How to ignore differences between negative signs of numbers in the diff command?

Question

I have two large files consisting mainly of numbers in matrix form, and I'd like to use diff (or similar command) to compare these files and determine which numbers are different.

Unfortunately, quite a lot of these numbers differ only by sign, and I'm not interested in those differences. I only care when two numbers are different in magnitude. (i.e. I want 0.523 vs. 0.623, but NOT 0.523 vs. -0.523)

Is it possible to make diff ignore the sign and only print numbers that are different in magnitude?

EDIT: Some input examples, as requested:

File 1:

21   -0.0081318   0.0000000   0.0000000   0.0000000  -0.0138079
22    0.0000000   0.0000000   0.0000000   0.1156119   0.0000000
23    0.0000000   0.0047536   0.0000000   0.0000000   0.0000000

File 2:

21   -0.0081318   0.0000000   0.0000000   0.0000000   0.0032533
22    0.0000000   0.0000000   0.0000000  -0.0250637   0.0000000
23    0.0000000  -0.0047536   0.0000000   0.0000000   0.0000000

Assuming my files are formated mostly like this (except much, MUCH longer), I want to print out the differences, but ignore such differences when they're only in sign. For example, I don't care for 0.0047536 vs. -0.0047536, but I do want to print 0.1156119 vs. -0.0250637.

Answer 1

Given your shell provided "process substitution" (likes recent bashes), try

diff <(tr '-' ' ' <file1) <(tr '-' ' '<file2)
1,2c1,2
< 21    0.0081318   0.0000000   0.0000000   0.0000000   0.0138079
< 22    0.0000000   0.0000000   0.0000000   0.1156119   0.0000000
---
> 21    0.0081318   0.0000000   0.0000000   0.0000000   0.0032533
> 22    0.0000000   0.0000000   0.0000000   0.0250637   0.0000000

Answer 2

$ xdiff(){ diff -bu <($1 "$2") <($1 "$3"); }
$ xdiff 'sed s/-\([.0-9]\)/\1/g' file1 file2

you can do other normalization to the data. for instance, to treat all of 0.01, .01, -.0100, -.01e as the same:

$ norm(){ awk '{for(i=1;i<=NF;i++){$i=$i<0?-$i:+$i};print}' "$@"; }
$ xdiff norm file1 file2

Answer 3

To print lines from file2 whose corresponding absolute values differ from the corresponding fields from the same line in file1, save the lines from file1 in memory, the compare their absolute values:

function abs(x) {
  return x < 0 ? -x : x;
}

# file 1
NR == FNR {
  file1[$1]=$2" "$3" "$4" "$5" "$6
}

# file 2
NR != FNR {
  split(file1[$1], file1fields);
  if ( abs($2) - abs(file1fields[1]) ||
       abs($3) - abs(file1fields[2]) ||
       abs($4) - abs(file1fields[3]) ||
       abs($5) - abs(file1fields[4]) ||
       abs($6) - abs(file1fields[5]) )
        print;
}

Save that in a file, then run awk -f /path/to/that/file file1 file2