# Concatenating a table of ordered pairs

probs = Sort[
loadFiles["/Users/boymommy148/Desktop/fall2017ResearchStuff/path/",
"*fsv*"], #1[[1]] < #2[[1]] &];
probs = Table[
Table[{probs[[i, 1]], probs[[i, 2, j]]}, {i, 1,
Length[probs]}], {j, 1, Length[probs[[1, 2]]]}];
For[i = 1, i <= Length[probs], i++,
For[j = 1, j <= Length[probs[[i]]], j++,
If[probs[[i, j, 2]] <= 0.1,
probs[[i, j, 2]] = Round[probs[[i, j, 2]], 0.001],
If[probs[[i, j, 2]] <= 0.25,
probs[[i, j, 2]] = Round[probs[[i, j, 2]], 0.01],
probs[[i, j, 2]] = Round[probs[[i, j, 2]], 0.1]
];
]
]
]


Hi there everyone! So this code here is creating a table for me consisting of ordered pairs of the form (x,y) where x is the electric field value, and y is the amplitude in a specified state. An example of probs is the following table:

{{0., 1.}, {0.073, 1.}, {0.369, 1.}, {0.664, 1.}, {0.96, 1.}, {1.255,
1.}, {1.506, 1.}, {1.757, 1.}, {2.008, 1.}, {2.259, 1.}, {2.51,
1.}, {2.761, 1.}, {3.012, 1.}, {3.263, 1.}, {3.514, 1.}, {3.765,
1.}, {4.017, 1.}, {4.267, 1.}, {4.517, 1.}, {4.767, 1.}, {5.017,
1.}, {5.267, 1.}, {5.518, 1.}, {5.77, 1.}, {6.022, 1.}, {6.272,
1.}, {6.522, 1.}, {6.774, 1.}, {7.024, 1.}, {7.276, 1.}, {7.528,
1.}, {7.779, 1.}, {8.03, 1.}, {8.281, 1.}, {8.532, 1.}, {8.784,
1.}, {9.035, 1.}, {9.285, 1.}, {9.537, 1.}, {9.788, 1.}, {10.038,
1.}, {10.288, 1.}, {10.539, 1.}, {10.79, 1.}, {11.04, 1.}, {11.29,
1.}, {11.541, 1.}, {11.792, 1.}, {12.044, 1.}, {12.295,
1.}, {12.546, 1.}, {12.797, 1.}, {13.048, 1.}, {13.3, 1.}, {13.551,
1.}, {13.802, 1.}, {14.053, 1.}, {14.304, 1.}, {14.555,
1.}, {14.805, 1.}, {15.056, 1.}, {15.306, 1.}, {15.556,
1.}, {15.806, 1.}, {16.056, 1.}, {16.306, 1.}, {16.556,
1.}, {16.807, 1.}, {17.057, 1.}, {17.308, 0.22}, {17.558,
0.23}, {17.808, 0.23}, {18.058, 0.23}, {18.308, 0.23}, {18.559,
0.23}, {18.81, 0.23}, {19.06, 0.23}, {19.31, 0.23}, {19.561,
0.23}, {19.811, 0.23}, {20.061, 0.23}, {20.311, 0.23}, {20.561,
0.23}, {20.812, 0.23}, {21.062, 0.23}, {21.312, 0.23}, {21.562,
0.23}, {21.812, 0.23}, {22.063, 0.23}, {22.313, 0.23}, {22.564,
0.23}, {22.815, 0.23}, {23.066, 0.23}, {23.316, 0.23}, {23.566,
0.23}, {23.817, 0.23}, {24.067, 0.23}, {24.318, 0.23}, {24.569,
0.23}, {24.82, 0.23}, {25.07, 0.23}, {25.32, 0.23}, {25.571,
0.23}, {25.821, 0.23}, {26.071, 0.23}, {26.322, 0.23}, {26.573,
0.23}, {26.823, 0.23}, {27.074, 0.23}, {27.324, 0.23}, {27.575,
0.23}, {27.825, 0.23}, {28.075, 0.23}, {28.325, 0.23}, {28.576,
0.23}, {28.827, 0.23}, {29.078, 0.23}, {29.329, 0.23}, {29.579,
0.23}, {29.829, 0.23}, {30.079, 0.23}, {30.33, 0.23}, {30.58,
0.23}, {30.831, 0.23}, {31.082, 0.23}, {31.332, 0.23}, {31.582,
0.23}, {31.832, 0.23}, {32.082, 0.23}, {32.333, 0.23}, {32.583,
0.23}, {32.833, 0.23}, {33.083, 0.23}, {33.333, 0.23}, {33.583,
0.23}, {33.834, 0.23}, {34.085, 0.23}, {34.336, 0.23}, {34.587,
0.23}, {34.838, 0.23}, {35.089, 0.23}, {35.339, 0.23}, {35.589,
0.23}, {35.839, 0.23}, {36.091, 0.23}, {36.342, 0.23}, {36.594,
0.23}, {36.845, 0.23}, {37.095, 0.23}, {37.347, 0.23}, {37.597,
0.23}, {37.848, 0.23}, {38.098, 0.23}, {38.348, 0.23}, {38.598,
0.23}, {38.85, 0.23}, {39.101, 0.23}, {39.353, 0.23}, {39.604,
0.23}, {39.854, 0.23}, {40.104, 0.23}, {40.354, 0.23}, {40.604,
0.23}, {40.855, 0.23}, {41.106, 0.23}, {41.357, 0.23}, {41.607,
0.23}, {41.859, 0.23}, {42.111, 0.23}, {42.361, 0.23}, {42.613,
0.23}, {42.863, 0.23}, {43.113, 0.23}, {43.365, 0.23}, {43.616,
0.23}, {43.867, 0.23}, {44.117, 0.23}, {44.368, 0.23}, {44.619,
0.23}, {44.871, 0.23}, {45.122, 0.23}, {45.373, 0.23}, {45.624,
0.23}, {45.876, 0.23}, {46.128, 0.23}, {46.379, 0.23}, {46.631,
0.23}, {46.881, 0.23}, {47.131, 0.23}, {47.382, 0.23}, {47.634,
0.23}, {47.887, 0.23}, {48.137, 0.23}, {48.387, 0.23}, {48.639,
0.23}, {48.889, 0.23}, {49.141, 0.23}, {49.391, 0.23}, {49.643,
0.23}, {49.895, 0.23}, {50.147, 0.23}, {50.399, 0.23}, {50.649,
