How can I sort set of points using awk or sed within a given interval - bash

Question

How can I sort the following file.txt that contains a set of points using awk or sed
1.0 -0.6486
0.8 -0.2384
-0.2 0.0750
-0.2 0.0750
0.6 0.0754
0.4 0.3150
0.2 0.4985
0.1 0.5742
-0.1 0.7003
-0.2 0.7528
-0.4 0.8416
-0.6 0.9133
-0.8 0.9721
-1.0 1.0208
1.0 2.4600
0.8 2.5526
0.6 2.6431
0.4 2.7286
0.2 2.8070
0.1 2.8433
-0.1 2.9098
-0.2 2.9400
-0.4 2.9948
-0.6 3.0428
-0.8 3.0849
-1.0 3.1218
I want to delete the lines {-0.2, 0.0750} and (-0.2, 0.0750) and have final form of the file as:
1.0 -0.6486
0.8 -0.2384
0.6 0.0754
0.4 0.3150
0.2 0.4985
0.1 0.5742
-0.1 0.7003
-0.2 0.7528
-0.4 0.8416
-0.6 0.9133
-0.8 0.9721
-1.0 1.0208
1.0 2.4600
0.8 2.5526
0.6 2.6431
0.4 2.7286
0.2 2.8070
0.1 2.8433
-0.1 2.9098
-0.2 2.9400
-0.4 2.9948
-0.6 3.0428
-0.8 3.0849
-1.0 3.1218
I need a script that can check from 1.0 to -1.0 in steps on 0.1 and delete any line not following the decreasing order, in this case the two points -0.2 and write the 'sorted' set to a new file.
I am new to Linux.

Answer 1

First off, your question has a problem, in that you say you want to "delete any line not following the decreasing order", but -0.2 is a decrease from 0.8. But if you meant decreasing order to refer to "in steps on 0.1", then there is another problem, which is that most of your data points decrease in steps of 0.2, and only a few decrease by 0.1.
The unstated requirement from your data is that an empty line resets the script so that it starts from 1.0 again.
So I've parameterized your question as "The x value in each sub-list must decrease by 1 or 2 steps of 0.1", and written the following awk one liner (I added the newlines for clarity, but you can leave them out to use it directly from the command line, as I did):
awk 'function NewList() {
xPrev=1.0+delta
};
BEGIN {
delta=0.1;
maxSteps=2;
epsilon=0.0000001;
NewList()
};
NF {
if (($1-epsilon <= xPrev - delta) && ($1+epsilon >= xPrev - delta*maxSteps)) {
print;
xPrev=$1
}
next
};
{
NewList();
print ""
}'
Note that the "epsilon" variable gets around the inaccuracy of computer floating-point math; without it, the program may (did on my system) stop printing output after a few points, due to tiny (and not displayed) differences from the decimal values.