English
资源说明：Collection of simple utilities / notes
## Pairing
szudzik & cantor
```
pairing.pl [-cantor|-szudzik] stdin|file # -szudzik is default
Given pairs of input: output the pairing function value (using cantor or szudzik)
Given single inputs: output the original pairs
Examples
--------
$ cat /tmp/data
4 5
3 9
12 300
$ pairing.pl /tmp/data
29
84
90012
$ pairing.pl /tmp/data | pairing.pl
4 5
3 9
12 300
```
## mat.py - Align data into matrix like format with columns aligned
```
usage: mat.py [-h] [-c COLS] [-r ROWS] [-p PAD] [-s] [-j] [file]
positional arguments:
file file|stdin
optional arguments:
-h, --help show this help message and exit
-c COLS, --cols COLS number of columns
-r ROWS, --rows ROWS number of rows
-p PAD, --pad PAD number of additional spaces between row elements
-s, --square square output
-j, --justify right justification, default is left justification
$ cat data
one
two
three
four
five
six
seven
eight
nine
ten
$ mat.py data # default is an attempt to square
one two three
four five six
seven eight nine
ten
$ mat.py -r 3 data # 3 rows
one two three four
five six seven eight
nine ten
$ mat.py -c 5 -p 3 < data # 5 columns with 3 additional spaces added
one two three four five
six seven eight nine ten
$ series 1 30 | mat.py -p 1 -c 7 # 7 columns, 1 additional space
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30
$ series 1 144 | mat.py -j # right justify each element within the column
1 2 3 4 5 6 7 8 9 10 11 12
13 14 15 16 17 18 19 20 21 22 23 24
25 26 27 28 29 30 31 32 33 34 35 36
37 38 39 40 41 42 43 44 45 46 47 48
49 50 51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70 71 72
73 74 75 76 77 78 79 80 81 82 83 84
85 86 87 88 89 90 91 92 93 94 95 96
97 98 99 100 101 102 103 104 105 106 107 108
109 110 111 112 113 114 115 116 117 118 119 120
121 122 123 124 125 126 127 128 129 130 131 132
133 134 135 136 137 138 139 140 141 142 143 144
```
## mi - Music Info
Utility to extract tag information from various music file formats or
display a pretty-printed album style summary from a directory or set of files
Examples
--------
```
$ mi --summary /music/a/AC-DC/Volts
AC/DC
Volts (1977)
Playing Time: 57:09
1. Dirty Eyes ................................................ 3:21
2. Touch Too Much ............................................ 6:34
3. If You Want Blood (You've Got It) ......................... 4:26
4. Back Seat Confidential .................................... 5:23
5. Get It Hot ................................................ 4:15
6. Sin City .................................................. 4:53
7. She's Got Balls ........................................... 7:56
8. School Days ............................................... 5:21
9. It's A Long Way To The Top (If You Wanna Rock 'N' Roll) ... 5:16
10. Ride On ................................................... 9:44
$ mi "/music/b/Buddaheads/Howlin' At The Moon/01. Long Way Down.mp3"
title: Long Way Down
artist: Buddaheads
album: Howlin' At The Moon
genre: Blues
year: 2004
track: 1
time: 5:16
vbr: yes
encoder: LAME3.97
version: ID3v2.3.0, ID3v1.1
bitrate: 270
$ mi "/music/Loseless/Donna The Buffalo/Rockin' In The Weary Land/01. Tides Of Time.flac"
title: Tides Of Time
artist: Donna The Buffalo
album: Rockin' In The Weary Land