0.23}, {50.899, 0.23}, {51.15, 0.23}, {51.401, 0.23}, {51.653,
0.23}, {51.903, 0.23}, {52.153, 0.23}, {52.403, 0.23}, {52.653,
0.23}, {52.904, 0.23}, {53.155, 0.23}, {53.408, 0.23}, {53.66,
0.23}, {53.913, 0.23}, {54.166, 0.23}, {54.416, 0.23}, {54.668,
0.23}, {54.918, 0.23}, {55.17, 0.23}, {55.422, 0.23}, {55.675,
0.23}, {55.925, 0.23}, {56.175, 0.23}, {56.425, 0.23}, {56.675,
0.23}, {56.925, 0.23}, {57.178, 0.23}, {57.431, 0.23}, {57.682,
0.23}, {57.935, 0.23}, {58.185, 0.23}, {58.436, 0.23}, {58.688,
0.23}, {58.94, 0.23}, {59.192, 0.23}, {59.445, 0.23}, {59.698,
0.23}, {59.948, 0.23}, {60.198, 0.23}, {60.448, 0.23}, {60.698,
0.23}, {60.95, 0.23}, {61.2, 0.23}, {61.453, 0.23}, {61.703, 0.23},
{61.954, 0.23}, {62.205, 0.23}, {62.456, 0.23}, {62.708,
0.23}, {62.96, 0.23}, {63.21, 0.23}, {63.461, 0.23}, {63.713,
0.23}, {63.965, 0.23}, {64.217, 0.23}, {64.469, 0.23}, {64.721,
0.23}, {64.974, 0.23}, {65.227, 0.23}, {65.477, 0.23}, {65.728,
0.23}, {65.979, 0.23}, {66.23, 0.23}, {66.483, 0.23}, {66.734,
0.23}, {66.986, 0.23}, {67.238, 0.23}, {67.488, 0.23}, {67.739,
0.23}, {67.99, 0.23}, {68.241, 0.23}, {68.493, 0.23}, {68.745,
0.23}, {68.997, 0.23}, {69.249, 0.23}, {69.499, 0.23}, {69.751,
0.23}, {70.004, 0.23}, {70.257, 0.23}, {70.51, 0.23}, {70.763,
0.23}, {71.014, 0.23}, {71.266, 0.23}, {71.517, 0.23}, {71.769,
0.23}, {72.021, 0.23}, {72.273, 0.23}, {72.526, 0.001}, {72.777,
0.001}, {73.029, 0.001}, {73.281, 0.001}, {73.534, 0.001}, {73.786,
0.001}, {74.039, 0.001}, {74.291, 0.001}, {74.542, 0.001}, {74.792,
0.001}, {75.043, 0.001}, {75.294, 0.001}, {75.545, 0.15}, {75.798,
0.2}, {76.049, 0.2}, {76.299, 0.2}, {76.55, 0.2}, {76.802,
0.2}, {77.053, 0.2}, {77.304, 0.2}, {77.556, 0.2}, {77.806,
0.2}, {78.059, 0.2}, {78.312, 0.2}, {78.562, 0.2}, {78.814,
0.005}, {79.067, 0.005}, {79.32, 0.005}, {79.57, 0.005}, {79.823,
0.005}, {80.073, 0.005}, {80.324, 0.005}, {80.574, 0.005}, {80.824,
0.005}, {81.074, 0.005}, {81.326, 0.005}, {81.579, 0.006}, {81.829,
0.005}, {82.081, 0.004}, {82.333, 0.17}, {82.585, 0.21}, {82.838,
0.2}, {83.091, 0.2}, {83.344, 0.21}, {83.597, 0.2}, {83.847,
0.2}, {84.1, 0.2}, {84.353, 0.2}, {84.605, 0.2}, {84.858,
0.2}, {85.108, 0.2}, {85.359, 0.2}, {85.61, 0.2}, {85.862,
0.002}, {86.113, 0.003}, {86.365, 0.003}, {86.617, 0.003}, {86.869,
0.003}, {87.122, 0.003}, {87.374, 0.003}, {87.625, 0.003}, {87.876,
0.003}, {88.128, 0.003}, {88.381, 0.003}, {88.631, 0.003}, {88.884,
0.003}, {89.134, 0.003}, {89.384, 0.003}, {89.637, 0.003}, {89.887,
0.003}, {90.137, 0.002}, {90.388, 0.015}, {90.638, 0.19}, {90.888,
0.19}, {91.141, 0.19}, {91.391, 0.19}, {91.641, 0.19}, {91.891,
0.19}, {92.142, 0.19}, {92.392, 0.19}, {92.643, 0.19}, {92.894,
0.19}, {93.145, 0.19}, {93.395, 0.19}, {93.646, 0.19}, {93.897,
0.19}, {94.147, 0.19}, {94.397, 0.19}, {94.65, 0.18}, {94.9,
0.019}, {95.15, 0.02}, {95.401, 0.02}, {95.651, 0.02}, {95.901,
0.02}, {96.151, 0.02}, {96.401, 0.02}, {96.651, 0.02}, {96.901,
0.02}, {97.151, 0.02}, {97.404, 0.02}, {97.656, 0.02}, {97.909,
0.02}, {98.162, 0.02}, {98.415, 0.02}, {98.668, 0.02}, {98.92,
0.02}, {99.173, 0.019}, {99.425, 0.021}, {99.678, 0.024}, {99.93,
0.031}, {100.182, 0.14}, {100.433, 0.15}, {100.686, 0.15}, {100.936,
0.15}, {101.187, 0.15}, {101.439, 0.15}, {101.69, 0.15}, {101.942,
0.15}, {102.193, 0.15}, {102.444, 0.15}, {102.695, 0.15}, {102.946,
0.15}, {103.197, 0.15}, {103.448, 0.15}, {103.699, 0.15}, {103.949,
0.15}, {104.199, 0.15}, {104.449, 0.15}, {104.7, 0.037}, {104.951,
0.057}, {105.202, 0.059}, {105.453, 0.06}, {105.704,
0.06}, {105.955, 0.06}, {106.206, 0.059}, {106.457, 0.06}, {106.708,
0.06}, {106.959, 0.06}, {107.212, 0.06}, {107.465, 0.06}, {107.715,
0.06}, {107.967, 0.06}, {108.218, 0.06}, {108.469, 0.06}, {108.72,
0.06}, {108.971, 0.06}, {109.222, 0.059}, {109.474,
0.059}, {109.725, 0.06}, {109.976, 0.06}, {110.226,
