divide each column by max value/last value - matrix

Question

I have a matrix like this:
A 25 27 50
B 35 37 475
C 75 78 80
D 99 88 76
0 234 230 681
The last row is the sum of all elements in the column - and it is also the maximum value.
What I would like to get is the matrix in which each value is divided by the last value in the column (e.g. for the first number in column 2, I would want "25/234="):
A 0.106837606837607 0.117391304347826 0.073421439060206
B 0.14957264957265 0.160869565217391 0.697503671071953
C 0.320512820512821 0.339130434782609 0.117474302496329
D 0.423076923076923 0.382608695652174 0.11160058737151
An answer in another thread gives an acceptable result for one column, but I was not able to loop it over all columns.
$ awk 'FNR==NR{max=($2+0>max)?$2:max;next} {print $1,$2/max}' file file
(this answer was provided here: normalize column data with maximum value of that column)
I would be grateful for any help!

Answer 1

In addition to the great approaches by #RavinderSingh13, you can also isolate the last line in the input file with, e.g. tail -n1 Input_file and then use the split() command in the BEGIN rule to separate the values. You can then make a single-pass through the file with awk to update the values as you indicate. In the end, you can pipe the output to head -n-1 to remove the unneeded final row, e.g.
awk -v lline="$(tail -n1 Input_file)" '
BEGIN { split(lline,a," ") }
{
printf "%s", $1
for(i=2; i<=NF; i++)
printf " %.15lf", $i/a[i]
print ""
}
' Input_file | head -n-1
Example Use/Output
$ awk -v lline="$(tail -n1 Input_file)" '
> BEGIN { split(lline,a," ") }
> {
> printf "%s", $1
> for(i=2; i<=NF; i++)
> printf " %.15lf", $i/a[i]
> print ""
> }
> ' Input_file | head -n-1
A 0.106837606837607 0.117391304347826 0.073421439060206
B 0.149572649572650 0.160869565217391 0.697503671071953
C 0.320512820512821 0.339130434782609 0.117474302496329
D 0.423076923076923 0.382608695652174 0.111600587371512
(note: this presumes you don't have trailing blank lines in your file and you really don't have blank lines between every row. If you do, let me know)
The differences between the approaches are largely negligible. In each case you are making a total of 3-passes through the file. Here with tail, awk and then head. In the other case with wc and then two-passes with awk.
Let either of us know if you have questions.

Answer 2

1st solution: Could you please try following, written and tested with shown samples in GNU awk. With exact 15 floating points as per OP's shown samples:
awk -v lines=$(wc -l < Input_file) '
FNR==NR{
if(FNR==lines){
for(i=2;i<=NF;i++){ arr[i]=$i }
}
next
}
FNR<lines{
for(i=2;i<=NF;i++){ $i=sprintf("%0.15f",(arr[i]?$i/arr[i]:"NaN")) }
print
}
' Input_file Input_file
2nd solution: If you don't care of floating points to be specific points then try following.
awk -v lines=$(wc -l < Input_file) '
FNR==NR && FNR==lines{
for(i=2;i<=NF;i++){ arr[i]=$i }
next
}
FNR<lines && FNR!=NR{
for(i=2;i<=NF;i++){ $i=(arr[i]?$i/arr[i]:"NaN") }
print
}
' Input_file Input_file
OR(placing condition of FNR==lines inside FNR==NR condition):
awk -v lines=$(wc -l < Input_file) '
FNR==NR{
if(FNR==lines){
for(i=2;i<=NF;i++){ arr[i]=$i }
}
next
}
FNR<lines{
for(i=2;i<=NF;i++){ $i=(arr[i]?$i/arr[i]:"NaN") }
print
}
' Input_file Input_file
Explanation: Adding detailed explanation for above.
awk -v lines=$(wc -l < Input_file) ' ##Starting awk program from here, creating lines which variable which has total number of lines in Input_file here.
FNR==NR{ ##Checking condition FNR==NR which will be TRUE when first time Input_file is being read.
if(FNR==lines){ ##Checking if FNR is equal to lines then do following.
for(i=2;i<=NF;i++){ arr[i]=$i } ##Traversing through all fields here of current line and creating an array arr with index of i and value of current field value.
}
next ##next will skip all further statements from here.
}
FNR<lines{ ##Checking condition if current line number is lesser than lines, this will execute when 2nd time Input_file is being read.
for(i=2;i<=NF;i++){ $i=sprintf("%0.15f",(arr[i]?$i/arr[i]:"NaN")) } ##Traversing through all fields here and saving value of divide of current field with arr current field value with 15 floating points into current field.
print ##Printing current line here.
}
' Input_file Input_file ##Mentioning Input_file names here.