genre: Alternative Country
year: 1998
track: 01/12
time: 3:27
encoder: flac --best
bitrate: 16 bits per sample @ 44100Hz
$ mi "/music/p/Paul Reddick & The Sidemen/Rattlebag/13. Smokehouse.ogg "
title: Smokehouse
artist: Paul Reddick & The Sidemen
album: Rattlebag
genre: Blues
year: 2001
track: 13
time: 2:54
encoder: Xiph.Org libVorbis I 20030909
bitrate: 118
```
## corr - Pearson Product Moment Correlation Coefficient
Reads 2 columns, skipping non-numerics and outputs the
Pearson Product Moment Correlation Coefficient
Examples
--------
```
$ cat data # mixture of text/data and differing whitespace
Col1 Col2
---- ----
1 3
non-data
3 9
5 8
$ corr /tmp/data
N = 3, r = 0.777713771047819
```
## cdataEncode - XML CDATA Encoder
Encode the input XML as CDATA, handling nested CDATA statements
Examples
--------
```
$ echo 'hello world' | cdataEncode
$ echo 'hello world' | cdataEncode | cdataEncode
]]>
```
## cutcol -- Generalized Column Cutter
Cut columns in various ways
```
cutcol.pl -statfile file.stats -field range -col RE [-delim str] [-outdelim str] [-(no)re] [-(no)label] [-preserve] [-quiet]
-statfile file.stats stats file
-field range column # or range
-col STR string matching column label in the stats file
-re treat -col STR as regular expression (default)
-label output the column label
-delim delim delimiter to split fields on (defaults to tab)
-outdelim delim output delimiter (defaults to delim) [use '\t' for tab]
-preserve output selected columns in original statfile order
-quiet die silently on error
Examples:
Given the following tab separated input in file 'test.stats':
grade Predicted id
2 3 1
1 2 2
1 1 3
# output columns 'grade' and 'Predicted'
cutcol.pl -col grade -col Predicted test.stats
cutcol.pl -field 1 -field 2 test.stats
# output columns 'grade' and 'Predicted'
cutcol.pl -col gr -col Pre test.stats
cutcol.pl -f 1-2 test.stats
# output columns 'Predicted' and 'grade'
cutcol.pl -col 'ed$' -col 'de$' test.stats
cutcol.pl -f 2 -f 1 test.stats
# output columns 'Predicted' and 'id'
cutcol.pl -col '(?i)pre' -col 'id' test.stats
# output all columns comma separated
cutcol.pl -col . -outdelim=, test.stats
# output columns 'id' and 'grade'
cutcol.pl -col id -col grade test.stats
# output columns 'grade' and 'id'
cutcol.pl -preserve -col id -col grade test.stats
# output all columns comma separated, then convert back to tab
cutcol.pl -col=. -outdelim=, -statfile=test.stats | cutcol.pl -delim=, -col=. -outdelim='\t' -
```
## squeezeCommand -- Command Line Squeezebox Controller
Basic command line control of a Slimserver Squeezebox (play, pause, power, info, list, etc.)
Examples
--------
```
squeezeboxCommand.pl [-player|-id] cmd [args]
cmd:
players -- show information on known players
info -- show summary of the music library and players
add file|dir [...] -- add content to the current playlist
pl(ay) file|dir [...] -- clear current playlist, then add content
pa(use) -- pause toggle
po(wer) [on|off] -- power query and control
list -- show song/album/artist in the current playlist
n(ext) [-#|+#] -- jump +/- in playlist, default is +1
v(olume) [-#|+#|#] -- volume query, +/- adjust, or set
mi -- run external "mi" utility on the current music file
$ squeezeboxCommand.pl -list # current track is displayed in reverse video (not shown below)
