0
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graph of multi-valued function

The graphed data look like this. I need to extract the data for each curve individually and use Interpolation to create a differentiable function for each curve. Can you show how to do this?

I will need to select data that falls between certain ranges. Ideally, I need to define a function xmin[t] and xmax[t] and select all data that falls between those limits.

Here is the data:

{{0.0001, {3.33812, 0.291642, 1.25777, 2.22443}}, {0.0002, {3.4381, 
0.320099, 1.28631, 2.25285}}, {0.0003, {3.53812, 0.341598, 2.27456,
1.3081}}, {0.0004, {3.6381, 0.358445, 2.29152, 
1.32505}}, {0.0005, {3.73812, 0.372028, 2.30516, 
1.33859}}, {0.0006, {3.8381, 2.31621, 1.3496, 
0.383104}}, {0.0007, {3.93812, 2.32534, 1.35872, 
0.392211}}, {0.0008, {4.03811, 2.33303, 1.36642, 
0.399914}}, {0.0009, {4.13811, 2.33961, 1.37303, 
0.406549}}, {0.001, {4.23811, 2.34531, 1.37876, 
0.412299}}, {0.0011, {4.33811, 2.35031, 1.38379, 
0.417339}}, {0.0012, {4.43812, 2.35474, 0.421802, 
1.38826}}, {0.0013, {4.5381, 1.39232, 2.3587, 
0.425801}}, {0.0014, {4.63812, 1.39593, 2.36227, 
0.429397}}, {0.0015, {4.7381, 1.39919, 2.3655, 
0.432651}}, {0.0016, {4.83812, 1.40215, 2.36846, 
0.435615}}, {0.0017, {4.9381, 1.40487, 2.37117, 
0.438333}}, {0.0018, {5.03811, 1.40737, 2.37368, 
0.440839}}, {0.0019, {5.1381, 1.40969, 2.37601, 
0.443162}}, {0.002, {5.23811, 1.41184, 2.37819, 
0.445325}}, {0.0021, {5.33811, 1.41385, 2.38022, 
0.447348}}, {0.0022, {5.43811, 1.41574, 2.38214, 
0.449249}}, {0.0023, {5.53812, 1.41752, 2.38395, 
0.451041}}, {0.0024, {5.6381, 1.41921, 2.38566, 
0.452738}}, {0.0025, {5.73812, 1.42081, 2.38729, 
0.45435}}, {0.0026, {2.38885, 5.8381, 1.42233, 
0.455887}}, {0.0027, {2.39031, 5.93812, 1.42379, 
0.457356}}, {0.0028, {6.0381, 1.42518, 0.458765, 
2.39172}}, {0.0029, {6.13811, 1.42652, 0.460121, 
2.39308}}, {0.003, {6.23811, 1.42781, 0.461429, 
2.39438}}, {0.0031, {6.33811, 1.42906, 0.462694, 
2.39564}}, {0.0032, {6.43812, 1.43028, 0.46392, 
2.39686}}, {0.0033, {6.5381, 1.43145, 0.465113, 
2.39805}}, {0.0034, {6.63812, 1.4326, 0.466276, 
2.39921}}, {0.0035, {6.7381, 0.467414, 1.43372, 
2.40034}}, {0.0036, {6.83812, 0.468534, 1.43482, 
2.40144}}, {0.0037, {6.9381, 0.469631, 1.43589, 
2.40252}}, {0.0038, {7.03812, 0.470709, 1.43695, 
2.40359}}, {0.0039, {7.1381, 0.471771, 1.43799, 
2.40464}}, {0.004, {7.23811, 0.472818, 1.43902, 
2.40567}}, {0.0041, {7.33811, 0.473854, 1.44004, 
2.4067}}, {0.0042, {7.43811, 0.474881, 1.44105, 
2.40771}}, {0.0043, {7.53812, 0.4759, 1.44206, 
2.40872}}, {0.0044, {7.63811, 0.476915, 1.44306, 
2.40973}}, {0.0045, {7.73812, 0.477927, 1.44406, 
