How to interpolate my list of results?

Question

I have the results

{{{0, 10, 10}, {0.114129, 9, 10}, {0.115385, 11, 10}, {0.118755, 11, 9}, 
{0.160154, 10, 9}, {0.193103, 9, 9}, {0.194063, 8, 10}, {0.208447, 8, 9} 
{0.235062, 7, 9}, {0.243287, 6, 9}, {0.248032, 5, 9}, {0.358482, 7, 9}, 
{0.393213, 7, 8}, {0.405397, 7, 7}, {0.461576, 6, 7}, {0.523134, 6, 6}, 
{0.635241, 6, 8}, {0.726211, 5, 8}, {0.829014, 4, 8}, {0.903913, 4, 7}, 
{1.32181, 6, 7}, {1.59651, 6, 6}, {1.64345, 6, 8}, {1.64803, 5, 8}, 
{1.65241, 5, 7}, {1.80486, 4, 7}, {1.97205,4, 6}, {2.78093, 4, 5}, 
{2.94957,4, 6}, {2.98843, 4, 6}, {3.1374,3, 6}, {3.44895, 2, 6}, 
{3.98122,2, 8}, {4.24663, 2, 10}, {4.45249, 2, 9}, {4.59911, 2, 9}, 
{5.14028, 3, 10}, {5.1964, 3, 12}, {5.20448, 3, 12}, {5.34628, 2, 13}, 
{5.39089, 2, 15}, {5.47021, 2, 16}, {5.49031, 2, 18}, {5.68693, 2, 18}, 
{5.90643, 3, 18}, {5.95821, 3, 17}, {6.04493, 4, 17}, {6.07941, 4, 16}, 
{6.18949, 4, 15}, {6.20035, 4, 14}, {6.31346, 4, 13}, {6.35271, 3, 13}, 
{6.58122, 3, 12}, {6.72382, 3, 11}, {6.74931, 3, 10}, {6.9862, 4, 11}, 
{7.11951,4, 10}, {7.17143, 3, 10}, {7.21791, 2, 11}, {7.33074, 2, 12}, 
{7.40083, 2, 11}, {7.43524, 4, 11}, {7.55296, 4, 10}, {7.62666, 3, 10}, 
{7.84643, 3, 9}, {8.0184, 3, 8}, {8.06468, 2, 8}, {8.11406, 2, 9}, 
{8.14889, 1, 9}, {8.27048, 0, 9}, {8.47532,0, 11}, {8.69576, 0, 13}, 
{8.97068, 1, 14}, {9.02658, 2, 14}, {9.08941, 2, 13}, {9.33396, 2, 13}, 
{9.50241, 2, 12}, {9.81107, 2, 13}, {9.86563, 2, 15}, {10.0441, 2, 14}}, 
{{0, 10, 10}, {0.00157025, 10, 9}, {0.0123142, 9, 9}, {0.0798253, 9, 8}, 
{0.0989871, 9, 7}, {0.159716, 8, 7}, {0.233333, 8, 6}, {0.284473, 9, 7}, 
{0.428241, 8, 7}, {0.566031, 8, 6}, {0.580869, 7, 6}, {0.59721, 6, 7}, 
{0.606727, 5, 7}, {0.650175,5, 6}, {0.784228, 5, 8}, {0.910743, 4, 8}, 
{1.04667, 4, 7}, {1.05059, 5, 7}, {1.11214, 4, 7}, {1.11664, 4, 6}, 
{1.11731, 6,6}, {1.34928, 5, 6}, {1.40728, 4, 6}, {1.51868, 4, 8}, 
{1.61049,4, 7}, {1.74908, 3, 7}, {1.79889, 3, 6}, {1.84876, 5, 6}, 
{2.18662,4, 6}, {3.0228, 4, 5}, {3.0609, 3, 5}, {3.10427, 3, 4}, 
{3.3269, 3, 6}, {3.38352, 3, 5}, {3.42096, 4, 5}, {3.57648, 3, 6},   
{3.6044, 3, 8}, {3.82802, 3, 10}, {3.89249, 2, 10}, {4.03572, 4, 10}, 