+----------------------------+-------+----------+-------------------+
| Track | Time | Album | Artist |
+----------------------------+-------+----------+-------------------+
| Restless | 3:35 | Restless | Eric Jerardi Band |
| Easy To Love, Easy To Hate | 4:47 | Restless | Eric Jerardi Band |
| Let It Ride | 3:46 | Restless | Eric Jerardi Band |
| Self Defense | 5:09 | Restless | Eric Jerardi Band |
| My Dog | 3:18 | Restless | Eric Jerardi Band |
| Jail | 2:52 | Restless | Eric Jerardi Band |
| Going Through The Motions | 2:37 | Restless | Eric Jerardi Band |
| Kaboom | 2:34 | Restless | Eric Jerardi Band |
| L.A. Prelude | 1:28 | Restless | Eric Jerardi Band |
| L.A. | 5:38 | Restless | Eric Jerardi Band |
| Get Back | 4:16 | Restless | Eric Jerardi Band |
| Such A Crime | 3:35 | Restless | Eric Jerardi Band |
| Dent | 1:54 | Restless | Eric Jerardi Band |
| Wish I Could | 3:41 | Restless | Eric Jerardi Band |
+----------------------------+-------+----------+-------------------+
$ squeezeboxCommand.pl -info
Slimserver Version: 7.5.5
Players:
player index: 0
player id: 00:01:02:03:04:05
player ip: 192.168.36.14:61859
player name: Basement
player model: squeezebox2
player index: 1
player id: ab:cd:ef:01:02:03
player ip: 192.168.36.15:46309
player name: Living Room
player model: squeezebox
Library:
Artists: 2692
Albums: 8426
Songs: 103253
Basement power is: on
Basement current volume: 50
$ squeezeboxCommand.pl -vol=+5
Basement new volume: 55
$ squeezeboxCommand.pl -vol 42
Basement new volume: 42
$ squeezeboxCommand.pl -mi
Basement: /music/e/Eric\ Jerardi\ Band/Restless/08.\ Kaboom.mp3
title: Kaboom
artist: Eric Jerardi Band
album: Restless
genre: Blues
year: 2007
track: 08/14
time: 2:34
vbr: yes
encoder: LAME3.99r
version: ID3v2.3.0
bitrate: 261
```
## sound.help -- self displaying sed script of sound utility notes
```
# various notes gathered over the years related to audio/video files
#
---------------------------------------------------------------------
To read the complete media from a CD-ROM writing the data
to the file cdimage.raw:
readcd dev=0,0,0 f=cdimage.raw
---------------------------------------------------------------------
With CD-Record:
---------------
CD-Writing HowTo:
http://howto.linuxberg.com/ptHOWTO/CD-Writing-HOWTO
For example:
cdrecord -v speed=4 dev=1,0,0 mandrake.iso
You get the number on the SCSI bus number with "cdrecord --scanbus"
On Mac:
cdrecord -v dev=IODVDServices/0 -dao *.wav
---------------------------------------------------------------------
With nautilus-cd-burner:
/usr/bin/nautilus-cd-burner --source-iso=/home/farnham/Download/ubuntu-7.04-desktop-i386.iso
---------------------------------------------------------------------
Creating an iso image:
mkisofs -o /tmp/proj.iso -R proj
---------------------------------------------------------------------
To create an iso image from a CD (no need to mount)
cat /dev/cdrom > image.iso
---------------------------------------------------------------------
Blanking a CD-RW:
cdrecord dev=1,0,0 speed=4 blank=all
cdrecord dev=1,0,0 speed=4 blank=fast
all Blank the entire disk. This may take a
long time.
fast Minimally blank the disk. This results
in erasing the PMA, the TOC and the
pregap.