2.41074}}, {0.0046, {7.8381, 0.478939, 1.44506, 
2.41174}}, {0.0047, {7.93812, 0.479952, 1.44606, 
2.41274}}, {0.0048, {8.0381, 0.480969, 1.44707, 
2.41375}}, {0.0049, {8.13812, 0.481992, 1.44809, 
2.41477}}, {0.005, {8.2381, 0.483024, 1.44911, 
2.41579}}, {0.0051, {8.33811, 0.484065, 1.45015, 
2.41682}}, {0.0052, {8.43811, 0.48512, 1.45119, 
2.41787}}, {0.0053, {8.53811, 0.486191, 1.45226, 
2.41894}}, {0.0054, {8.63811, 0.487279, 1.45335, 
2.42002}}, {0.0055, {8.7381, 0.488389, 1.45445, 
2.42112}}, {0.0056, {0.489522, 1.45559, 2.42225, 
8.83811}}, {0.0057, {0.490683, 1.45675, 2.42341, 
8.93811}}, {0.0058, {0.491875, 1.45794, 
2.42459}}, {0.0059, {0.493101, 1.45917, 
2.42582}}, {0.006, {0.494366, 1.46044, 
2.42708}}, {0.0061, {0.495675, 1.46175, 
2.42839}}, {0.0062, {0.497032, 1.46312, 
2.42974}}, {0.0063, {0.498444, 1.46454, 
2.43115}}, {0.0064, {0.499918, 1.46603, 
2.43263}}, {0.0065, {0.50146, 1.46759, 
2.43419}}, {0.0066, {0.503079, 1.46923, 
2.43582}}, {0.0067, {0.504785, 1.47096, 
2.43755}}, {0.0068, {0.506588, 1.47279, 
2.43937}}, {0.0069, {0.508502, 1.47473, 
2.4413}}, {0.007, {0.510541, 1.47681, 
2.44336}}, {0.0071, {0.512723, 1.47904, 
2.44556}}, {0.0072, {1.48141, 0.515068, 
2.44792}}, {0.0073, {0.517602, 2.45048, 
1.48397}}, {0.0074, {0.520354, 2.45325, 
1.48675}}, {0.0075, {0.52336, 2.45627, 
1.48978}}, {0.0076, {0.526663, 2.4596, 
1.49312}}, {0.0077, {0.53032, 2.46327, 
1.4968}}, {0.0078, {0.534398, 2.46737, 
1.50091}}, {0.0079, {0.538986, 2.47197, 
1.50551}}, {0.008, {0.544197, 2.47719, 
1.51073}}, {0.0081, {0.55018, 1.51669, 
2.48316}}, {0.0082, {0.557127, 2.49011, 
1.52359}}, {0.0083, {2.49817, 1.53163, 
0.56518}}, {0.0084, {2.50771, 1.54117, 
0.574717}}, {0.0085, {2.5192, 1.55267, 
0.586233}}, {0.0086, {2.53335, 0.600412, 
1.56688}}, {0.0087, {1.58491, 2.55123, 
0.61839}}, {0.0088, {1.60793, 0.641552, 
2.57447}}, {0.0089, {0.672227, 1.63838, 
2.60505}}, {0.009, {0.713472, 2.64647, 
1.67997}}, {0.0091, {2.70345, 1.73691, 
0.770497}}, {0.0092, {2.78061, 0.847133, 
1.81329}}, {0.0093, {2.87386, 1.90741, 
0.940996}}, {0.0094, {2.97355, 1.03865, 2.00498, 0.0873681, 
0.0488886}}, {0.0095, {3.07352, 2.08944, 0.156519, 1.123, 
0.0220564}}, {0.0096, {3.17355, 2.15397, 1.18737, 
0.22091}}, {0.0097, {2.20105, 3.27352, 1.23452, 
0.268062}}, {0.0098, {3.37354, 0.302724, 1.26878, 
2.23542}}, {0.0099, {3.47353, 0.328366, 2.26121, 
1.29471}}, {0.01, {3.57354, 0.348013, 2.28102, 
1.31458}}, {0.0101, {3.67353, 0.363577, 2.29666, 
1.33018}}, {0.0102, {3.77354, 0.376234, 2.30933, 
1.34274}}, {0.0103, {3.87354, 2.31963, 1.35302, 
0.386513}}, {0.0104, {3.97353, 2.32821, 1.36159, 
0.395083}}, {0.0105, {4.07355, 2.33548, 1.36888, 
0.402378}}, {0.0106, {4.17353, 2.34172, 1.37515, 