{4.14792, 3, 10}, {4.29539, 3, 9}, {4.62608, 5, 9}, {4.67712, 7, 9}, 
{4.70763, 7, 8}, {4.8375, 6, 9}, {4.87401, 6, 8}, {4.99582, 6, 7}, 
{5.00558, 5, 7}, {5.03584, 5, 8}, {5.17234, 5, 7}, {5.26621,4, 8}, 
{5.49947, 4, 7}, {5.53808, 4, 6}, {5.63194, 4, 6}, {5.66884, 3, 6}, 
{5.79289, 3, 5}, {5.79674, 5, 5}, {5.93102, 5,4}, {6.04469, 5, 3}, 
{6.2474, 7, 3}, {6.32087, 8, 4}, {6.34615, 10, 4}, {6.45538, 9, 4}, 
{6.49163, 10, 5}, {6.49456, 9, 5}, {6.64491, 9, 4}, {6.72716, 10, 5}, 
{6.8513, 10, 4}, {6.86975, 9, 4}, {6.91351, 9, 3}, {7.48925, 8, 3},
{7.53343, 7, 3}, {7.7141, 9, 3}, {7.74821, 8, 3}, {7.82409, 10, 3}, 
{7.92441, 9, 3}, {8.03961, 8, 3}, {8.13332, 10, 3}, {8.2045, 9, 3}, 
{8.62925, 8, 3}, {8.7584, 7, 3}, {9.01221, 7, 2}, {9.18724, 9, 2}, 
{9.34235, 8, 2}, {9.44694, 7, 2}, {9.65845, 7, 4}, {9.67498, 6, 4},  
{9.69573, 8, 4}, {9.76277, 10, 4}, {9.77852, 9, 4}, {9.80974, 8, 4}, 
{9.85812, 7, 4}, {9.91486, 9, 4}, {10.0656, 9, 6}}, 
{{0, 10, 10}, {0.0786173, 10, 9}, {0.159432, 9, 9}, {0.241794, 8, 10}, 
{0.285418, 7, 10}, {0.364088, 7, 9}, {0.393744, 7, 8}, {0.41457, 7, 7}, 
{0.437014, 7, 6}, {0.437701, 8, 5}, {0.596505,10, 5}, {0.846736, 10, 4}, 
{1.18815, 10, 3}, {1.34252, 9, 3}, {1.48486, 11, 3}, {1.55601, 13, 3}, 
{1.88043, 16, 2}, {1.88406, 18, 2}, {1.94665, 18, 1}, {2.50657, 17, 1}, 
{2.64969, 16, 1}, {2.70897, 18, 1}, {2.82536, 17, 1}, {3.12088, 19, 1}, 
{3.34407, 18, 1}, {3.40552, 19, 2}, {3.50199, 18, 2}, {3.60667, 17, 2}, 
{3.62172, 16, 2}, {3.64203, 15, 2}, {3.74326, 14, 2}, {3.76458, 13, 2}, 
{3.84473, 12, 2}, {3.88209, 11, 2}, {3.90626, 10, 2}, {3.97077, 9, 2}, 
{3.99447, 8, 2}, {4.10467, 8, 1}, {4.1746, 9, 2}, {4.17579, 8, 2}, 
{4.1864, 7, 2}, {4.74247, 8, 1}, {5.21633, 7, 1}, {5.91447, 6, 1}, 
{6.69129, 7, 0}, {7.45429, 9, 0}, {7.59871, 10, 1}, {7.6605, 9, 1}, 
{7.76442, 8, 1}, {7.93861, 9, 2}, {8.24453, 10, 3}, {8.39746, 10, 2}, 
{8.40362, 9, 2}, {8.4071, 10, 3}, {8.62252, 9, 3}, {8.77215, 9, 5}, 
{8.7814, 11,5}, {8.82388, 11, 4}, {8.86246, 10, 4}, {9.03635, 10, 3}, 
{9.06071, 9, 3}, {9.43662, 8, 3}, {9.50551, 7, 3}, {9.60883, 6,3}, 
{9.83946, 5, 3}, {9.92444, 4, 3}, {9.93336, 4, 5}, {9.93849, 4, 4}, 
{10.0484, 6, 4}}}