---------------------------------------------------------------------
Ripping to WAV storing each track in a separate file:
cdparanoia -B
cdparanoia -d /dev/dvd1 -B
Recording the WAV's:
cdrecord -v speed=4 dev=1,0,0 -audio *.wav
Checking to see if double speed would work:
cdrecord -v -dummy speed=2 dev=1,0,0 -audio *.wav
To copy an audio CD:
cdda2wav -x -D1,0,0 -B
cdrecord -v dev=1,0,0 -dao *.wav
cdrecord -v dev=/dev/scd1 -pad -dao *.wav
To copy an audio CD with CDDB lookup for track names:
cdda2wav --dev=1,0,0 --max --alltracks --cddb=1
To rename audio*.wav to track names:
~/bin/renameTracks.pl audio.cddb
To record the WAV's to a blank CDR:
cdrecord -v speed=4 dev=1,0,0 *.wav
---------------------------------------------------------------------
Wax -> Digital
aumix # set recording levels
rec -w -c 2 -r 44100 file.wav # SOX rec
gramofile # find and split tracks
---------------------------------------------------------------------
Downsampling:
# create intermediate CAF file
# input.wav: RIFF (little-endian) data, WAVE audio, Microsoft PCM, 24 bit, stereo 96000 Hz
afconvert -d 0 -f caff input.wav intermediate.caf
afconvert -d LEI16@44100 intermediate.caf outut.wav
# output.wav: RIFF (little-endian) data, WAVE audio, Microsoft PCM, 16 bit, stereo 44100 Hz
or
afconvert -d LEI16@44100 -f WAVE input.wav output.wav
or
/usr/local/sox-14.3.0/bin/sox input.wav -b 16 -r 44100 output.wav
---------------------------------------------------------------------
Converting flac to alac:
flac -d file.flac
afconvert -d alac file.wav file.m4a
---------------------------------------------------------------------
Converting m4a to WAV:
faad -o file.wav file.m4a
or
mplayer -vc dummy -vo null -ao pcm:file=music.wav music.m4a
or
afconvert -d LEI16 -f WAVE file.m4a file.wav
or
ffmpeg -i file.m4a file.wav
---------------------------------------------------------------------
Copying m4a to strip tags
ffmpeg -loglevel 0 -i input.m4a -vn -c:a copy output.m4a
ffmpeg -loglevel 0 -i input.m4a -vn -acodec copy output.m4a
or
MP4Box -add infile.m4a#audio output.m4a
---------------------------------------------------------------------
Converting mp3 to WAV:
madplay -o file.wav file.mp3
or
sox file.mp3 file.wav
or
mplayer -vc dummy -vo null -ao pcm:file=music.wav music.mp3
or
notlame --decode file.mp3 file.wav
or
afconvert -d LEI16 -f WAVE file.mp3 file.wav
---------------------------------------------------------------------
Converting WAV to m4a:
faac -q 120 -c 20000 -w file.wav # encodes to file.m4a
#faac -q 130 -c 22000 -m 4 (~218 kbps)
#faac -q 120 -c 20000 -m 4 (~194 kbps)
#faac -q 110 -c 18000 -m 4 (~158 kbps)
#faac -q 100 -c 16000 -m 4 (~129 kbps)
#faac -q 90 -c 14000 -m 4 (~103 kbps)
#faac -q 80 -c 12000 -m 4 (~79 kbps)
#faac -q 70 -c 10000 -m 4 (~62 kbps)
On a Mac (intermediate caf file):
afconvert file.wav intermediate.caf -d 0 -f caff --soundcheck-generate
afconvert intermediate.caf -d aac -f m4af -u pgcm 2 --soundcheck-read -b 256000 -q 127 -s 2 file.m4a
---------------------------------------------------------------------
Converting WAV to mp3:
notlame -h -V 0 -b 112 file.wav file.mp3
or
xingmp3enc -B 192 file.wav
---------------------------------------------------------------------
Converting WAV to ogg: --quality=6 is ~190 kbps
oggenc --artist='Dire Straits' \
--album='Alchemy: Dire Straits Live' \
--title='Sultans Of Swing' \
--track=6 \
--genre=Rock \
--date=1984 \
--quality=6 \
06.\ Sultans\ Of\ Swing.wav
Listing the ogg tags:
% vorbiscomment -l 06.\ Sultans\ Of\ Swing.ogg
Tagging an ogg file using a text file:
% cat tags
title=Sultans Of Swing
artist=Dire Straits
genre=Rock
date=1984
