How to find the max values from columns - awk

Question

I am trying to find the maxima in three columns of a file called data.dat. The idea is
5414 6267 3157
4521 1235 5418
1366 6472 4598
5153 7814 5648
5414
7814
5648
I'm trying to use awk as
for k in {1..3};awk 'BEGIN {max = 0} {if ('$k'>max) max='$k'} END {print max}' data.dat;done
but I have not been lucky.

Answer 1

Could you please try following, written and tested with shown samples in GNU awk.
awk '
{
for(i=1;i<=NF;i++){
arr[i]=(arr[i]>$i?arr[i]:$i)
}
}
END{
for(k=1;k<=NF;k++){
print arr[k]
}
}' Input_file
Explanation: Adding detailed explanation for above.
awk ' ##Starting awk program from here.
{
for(i=1;i<=NF;i++){ ##Start a for loop from 1st field to last field of current line.
arr[i]=(arr[i]>$i?arr[i]:$i) ##Creating array arr with index of column number and keeping only greater value by comparing its [revious value in each iteration.
}
}
END{ ##Starting END block of this awk program from here.
for(k=1;k<=NF;k++){ ##Starting a loop from k=1 to till number of fields here.
print arr[k] ##Printing value of arr with index of k here.
}
}' Input_file ##Mentioning Input_file name here.

Answer 2

This is what awk arrays are made for. You can simply loop over each field, using the field number as the array index and comparing the value against the current field value. If it is greater, update the value at that index with the current value, e.g.
awk '{
for (i=1; i<=NF; i++)
if ($i > a[i])
a[i] = $i
}
END {
for (j = 1; j < i; j++)
print a[j]
}' file
Example Use/Output
For example, with your data in the filename file, you can just open an xterm and select-copy the awk script above and middle-mouse paste in the current directory containing file to test, e.g.
$ awk '{
> for (i=1; i<=NF; i++)
> if ($i > a[i])
> a[i] = $i
> }
> END {
> for (j = 1; j < i; j++)
> print a[j]
> }' file
5414
7814
5648