0.059}, {110.479, 0.057}, {110.732, 0.057}, {110.982,
0.061}, {111.233, 0.081}, {111.484, 0.19}, {111.734, 0.2}, {111.985,
0.19}, {112.236, 0.19}, {112.486, 0.18}, {112.737, 0.19}, {112.987,
0.19}, {113.237, 0.19}, {113.489, 0.19}, {113.741, 0.19}, {113.992,
0.19}, {114.245, 0.19}, {114.498, 0.19}, {114.751, 0.19}, {115.004,
0.19}, {115.257, 0.19}, {115.51, 0.19}, {115.763, 0.19}, {116.015,
0.19}, {116.267, 0.18}, {116.519, 0.17}, {116.769, 0.083}, {117.022,
0.001}, {117.272, 0.001}, {117.522, 0.003}, {117.773,
0.004}, {118.025, 0.004}, {118.276, 0.004}, {118.526,
0.003}, {118.777, 0.004}, {119.028, 0.004}, {119.278,
0.004}, {119.528, 0.004}, {119.778, 0.004}, {120.029,
0.004}, {120.281, 0.004}, {120.533, 0.004}, {120.785,
0.004}, {121.035, 0.004}, {121.288, 0.004}, {121.538,
0.004}, {121.791, 0.004}, {122.041, 0.004}, {122.294,
0.004}, {122.547, 0.004}, {122.8, 0.003}, {123.051,
0.004}, {123.301, 0.004}, {123.551, 0.004}, {123.802,
0.003}, {124.054, 0.002}, {124.304, 0.003}, {124.557,
0.008}, {124.809, 0.081}, {125.062, 0.19}, {125.315, 0.2}, {125.568,
0.2}, {125.82, 0.2}, {126.071, 0.2}, {126.321, 0.2}, {126.574,
0.2}, {126.824, 0.2}, {127.075, 0.2}, {127.327, 0.2}, {127.58,
0.2}, {127.832, 0.2}, {128.085, 0.2}, {128.337, 0.2}, {128.589,
0.2}, {128.842, 0.2}, {129.093, 0.2}, {129.343, 0.2}, {129.596,
0.2}, {129.849, 0.2}, {130.102, 0.2}, {130.352, 0.2}, {130.603,
0.2}, {130.855, 0.2}, {131.107, 0.2}, {131.359, 0.2}, {131.61,
0.2}, {131.862, 0.2}, {132.113, 0.2}, {132.364, 0.2}, {132.616,
0.2}, {132.868, 0.2}, {133.12, 0.15}, {133.373, 0.1}, {133.623,
0.093}, {133.874, 0.096}, {134.125, 0.1}, {134.376, 0.1}, {134.627,
0.1}, {134.877, 0.1}, {135.128, 0.1}, {135.378, 0.1}, {135.63,
0.1}, {135.882, 0.1}, {136.133, 0.1}, {136.384, 0.1}, {136.637,
0.1}, {136.89, 0.1}, {137.14, 0.1}, {137.39, 0.1}, {137.641,
0.1}, {137.891, 0.1}, {138.142, 0.1}, {138.392, 0.1}, {138.645,
0.1}, {138.897, 0.1}, {139.148, 0.1}, {139.399, 0.1}, {139.651,
0.1}, {139.903, 0.1}, {140.153, 0.1}, {140.403, 0.1}, {140.654,
0.1}, {140.904, 0.1}, {141.155, 0.1}, {141.406, 0.098}, {141.656,
0.077}, {141.908, 0.019}, {142.16, 0.064}, {142.412,
0.086}, {142.663, 0.091}, {142.915, 0.089}, {143.165,
0.089}, {143.415, 0.089}, {143.666, 0.088}, {143.917,
0.089}, {144.168, 0.089}, {144.419, 0.089}, {144.67,
0.089}, {144.92, 0.089}, {145.173, 0.089}, {145.426,
0.089}, {145.678, 0.089}, {145.93, 0.089}, {146.18, 0.089}, {146.43,
0.089}, {146.682, 0.089}, {146.933, 0.089}, {147.184,
0.089}, {147.436, 0.089}, {147.687, 0.089}, {147.939,
0.089}, {148.19, 0.089}, {148.443, 0.089}, {148.695,
0.089}, {148.948, 0.089}, {149.198, 0.089}, {149.449,
0.089}, {149.7, 0.089}, {149.952, 0.089}, {150.205,
0.089}, {150.457, 0.089}, {150.709, 0.089}, {150.962,
0.089}, {151.214, 0.089}, {151.466, 0.089}, {151.716,
0.089}, {151.966, 0.089}, {152.217, 0.089}, {152.469,
0.089}, {152.722, 0.089}, {152.972, 0.089}, {153.222,
0.089}, {153.472, 0.089}, {153.722, 0.089}, {153.972,
0.089}, {154.223, 0.089}, {154.473, 0.089}, {154.723,
0.089}, {154.973, 0.089}, {155.226, 0.089}, {155.477,
0.089}, {155.728, 0.089}, {155.981, 0.089}, {156.233,
0.089}, {156.486, 0.089}, {156.739, 0.089}, {156.992,
0.089}, {157.245, 0.089}, {157.495, 0.089}, {157.745,
0.089}, {157.998, 0.089}, {158.251, 0.089}, {158.501,
0.089}, {158.752, 0.089}, {159.003, 0.089}, {159.255,
0.088}, {159.507, 0.09}, {159.76, 0.088}, {160.012, 0.09}, {160.265,
0.088}, {160.515, 0.089}, {160.768, 0.089}, {161.018,
0.088}, {161.268, 0.089}, {161.518, 0.089}, {161.77,
0.089}, {162.02, 0.089}, {162.272, 0.089}, {162.523,
0.089}, {162.775, 0.089}, {163.028, 0.089}, {163.28,
0.089}, {163.533, 0.089}, {163.786, 0.089}, {164.039,
0.089}, {164.289, 0.089}, {164.54, 0.089}, {164.791,
0.089}, {165.042, 0.089}, {165.293, 0.089}, {165.544,
