Pave is a time management tool that helps improve and enhance productivity in one of the most reliable ways possible. It is easily customizable to the needs of the user to ensure they stay organized on all their tasks and activities.
View ProjectTilde is a gesture control, magic wand tool for interacting and controlling other applications accross external devices such as a laptop, desktop or tablet.
Swipe is an all in one application to manage transactions from all your bank accounts and credit cards. Filter reports by category to see spending habits and save up for specific goals automatically.
Settle up is a tool for friends and roommates to track bills and other shared expenses, so that everyone gets paid back.Easily connect your account to the app and request money or pay friends with a few clicks.
Hash is an iPhone application that connects to your desktop device and web extensions in order to successfully authenticate several user accounts seamlessly using your fingerprint via touch ID.
42 Sttom is a digital multi media company aimed to create, capture and convey emotionally powerful messages by exploring stories and talents through art, pictures and videos.
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Being in my first year of career I had the idea of a game with balls that would orbitate around planets and compite between them in order to stand in the orbit. That same year, after a week of hard work I had already the first version of the game. I found the mechanics so funny, but the game fell into oblivion.
Three years later, when I discover the Three Headed Monkey Awards, I decide this could be a good place to show the project to the world. Unfortunately, the contest application time was ending in only five days. With the colaboration of my flatmate, Paco, we worked hard to get a good version to present. And here is to you.
To Julien, my good friend, for the awesome music of the main menu; to Samuel Soutullo and Cristofer Canosa, who were with me in that early development and even played against me and had a lot of fun together; to Paco, for standing me even when I was too nervous; to my parents, Ángeles and Arturo, who allowed me to make real many of my dreams, payed my studies and always supported me; and of course, to you, who are playing my humble, little creation.
"Curves" and "Beat Culture" by "Larry Groove" (Julien), whose music you can find in soundcloud.com/larrygroove. Worth to take a look through.
"Ion Cannon" by "Zythian & Xivine" is licensed under a Creative Commons License.
http://bit.ly/ZythianIonCannon
https://youtu.be/bmgngsmyXq0
"Bring It Back" by "Zythian" is licensed under a Creative Commons License
https://soundcloud.com/zythian
https://soundcloud.com/zythian/bring-it-back
"Space And Time" by "Voirnox" is licensed under a Creative Commons License.
https://soundcloud.com/k9dubstep-voirnox
https://soundcloud.com/k9dubstep-voirnox/voirnox-space-and-time
Game background is licensed under a Creative Commons License.
Author: Palms
Some of the sound effects are taken from the Bank of Images and Sounds, of the Spanish Ministery of Education, Culture and Sport.


{% extends 'landing/base.html' %}
{% block content %}
first_name = {{artist.first_name}}
added_by = {{artist.added_by}}
born = {{artist.born}}
description = {{artist.description}}
contry_origin = {{artist.contry_origin}}
died = {{artist.died}}
is_active = {{artist.is_active}}
last_name = {{artist.last_name}}
stage_name = {{artist.stage_name}}
{% endblock %}


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--- layout: page title: About Me background: '/img/bg-about.jpg' ---
I’m a second year industrial PhD student collaborating with Siteimprove under the supervision of Anders Søgaard at the CoAStaL group, University of Copenhagen, Denmark. The focus of my PhD currently is on improving the quality of Grammatical Error Correction systems, specifically focusing on low-resource approaches. I am also interested in the use of reinforcement learning as a way to improve NLP systems.


This file documents version 4.2.1 of GNU sed, a stream editor.
Copyright © 1998, 1999, 2001, 2002, 2003, 2004 Free Software Foundation, Inc.
This document is released under the terms of the GNU Free Documentation License as published by the Free Software Foundation; either version 1.1, or (at your option) any later version.
You should have received a copy of the GNU Free Documentation License along with GNU sed; see the file COPYING.DOC. If not, write to the Free Software Foundation, 59 Temple Place - Suite 330, Boston, MA 02110-1301, USA.
There are no Cover Texts and no Invariant Sections; this text, along with its equivalent in the printed manual, constitutes the Title Page.
--- The detailed node listing ---
sed Programs:
Examples:
sed is a stream editor. A stream editor is used to perform basic text transformations on an input stream (a file or input from a pipeline). While in some ways similar to an editor which permits scripted edits (such as ed), sed works by making only one pass over the input(s), and is consequently more efficient. But it is sed's ability to filter text in a pipeline which particularly distinguishes it from other types of editors.