album=Alchemy: Dire Straits Live
tracknumber=6
% vorbiscomment -w -c tags file.ogg
Playing an ogg file:
% mplayer file.ogg
or
% ogg123 file.ogg
or
% xmms file.ogg
---------------------------------------------------------------------
Converting ogg to WAV:
oggdec -o file.wav file.ogg
for f in *.ogg; do oggdec -o "${f%.ogg}.wav" "$f"; done
---------------------------------------------------------------------
Converting WMA to WAV:
mplayer -vc dummy -vo null -ao pcm:file=music.wav music.wma
or
ffmpeg -i file.wma -f wav file.wav
---------------------------------------------------------------------
Concatinating 2 WAV's:
sox file1.wav -r 44100 -c 2 -s -w file1.raw
sox file2.wav -r 44100 -c 2 -s -w file2.raw
cat file1.raw file2.raw > file.raw
sox -r 44100 -c 2 -s -w file.raw file.wav
---------------------------------------------------------------------
Playing a DVD from a directory
mplayer dvd:// -dvd-device /path/to/dir
---------------------------------------------------------------------
Pulling the MP2 audio track off a DVD:
mplayer dvd:// -dvd-device /path/to/dir -dumpaudio -dumpfile stream.mp2
Convert the compressed audio (48000Hz MP2) to a 44100Hz 2ch Signed 16-bit WAV
mplayer stream.mp2 -af resample=44100 -ao pcm:file=stream.wav
or from the DVD device (dvd://1)
mplayer -vo null -vc dummy -ao pcm:file=music.wav dvd://1
mplayer -vo null -vc dummy -ao pcm:file=stream.wav /export/data/public/Music/WP_EARTH_TO_ATLANTA_2.ISO
mplayer -vo null -vc null -ao pcm:file=stream.wav dvd:// /media/dvdrecorder
followed by (dvd://2)
mplayer -vc null -vo null -ao pcm:file=music.wav dvd://2 -dvd-device ./Gary_Moore
Pull the mp2 track off and resample
mplayer -vo null -vc dummy -af resample=44100 -ao pcm:file=stream.wav LIVE_BABY_LIVE.ISO
Pull the audio track with id 130 (-aid 130, use -v to find id's), resample.
mplayer -vo null -vc dummy -aid 130 -af resample=44100 -ao pcm:fast:file=stream130.wav LIVE_BABY_LIVE.ISO
Pull the audio track with id 160 resample.
mplayer -vo null -vc dummy -aid 160 -af resample=44100 -ao pcm:fast:waveheader:file=music.wav dvd://2
Split into individual tracks.
foreach f ( `series 1 16` )
foreach? mplayer -vo null -vc dummy -aid 160 -af resample=44100 -ao pcm:fast:file=$f.wav -chapter $f-$f dvd://2
foreach? end
Pull the audio track with id 129, resample -- dvd is mounted as "/dev/cdrom1" which is device "/dev/dvd1"
mplayer -vo null -vc dummy -aid 129 -af resample=44100 -ao pcm:fast:waveheader:file=stream.wav dvd:// -dvd-device /dev/dvd1
---------------------------------------------------------------------
Increase volume of a wav file to a target amplitude of -12dBFS
normalize -a -12dBFS file.wav
---------------------------------------------------------------------
Backup a directory to a dvd
growisofs -J -R -Z /dev/dvdwriter -speed=2 /path/to/dir
---------------------------------------------------------------------
Erasing a dvd-rw
dvd+rw-format -force /dev/dvd
---------------------------------------------------------------------
To copy a DVD using DVD Shrink
wine .wine/drive_c/Program\ Files/DVD\ Shrink/DVD\ Shrink\ 3.2.exe
Write from the ripped directory to dvd
growisofs -dvd-compat -Z /dev/dvdwriter -dvd-video -V LABEL /path/to/dvd/image/
Write from the iso to dvd
growisofs -dvd-compat -Z /dev/dvdrw=/export/data/public/Music/BORAT_16X9.ISO
---------------------------------------------------------------------
To burn a DVD iso on a Mac
hdiutil burn DESPICABLE_ME.ISO
---------------------------------------------------------------------
To convert wma to wav
foreach f ( *.wma )
foreach? mplayer -vo null -quiet -srate 44100 -channels 2 -vc dummy -ao pcm:waveheader:fast:file="$f.wav" "$f"
