2
$\begingroup$ 
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}, {221.664, 0.082}, {221.917, 0.082}, {222.17, 
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  0.035}, {226.965, 0.035}, {227.219, 0.034}, {227.473, 
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  0.032}, {228.477, 0.033}, {228.729, 0.034}, {228.981, 
  0.033}, {229.233, 0.031}, {229.484, 0.027}, {229.735, 
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  0.14}, {231.75, 0.14}, {232.004, 0.14}, {232.257, 0.14}, {232.511, 
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   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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   0.031}, {246.395, 0.03}, {246.645, 0.031}, {246.896, 
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  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, 
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  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, 
  0.03}, {259.259, 0.03}, {259.512, 0.03}, {259.765, 0.03}, {260.017, 
  0.03}, {260.27, 0.03}, {260.522, 0.03}, {260.774, 0.03}, {261.026, 
  0.03}, {261.279, 0.03}, {261.531, 0.03}, {261.783, 0.03}, {262.035, 
  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, 
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  0.03}, {265.065, 0.03}, {265.318, 0.03}, {265.571, 0.03}, {265.824, 
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  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, 
  0.031}, {271.119, 0.03}, {271.371, 0.03}, {271.623, 
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  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, 
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  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, 
  0.03}, {290.055, 0.03}, {290.309, 0.03}, {290.563, 0.03}, {290.818, 
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  0.077}, {295.386, 0.077}, {295.64, 0.077}, {295.894, 
  0.077}, {296.148, 0.035}, {296.402, 0.003}, {296.656, 
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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, 
  0.003}, {301.454, 0.003}, {301.706, 0.003}, {301.957, 
  0.003}, {302.209, 0.003}, {302.461, 0.003}, {302.713, 
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   0.003}, {305.48, 0.003}, {305.735, 0.003}, {305.985, 
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  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, 
  0.003}, {318.351, 0.003}, {318.606, 0.003}, {318.86, 
  0.003}, {319.114, 0.003}, {319.368, 0.003}, {319.621, 
  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, 
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  0.067}, {326.671, 0.06}, {326.925, 0.041}, {327.179, 
  0.036}, {327.433, 0.032}, {327.687, 0.031}, {327.941, 
  0.031}, {328.191, 0.03}, {328.441, 0.029}, {328.695, 
  0.029}, {328.949, 0.028}, {329.201, 0.028}, {329.454, 
  0.027}, {329.706, 0.027}, {329.959, 0.026}, {330.211, 
  0.026}, {330.463, 0.025}, {330.714, 0.024}, {330.966, 
  0.024}, {331.218, 0.023}, {331.47, 0.023}, {331.722, 
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  0.021}, {332.725, 0.02}, {332.975, 0.02}, {333.225, 0.02}, {333.479,
   0.019}, {333.729, 0.019}, {333.983, 0.019}, {334.237, 
  0.018}, {334.491, 0.018}, {334.745, 0.018}, {334.999, 
  0.017}, {335.253, 0.017}, {335.506, 0.017}, {335.759, 
  0.016}, {336.011, 0.016}, {336.264, 0.016}, {336.516, 
  0.016}, {336.768, 0.016}, {337.02, 0.015}, {337.271, 
  0.015}, {337.523, 0.015}, {337.774, 0.015}, {338.024, 
  0.015}, {338.275, 0.015}, {338.525, 0.015}, {338.776, 
  0.014}, {339.026, 0.014}, {339.276, 0.014}, {339.526, 
  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

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ what should the x-coordinate be for the concatenated pairs? $\endgroup$ – user42582 Dec 3 '17 at 18:02
  • $\begingroup$ With data being the list of pairs, does GatherBy[data, Last -> Identity] orGatherBy[data, Last -> First] answer your question? $\endgroup$ – Henrik Schumacher Dec 3 '17 at 18:20
  • 1
    $\begingroup$ @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? $\endgroup$ – Lopey Tall Dec 4 '17 at 3:24
0
$\begingroup$

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.

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1
  • $\begingroup$ AHHHH fantastic I can't believe I didn't see this! Thank you so much for the elaboration. Cheers! $\endgroup$ – Lopey Tall Dec 4 '17 at 16:30
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$\begingroup$

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}}
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3
  • $\begingroup$ 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? $\endgroup$ – Lopey Tall Dec 4 '17 at 3:18
  • $\begingroup$ correction: {{0., 1.}, {17.057, 1.}, {17.308, 0.22}, {17.558, 0.23}, {72.273, 0.23}, {72.526, 0.001}...} $\endgroup$ – Lopey Tall Dec 4 '17 at 3:26
  • $\begingroup$ @LopeyTall but the code I posted does exactly this? You just need to extract the values from the association. I will add this now. $\endgroup$ – Nasser Dec 4 '17 at 3:47

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