Normally sed is invoked like this:
sed SCRIPT INPUTFILE...
The full format for invoking sed is:
sed OPTIONS... [SCRIPT] [INPUTFILE...]
If you do not specify INPUTFILE, or if INPUTFILE is -, sed filters the contents of the standard input. The script is actually the first non-option parameter, which sed specially considers a script and not an input file if (and only if) none of the other options specifies a script to be executed, that is if neither of the -e and -f options is specified.
sed may be invoked with the following command-line options:
--version
--help
-n
--quiet
--silent
sed
works).
These options disable this automatic printing,
and sed only produces output when explicitly told to
via the p
command.
-e
script--expression=
script-f
script-file--file=
script-file-i[
SUFFIX]
--in-place[=
SUFFIX]
This option implies -s.
When the end of the file is reached, the temporary file is renamed to the output file's original name. The extension, if supplied, is used to modify the name of the old file before renaming the temporary file, thereby making a backup copy2).
This rule is followed: if the extension doesn't contain a *
,
then it is appended to the end of the current filename as a
suffix; if the extension does contain one or more *
characters, then each asterisk is replaced with the
current filename. This allows you to add a prefix to the
backup file, instead of (or in addition to) a suffix, or
even to place backup copies of the original files into another
directory (provided the directory already exists).
If no extension is supplied, the original file is
overwritten without making a backup.
-l
N--line-length=
Nl
command.
A length of 0 (zero) means to never wrap long lines. If
not specified, it is taken to be 70.
--posix
POSIXLY_CORRECT
variable
to a non-empty value.
-b
--binary
--follow-symlinks
-r
--regexp-extended
-s
--separate
$
refers to the last line of each file,
and files invoked from the R
commands are rewound at the
start of each file.
-u
--unbuffered
If no -e, -f, --expression, or --file options are given on the command-line, then the first non-option argument on the command line is taken to be the script to be executed.
If any command-line parameters remain after processing the above, these parameters are interpreted as the names of input files to be processed. A file name of - refers to the standard input stream. The standard input will be processed if no file names are specified.
A sed program consists of one or more sed commands, passed in by one or more of the -e, -f, --expression, and --file options, or the first non-option argument if zero of these options are used. This document will refer to “the” sed script; this is understood to mean the in-order catenation of all of the scripts and script-files passed in.
Each sed
command consists of an optional address or
address range, followed by a one-character command name
and any additional command-specific code.
sed maintains two data buffers: the active pattern space, and the auxiliary hold space. Both are initially empty.
sed operates by performing the following cycle on each lines of input: first, sed reads one line from the input stream, removes any trailing newline, and places it in the pattern space. Then commands are executed; each command can have an address associated to it: addresses are a kind of condition code, and a command is only executed if the condition is verified before the command is to be executed.
When the end of the script is reached, unless the -n option is in use, the contents of pattern space are printed out to the output stream, adding back the trailing newline if it was removed.3 Then the next cycle starts for the next input line.
Unless special commands (like D) are used, the pattern space is deleted between two cycles. The hold space, on the other hand, keeps its data between cycles (see commands h, H, x, g, G to move data between both buffers).
Addresses in a sed script can be in any of the following forms:
~
step1~2
;
to pick every third line starting with the second, 2~3 would be used;
to pick every fifth line starting with the tenth, use 10~5;
and 50~0 is just an obscure way of saying 50
.
$
/
regexp/
/
characters,
each must be escaped by a backslash (\
).
The empty regular expression // repeats the last regular
expression match (the same holds if the empty regular expression is
passed to the s
command). Note that modifiers to regular expressions
are evaluated when the regular expression is compiled, thus it is invalid to
specify them together with the empty regular expression.
\%
regexp%
%
may be replaced by any other single character.)
This also matches the regular expression regexp,
but allows one to use a different delimiter than /
.
This is particularly useful if the regexp itself contains
a lot of slashes, since it avoids the tedious escaping of every /
.
If regexp itself includes any delimiter characters,
each must be escaped by a backslash (\
).
/
regexp/I
\%
regexp%I
I
modifier to regular-expression matching is a GNU
extension which causes the regexp to be matched in
a case-insensitive manner.