0.408677}}, {0.0107, {4.27355, 2.34716, 1.38061, 
0.414158}}, {0.0108, {4.37353, 1.38543, 2.35194, 
0.41898}}, {0.0109, {4.47354, 2.35619, 0.423268, 
1.38972}}, {0.011, {4.57353, 1.39364, 2.36001, 
0.427118}}, {0.0111, {4.67354, 1.39712, 2.36345, 
0.430586}}, {0.0112, {4.77353, 1.40027, 2.36658, 
0.433732}}, {0.0113, {4.87354, 1.40314, 2.36945, 
0.436605}}, {0.0114, {4.97354, 1.40578, 2.37209, 
0.439244}}, {0.0115, {5.07353, 1.40821, 2.37453, 
0.441682}}, {0.0116, {5.17355, 1.41047, 2.3768, 
0.443945}}, {0.0117, {5.27353, 1.41257, 2.37892, 
0.446057}}, {0.0118, {5.37355, 1.41454, 2.38091, 
0.448035}}, {0.0119, {5.47353, 1.41639, 2.38279, 
0.449895}}, {0.012, {5.57355, 1.41813, 2.38457, 
0.451653}}, {0.0121, {5.67353, 1.41978, 2.38625, 
0.453319}}, {0.0122, {5.77354, 1.42135, 2.38785, 
0.454903}}, {0.0123, {2.38937, 5.87353, 1.42285, 
0.456415}}, {0.0124, {2.39082, 5.97354, 1.42429, 
0.457862}}, {0.0125, {6.07355, 1.42566, 0.459252, 
2.39221}}, {0.0126, {6.17353, 1.42698, 0.46059, 
2.39354}}, {0.0127, {6.27355, 1.42826, 0.461882, 
2.39483}}, {0.0128, {6.37353, 1.4295, 0.463132, 
2.39608}}, {0.0129, {6.47355, 1.4307, 0.464347, 
2.39729}}, {0.013, {6.57352, 1.43186, 0.465528, 
2.39847}}, {0.0131, {6.67354, 1.433, 0.466681, 
2.39961}}, {0.0132, {6.77353, 0.467814, 1.43411, 
2.40073}}, {0.0133, {6.87354, 0.468925, 1.4352, 
2.40183}}, {0.0134, {6.97354, 0.470015, 1.43627, 
2.4029}}, {0.0135, {7.07353, 0.471087, 1.43732, 
2.40396}}, {0.0136, {7.17354, 0.472143, 1.43836, 
2.405}}, {0.0137, {7.27353, 0.473186, 1.43938, 
2.40604}}, {0.0138, {7.37355, 0.474219, 1.4404, 
2.40706}}, {0.0139, {7.47353, 0.475242, 1.44141, 
2.40807}}, {0.014, {7.57355, 0.47626, 1.44241, 
2.40908}}, {0.0141, {7.67353, 0.477274, 1.44341, 
2.41009}}, {0.0142, {7.77355, 0.478285, 1.44441, 
2.41109}}, {0.0143, {7.87353, 0.479297, 1.44541, 
2.41209}}, {0.0144, {7.97354, 0.480312, 1.44642, 
2.4131}}, {0.0145, {8.07353, 0.481331, 1.44743, 
2.41411}}, {0.0146, {8.17354, 0.482357, 1.44845, 
2.41513}}, {0.0147, {8.27354, 0.483391, 1.44948, 
2.41615}}, {0.0148, {8.37353, 0.484438, 1.45052, 
2.41719}}, {0.0149, {8.47355, 0.485498, 1.45157, 
2.41825}}, {0.015, {8.57353, 0.486574, 1.45264, 
2.41932}}, {0.0151, {8.67355, 0.48767, 1.45374, 
2.42041}}, {0.0152, {8.77353, 0.488787, 1.45485, 
2.42152}}, {0.0153, {0.48993, 1.45599, 8.87354, 
2.42266}}, {0.0154, {0.491101, 1.45717, 2.42382, 
8.97354}}, {0.0155, {0.492305, 1.45837, 
2.42502}}, {0.0156, {0.493544, 1.45961, 
2.42626}}, {0.0157, {0.494824, 1.4609, 
2.42754}}, {0.0158, {0.49615, 1.46223, 
2.42886}}, {0.0159, {0.497526, 1.46362, 
2.43024}}, {0.016, {0.498959, 1.46506, 
2.43167}}, {0.0161, {0.500456, 1.46657, 
2.43317}}, {0.0162, {0.502024, 1.46816, 
