Interpolating a list

Question

Here is a sample list

data = {{1, 2.1, 55.2}, {2, 2.7, 60}, {3, 3.1, 65}, {4, 3.5, 67}, {5, 4.5, 72}, {6, 4.2, 77}, {7, 5.9, 80}}

which contains three rows.

Now, let's create another list

ti = 2.;
tf = 6.;
nmax = 200;
dt = (tf - ti)/(nmax - 1);
times = Table[i, {i, ti, tf, dt}];

So, we created a list containing 200 equally spaced numbers in the interval [2,6]. These numbers correspond to the second row of the initial data list.

Now, I want to interpolate the initial data list so as to be able to predict what would be the values of the first and third columns using the 200 list as a second row. So we should obtain a new list data2 containing as a second row the 200 equally spaced data from times list and as first and third columns the interpolated ones. Finally, if possible, I would like to merge data and data2 with ordered columns.

Any ideas?

Answer 1

With simple interpolation based on 2nd column:

ti = 2.;
tf = 6.;
nmax = 200;
dt = (tf - ti)/(nmax - 1);
int1 = Interpolation[data[[;; , {2, 1}]]] /@ Range[ti, tf, dt] // Quiet;
int2 = Interpolation[data[[;; , {2, 2}]]] /@ Range[ti, tf, dt] // Quiet;
int3 = Interpolation[data[[;; , {2, 3}]]] /@ Range[ti, tf, dt] // Quiet;

newdata = Transpose[{int1, int2, int3}]

Answer 2

1. Re-arrange data into two lists of {time, value} pairs rdata = data[[All, {2, #}]] & /@ {1, 3}.
2. Use TemporalData with the option ResamplingMethod on rdata to get a temporal data object td.
3. Use td["PathFunctions"] to get the two interpolating functions.
4. Map the interpolating functions to your times.

td = TemporalData[data[[All, {2, #}]] & /@ {1, 3}, 
   ResamplingMethod -> {"Interpolation", InterpolationOrder -> 1}];

Show[ListPlot[td, PlotMarkers -> Automatic],
 ListPlot[Quiet@Through[td["PathFunctions"]@times], 
  PlotStyle -> {Red, Green}, BaseStyle -> PointSize[Small], 
  Joined -> False, DataRange -> {2, 6}], ImageSize -> Large]

To get data2 use

data2 = Quiet @
 Transpose[{td["PathFunctions"][[1]] @ #, #, td["PathFunctions"][[2]] @ #}]& @ times