/
regexp/M
\%
regexp%M
M
modifier to regular-expression matching is a GNU sed
extension which causes ^
and $
to match respectively
(in addition to the normal behavior) the empty string after a newline,
and the empty string before a newline. There are special character
sequences
(\`
and \'
)
which always match the beginning or the end of the buffer.
M
stands for multi-line.
If no addresses are given, then all lines are matched; if one address is given, then only lines matching that address are matched.
An address range can be specified by specifying two addresses
separated by a comma (,
). An address range matches lines
starting from where the first address matches, and continues
until the second address matches (inclusively).
If the second address is a regexp, then checking for the ending match will start with the line following the line which matched the first address: a range will always span at least two lines (except of course if the input stream ends).
If the second address is a number less than (or equal to) the line matching the first address, then only the one line is matched.
GNU sed also supports some special two-address forms; all these are GNU extensions:
0,/
regexp/
0
can be used in an address specification like
0,/
regexp/
so that sed will try to match
regexp in the first input line too. In other words,
0,/
regexp/
is similar to 1,/
regexp/
,
except that if addr2 matches the very first line of input the
0,/
regexp/
form will consider it to end the range, whereas
the 1,/
regexp/
form will match the beginning of its range and
hence make the range span up to the second occurrence of the
regular expression.
Note that this is the only place where the 0
address makes
sense; there is no 0-th line and commands which are given the 0
address in any other way will give an error.
,+
N,~
NAppending the !
character to the end of an address
specification negates the sense of the match.
That is, if the !
character follows an address range,
then only lines which do not match the address range
will be selected.
This also works for singleton addresses,
and, perhaps perversely, for the null address.
To know how to use sed, people should understand regular expressions (regexp for short). A regular expression is a pattern that is matched against a subject string from left to right. Most characters are ordinary: they stand for themselves in a pattern, and match the corresponding characters in the subject. As a trivial example, the pattern
The quick brown fox
matches a portion of a subject string that is identical to itself. The power of regular expressions comes from the ability to include alternatives and repetitions in the pattern. These are encoded in the pattern by the use of special characters, which do not stand for themselves but instead are interpreted in some special way. Here is a brief description of regular expression syntax as used in sed.
*
\
, a .
, a grouped regexp
(see below), or a bracket expression. As a GNU extension, a
postfixed regular expression can also be followed by *
; for
example, a**
is equivalent to a*
. POSIX
1003.1-2001 says that *
stands for itself when it appears at
the start of a regular expression or subexpression, but many
nonGNU implementations do not support this and portable
scripts should instead use \*
in these contexts.
\+
*
, but matches one or more. It is a GNU extension.
\?
*
, but only matches zero or one. It is a GNU extension.
\{
i\}
*
, but matches exactly i sequences (i is a
decimal integer; for portability, keep it between 0 and 255
inclusive).
\{
i,
j\}
\{
i,\}
\(
regexp\)
\(abcd\)*
:
this will search for zero or more whole sequences
of abcd, while abcd*
would search
for abc followed by zero or more occurrences
of d. Note that support for \(abcd\)*
is
required by POSIX 1003.1-2001, but many non-GNU
implementations do not support it and hence it is not universally
portable.
.
^
In most scripts, pattern space is initialized to the content of each
line (see How sed
works). So, it is a
useful simplification to think of ^#include
as matching only
lines where #include is the first thing on line—if there are
spaces before, for example, the match fails. This simplification is
valid as long as the original content of pattern space is not modified,
for example with an s
command.
^
acts as a special character only at the beginning of the
regular expression or subexpression (that is, after \(
or
\|
). Portable scripts should avoid ^
at the beginning of
a subexpression, though, as POSIX allows implementations that
treat ^
as an ordinary character in that context.
$
^
, but refers to end of pattern space.
$
also acts as a special character only at the end
of the regular expression or subexpression (that is, before \)
or \|
), and its use at the end of a subexpression is not
portable.
[
list]
[^
list]
[aeiou]
matches all vowels. A list may include
sequences like char1-
char2, which
matches any character between (inclusive) char1
and char2.
A leading ^
reverses the meaning of list, so that
it matches any single character not in list. To include
]
in the list, make it the first character (after
the ^
if needed), to include -
in the list,
make it the first or last; to include ^
put
it after the first character.