foreach? end
---------------------------------------------------------------------
To split a flac file with associated cue file into wav tracks
# Disc5.flac is entire disc with Disc5.cue describing the tracks.
# Output files named (track01,track02...) via "-a track"
cuebreakpoints Disc5.cue | shnsplit -a track -o wav Disc5.flac
---------------------------------------------------------------------
To set flac tags
metaflac --set-tag=Artist='B.B. King' --set-tag=Album='Live At The Royal Albert Hall 2011' --set-tag=Genre=Blues --set-tag=Date=2011 *.flac
tagit.flac
tracks.flac
metaflac --set-tag='Encoded-by=flac --best' *.flac
---------------------------------------------------------------------
Using ape (Monkey Audio File)
Examples:
Compress: mac file.wav output.ape -c2000
Decompress: mac file.ape file.wav -d
ffmpeg -i file.ape output.wav
java -jar jmac.jar d file.ape output.wav
java -jar jmac-1.74/distributables/jmac.jar c1 CaffeinatedRattlesnake.wav CaffeinatedRattlesnake.ape
---------------------------------------------------------------------
Mounting an ISO on a Mac
hdiutil attach -imagekey diskimage-class=CRawDiskImage -mount file.iso
# command responds with device "/dev/disk2"
hdiutil mount /dev/disk2
---------------------------------------------------------------------
Burning .iso on Mac
DON'T burn the .iso directly
DO convert it to a .cdr first, then burn it! Here's how:
1. Open Disk Utility
2. Drag & drop the .iso onto the left panel (under where you see your HD listed), or in some other manner get it into the left panel (may vary with the version of OSX you are using)
3. Highlight the .iso
4. Choose "Convert" at the top
5. IMPORTANT: Choose "DVD/CD master" for the image format
6. For encryption choose "none"
7. Click "Save", and make sure the file type is ".cdr" (you can keep the .iso if you want as well)
8. After some time, you will have another image; burn that image
9. Insert a writable CD or DVD, and choose the slowest possible burn time (for safety)
10. Choose to verify the disk you are burning as well, then click "Burn"
11. Depending on what OS built the .iso, the result may not be readable by your Mac, but the PC or hypervisor where you will install it will be able to read and boot it
---------------------------------------------------------------------
MP3 Compilation tag
eyeD3 --text-frame=TCMP:1
---------------------------------------------------------------------
flac to alac
for f in *.flac; do ffmpeg -loglevel 0 -i "$f" -acodec alac "${f%.flac}.m4a"; done
---------------------------------------------------------------------
remove all m4a tags
for f in *.m4a; do MP4Box -itags all=NULL "$f"; done
```
## utf8norm -- UTF8 Normalization
```
Usage: utf8norm [-help] [-para] [-squeeze] [-output file] file|stdin
Available options:
-h, --help Help
-o, --output= Output File
-p, --paragraph Read in Perl style paragraph mode
-s, --squeeze Squeeze Whitespace
```
## hexbytes -- I/O in hex
```
hexbytes [-nmrs] file|stdin
-n output a trailing newline
-m i/o in ModHex (mapping: cbdefghijklnrtuv => 0123456789abcdef)