2.43476}}, {0.0163, {0.503673, 1.46983, 
2.43642}}, {0.0164, {0.505412, 1.47159, 
2.43818}}, {0.0165, {0.507253, 1.47346, 
2.44004}}, {0.0166, {0.509209, 1.47545, 
2.44201}}, {0.0167, {0.511296, 1.47758, 
2.44412}}, {0.0168, {1.47987, 0.513534, 
2.44638}}, {0.0169, {0.515943, 2.44881, 1.4823}}, {0.017, {0.51855,
 2.45143, 1.48493}}, {0.0171, {0.521388, 2.45429, 
1.48779}}, {0.0172, {0.524493, 2.45741, 
1.49093}}, {0.0173, {0.527915, 2.46085, 
1.49438}}, {0.0174, {0.531713, 2.46467, 
1.4982}}, {0.0175, {0.53596, 2.46893, 
1.50248}}, {0.0176, {0.540754, 2.47374, 
1.50728}}, {0.0177, {0.546219, 2.47921, 
1.51274}}, {0.0178, {0.552521, 1.51901, 
2.48548}}, {0.0179, {2.49282, 1.52629, 
0.559833}}, {0.018, {2.50136, 1.53482, 
0.568369}}, {0.0181, {2.51153, 1.54499, 
0.57854}}, {0.0182, {2.52386, 1.55735, 
0.590906}}, {0.0183, {2.53918, 0.606305, 
1.57274}}, {0.0184, {1.5924, 2.55876, 0.625895}}, {0.0185, {1.6177,
 2.58433, 0.651412}}, {0.0186, {0.685375, 1.65168, 
2.61827}}, {0.0187, {0.731725, 2.66467, 
1.69818}}, {0.0188, {1.76178, 2.72803, 
0.795243}}, {0.0189, {2.81221, 0.878696, 
1.84513}}, {0.019, {1.94265, 2.90897, 
0.976116}}, {0.0191, {3.00897, 1.07048, 2.03706, 0.104111, 
0.0366898}}, {0.0192, {3.10896, 1.14814, 0.181627, 0.0157184, 
2.1146}}, {0.0193, {3.20897, 2.17229, 0.239378, 
1.20583}}, {0.0194, {3.30896, 1.24784, 0.281525, 
2.21446}}, {0.0195, {3.40896, 0.312661, 1.27876, 
2.24534}}, {0.0196, {3.50897, 0.335892, 2.26881, 
1.30233}}, {0.0197, {3.60896, 0.353921, 2.28697, 
1.32052}}, {0.0198, {3.70898, 0.368347, 2.30149, 
1.33493}}, {0.0199, {0.380122, 3.80896, 2.31321, 
1.34661}}, {0.02, {3.90897, 2.32285, 1.35623, 
0.389715}}, {0.0201, {4.00896, 2.33092, 1.36431, 
0.397794}}, {0.0202, {4.10897, 2.33779, 1.3712, 
0.404715}}, {0.0203, {4.20895, 2.34373, 1.37717, 
0.410703}}, {0.0204, {4.30897, 2.34892, 1.38239, 
0.415935}}, {0.0205, {4.40896, 1.38701, 2.3535, 
0.420554}}, {0.0206, {4.50896, 1.39119, 2.35759, 
0.42468}}, {0.0207, {4.60897, 1.39491, 2.36126, 
0.428387}}, {0.0208, {4.70896, 1.39827, 2.36459, 
0.431734}}, {0.0209, {4.80897, 1.40132, 2.36762, 
0.434778}}, {0.021, {4.90896, 1.4041, 2.37041, 
0.437565}}, {0.0211, {5.00898, 1.40666, 2.37297, 
0.440129}}, {0.0212, {5.10895, 1.40903, 2.37535, 
0.442502}}, {0.0213, {5.20897, 1.41123, 2.37757, 
0.44471}}, {0.0214, {5.30895, 1.41328, 2.37964, 
0.446772}}, {0.0215, {5.40897, 1.4152, 2.38159, 
0.448706}}, {0.0216, {5.50896, 1.41702, 2.38343, 
0.450529}}, {0.0217, {5.60897, 1.41873, 2.38517, 
0.452253}}, {0.0218, {5.70897, 1.42035, 2.38683, 
0.453889}}, {0.0219, {5.80896, 1.42189, 2.3884, 
0.455446}}, {0.022, {2.38989, 5.90897, 1.42337, 
0.456934}}, {0.0221, {6.00896, 1.42478, 0.458361, 