The characters $
, *
, .
, [
, and \
are normally not special within list. For example, [\*]
matches either \ or *, because the \
is not
special here. However, strings like [.ch.]
, [=a=]
, and
[:space:]
are special within list and represent collating
symbols, equivalence classes, and character classes, respectively, and
[
is therefore special within list when it is followed by
.
, =
, or :
. Also, when not in
POSIXLY_CORRECT mode, special escapes like \n
and
\t
are recognized within list. See Escapes.
\|
regexp2\|
, ^
, and
$
, but less tightly than the other regular expression
operators.
\
digit\(...\)
parenthesized
subexpression in the regular expression. This is called a back
reference. Subexpressions are implicity numbered by counting
occurrences of \(
left-to-right.
\n
\
char$
,
*
, .
, [
, \
, or ^
.
Note that the only C-like
backslash sequences that you can portably assume to be
interpreted are \n
and \\
; in particular
\t
is not portable, and matches a t under most
implementations of sed, rather than a tab character.
Note that the regular expression matcher is greedy, i.e., matches are attempted from left to right and, if two or more matches are possible starting at the same character, it selects the longest.
Examples:
If you use sed at all, you will quite likely want to know these commands.
#
The #
character begins a comment;
the comment continues until the next newline.
If you are concerned about portability, be aware that
some implementations of sed (which are not posix
conformant) may only support a single one-line comment,
and then only when the very first character of the script is a #
.
Warning: if the first two characters of the sed script
are #n
, then the -n (no-autoprint) option is forced.
If you want to put a comment in the first line of your script
and that comment begins with the letter n
and you do not want this behavior,
then be sure to either use a capital N,
or place at least one space before the n.
q [
exit-code]
Exit sed without processing any more commands or input.
Note that the current pattern space is printed if auto-print is
not disabled with the -n options. The ability to return
an exit code from the sed script is a GNU sed extension.
d
p
n
{
commands }
{
and }
characters.
This is particularly useful when you want a group of commands
to be triggered by a single address (or address-range) match.
s
CommandThe syntax of the s
(as in substitute) command is
s/regexp/replacement/flags. The /
characters may be uniformly replaced by any other single
character within any given s
command. The /
character (or whatever other character is used in its stead)
can appear in the regexp or replacement
only if it is preceded by a \
character.
The s
command is probably the most important in sed
and has a lot of different options. Its basic concept is simple:
the s
command attempts to match the pattern
space against the supplied regexp; if the match is
successful, then that portion of the pattern
space which was matched is replaced with replacement.
The replacement can contain \
n (n being
a number from 1 to 9, inclusive) references, which refer to
the portion of the match which is contained between the nth
\(
and its matching \)
.
Also, the replacement can contain unescaped &
characters which reference the whole matched portion
of the pattern space.
Finally, as a GNU sed extension, you can include a
special sequence made of a backslash and one of the letters
L
, l
, U
, u
, or E
.
The meaning is as follows:
\L
\U
or \E
is found,
\l
\U
\L
or \E
is found,
\u
\E
\L
or \U
.
To include a literal \
, &
, or newline in the final
replacement, be sure to precede the desired \
, &
,
or newline in the replacement with a \
.
The s
command can be followed by zero or more of the
following flags:
g
Note: the posix standard does not specify what should happen
when you mix the g
and number modifiers,
and currently there is no widely agreed upon meaning
across sed implementations.
For GNU sed, the interaction is defined to be:
ignore matches before the numberth,
and then match and replace all matches from
the numberth on.
p
Note: when both the p
and e
options are specified,
the relative ordering of the two produces very different results.
In general, ep
(evaluate then print) is what you want,
but operating the other way round can be useful for debugging.
For this reason, the current version of GNU sed interprets
specially the presence of p
options both before and after
e
, printing the pattern space before and after evaluation,
while in general flags for the s
command show their
effect just once. This behavior, although documented, might
change in future versions.
w
file-namee
I
i
I
modifier to regular-expression matching is a GNU
extension which makes sed match regexp in a
case-insensitive manner.
M
m
M
modifier to regular-expression matching is a GNU sed
extension which causes ^
and $
to match respectively
(in addition to the normal behavior) the empty string after a newline,
and the empty string before a newline. There are special character
sequences
(\`
and \'
)
which always match the beginning or the end of the buffer.