These triplets of results represents {time, amount in population1, amount in population2}, from a simulation that I repeated 3 times to get 3 realisations and is stored as a list called RESULTS. As you can see, the times in my results are continuous, however, I wish to change them to discrete times, specifically (0, 0.01, 0.02, ..., 10), so I can compare each of the realisations.

In other words I want to transform my data such that I can see the amounts in each population at discrete moments in time.

I believe I have to use INTERPOLATION to do this, however, my attempts don't seem to be working.

For a single realisation, I do the following. Where resultsare my results for a single realisation, not a list of realisations.

My resultsare

{{0, 10, 10}, {0.0517339, 9, 10}, {0.0652198, 9, 9}, {0.10149, 8, 9}, 
{0.129424, 7, 9}, {0.195224, 7, 8}, {0.342889, 7, 7}, {0.432865,7, 6}, 
{0.440611, 9, 6}, {0.591368, 9, 5}, {0.595538, 9, 4}, {0.652285, 8, 4}, 
{0.692064, 7, 4}, {0.838426, 7, 3}, {1.00484, 9, 3}, {1.03923, 11, 3}, 
{1.25564, 10, 5}, {1.26416, 9, 5}, {1.30464, 8, 5}, {1.38528, 7, 5}, 
{1.40261, 7, 4}, {1.43688, 8, 3}, {1.62686, 7, 3}, {1.68806, 6, 3}, 
{1.69626, 6, 5}, {1.8633, 6, 4}, {1.89874, 5, 4}, {1.95469, 5, 3}, 
{2.03057, 6, 4}, {2.08386, 5, 4}, {2.42979, 4, 4}, {2.77053, 4, 6}, 
{2.81467, 4, 5}, {2.9406, 4, 4}, {2.99647, 3, 4}, {3.23748, 3, 3}, 
{3.64886, 3, 2}, {3.79736, 3, 1}, {5.15426, 5, 1}, {5.21834, 7, 1}, 
{5.33466, 8, 2}, {5.45287, 7, 2}, {5.62627, 7, 4}, {5.7219, 6, 4},
{6.13589, 5, 4}, {6.22153, 5, 3}, {6.26948, 4, 3}, {6.35013, 6, 3}, 
{6.57652, 8, 3}, {6.71548, 7, 3}, {6.91989, 9, 3}, {7.32093, 8, 3}, 
{7.41391, 9, 4}, {7.4232, 9, 3}, {7.57311, 8, 5}, {7.59601, 10, 5}, 
{7.62954, 11, 6}, {7.67323, 10, 6}, {7.72092, 9, 6}, {7.80297, 8, 7}, 
{7.81821, 8, 6}, {7.85965, 7, 6}, {7.93377, 6, 6}, {8.00356, 6, 8}, 
{8.03843, 6, 7}, {8.30788, 5, 7}, {8.36661, 4, 7}, {8.47783, 3, 7}, 
{8.72014, 3, 6}, {8.90535, 3, 8}, {9.22095, 3, 8}, {9.31672, 2, 8}, 
{9.32869, 4, 8}, {9.5083, 4, 10}, {9.77343, 3, 11}, {9.86772, 5, 11}, 
{9.88329, 4, 11}, {9.91103, 5, 12}, {9.94773, 5, 14}, {9.9559, 4, 14}, 
{10.0996, 4, 13}}

p1F = Interpolation[results[[All, {1, 2}]], InterpolationOrder -> 0];
p1resampled = Table[{t, p1F[t]}, {t, 0, 10, 0.1}]