0.089}, {165.795, 0.089}, {166.046, 0.089}, {166.298,
0.089}, {166.55, 0.089}, {166.802, 0.089}, {167.055,
0.089}, {167.305, 0.089}, {167.556, 0.089}, {167.808,
0.089}, {168.06, 0.089}, {168.311, 0.089}, {168.561,
0.089}, {168.811, 0.089}, {169.061, 0.089}, {169.312,
0.089}, {169.563, 0.089}, {169.815, 0.089}, {170.067,
0.089}, {170.317, 0.089}, {170.567, 0.089}, {170.818,
0.089}, {171.07, 0.089}, {171.322, 0.089}, {171.572,
0.089}, {171.822, 0.089}, {172.073, 0.089}, {172.323,
0.089}, {172.574, 0.089}, {172.825, 0.089}, {173.076,
0.089}, {173.329, 0.089}, {173.579, 0.089}, {173.83,
0.089}, {174.081, 0.089}, {174.333, 0.089}, {174.584,
0.089}, {174.835, 0.089}, {175.087, 0.089}, {175.337,
0.089}, {175.587, 0.089}, {175.838, 0.089}, {176.089,
0.089}, {176.341, 0.089}, {176.591, 0.089}, {176.841,
0.089}, {177.091, 0.089}, {177.342, 0.089}, {177.593,
0.089}, {177.844, 0.089}, {178.096, 0.089}, {178.347,
0.089}, {178.597, 0.089}, {178.847, 0.089}, {179.098,
0.089}, {179.351, 0.089}, {179.604, 0.089}, {179.857,
0.089}, {180.107, 0.089}, {180.357, 0.087}, {180.607,
0.088}, {180.857, 0.091}, {181.108, 0.088}, {181.358,
0.089}, {181.609, 0.088}, {181.859, 0.089}, {182.11,
0.092}, {182.361, 0.089}, {182.613, 0.088}, {182.865,
0.087}, {183.118, 0.086}, {183.371, 0.087}, {183.625,
0.09}, {183.878, 0.089}, {184.128, 0.088}, {184.382,
0.089}, {184.632, 0.089}, {184.882, 0.088}, {185.133,
0.089}, {185.384, 0.089}, {185.636, 0.089}, {185.888,
0.089}, {186.139, 0.089}, {186.391, 0.089}, {186.644,
0.089}, {186.896, 0.089}, {187.149, 0.089}, {187.402,
0.089}, {187.656, 0.089}, {187.91, 0.089}, {188.16,
0.089}, {188.413, 0.089}, {188.665, 0.089}, {188.915,
0.089}, {189.166, 0.089}, {189.417, 0.089}, {189.668,
0.089}, {189.92, 0.089}, {190.172, 0.089}, {190.424,
0.089}, {190.676, 0.089}, {190.929, 0.089}, {191.179,
0.089}, {191.43, 0.089}, {191.681, 0.089}, {191.933,
0.089}, {192.184, 0.089}, {192.435, 0.089}, {192.685,
0.089}, {192.936, 0.089}, {193.186, 0.089}, {193.437,
0.089}, {193.688, 0.089}, {193.94, 0.089}, {194.194,
0.089}, {194.448, 0.089}, {194.698, 0.088}, {194.948,
0.091}, {195.198, 0.089}, {195.449, 0.086}, {195.703,
0.089}, {195.957, 0.094}, {196.211, 0.093}, {196.465,
0.088}, {196.719, 0.086}, {196.969, 0.086}, {197.22,
0.086}, {197.473, 0.085}, {197.726, 0.085}, {197.979,
0.088}, {198.232, 0.09}, {198.486, 0.089}, {198.74,
0.086}, {198.993, 0.086}, {199.245, 0.088}, {199.497,
0.089}, {199.749, 0.087}, {200.001, 0.086}, {200.255,
0.087}, {200.505, 0.088}, {200.755, 0.087}, {201.006,
0.086}, {201.257, 0.087}, {201.508, 0.088}, {201.759,
0.087}, {202.01, 0.086}, {202.261, 0.087}, {202.512,
0.088}, {202.762, 0.088}, {203.012, 0.086}, {203.263,
0.085}, {203.515, 0.087}, {203.767, 0.091}, {204.02,
0.096}, {204.273, 0.099}, {204.526, 0.093}, {204.779,
0.092}, {205.033, 0.094}, {205.287, 0.089}, {205.54,
0.083}, {205.794, 0.082}, {206.048, 0.083}, {206.301,
0.083}, {206.555, 0.083}, {206.805, 0.083}, {207.055,
0.082}, {207.305, 0.082}, {207.556, 0.083}, {207.806,
0.082}, {208.057, 0.082}, {208.308, 0.082}, {208.559,
0.083}, {208.811, 0.083}, {209.062, 0.083}, {209.313,
0.083}, {209.565, 0.083}, {209.817, 0.082}, {210.07,
0.083}, {210.322, 0.082}, {210.575, 0.083}, {210.828,
0.083}, {211.081, 0.083}, {211.335, 0.083}, {211.588,
0.082}, {211.842, 0.083}, {212.096, 0.083}, {212.346,
0.083}, {212.596, 0.083}, {212.846, 0.083}, {213.096,
0.083}, {213.351, 0.083}, {213.606, 0.083}, {213.856,
0.083}, {214.106, 0.083}, {214.357, 0.083}, {214.607,
0.083}, {214.858, 0.083}, {215.109, 0.082}, {215.361,
0.083}, {215.615, 0.083}, {215.868, 0.083}, {216.121,
0.082}, {216.373, 0.083}, {216.625, 0.082}, {216.877,
0.083}, {217.13, 0.083}, {217.382, 0.082}, {217.635,
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0.082}, {220.157, 0.082}, {220.407, 0.082}, {220.662,
0.082}, {220.912, 0.082}, {221.162, 0.082}, {221.412,