M
stands for multi-line.
Though perhaps less frequently used than those in the previous section, some very small yet useful sed scripts can be built with these commands.
y/
source-chars/
dest-chars/
/
characters may be uniformly replaced by
any other single character within any given y
command.)
Transliterate any characters in the pattern space which match any of the source-chars with the corresponding character in dest-chars.
Instances of the /
(or whatever other character is used in its stead),
\
, or newlines can appear in the source-chars or dest-chars
lists, provide that each instance is escaped by a \
.
The source-chars and dest-chars lists must
contain the same number of characters (after de-escaping).
a\
Queue the lines of text which follow this command
(each but the last ending with a \
,
which are removed from the output)
to be output at the end of the current cycle,
or when the next input line is read.
Escape sequences in text are processed, so you should
use \\
in text to print a single backslash.
As a GNU extension, if between the a
and the newline there is
other than a whitespace-\
sequence, then the text of this line,
starting at the first non-whitespace character after the a
,
is taken as the first line of the text block.
(This enables a simplification in scripting a one-line add.)
This extension also works with the i
and c
commands.
i\
Immediately output the lines of text which follow this command
(each but the last ending with a \
,
which are removed from the output).
c\
\
,
which are removed from the output)
in place of the last line
(or in place of each line, if no addresses were specified).
A new cycle is started after this command is done,
since the pattern space will have been deleted.
=
Print out the current input line number (with a trailing newline).
l
n\
character)
are printed in C-style escaped form; long lines are split,
with a trailing \
character to indicate the split;
the end of each line is marked with a $
.
n specifies the desired line-wrap length;
a length of 0 (zero) means to never wrap long lines. If omitted,
the default as specified on the command line is used. The n
parameter is a GNU sed extension.
r
filenameQueue the contents of filename to be read and inserted into the output stream at the end of the current cycle, or when the next input line is read. Note that if filename cannot be read, it is treated as if it were an empty file, without any error indication.
As a GNU sed extension, the special value /dev/stdin
is supported for the file name, which reads the contents of the
standard input.
w
filenameThe file will be created (or truncated) before the
first input line is read; all w
commands
(including instances of w
flag on successful s
commands)
which refer to the same filename are output without
closing and reopening the file.
D
N
P
h
H
g
G
x
In most cases, use of these commands indicates that you are probably better off programming in something like awk or Perl. But occasionally one is committed to sticking with sed, and these commands can enable one to write quite convoluted scripts.
:
labelSpecify the location of label for branch commands.
In all other respects, a no-op.
b
labelt
labels
ubstitution
since the last input line was read or conditional branch was taken.
The label may be omitted, in which case the next cycle is started.
These commands are specific to GNU sed, so you must use them with care and only when you are sure that hindering portability is not evil. They allow you to check for GNU sed extensions or to do tasks that are required quite often, yet are unsupported by standard seds.
e [
command]
e
command
executes the command that is found in pattern space and
replaces the pattern space with the output; a trailing newline
is suppressed.
If a parameter is specified, instead, the e
command
interprets it as a command and sends its output to the output stream
(like r
does). The command can run across multiple
lines, all but the last ending with a back-slash.
In both cases, the results are undefined if the command to be
executed contains a nul character.
L
nfmt
does; if n is omitted, the default as specified
on the command line is used. This command is considered a failed
experiment and unless there is enough request (which seems unlikely)
will be removed in future versions.
Q [
exit-code]
This command is the same as q
, but will not print the
contents of pattern space. Like q
, it provides the
ability to return an exit code to the caller.
This command can be useful because the only alternative ways to accomplish this apparently trivial function are to use the -n option (which can unnecessarily complicate your script) or resorting to the following snippet, which wastes time by reading the whole file without any visible effect:
:eat $d Quit silently on the last line N Read another line, silently g Overwrite pattern space each time to save memory b eat
R
filenameAs with the r
command, the special value /dev/stdin
is supported for the file name, which reads a line from the
standard input.
T
labels
ubstitutions since the last input line was read or
conditional branch was taken. The label may be omitted,
in which case the next cycle is started.
v
version4.0.5
. The default is 4.0
because that is the first version that implemented this command.
