swapping fields in columns by fixed pattern (yes, no, no, yes)

Question

I want to produce a following list of pages (for imposition work); (number of pages is variable, but I make a sample of my needs using a list of 16 pages, logic is the same for longer lists)

1,16
8,9
15,2
10,7
3,14
6,11
13,4
12,5

I written this for cycle:

for ((x=16, y=1, z=8, w=9;x>=4, y<=4, z>=12, w<=12;x--, y++, z--, w++)); do echo "$x $y;$z $w"; done | tr ";" "\n" | tr " " ","

that, however, produces:

16,1
8,9
15,2
7,10
14,3
6,11
13,4
5,12

and not the list of pages I want. So, I need, with awk or other commands, to swap fields in some columns following this pattern (repeating every 4 couple of pages)

swap fields

no swap fields

no swap fields

swap fields

16,1 (swap: becomes: 1,16
8,9  (no swap: remains 8,9
15,2 (no swap: remains 15,2
7,10 (swap: becomes: 10,7
14,3 (swap: becomes: 3,14
6,11 (no swap: remains 6,11
13,4 (no swap: remains 13,4
5,12 (swap: becomes: 12,5

generalizing the logic of this imposition (I need to impose a single copy of an A6 book across an A4 page format) I wrote a more generalized script

#!/bin/sh
pages=$1
halfpages="`let DIVISION=$pages/2; echo $DIVISION`"
incr="$(echo "scale=0; $halfpages+1" |bc -l)"
dividedby4="$(echo "scale=0; $pages/4" |bc -l)"
lastupperpage="$(echo "scale=0; $pages-$dividedby4" |bc -l)"
u="u"
for ((x=$pages, y=1, z=$halfpages, w=$incr;x>=4, y<=4, z>=$lastupperpage, w<=$lastupperpage;x--, y++, z--, w++)); do echo "$x$u $y$u;$z $w"; done | tr ";" "\n" | tr " " "," | tr "\n" ","
exit 0

however I'm only able to produce:

16u,1u,8,9,15u,2u,7,10,14u,3u,6,11,13u,4u,5,12

instead of right:

1u,16u,8,9,15u,2u,10,7,3u,14u,6,11,13u,4u,12,5

that I pass to Multivalent.jar

• http://ifile.it/iqpjo4s/Multivalent.jar

I attach a picture of right imposition of an A6 across an A4 to show the right sequence of imposition

what I try to obtain is a way to impose a whole A6 book across an A4 page in ONE signature consisting in all its pages (not the 8-Page Imposition), in order to cut at half A4 page, close the two halves one over another, reverse sheet obtained, cut at half and applying glue to left edge in order to apply cover

to perform this task I need or to rethink my script from scratch or find a way to swap fields in columns by a fixed pattern (swap, no swap, no swap, swap) in order to correct wrong order produced by my script

EDIT

solved sending standard output of script to awk with this syntax:

awk -F "," '{
    print $2 "," $1;
    getline; print;
    getline; print;
    getline; print $2 "," $1
}' 

Answer 1

The following script is a much cleaner way of obtaining the output you want.

#!/usr/bin/env bash

(($# == 0)) && {
    echo "Usage: $0 <page_count>"
    exit 1
} >&2

# nTotal = $1 rounded up to a multiple 8
nTotal=$(($1 + 7))
nTotal=$((nTotal - nTotal % 8))
nHalf=$((nTotal / 2))
nQuarter=$((nTotal / 4))

# print page numbers in groups of 4, 2 groups at a time
for ((x=0; x < nQuarter; x+=2)); do
    printf '%du,%du\n%d,%d\n' \
        $((x + 1)) $((nTotal - x)) $((nHalf - x)) $((nHalf + x + 1))
    printf '%du,%du\n%d,%d\n' \
        $((nTotal - (x + 1))) $((x + 2)) \
        $((nHalf + x + 2)) $((nHalf - x - 1))
done

Example

$ ./imposition8 16
1u,16u
8,9
15u,2u
10,7
3u,14u
6,11
13u,4u
12,5

---

I rewrote your script because there were several problems with the original.

• You used non-sh compatible bash specific syntax, so I corrected the shebang line to match.

• The entire thing can be done in pure bash. The use of multiple tr invocations, an external awk, and bc is inefficient. In particular, you should know that bash and even POSIX-compliant sh can do math internally.

Answer 2

Here is a script which does it cleanly (hopefully).. I'm not up with printing/binding methods, so I'm not sure if the sequencing is correct, but it certainly works from the center out... I just don't knwo the folding/cutting sequence you require (beyond your 16 page example)... I've included a sample 24 page output.

pages=${1:-16}
pagesPerSheet=4
sheets=$((  (pages/pagesPerSheet) 
          +((pages%pagesPerSheet)>0) ))
pagesTot=$((sheets*pagesPerSheet))

Ob=0               # overall begin
Ox=$((pagesTot+1)) # overall max 
Hb=$((Ox/2))       # 2nd Half begin
hx=$((Hb+1))       # 1st half max

for ((s=sheets;s>0;s-=2)) ;do
   printf '%su,%su,%s,%s,%su,%su,%s,%s%s' \
           $((Ob+=1)) $((Ox-=1)) \
           $((hx-=1)) $((Hb+=1)) \
           $((Ox-=1)) $((Ob+=1)) \
           $((Hb+=1)) $((hx-=1)) \
           $(((s>2)) && echo ,)
done; echo  

output

# 16 page
1u,16u,8,9,15u,2u,10,7,3u,14u,6,11,13u,4u,12,5
# 24 page
1u,24u,12,13,23u,2u,14,11,3u,22u,10,15,21u,4u,16,9,5u,20u,8,17,19u,6u,18,7

---

This code snippet prints a graphical view

Ob=0               # overall begin
Ox=$((pagesTot+1)) # overall max 
Hb=$((Ox/2))       # 2nd Half begin
hx=$((Hb+1))       # 1st half max

for ((s=sheets;s>0;s-=2)) ;do
   printf '%2su %2su | %2su %2su\n%2s  %2s  | %2s  %2s\n-------   -------\n' \
           $((Ob+=1)) $((Ox-=1)) $((Ox-=1)) $((Ob+=1)) \
           $((hx-=1)) $((Hb+=1)) $((Hb+=1)) $((hx-=1))
done

output

# 16 page
 1u 16u | 15u  2u
 8   9  | 10   7
-------   -------
 3u 14u | 13u  4u
 6  11  | 12   5
-------   -------

# 24 page
 1u 24u | 23u  2u
12  13  | 14  11
-------   -------
 3u 22u | 21u  4u
10  15  | 16   9
-------   -------
 5u 20u | 19u  6u
 8  17  | 18   7
-------   -------

Answer 3

I understand the desire to derive a formula, but wouldn't it be much more easy, and therefore better, from a maintenance perspective, to use something like this:

#!/bin/bash
arr=(1 16 8 9 15 2 10 7 3 14 6 11 13 4 12 5)
for i in {0..3}; do 
    for n in ${arr[*]}; do 
        echo -n $((n+16*i))","
    done
    echo
done | sed -r 's/([^,]+,[^,]+),/\1\n/g' 

Or doesn't the pattern repeat like this:

1,16
8,9
15,2
10,7
3,14
6,11
13,4
12,5

17,32
24,25
31,18
26,23
19,30
22,27
29,20
28,21

...