0.082}, {221.664, 0.082}, {221.917, 0.082}, {222.17,
0.082}, {222.424, 0.082}, {222.677, 0.082}, {222.928,
0.082}, {223.18, 0.082}, {223.432, 0.081}, {223.684,
0.082}, {223.936, 0.081}, {224.188, 0.08}, {224.441,
0.084}, {224.694, 0.088}, {224.944, 0.084}, {225.194,
0.066}, {225.444, 0.036}, {225.694, 0.012}, {225.949,
0.012}, {226.203, 0.022}, {226.457, 0.03}, {226.711,
0.035}, {226.965, 0.035}, {227.219, 0.034}, {227.473,
0.031}, {227.723, 0.03}, {227.974, 0.03}, {228.226,
0.032}, {228.477, 0.033}, {228.729, 0.034}, {228.981,
0.033}, {229.233, 0.031}, {229.484, 0.027}, {229.735,
0.024}, {229.985, 0.021}, {230.236, 0.024}, {230.486,
0.059}, {230.738, 0.11}, {230.99, 0.13}, {231.243, 0.13}, {231.497,
0.14}, {231.75, 0.14}, {232.004, 0.14}, {232.257, 0.14}, {232.511,
0.14}, {232.765, 0.14}, {233.017, 0.14}, {233.269, 0.14}, {233.521,
0.14}, {233.775, 0.14}, {234.029, 0.14}, {234.284, 0.14}, {234.539,
0.14}, {234.794, 0.14}, {235.049, 0.14}, {235.299, 0.14}, {235.549,
0.14}, {235.799, 0.14}, {236.049, 0.14}, {236.303, 0.14}, {236.557,
0.14}, {236.812, 0.14}, {237.062, 0.14}, {237.313, 0.14}, {237.564,
0.14}, {237.815, 0.14}, {238.067, 0.14}, {238.319, 0.14}, {238.571,
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0.14}, {239.829, 0.14}, {240.081, 0.14}, {240.334, 0.14}, {240.587,
0.14}, {240.84, 0.14}, {241.093, 0.14}, {241.347, 0.14}, {241.601,
0.14}, {241.855, 0.14}, {242.109, 0.14}, {242.363, 0.14}, {242.617,
0.15}, {242.87, 0.032}, {243.124, 0.03}, {243.378, 0.031}, {243.628,
0.031}, {243.883, 0.031}, {244.138, 0.03}, {244.393,
0.03}, {244.643, 0.031}, {244.893, 0.03}, {245.143,
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0.03}, {249.159, 0.03}, {249.411, 0.03}, {249.662, 0.03}, {249.914,
0.03}, {250.166, 0.03}, {250.418, 0.03}, {250.67, 0.03}, {250.923,
0.03}, {251.175, 0.03}, {251.427, 0.03}, {251.679, 0.03}, {251.932,
0.03}, {252.184, 0.03}, {252.437, 0.03}, {252.689, 0.03}, {252.942,
0.03}, {253.195, 0.03}, {253.447, 0.03}, {253.7, 0.03}, {253.952,
0.03}, {254.205, 0.03}, {254.457, 0.03}, {254.71, 0.03}, {254.963,
0.03}, {255.215, 0.03}, {255.468, 0.03}, {255.721, 0.03}, {255.974,
0.03}, {256.227, 0.03}, {256.48, 0.03}, {256.733, 0.03}, {256.985,
0.03}, {257.238, 0.03}, {257.49, 0.03}, {257.743, 0.03}, {257.995,
0.03}, {258.247, 0.03}, {258.5, 0.03}, {258.752, 0.03}, {259.006,
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0.03}, {262.288, 0.03}, {262.542, 0.03}, {262.796, 0.03}, {263.048,
0.03}, {263.3, 0.031}, {263.552, 0.03}, {263.805, 0.03}, {264.057,
0.031}, {264.309, 0.031}, {264.561, 0.03}, {264.813,
0.03}, {265.065, 0.03}, {265.318, 0.03}, {265.571, 0.03}, {265.824,
0.03}, {266.077, 0.031}, {266.329, 0.031}, {266.581,
0.031}, {266.833, 0.031}, {267.085, 0.03}, {267.337,
0.03}, {267.589, 0.031}, {267.841, 0.03}, {268.093, 0.03}, {268.346,
0.031}, {268.598, 0.03}, {268.851, 0.031}, {269.103,
0.03}, {269.356, 0.031}, {269.608, 0.03}, {269.86, 0.031}, {270.112,
0.03}, {270.364, 0.031}, {270.615, 0.03}, {270.867,
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0.031}, {271.875, 0.031}, {272.127, 0.031}, {272.38,
0.031}, {272.631, 0.031}, {272.883, 0.03}, {273.135,
0.03}, {273.386, 0.03}, {273.638, 0.031}, {273.889, 0.03}, {274.141,
0.031}, {274.392, 0.03}, {274.644, 0.03}, {274.895,
0.03}, {275.146, 0.03}, {275.398, 0.03}, {275.65, 0.03}, {275.901,
0.03}, {276.152, 0.03}, {276.403, 0.03}, {276.654, 0.031}, {276.905,
0.03}, {277.155, 0.03}, {277.406, 0.03}, {277.657,
0.031}, {277.907, 0.03}, {278.158, 0.03}, {278.409, 0.03}, {278.659,
0.03}, {278.91, 0.03}, {279.16, 0.03}, {279.411, 0.03}, {279.661,
0.03}, {279.911, 0.03}, {280.161, 0.03}, {280.411, 0.03}, {280.661,
0.03}, {280.911, 0.03}, {281.166, 0.03}, {281.416, 0.03}, {281.671,
0.03}, {281.926, 0.03}, {282.181, 0.03}, {282.436, 0.03}, {282.691,