2.39132}}, {0.0222, {6.10898, 1.42614, 0.459731, 
2.39269}}, {0.0223, {6.20895, 1.42744, 0.461052, 
2.39401}}, {0.0224, {6.30897, 1.4287, 0.462329, 
2.39528}}, {0.0225, {6.40896, 1.42993, 0.463567, 
2.39651}}, {0.0226, {6.50897, 1.43111, 0.464769, 
2.39771}}, {0.0227, {6.60896, 1.43227, 0.46594, 
2.39888}}, {0.0228, {6.70896, 0.467083, 1.4334, 
2.40001}}, {0.0229, {6.80897, 0.46821, 1.4345, 
2.40112}}, {0.023, {6.90896, 0.469314, 1.43558, 
2.40221}}, {0.0231, {7.00898, 0.470397, 1.43664, 
2.40328}}, {0.0232, {7.10895, 0.471463, 1.43769, 
2.40433}}, {0.0233, {7.20897, 0.472514, 1.43872, 
2.40537}}, {0.0234, {7.30896, 0.473553, 1.43974, 
2.4064}}, {0.0235, {7.40897, 0.474582, 1.44076, 
2.40742}}, {0.0236, {7.50896, 0.475604, 1.44177, 
2.40843}}, {0.0237, {7.60897, 0.476619, 1.44277, 
2.40944}}, {0.0238, {7.70896, 0.477632, 1.44377, 
2.41044}}, {0.0239, {7.80896, 0.478644, 1.44477, 
2.41145}}, {0.024, {7.90897, 0.479656, 1.44577, 
2.41245}}, {0.0241, {8.00896, 0.480672, 1.44678, 
2.41346}}, {0.0242, {8.10897, 0.481693, 1.44779, 
2.41447}}, {0.0243, {8.20896, 0.482722, 1.44881, 
2.41549}}, {0.0244, {8.30897, 0.483761, 1.44984, 
2.41652}}, {0.0245, {8.40896, 0.484811, 1.45089, 
2.41756}}, {0.0246, {8.50897, 0.485877, 1.45195, 
2.41862}}, {0.0247, {8.60896, 0.48696, 1.45303, 
2.4197}}, {0.0248, {8.70897, 0.488063, 1.45413, 
2.4208}}, {0.0249, {0.489189, 1.45525, 2.42192, 
8.80897}}, {0.025, {0.490342, 1.4564, 2.42307, 
8.90896}}, {0.0251, {0.491524, 1.45759, 
2.42424}}, {0.0252, {0.49274, 1.45881, 
2.42546}}, {0.0253, {0.493993, 1.46006, 
2.42671}}, {0.0254, {0.495288, 1.46137, 
2.428}}, {0.0255, {0.496631, 1.46272, 
2.42934}}, {0.0256, {0.498027, 1.46412, 
2.43074}}, {0.0257, {0.499482, 1.46559, 
2.43219}}, {0.0258, {0.501003, 1.46713, 
2.43373}}, {0.0259, {0.502599, 1.46874, 
2.43534}}, {0.026, {0.504278, 1.47044, 
2.43704}}, {0.0261, {0.506052, 1.47224, 
2.43883}}, {0.0262, {0.507932, 1.47415, 
2.44073}}, {0.0263, {0.509933, 1.47619, 
2.44274}}, {0.0264, {0.512071, 1.47837, 
2.4449}}, {0.0265, {1.48071, 0.514367, 
2.44722}}, {0.0266, {0.516843, 2.44971,1.48321}}, {0.0267, {0.519527, 
2.45242, 
1.48592}}, {0.0268, {0.522455, 2.45536, 
1.48887}}, {0.0269, {0.525667, 2.45859, 
1.49211}}, {0.027, {0.529214, 2.46216, 
1.49569}}, {0.0271, {0.533161, 2.46612, 
1.49966}}, {0.0272, {0.53759, 2.47057, 
1.50411}}, {0.0273, {0.542606, 2.4756, 
1.50914}}, {0.0274, {0.548346, 1.51486, 
2.48133}}, {0.0275, {0.554995, 2.48799, 
1.52147}}, {0.0276, {2.49569, 1.52915, 
0.562696}}, {0.0277, {2.50475, 1.53821, 
0.571759}}, {0.0278, {2.51562, 1.54908, 
0.582638}}, {0.0279, {2.5289, 1.5624, 0.59595}}, {0.028, {1.57922, 
2.54554, 0.612701}}, {0.0281, {2.56706, 1.60059, 
