Modify text file with math expression - language-agnostic

Question

I have a file called POSCAR that looks like this.
Pt-FCC
3.975
3.975000 0.000000 0.000000
0.000000 3.975000 0.000000
0.000000 0.000000 3.975000
I need to change the 3x3x3 matrix several times, to take the following shape and values, where d ranges from 0.005 to 0.025 with a 0.005 increment.
Pt-FCC
3.975
1+d 0.000000 0.000000
0.000000 1-d 0.000000
0.000000 0.000000 1/(1-d^2)
For example, for d=0.005:
Pt-FCC
3.975
1.005000 0.000000 0.000000
0.000000 0.995000 0.000000
0.000000 0.000000 1.000025
I cannot assign a variable inside the file and use expr and echo to evaluate it, because the simulation program does not understand this. I am attempting to use a loop that iterates through all the values of d and copies the original POSCAR file, then uses perl, sed, or awk to modify the matrix while keeping the spacing constant.
for i in $(seq 0.005 0.005 0.025)
do
cp POSCAR POSCAR_pure_shear/POSCAR_pure_$i
perl -pi .................. POSCAR_pure_$i
done
I understand this is a long question and I appreciate any help that might shift me in the right direction. I am still a beginner!

Answer 1

You can do something like this:
awk -v d=0.005 'FNR==3 {$1=sprintf("%0.6f", 1+d)}
FNR==4 {$2=sprintf("%0.6f",1-d)}
FNR==5 {$3=sprintf("%0.6f",1/(1-d**2))}
1' file
Prints:
Pt-FCC
3.975
1.005000 0.000000 0.000000
0.000000 0.995000 0.000000
0.000000 0.000000 1.000025
Plugging that into your loop:
for i in $(seq 0.005 0.005 0.025)
do
awk -v d="$i" 'FNR==3 {$1=sprintf("%0.6f", 1+d)}
FNR==4 {$2=sprintf("%0.6f",1-d)}
FNR==5 {$3=sprintf("%0.6f",1/(1-d**2))}
1' file
done