0.03}, {282.946, 0.03}, {283.2, 0.03}, {283.45, 0.03}, {283.704,
0.03}, {283.954, 0.03}, {284.208, 0.03}, {284.463, 0.03}, {284.717,
0.03}, {284.972, 0.03}, {285.226, 0.03}, {285.481, 0.03}, {285.735,
0.03}, {285.989, 0.03}, {286.244, 0.03}, {286.498, 0.03}, {286.752,
0.03}, {287.006, 0.03}, {287.26, 0.03}, {287.515, 0.03}, {287.768,
0.03}, {288.022, 0.03}, {288.277, 0.03}, {288.531, 0.03}, {288.785,
0.03}, {289.039, 0.03}, {289.293, 0.03}, {289.547, 0.03}, {289.801,
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0.03}, {291.071, 0.03}, {291.324, 0.03}, {291.578, 0.03}, {291.832,
0.03}, {292.086, 0.03}, {292.34, 0.03}, {292.595, 0.03}, {292.849,
0.03}, {293.103, 0.031}, {293.357, 0.03}, {293.611,
0.032}, {293.865, 0.03}, {294.119, 0.002}, {294.372,
0.071}, {294.625, 0.08}, {294.878, 0.077}, {295.132,
0.077}, {295.386, 0.077}, {295.64, 0.077}, {295.894,
0.077}, {296.148, 0.035}, {296.402, 0.003}, {296.656,
0.003}, {296.91, 0.003}, {297.163, 0.003}, {297.417,
0.003}, {297.669, 0.003}, {297.92, 0.003}, {298.173,
0.003}, {298.426, 0.003}, {298.679, 0.003}, {298.932,
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0.003}, {299.945, 0.003}, {300.198, 0.003}, {300.45,
0.003}, {300.702, 0.003}, {300.953, 0.003}, {301.203,
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0.003}, {304.475, 0.003}, {304.73, 0.003}, {304.98, 0.003}, {305.23,
0.003}, {305.48, 0.003}, {305.735, 0.003}, {305.985,
0.003}, {306.239, 0.003}, {306.489, 0.003}, {306.743,
0.003}, {306.997, 0.003}, {307.25, 0.003}, {307.502,
0.003}, {307.754, 0.003}, {308.006, 0.003}, {308.26,
0.003}, {308.513, 0.003}, {308.766, 0.003}, {309.019,
0.003}, {309.272, 0.003}, {309.525, 0.003}, {309.778,
0.003}, {310.03, 0.003}, {310.282, 0.003}, {310.532,
0.003}, {310.782, 0.003}, {311.032, 0.003}, {311.283,
0.003}, {311.534, 0.003}, {311.786, 0.003}, {312.038,
0.003}, {312.289, 0.003}, {312.541, 0.003}, {312.792,
0.003}, {313.043, 0.003}, {313.293, 0.003}, {313.547,
0.003}, {313.801, 0.003}, {314.055, 0.003}, {314.309,
0.003}, {314.563, 0.003}, {314.813, 0.003}, {315.064,
0.003}, {315.314, 0.003}, {315.564, 0.003}, {315.815,
0.003}, {316.07, 0.003}, {316.324, 0.003}, {316.578,
0.003}, {316.831, 0.003}, {317.083, 0.003}, {317.336,
0.003}, {317.589, 0.003}, {317.842, 0.003}, {318.097,
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0.003}, {319.873, 0.003}, {320.125, 0.003}, {320.376,
0.003}, {320.628, 0.003}, {320.88, 0.003}, {321.131,
0.003}, {321.385, 0.002}, {321.638, 0.001}, {321.892,
0.036}, {322.145, 0.066}, {322.398, 0.068}, {322.649,
0.066}, {322.9, 0.066}, {323.151, 0.066}, {323.402,
0.066}, {323.653, 0.065}, {323.903, 0.065}, {324.153,
0.065}, {324.404, 0.064}, {324.656, 0.064}, {324.908,
0.064}, {325.16, 0.063}, {325.412, 0.063}, {325.662,
0.061}, {325.912, 0.062}, {326.162, 0.064}, {326.416,
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0.036}, {327.433, 0.032}, {327.687, 0.031}, {327.941,
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0.019}, {333.729, 0.019}, {333.983, 0.019}, {334.237,
0.018}, {334.491, 0.018}, {334.745, 0.018}, {334.999,
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0.014}, {339.776, 0.014}, {340.026, 0.014}, {340.28,
0.014}, {340.534, 0.014}, {340.788, 0.014}, {341.041,
0.014}, {341.293, 0.014}, {341.545, 0.014}, {341.799,
0.014}, {342.052, 0.014}, {342.305, 0.014}, {342.558,
0.014}, {342.811, 0.014}, {343.064, 0.014}, {343.316,
0.014}, {343.569, 0.014}, {343.821, 0.014}, {344.071,
0.014}, {344.321, 0.014}, {344.575, 0.014}, {344.826,
0.014}, {345.077, 0.013}, {345.328, 0.013}, {345.579,
0.013}, {345.83, 0.013}, {346.081, 0.013}, {346.332,
0.013}, {346.582, 0.012}, {346.832, 0.012}, {347.086,
0.012}, {347.339, 0.011}, {347.591, 0.01}, {347.843,
0.01}, {348.095, 0.009}, {348.349, 0.009}, {348.603,
0.008}, {348.857, 0.007}, {349.111, 0.007}}


