How to obtain a specific text from a file?

I generated a data file with the following format:

0.1
Analytic value = 340.347685734
Approximated value = 332.45634555
--
0.2
Analytic value = 340.936745872
Approximated value = 332.57893789
--
0.3
... and so on

I want to plot the analytic and approximate values in matplotlib/gnuplot against the input parameter (0.1, 0.2, etc). Usually, before generating the data file, I use to generate them with an awk script that puts the three values in three columns which is very easy to plot. However, here I accidentally generated the data file in a different format. How can I convert this text file to the following (maybe using regex or awk!):

0.1 340.347685734 332.45634555 
0.2 340.936745872 332.57893789
0.3 ... and so on

Or is there a way that I can plot the data without converting the format using gnuplot/matplotlib?

EDIT:
I have attempted to do it using python3. The following is my code:

file = open("myFile.dat",'r')
newFile = open("newFile.dat", 'a')
for i in range(4000):
  col1 = file.readline().split[-1]
  col2 = file.readline().split[-1]
  col3 = file.readline().split[-1]
  _ = file.readline().split[-1]
  line = col1 + " " + col2 + " " + col3
  newFile.write(line)

However, I was getting some error TypeError: 'builtin_function_or_method' object is not subscriptable which I didn't understand and I think this is a very inefficient code. That's why I asked in the SE. All the solutions presented so far work quite well. I marked the solution with awk as the accepted answer because it's simple and elegant. Also, I appreciate the solution that uses gnuplot only which also uncover a side of gnuplot for me.

No Regex needed here. Just 4 simple replacements:

Two replacements for the unwanted text, one replacement to remove the line breaks and one replacement to insert a linebreak again.

file = """0.1
Analytic value = 340.347685734
Approximated value = 332.45634555
--
0.2
Analytic value = 340.936745872
Approximated value = 332.57893789
--
0.3
... and so on
"""

file = file.replace("Analytic value = ","")
file = file.replace("Approximated value = ","")
file = file.replace("\n"," ")
file = file.replace("-- ","\n")
print(file)

Result:

0.1 340.347685734 332.45634555 
0.2 340.936745872 332.57893789 
0.3 ... and so on 

I would harness GNU AWK for this task following way, let file.txt content be

0.1
Analytic value = 340.347685734
Approximated value = 332.45634555
--
0.2
Analytic value = 340.936745872
Approximated value = 332.57893789
--

then

awk '/^--$/{print "";next}{printf "%s ",$NF}' file.txt

doess output

0.1 340.347685734 332.45634555 
0.2 340.936745872 332.57893789

Explanation: for line being -- just print newline and go to next one, for all others lines do output last field followed by space and not newline. If you want to know more about NF then read 8 Powerful Awk Built-in Variables – FS, OFS, RS, ORS, NR, NF, FILENAME, FNR

(tested in GNU Awk 5.1.0)

There are many ways to solve this problem, and the choice will among others depend on the file size. Here is a simple solution for a case when you cannot load the whole file at once - you have to process it line by line,

raw_data_file = 'data.txt'
out_data_file = 'data_final.txt'

counter = 0
with open(raw_data_file, 'r') as fin, open(out_data_file, 'w') as fout:
    temp_line = []
    for line in fin:

        if counter == 0:
            # First column
            temp_line.append(line.strip())
            counter += 1
            continue
        elif counter == 1:
            # Analytic value column
            temp_line.append(line.strip().split()[-1])
            counter += 1
            continue
        elif counter == 2:
            # Approximate value column
            temp_line.append(line.strip().split()[-1])
            counter += 1
        elif counter == 3:
            # Skip the -- and reset the counter
            counter = 0
            continue

        # Write the rearranged data to file
        fout.write((' ').join(temp_line))
        fout.write('\n')
        temp_line = []

Note that this solution relies tightly on the structure of the file that you provided.

> Or is there a way that I can plot the data without converting the format using gnuplot/matplotlib?

Yes, there is! Here is a platform-independent gnuplot-only solution. No need for external extra data preparation tools.

If you are plotting from a file, skip the $Data <<EOD ... EOD section and use plot 'yourFile.dat' ... .

Script: (works for gnuplot>=5.0.6, March 2017)

### plot special data format
reset session

$Data <<EOD
0.1
Analytic value = 340.347685734
Approximated value = 332.45634555
--
0.2
Analytic value = 340.936745872
Approximated value = 332.57893789
--
0.3
Analytic value = 341.936745872
Approximated value = 333.57893789
EOD

set datafile missing NaN
set key out
myFilter(colD,colF,valF) = strcol(colF) eq valF ? column(colD) : NaN

plot $Data u (valid(1)?x0=$1:x0):(myFilter(4,1,"Analytic"))     w lp pt 7 lc "red"  ti "analytic", \
        '' u (valid(1)?x0=$1:x0):(myFilter(4,1,"Approximated")) w lp pt 7 lc "blue" ti "approximated"
### end of script

Result:

Using any awk:

$ awk '{n=(NR%4); val[n]=$NF} n==0{print val[1], val[2], val[3]}' file
0.1 340.347685734 332.45634555
0.2 340.936745872 332.57893789