This command enables all GNU extensions even if
POSIXLY_CORRECT is set in the environment.
W
filenamew
command about
file handling holds here too.
z
Until this chapter, we have only encountered escapes of the form \^, which tell sed not to interpret the circumflex as a special character, but rather to take it literally. For example, \* matches a single asterisk rather than zero or more backslashes.
This chapter introduces another kind of escape6—that is, escapes that are applied to a character or sequence of characters that ordinarily are taken literally, and that sed replaces with a special character. This provides a way of encoding non-printable characters in patterns in a visible manner. There is no restriction on the appearance of non-printing characters in a sed script but when a script is being prepared in the shell or by text editing, it is usually easier to use one of the following escape sequences than the binary character it represents:
The list of these escapes is:
\a
\f
\n
\r
\t
\v
\c
x\d
xxx\o
xxx\x
xx\b (backspace) was omitted because of the conflict with the existing “word boundary” meaning.
Other escapes match a particular character class and are valid only in regular expressions:
\w
\W
\b
\B
\`
^
in multi-line mode.
\'
$
in multi-line mode.
Here are some sed scripts to guide you in the art of mastering sed.
Some exotic examples:
Emulating standard utilities:
This script centers all lines of a file on a 80 columns width.
To change that width, the number in \{...\}
must be
replaced, and the number of added spaces also must be changed.
Note how the buffer commands are used to separate parts in the regular expressions to be matched—this is a common technique.
#!/usr/bin/sed -f # Put 80 spaces in the buffer 1 { x s/^$/ / s/^.*$/&&&&&&&&/ x } # del leading and trailing spaces y/tab/ / s/^ *// s/ *$// # add a newline and 80 spaces to end of line G # keep first 81 chars (80 + a newline) s/^\(.\{81\}\).*$/\1/ # \2 matches half of the spaces, which are moved to the beginning s/^\(.*\)\n\(.*\)\2/\2\1/
This script is one of a few that demonstrate how to do arithmetic in sed. This is indeed possible,7 but must be done manually.
To increment one number you just add 1 to last digit, replacing it by the following digit. There is one exception: when the digit is a nine the previous digits must be also incremented until you don't have a nine.
This solution by Bruno Haible is very clever and smart because
it uses a single buffer; if you don't have this limitation, the
algorithm used in Numbering lines, is faster.
It works by replacing trailing nines with an underscore, then
using multiple s
commands to increment the last digit,
and then again substituting underscores with zeros.
#!/usr/bin/sed -f
/[^0-9]/ d
# replace all leading 9s by _ (any other character except digits, could
# be used)
:d
s/9\(_*\)$/_\1/
td
# incr last digit only. The first line adds a most-significant
# digit of 1 if we have to add a digit.
#
# The tn
commands are not necessary, but make the thing
# faster
s/^\(_*\)$/1\1/; tn
s/8\(_*\)$/9\1/; tn
s/7\(_*\)$/8\1/; tn
s/6\(_*\)$/7\1/; tn
s/5\(_*\)$/6\1/; tn
s/4\(_*\)$/5\1/; tn
s/3\(_*\)$/4\1/; tn
s/2\(_*\)$/3\1/; tn
s/1\(_*\)$/2\1/; tn
s/0\(_*\)$/1\1/; tn
:n
y/_/0/
This is a pretty strange use of sed. We transform text, and transform it to be shell commands, then just feed them to shell. Don't worry, even worse hacks are done when using sed; I have seen a script converting the output of date into a bc program!
The main body of this is the sed script, which remaps the name from lower to upper (or vice-versa) and even checks out if the remapped name is the same as the original name. Note how the script is parameterized using shell variables and proper quoting.