My objective is to have all the points with the same y value be concatenated. So in the example above, the table would go from {0.,1.} all the way to {17.308, 0.22}. Then all the ordered pairs from {0., 1.} to {17.057, 1.} would be only one or two ordered pairs. Runtime is not an issue. I don't need this to be efficient for the time being. Thank you in advance. Cheers

• what should the x-coordinate be for the concatenated pairs? Dec 3 '17 at 18:02
• With data being the list of pairs, does GatherBy[data, Last -> Identity] orGatherBy[data, Last -> First] answer your question? Dec 3 '17 at 18:20
• @user42582 they should remain the same. Basically just deleted ordered pairs, not changing the data. So basically what I mean by that is, I want to keep the integrity, shape, of the data set (probs), I do however want to delete some of the points in probs. Notably any points (ordered pairs, (x,y)) where the y value is the same for consecutive values. I would like probs to eventually look like: {{0., 1.}, {17.057, 1.}, {17.308, 0.22}, {17.558, 0.23}, {72.273, 0.23}, {72.526, 0.001}...} and so on. You see what I mean by first and last ordered pair with the same y value? Dec 4 '17 at 3:24

## 2 Answers

First we need to Gather the input data according to their Last entry (their y-coordinate)

GatherBy[data, Last]


(let data stand for the large list of input in the question). The output of this evaluation is large enough not to include it here; a small portion of it is

{
{ {0., 1.}, {0.073, 1.}, ..., {17.057, 1.} },
...

{ {348.857, 0.007}, {349.111, 0.007} }
}


namely, it groups the input data wrt the y-coordinate in sub-lists, and returns them in a list. Please note, that each sub-list is not ordered unless the input is ordered ( see GatherBy ).

It seems that the input data are ordered wrt to their first component, but in the following code we'll assume that they are not. Making sure beforehand that the input is appropriately ordered can save some time.

Next, we need to extract the First and Last elements in each sub-list and Flatten out the output:

f = Through[{First, Last}[Sort@{##}]] &

Flatten[Apply[f, GatherBy[data, Last], 1], 1]


Through, effectively returns the First and Last item in the sorted list of grouped entries it is passed as an argument (actually, the way f is coded, it receives many arguments ie the grouped sublists, not a single argument, but that is simply an implementation detail).

The output of the last evaluation is

{
{0., 1.}, {17.057, 1.}, {17.308, 0.22}, {17.308, 0.22}, {17.558, 0.23},
{72.273, 0.23}, {72.526, 0.001}, {321.638, 0.001}, {75.545, 0.15},
{242.617, 0.15}, {75.798, 0.2}, {132.868, 0.2}, {78.814, 0.005},
{81.829, 0.005}, {81.579, 0.006}, {81.579, 0.006}, {82.081, 0.004},
{123.551, 0.004}, {82.333, 0.17}, {116.519, 0.17}, {82.585, 0.21},
{83.344, 0.21}, {85.862, 0.002}, {321.385, 0.002}, {86.113, 0.003},
{321.131, 0.003}, {90.388, 0.015}, {338.525, 0.015}, {90.638, 0.19},
{125.062, 0.19}, {94.65, 0.18}, {116.267, 0.18}, {94.9, 0.019},
{333.983, 0.019}, {95.15, 0.02}, {333.225, 0.02}, {99.425, 0.021},
{332.475, 0.021}, {99.678, 0.024}, {330.966, 0.024}, {99.93, 0.031},
{327.941, 0.031}, {100.182, 0.14}, {242.363, 0.14}, {104.7, 0.037},
{104.7, 0.037}, {104.951, 0.057}, {110.732, 0.057}, {105.202, 0.059},
{230.486, 0.059}, {105.453, 0.06}, {326.671, 0.06}, {110.982, 0.061},
{325.662, 0.061}, {111.233, 0.081}, {223.936, 0.081}, {116.769, 0.083},
{217.635, 0.083}, {124.557, 0.008}, {348.603, 0.008}, {133.373, 0.1},
{141.155, 0.1}, {133.623, 0.093}, {204.526, 0.093}, {133.874, 0.096},
{204.02, 0.096}, {141.406, 0.098}, {141.406, 0.098}, {141.656, 0.077},
{295.894, 0.077}, {142.16, 0.064}, {326.162, 0.064}, {142.412, 0.086},
{203.012, 0.086}, {142.663, 0.091}, {203.767, 0.091}, {142.915, 0.089},
{205.287, 0.089}, {143.666, 0.088}, {224.694, 0.088}, {159.507, 0.09},
{198.232, 0.09}, {180.357, 0.087}, {203.515, 0.087}, {182.11,0.092},
{204.779, 0.092}, {195.957, 0.094}, {205.033, 0.094}, {197.473, 0.085},
{203.263, 0.085}, {204.273, 0.099}, {204.273, 0.099}, {205.794, 0.082},
{223.684, 0.082}, {218.396, 0.079}, {218.396, 0.079}, {218.646, 0.08},
{294.625, 0.08}, {224.441, 0.084}, {224.944, 0.084}, {225.194, 0.066},
{323.402, 0.066}, {225.444, 0.036}, {327.179, 0.036}, {225.694, 0.012},
{347.086, 0.012}, {226.203, 0.022}, {331.974, 0.022}, {226.457, 0.03},
{328.191, 0.03}, {226.711, 0.035}, {296.148, 0.035}, {227.219, 0.034},
{228.729, 0.034}, {228.226, 0.032}, {327.433, 0.032}, {228.477, 0.033},
{228.981, 0.033}, {229.484, 0.027}, {329.706, 0.027}, {230.738, 0.11},
{230.738, 0.11}, {230.99, 0.13}, {231.243, 0.13}, {294.372, 0.071},
{294.372, 0.071}, {322.398, 0.068}, {322.398, 0.068}, {323.653, 0.065},
{324.153, 0.065}, {325.16, 0.063}, {325.412, 0.063}, {325.912, 0.062},
{325.912, 0.062}, {326.416, 0.067}, {326.416, 0.067}, {326.925, 0.041},
{326.925, 0.041}, {328.441, 0.029}, {328.695, 0.029}, {328.949, 0.028},
{329.201, 0.028}, {329.959, 0.026}, {330.211, 0.026}, {330.463, 0.025},
{330.463, 0.025}, {331.218, 0.023}, {331.47, 0.023}, {334.237, 0.018},
{334.745, 0.018}, {334.999, 0.017}, {335.506, 0.017}, {335.759, 0.016},
{336.768, 0.016}, {338.776, 0.014}, {344.826, 0.014}, {345.077, 0.013},
{346.332, 0.013}, {347.339, 0.011}, {347.339, 0.011}, {347.591, 0.01},
{347.843, 0.01}, {348.095, 0.009}, {348.349, 0.009}, {348.857, 0.007},
{349.111, 0.007}
}