0.634137}}, {0.0282, {0.662392, 1.62853, 
2.59522}}, {0.0283, {0.700052, 2.63303, 
1.66648}}, {0.0284, {2.68508, 1.7185, 
0.752084}}, {0.0285, {1.78907, 2.75548, 
0.822583}}, {0.0286, {0.912242, 2.84526, 
1.87877}}, {0.0287, {1.01085, 1.97738, 
2.94442}}, {0.0288, {1.10033, 3.04438, 2.06679, 0.133875, 
0.0280543}}, {0.0289, {0.0100796, 3.1444, 2.13728, 1.17065, 
0.204121}}, {0.029, {3.24438, 1.22238, 2.18874, 
0.255848}}, {0.0291, {3.3444, 0.2937, 1.25981, 
2.22647}}, {0.0292, {3.44438, 0.321624, 1.28786, 
2.2544}}, {0.0293, {3.5444, 0.342775, 2.27575, 
1.30929}}, {0.0294, {3.64438, 0.359383, 2.29246, 
1.32599}}, {0.0295, {3.7444, 0.372795, 2.30592, 
1.33935}}, {0.0296, {3.84438, 2.31683, 1.35022, 
0.383725}}, {0.0297, {3.9444, 2.32586, 1.35924, 
0.392733}}, {0.0298, {4.04439, 2.33348, 1.36687, 
0.40036}}, {0.0299, {4.14439, 2.33999, 1.37341, 
0.406934}}, {0.03, {4.2444, 2.34565, 1.37909, 
0.412635}}, {0.0301, {4.34439, 2.35061, 1.38409, 
0.417635}}, {0.0302, {4.4444, 2.355, 0.422066, 
1.38852}}, {0.0303, {4.54438, 1.39256, 2.35894, 
0.426039}}, {0.0304, {4.6444, 1.39614, 2.36248, 
0.429611}}, {0.0305, {4.74438, 1.39938, 2.3657, 
0.432845}}, {0.0306, {4.8444, 1.40233, 2.36864, 
0.435793}}, {0.0307, {4.94439, 1.40503, 2.37134, 
0.438497}}, {0.0308, {5.04439, 1.40752, 2.37383, 
0.44099}}, {0.0309, {5.14439, 1.40983, 2.37615, 
0.443302}}, {0.031, {5.24439, 1.41197, 2.37832, 
0.445456}}, {0.0311, {5.3444, 1.41398, 2.38035, 
0.447471}}, {0.0312, {5.44439, 1.41586, 2.38225, 
0.449364}}, {0.0313, {5.5444, 1.41763, 2.38406, 
0.451151}}, {0.0314, {5.64438, 1.41931, 2.38577, 
0.452842}}, {0.0315, {5.7444, 1.4209, 2.38739, 
0.454449}}, {0.0316, {2.38894, 5.84438, 1.42242, 
0.455981}}, {0.0317, {2.39041, 5.9444, 1.42387, 
0.457446}}, {0.0318, {6.04439, 1.42527, 0.458852, 
2.39181}}, {0.0319, {6.14439, 1.4266, 0.460205, 
2.39316}}, {0.032, {6.24439, 1.42789, 0.461509, 
2.39446}}, {0.0321, {6.34439, 1.42914, 0.462772, 
2.39572}}, {0.0322, {6.4444, 1.43035, 0.463996, 
2.39694}}, {0.0323, {6.54438, 1.43153, 0.465187, 
2.39813}}, {0.0324, {6.6444, 1.43267, 0.466348, 
2.39928}}, {0.0325, {6.74438, 0.467485, 1.43379, 
2.40041}}, {0.0326, {6.8444, 0.468603, 1.43488, 
2.40151}}, {0.0327, {6.94438, 0.4697, 1.43596, 
2.40259}}, {0.0328, {7.0444, 0.470777, 1.43702, 
2.40365}}, {0.0329, {7.14439, 0.471837, 1.43806, 
2.4047}}, {0.033, {7.24439, 0.472884, 1.43909, 
2.40574}}, {0.0331, {7.3444, 0.473919, 1.4401, 
2.40676}}, {0.0332, {7.44439, 0.474945, 1.44112, 
2.40778}}, {0.0333, {7.5444, 0.475964, 1.44212, 
2.40879}}, {0.0334, {7.64439, 0.476978, 1.44312, 
2.4098}}, {0.0335, {7.7444, 0.477991, 1.44412, 
2.4108}}, {0.0336, {7.84438, 0.479002, 1.44512, 2.4118}}}