Which returns the results

{{0., 9.}, {0.1, 8.}, {0.2, 7.}, {0.3, 7.}, {0.4, 7.}, {0.5, 9.}, {0.6, 8.}, 
{0.7, 7.}, {0.8, 7.}, {0.9, 9.}, {1., 9.}, {1.1, 10.}, {1.2, 10.}, {1.3,8.}, 
{1.4, 7.}, {1.5, 7.}, {1.6, 7.}, {1.7, 6.}, {1.8, 6.}, {1.9, 5.}, {2., 6.}, 
{2.1, 4.}, {2.2, 4.}, {2.3, 4.}, {2.4, 4.}, {2.5, 4.}, {2.6, 4.}, {2.7, 4.}, 
{2.8, 4.}, {2.9, 4.}, {3., 3.}, {3.1, 3.}, {3.2, 3.}, {3.3, 3.}, {3.4, 3.}, 
{3.5, 3.}, {3.6, 3.}, {3.7, 3.}, {3.8, 5.}, {3.9, 5.}, {4., 5.}, {4.1, 5.}, 
{4.2, 5.}, {4.3, 5.}, {4.4, 5.}, {4.5, 5.}, {4.6, 5.}, {4.7, 5.}, {4.8, 5.}, 
{4.9, 5.}, {5., 5.}, {5.1, 5.}, {5.2, 7.}, {5.3, 8.}, {5.4, 7.}, {5.5, 7.}, 
{5.6, 7.}, {5.7, 6.}, {5.8, 5.}, {5.9, 5.}, {6., 5.}, {6.1, 5.}, {6.2, 5.}, 
{6.3, 6.}, {6.4, 8.}, {6.5, 8.}, {6.6, 7.}, {6.7, 7.}, {6.8, 9.}, {6.9, 9.}, 
{7., 8.}, {7.1, 8.}, {7.2, 8.}, {7.3, 8.}, {7.4, 9.}, {7.5, 8.}, {7.6, 11.}, 
{7.7, 9.}, {7.8, 8.}, {7.9, 6.}, {8., 6.}, {8.1, 5.}, {8.2, 5.}, {8.3, 5.}, 
{8.4, 3.}, {8.5, 3.}, {8.6, 3.}, {8.7, 3.}, {8.8, 3.}, {8.9, 3.}, {9., 3.}, 
{9.1, 3.}, {9.2, 3.}, {9.3, 2.}, {9.4, 4.}, {9.5, 4.}, {9.6, 3.}, {9.7, 3.}, 
{9.8, 5.}, {9.9, 5.}, {10., 4.}}

Which as you can see is incorrect as the first few terms should be

{0,10}, {0.01,10}, {0.02,10}, {0.03,10}, {0.04,10}, {0.05,10}, {0.06,9},
{0.07,9}, {0.08,9}, {0.09,9}, {0.10,9}, {0.11,8}, {0.12,8}, {0.13,7}, ...and so on

How do I modify this code so that I achieve the right output? And then, how do I repeat the process but this time using my list of realisations RESULTS?

Answer 1

This code reads the triplet population vs time dataset results3 (renamed), and plots the 3 pairs of data after resampling. Resampled data is in array popRes[i,j], where {i,1,3} is the realization index, and {j,1,2} is the index representing population1 and population2 respectively.

(* This code reads the triplet population vs time dataset `results3` (renamed), and plots the 3 pairs of data after resampling. Resampled data is in array `popRes[i,j]`, where `{i,1,3}` is the realization index, and `{j,1,2}` is the index representing population1 and population2 respectively. *)

For[i=1,i<4,i++,
 time=results3[[i,All,1]];
 pop[i,1]=EventSeries[results3[[i,All,2]],{time}];
 pop[i,2]=EventSeries[results3[[i,All,3]],{time}];
 popRes[i,1]=TimeSeriesResample[pop[i,1],ResamplingMethod->{"Interpolation",InterpolationOrder->1}];
 popRes[i,2]=TimeSeriesResample[pop[i,2],ResamplingMethod->{"Interpolation",InterpolationOrder->1}]; ]

(* Verify that resampling is regular/uniform for the output data *)

RegularlySampledQ[popRes[1,1]]
RegularlySampledQ[popRes[1,2]]

OUT: True

OUT: True

(* Realization 1: Plot of population1 and population2 vs time BEFORE resampling *)
ListPlot[{pop[1,1],pop[1,2]}]

(* Realization 1: Plot of population1 and population2 vs time AFTER resampling *)
ListPlot[{popRes[1,1],popRes[1,2]},PlotLegends->{"popRes[1,1]","popRes[1,2]"},ImageSize->600,PlotStyle->Thick]

(* Realizations 1, 2 and 3: Plot of population1 and population2 vs time AFTER resampling *)
 ListLinePlot[{popRes[1,1],popRes[1,2],popRes[2,1],popRes[2,2],popRes[3,1],popRes[3,2]},PlotLegends->{"popRes[1,1]","popRes[1,2]","popRes[2,1]","popRes[2,2]","popRes[3,1]","popRes[3,2]"},ImageSize->600,PlotStyle->Thick]