Sorting Columns From File BASH

Note, as mentioned in the comments, a pure bash solution isn't pretty. There are a number of ways to do it, but this is probably the most straight forward. The following requires reading all values per line into the array, and saving the matrix stride so it can be transposed to read all column values into a row matrix and sorted. All sorted columns are inserted into new row matrix a2. Transposing that row matrix yields your original matrix back in column sort order.

Note this will work for any rank of column matrix in your file.

#!/bin/bash

test -z "$1" && {           ## validate number of input
    printf "insufficient input. usage:  %s <filename>\n" "${0//*\//}"
    exit 1;
}

test -r "$1" || {           ## validate file was readable
    printf "error: file not readable '%s'. usage:  %s <filename>\n" "$1" "${0//*\//}"
    exit 1;
}

## function: my sort integer array - accepts array and returns sorted array
## Usage: array=( "$(msia ${array[@]})" )
msia() {
    local a=( "$@" )
    local sz=${#a[@]}
    local _tmp
    [[ $sz -lt 2 ]] && { echo "Warning: array not passed to fxn 'msia'"; return 1; }
    for((i=0;i<$sz;i++)); do
        for((j=$((sz-1));j>i;j--)); do
        [[ ${a[$i]} -gt ${a[$j]} ]] && {
            _tmp=${a[$i]}
            a[$i]=${a[$j]}
            a[$j]=$_tmp
        }
        done
    done
    echo ${a[@]}
    unset _tmp
    unset sz
    return 0
}

declare -a a1               ## declare arrays and matrix variables
declare -a a2
declare -i cnt=0
declare -i stride=0
declare -i sz=0

while read line; do         ## read all lines into array
    a1+=( $line );
    (( cnt == 0 )) && stride=${#a1[@]}  ## calculate matrix stride
    (( cnt++ ))
done < "$1"

sz=${#a1[@]}                ## calculate matrix size
                            ## print original array
printf "\noriginal array:\n\n"
for ((i = 0; i < sz; i += stride)); do
    for ((j = 0; j < stride; j++)); do
        printf " %s" ${a1[i+j]}
    done
    printf "\n"
done

                            ## sort columns from stride array
for ((j = 0; j < stride; j++)); do
    for ((i = 0; i < sz; i += stride)); do
        arow+=( ${a1[i+j]} )
    done
    a2+=( $(msia ${arow[@]}) )  ## create sorted array
    unset arow
done
                            ## print the sorted array
printf "\nsorted array:\n\n"
for ((j = 0; j < cnt; j++)); do
    for ((i = 0; i < sz; i += cnt)); do
        printf " %s" ${a2[i+j]}
    done
    printf "\n"
done

exit 0

Output

$ bash sort_cols2.sh dat/matrix.txt

original array:

 1 1 1 1 1
 9 3 4 5 5
 6 7 8 9 7
 3 6 8 9 1
 3 4 2 1 4
 6 4 4 7 7

sorted array:

 1 1 1 1 1
 3 3 2 1 1
 3 4 4 5 4
 6 4 4 7 5
 6 6 8 9 7
 9 7 8 9 7

Awk script

awk '
{for(i=1;i<=NF;i++)a[i]=a[i]" "$i}      #Add to column array
END{
        for(i=1;i<=NF;i++){
                split(a[i],b)          #Split column
                x=asort(b)             #sort column
                for(j=1;j<=x;j++){     #loop through sort
                        d[j]=d[j](d[j]~/./?" ":"")b[j]  #Recreate lines
                }
        }
for(i=1;i<=NR;i++)print d[i]          #Print lines
}' file

Output

1 1 1 1 1
3 3 2 1 1
3 4 4 5 4
6 4 4 7 5
6 6 8 9 7
9 7 8 9 7

Here's my entry in this little exercise. Should handle an arbitrary number of columns. I assume they're space-separated:

#!/bin/bash

linenumber=0
while read line; do
        i=0
        # Create an array for each column.
        for number in $line; do
                [ $linenumber == 0 ] && eval "array$i=()"
                eval "array$i+=($number)"
                (( i++ ))
        done    
        (( linenumber++ ))
done <$1
IFS=$'\n'
# Sort each column
for j in $(seq 0 $i ); do
        thisarray=array$j
        eval array$j='($(sort <<<"${'$thisarray'[*]}"))'
done    
# Print each array's 0'th entry, then 1, then 2, etc...
for k in $(seq 0 ${#array0[@]}); do
        for j in $(seq 0 $i ); do
                eval 'printf ${array'$j'['$k']}" "'
        done    
        echo "" 
done

Not bash but i think this python code worths a look showing how this task can be achieved using built-in functions.

From the interpreter:

$ cat matrix.txt 
1 1 1 1 1
9 3 4 5 5
6 7 8 9 7
3 6 8 9 1
3 4 2 1 4
6 4 4 7 7

$ python
Python 2.7.3 (default, Jun 19 2012, 17:11:17) 
[GCC 4.4.3] on hp-ux11
Type "help", "copyright", "credits" or "license" for more information.
>>>
>>> f = open('./matrix.txt')
>>> for row in zip(*[sorted(list(a)) 
               for a in zip(*[a.split() for a in f.readlines()])]):
...    print ' '.join(row)
... 
1 1 1 1 1
3 3 2 1 1
3 4 4 5 4
6 4 4 7 5
6 6 8 9 7
9 7 8 9 7