I need to find data that falls within certain ranges. Can you show me how to separate out the data for each curve in the graph individually?

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  • $\begingroup$ It sounds like you already know what you need to do for this one (i.e. use Interpolation). Have you tried using Interpolation on each part of your dataset? $\endgroup$ – MassDefect Nov 4 at 23:35
1
$\begingroup$

Here's a start:

data = CloudGet[
   "https://www.wolframcloud.com/obj/55c838a4-7856-4dba-9e50-3317fdb0f33b"];

(curves = 
   Flatten[Thread /@ data, 1][[#]] & /@ 
    FindCurvePath[
     Flatten[Thread /@ 
       Thread[{Rescale@data[[All, 1]], Rescale@data[[All, 2]]}], 
      1]]) // ListLinePlot

enter image description here

fns = Interpolation /@ DeleteDuplicatesBy[First] /@ curves;
ListLinePlot[fns]

enter image description here

There are some problems with duplicated abscissae, but they can probably be handled by hand. Inspect:

curves[[{5, 6}]]
curves[[{8, 7}]]
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  • $\begingroup$ Thanks, this works. Can you help me - where do I find documentation on this Thread /@ data, 1][[#]] & /@ $\endgroup$ – Klandgren Nov 5 at 1:56
  • $\begingroup$ @Klandgren You can look up Thread and Function and Map. You can also enter & and /@ into the search bar of the documentation, or search this Q&A for the shortcut symbols: mathematica.stackexchange.com/a/25616/4999 $\endgroup$ – Michael E2 Nov 5 at 2:00
  • $\begingroup$ Perfect, thanks. I am re-writing into those commands that I understand better. You did some slick Mathematica programming. $\endgroup$ – Klandgren Nov 5 at 2:43

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