.2552114, 0.25014339999999996, 0.2485022, 0.2475529, 0.24493779999999998, 0.2358408, 0.2340855, 0.2329842, 0.2322835, 0.2317147, 0.2329453, 0.23787809999999998, 0.24544570000000004, 0.25218320000000005]