How can I interpolate a missed value depending on the previous and next value?

Question

I have a large file with two columns, I would like to interpret the value at 0.00, 0.50, 1.00, 1.50 ...etc (if it is not already exist) by calculating the mean from the previous value and the next value. For instance the corresponding value of 3.00 is missed so I want to add a line with 3.00 in the first column and a corresponding value in the second column =(2.99 + 3.56)/2=3.14 and do the same for 3.50, 4.00 , 4.50 ...etc this is my input

0.00  0.29
0.50  0.79
1.00  1.31
1.50  1.86
2.00  2.42
2.50  2.99
3.25  3.56
3.75  4.15
4.25  4.73
4.75  5.32
5.00  5.92
5.50  6.53
6.00  7.15

and this my desired output

0.00    0.29
0.50    0.79
1.00    1.31
1.50    1.86
2.00    2.42
2.50    2.99
3.00    3.28
3.50    3.86
4.00    4.44
4.50    5.03
5.00    5.92
5.50    6.53
6.00    7.15

Answer 1

I would do it in two steps.

First, interpolate the missing data. Here is an example with awk:

awk '
    ($1 - prev1) > 0.25 { printf "%.2f  %.2f\n", prev1 + 0.25, (prev2 + $2)/2 }
    { print; prev1 = $1; prev2 = $2 }
' data_file

It works like this:

• First, if we notice that a value in column 1 is missing (gap with previous value is > 0.25) we print the missing line by calculating an average for the column 2.
• Next, we print the current line and set the previous values for the next cycle

Finally, you can filter out the unwanted lines:

(previous awk command) | awk '$1 ~ /0$/'

This last awk command only displays the lines whose first value ends with a 0.