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Linear interpolation

Here is a problem that occurs often. One have a set of data files that contain 2 columns (x and y) for some calculated property. Here I have selected only two such sets.

Before

I want to be able to add them, subtract them or make an average. So, what is the problem? The problem is, that the data is sampled in the same region but on different grids i.e. the number of points is different.

   0.00    0.151576740
   6.51    0.157566880
  13.03    0.175107240
  19.54    0.202843140
...
3967.59   -0.000073200
3974.10   -0.000082352
3980.62   -0.000095120
3987.13   -0.000107504

   0.00    0.060664982
   7.41    0.063726254
  14.83    0.072136290
  22.24    0.083837971
...
3965.71   -0.000059534
3973.12   -0.000055689
3980.53   -0.000048746
3987.94   -0.000041886

One needs to have the values on the same grid to make some simple calculations. I am interested in the region x in [1500:4000] and with a small awk script I can do on-the-fly linear interpolation (which is good enough in this particular case). Here is how the interpolated data compares to the original.

1500 0.00488383
1501 0.0050328
1502 0.00518177
1503 0.00533075
...

1500 0.00410784
1501 0.00411207
1502 0.0041163
1503 0.00412054
...

The script is running over integer numbers for easier understanding, but could be easily modified to handle real numbers for the grid values.

interpolate-on-regular-grid.awk

#!/usr/bin/awk -f
BEGIN {
  minx= 1500;  # Range: lower limit
  maxx= 4000;  #        upper limit
  dx= 1;       #        increment
}

{
  # check if the lower limit has been reached
  if (($1 > minx ) && ($1 < maxx)){
    x2=$1; y2=$2;

    # for the defined range
    for (xi= minx; xi <= maxx; xi= xi+dx){
      # step forward if the current grid point is outside the [x1:x2] region
      if (xi > x2)  {
        while (($1<xi) && (getline!=0) ) {x1=x2; y1=y2; x2=$1; y2=$2}
      }
      yi= (y2-y1)/(x2-x1)*(xi-x1) + y1; # linear interpolation
      print xi, yi
    }
  }
  x1= $1; y1=$2
}

Here is the result: After

Warning

I have written the script for my purposes and tested it against my data. It works for all of my cases, but could fail in some unforeseen situations so, please, always make sure that your results are reasonable. Do not blindly use the scripts provided on this site.

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