-r input is hex, output decoded characters
-s strip trailing byte on input data
```
## mp3enc -- Front end to lame handling wav, aiff, m4a, ogg, flac
## itunesPlus -- afconvert wav, aiff, flac with appropriate flags
## prec -- C operator precedence/associativity chart
```
C operator precedence/associativity chart
Arity Operator Assoc
--------------------------------------------------------------
mixed () [] -> . l -> r
unary ! ~ ++ -- - (type) * & sizeof r -> l
binary * / % l -> r
binary + - l -> r
binary << >> l -> r
binary < <= > >= l -> r
binary == != l -> r
binary & l -> r
binary ^ l -> r
binary | l -> r
binary && l -> r
binary || l -> r
ternary ?: r -> l
binary = += -= *= /= %= >>= <<= &= ^= |= r -> l
binary , l -> r
--------------------------------------------------------------
```
## Procrustes -- Finding a rotation matrix
```
# Finding a rotation matrix: Orthogonal Procrustes problem
# http://en.wikipedia.org/wiki/Orthogonal_Procrustes_problem
#
# This problem was originally solved by Peter Schonemann in a 1964 thesis.
#
# This problem is equivalent to finding the nearest orthogonal matrix to a given matrix (M = A' * B).
# To find this orthogonal matrix R, one uses the singular value decomposition
#
# M=U*S*V' to write R=U*V'
#
##########################################
# Example demonstrating the basic concept:
#
# # Define matrix A
# A = matrix(c(10,4,8, -2,3,7, 11,-3,12), nrow = 3, ncol = 3, byrow = TRUE)
# > A
# [,1] [,2] [,3]
# [1,] 10 4 8
# [2,] -2 3 7
# [3,] 11 -3 12
#
#
#
# Rotation matricies around fixed axis (x, y, z)
#
# 1 0 0 cos(r) 0 -sin(r) cos(r) sin(r) 0
# X(r) = 0 cos(r) sin(r) Y(r) = 0 1 0 Z(r) = -sin(r) cos(r) 0
# 0 -sin(r) cos(r) sin(r) 0 cos(r) 0 0 1
#
#
#
# # Define an arbitrary rotation matrix (the one we'll solve for later)
#
# 30 degree (counter clockwise) rotation around the X axis
# R = matrix(c(1,0,0, 0,cos(pi/6),sin(pi/6), 0,-sin(pi/6),cos(pi/6)), nrow = 3, ncol = 3, byrow = TRUE)
#
# 90 degree (counter clockwise) rotation around the Z axis
# R = matrix(c(0,1,0, -1,0,0, 0,0,1), nrow = 3, ncol = 3, byrow = TRUE)
#
# > R
# [,1] [,2] [,3]
# [1,] 0 1 0
# [2,] -1 0 0
# [3,] 0 0 1
#
#
# # Define matrix B as a rotation of A
# > B = A %*% R
# > B
# [,1] [,2] [,3]
# [1,] -4 10 8
# [2,] -3 -2 7
# [3,] 3 11 12
#
#
# # Solve for R using svd
# s = svd(t(A) %*% B)
# > s$u
# [,1] [,2] [,3]
# [1,] -0.6770274541 -0.622683461 0.392299800
# [2,] -0.0324477139 0.557783557 0.829351946
# [3,] -0.7352421181 0.548764805 -0.397839436
#
# > s$v
# [,1] [,2] [,3]
# [1,] 0.0324477139 -0.557783557 -0.829351946
# [2,] -0.6770274541 -0.622683461 0.392299800
# [3,] -0.7352421181 0.548764805 -0.397839436
#
# > s$d
# [1] 440.0730908 49.6087753 26.3181339
#
#
# > R2 = s$u %*% t(s$v)
# > R2
# [,1] [,2] [,3]
# [1,] -2.33146835e-15 1.00000000e+00 1.38777878e-16
# [2,] -1.00000000e+00 -2.27595720e-15 2.44249065e-15
# [3,] 2.33146835e-15 3.60822483e-16 1.00000000e+00
#
# > round(R2, digits=9)
# [,1] [,2] [,3]
# [1,] 0 1 0
# [2,] -1 0 0
# [3,] 0 0 1
##########################################
```
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