Finally please note that for some values of the y-coordinate there is but one entry in the input data; if the output is expected to simply contain that single entry (not a pair of identical entries), then the code for f above should be modified to f = Union@Through[{First, Last}[Sort@{##}]] &.

This modification is needed because otherwise f applied to a single entry would output a pair of identical entries.

• AHHHH fantastic I can't believe I didn't see this! Thank you so much for the elaboration. Cheers! Dec 4 '17 at 16:30

I would like probs to eventually look like: {{0., 1.}, {17.057, 1.}, {17.308, 0.22}, {72.273, 0.23}, {72.526, 0.001}...} and so on.

This splits data by y, then takes first and last entries.

result=GroupBy[data,Last];
result=If[Length[#]>1,{First[#],Last[#]},#]&/@result;
newData=Values[result[[All,;;]]];
Flatten[newData,1]


Gives

{{0.,1.},{17.057,1.},{17.308,0.22},{17.558,0.23},{72.273,0.23},
{72.526,0.001},{321.638,0.001},{75.545,0.15},{242.617,0.15},{75.798,0.2},
{132.868,0.2},{78.814,0.005},{81.829,0.005},{81.579,0.006},{82.081,0.004},
{123.551,0.004},{82.333,0.17},{116.519,0.17},{82.585,0.21},{83.344,0.21},
{85.862,0.002},{321.385,0.002},{86.113,0.003},{321.131,0.003},{90.388,0.015},
{338.525,0.015},{90.638,0.19},{125.062,0.19},{94.65,0.18},{116.267,0.18},
{94.9,0.019},{333.983,0.019},{95.15,0.02},{333.225,0.02},{99.425,0.021},
{332.475,0.021},{99.678,0.024},{330.966,0.024},{99.93,0.031},{327.941,0.031},
{100.182,0.14},{242.363,0.14},{104.7,0.037},{104.951,0.057},{110.732,0.057},
{105.202,0.059},{230.486,0.059},{105.453,0.06},{326.671,0.06},{110.982,0.061},
{325.662,0.061},{111.233,0.081},{223.936,0.081},{116.769,0.083},{217.635,0.083},
{124.557,0.008},{348.603,0.008},{133.373,0.1},{141.155,0.1},{133.623,0.093},
{204.526,0.093},{133.874,0.096},{204.02,0.096},{141.406,0.098},{141.656,0.077},
{295.894,0.077},{142.16,0.064},{326.162,0.064},{142.412,0.086},{203.012,0.086},
{142.663,0.091},{203.767,0.091},{142.915,0.089},{205.287,0.089},{143.666,0.088},
{224.694,0.088},{159.507,0.09},{198.232,0.09},{180.357,0.087},{203.515,0.087},
{182.11,0.092},{204.779,0.092},{195.957,0.094},{205.033,0.094},{197.473,0.085},
{203.263,0.085},{204.273,0.099},{205.794,0.082},{223.684,0.082},{218.396,0.079},
{218.646,0.08},{294.625,0.08},{224.441,0.084},{224.944,0.084},{225.194,0.066},
{323.402,0.066},{225.444,0.036},{327.179,0.036},{225.694,0.012},{347.086,0.012},
{226.203,0.022},{331.974,0.022},{226.457,0.03},{328.191,0.03},{226.711,0.035},
{296.148,0.035},{227.219,0.034},{228.729,0.034},{228.226,0.032},{327.433,0.032},
{228.477,0.033},{228.981,0.033},{229.484,0.027},{329.706,0.027},{230.738,0.11},
{230.99,0.13},{231.243,0.13},{294.372,0.071},{322.398,0.068},{323.653,0.065},
{324.153,0.065},{325.16,0.063},{325.412,0.063},{325.912,0.062},{326.416,0.067},
{326.925,0.041},{328.441,0.029},{328.695,0.029},{328.949,0.028},{329.201,0.028},
{329.959,0.026},{330.211,0.026},{330.463,0.025},{331.218,0.023},{331.47,0.023},
{334.237,0.018},{334.745,0.018},{334.999,0.017},{335.506,0.017},{335.759,0.016},
{336.768,0.016},{338.776,0.014},{344.826,0.014},{345.077,0.013},{346.332,0.013},
{347.339,0.011},{347.591,0.01},{347.843,0.01},{348.095,0.009},{348.349,0.009},
{348.857,0.007},{349.111,0.007}}

• So basically what I mean by that is, I want to keep the integrity, shape, of the data set (probs), I do however want to delete some of the points in probs. Notably any points (ordered pairs, (x,y)) where the y value is the same for consecutive values. I would like probs to eventually look like: {{0., 1.}, {17.057, 1.}, {17.308, 0.22}, {72.273, 0.23}, {72.526, 0.001}...} and so on. You see what I mean by first and last ordered pair with the same y value? Dec 4 '17 at 3:18
• correction: {{0., 1.}, {17.057, 1.}, {17.308, 0.22}, {17.558, 0.23}, {72.273, 0.23}, {72.526, 0.001}...} Dec 4 '17 at 3:26
• @LopeyTall but the code I posted does exactly this? You just need to extract the values from the association. I will add this now. Dec 4 '17 at 3:47