Interpolation on shell script bash - bash

Question

I have a data file containing values of longitudes and latitudes (displayed on two columns) measured by a GPS along a profile at regular intervals. at a certain point on my profile, the GPS stopped working, hence in my data i have zeros instead of values of longitudes and latitudes. I want to interpolate between this fields to get values of longitudes and latitudes instead of zeros.
to be more clear here is a simple example of how my file looks like.
[12 7] ;
[14 8 ];
[0 0];
[0 0];
[20 11];
[22 12]
NB: the number are on two columns, it's the editor's problem
i want to interpolate where i got zeros. i am working on bash and i have no idea on how to do it

Answer 1

You might have luck with a linear regression done once for the first column and once for the second column.
Assume we're working on the first column. The input / x axis is the index of the measurement, and the output / y axis is the measurement itself. So your data can become ((1, 12), (2, 14), (3, 0), (4, 0), (5, 20), (6, 22)). Based on the known input-output relationships, for indices (1, 2, 5, 6), you need to deduce a formula of the form y = ax + b. So you basically need to find a and b. Once you have those you can find the y for input 3 as 3a + b and the y for input 4 as 4a + b.
You'll find a different a and b for the second column.
How to find a and b is a little bit complicated. You can look at this article for a nice introduction as well as the formulas for computing a and b (named b0 and b1 inside).
One last thing - I would not attempt doing such a thing in Bash. While it is possible, as Bash has support for arrays and math, it is not what it was designed for. Call out to Matlab/Octave or R, and use their results. Those tools have builtin support for reading files such as yours as well as for doing the regression.

Answer 2

You can do that with awk, here is a script:
script.awk
BEGIN { FS="[ [\\];]+"
# decide on the number of floating digits for the interpolated figures
FMTStr= "[%.1f, %.1f];\n"
}
{ if( ($2== 0) && ( $3 == 0) ) { zeroLines++ }
else {
for( i = 1; i <= zeroLines; i++ ) {
t1 = prev1 + (($2 - prev1) / (zeroLines + 1 )) * i
t2 = prev2 + (($3 - prev2) / (zeroLines + 1 ) ) * i
printf(FMTStr, t1, t2)
}
# either printf(FMTStr, $2, $3) #or
print $0
prev1 = $2
prev2 = $3
zeroLines = 0
}
}
Use it so: awk -f script.awk yourfile, it gives you
[12 7] ;
[14 8 ];
[16.0, 9.0];
[18.0, 10.0];
[20 11];
[22 12];