#! /bin/sh # rename files to lower/upper case... # # usage: # move-to-lower * # move-to-upper * # or # move-to-lower -R . # move-to-upper -R . # help() { cat << eof Usage: $0 [-n] [-r] [-h] files... -n do nothing, only see what would be done -R recursive (use find) -h this message files files to remap to lower case Examples: $0 -n * (see if everything is ok, then...) $0 * $0 -R . eof } apply_cmd='sh' finder='echo "$@" | tr " " "\n"' files_only= while : do case "$1" in -n) apply_cmd='cat' ;; -R) finder='find "$@" -type f';; -h) help ; exit 1 ;; *) break ;; esac shift done if [ -z "$1" ]; then echo Usage: $0 [-h] [-n] [-r] files... exit 1 fi LOWER='abcdefghijklmnopqrstuvwxyz' UPPER='ABCDEFGHIJKLMNOPQRSTUVWXYZ' case `basename $0` in *upper*) TO=$UPPER; FROM=$LOWER ;; *) FROM=$UPPER; TO=$LOWER ;; esac eval $finder | sed -n ' # remove all trailing slashes s/\/*$// # add ./ if there is no path, only a filename /\//! s/^/.\// # save path+filename h # remove path s/.*\/// # do conversion only on filename y/'$FROM'/'$TO'/ # now line contains original path+file, while # hold space contains the new filename x # add converted file name to line, which now contains # path/file-name\nconverted-file-name G # check if converted file name is equal to original file name, # if it is, do not print nothing /^.*\/\(.*\)\n\1/b # now, transform path/fromfile\n, into # mv path/fromfile path/tofile and print it s/^\(.*\/\)\(.*\)\n\(.*\)$/mv "\1\2" "\1\3"/p ' | $apply_cmd
This script strips the definition of the shell functions from the output of the set Bourne-shell command.
#!/bin/sh
set | sed -n '
:x
# if no occurrence of =() print and load next line
/=()/! { p; b; }
/ () $/! { p; b; }
# possible start of functions section
# save the line in case this is a var like FOO="() "
h
# if the next line has a brace, we quit because
# nothing comes after functions
n
/^{/ q
# print the old line
x; p
# work on the new line now
x; bx
'
This script can be used to reverse the position of characters in lines. The technique moves two characters at a time, hence it is faster than more intuitive implementations.
Note the tx
command before the definition of the label.
This is often needed to reset the flag that is tested by
the t
command.
Imaginative readers will find uses for this script. An example is reversing the output of banner.8
#!/usr/bin/sed -f /../! b # Reverse a line. Begin embedding the line between two newlines s/^.*$/\ &\ / # Move first character at the end. The regexp matches until # there are zero or one characters between the markers tx :x s/\(\n.\)\(.*\)\(.\n\)/\3\2\1/ tx # Remove the newline markers s/\n//g
This one begins a series of totally useless (yet interesting) scripts emulating various Unix commands. This, in particular, is a tac workalike.
Note that on implementations other than GNU sed this script might easily overflow internal buffers.
#!/usr/bin/sed -nf # reverse all lines of input, i.e. first line became last, ... # from the second line, the buffer (which contains all previous lines) # is *appended* to current line, so, the order will be reversed 1! G # on the last line we're done -- print everything $ p # store everything on the buffer again h
This script replaces cat -n; in fact it formats its output exactly like GNU cat does.
Of course this is completely useless and for two reasons: first, because somebody else did it in C, second, because the following Bourne-shell script could be used for the same purpose and would be much faster:
#! /bin/sh sed -e "=" $@ | sed -e ' s/^/ / N s/^ *\(......\)\n/\1 / '
It uses sed to print the line number, then groups lines two
by two using N
. Of course, this script does not teach as much as
the one presented below.
The algorithm used for incrementing uses both buffers, so the line
is printed as soon as possible and then discarded. The number
is split so that changing digits go in a buffer and unchanged ones go
in the other; the changed digits are modified in a single step
(using a y
command). The line number for the next line
is then composed and stored in the hold space, to be used in the
next iteration.
#!/usr/bin/sed -nf # Prime the pump on the first line x /^$/ s/^.*$/1/ # Add the correct line number before the pattern G h # Format it and print it s/^/ / s/^ *\(......\)\n/\1 /p # Get the line number from hold space; add a zero # if we're going to add a digit on the next line g s/\n.*$// /^9*$/ s/^/0/ # separate changing/unchanged digits with an x s/.9*$/x&/ # keep changing digits in hold space h s/^.*x// y/0123456789/1234567890/ x # keep unchanged digits in pattern space s/x.*$// # compose the new number, remove the newline implicitly added by G G s/\n// h
Emulating cat -b is almost the same as cat -n—we only have to select which lines are to be numbered and which are not.
The part that is common to this script and the previous one is not commented to show how important it is to comment sed scripts properly...
#!/usr/bin/sed -nf /^$/ { p b } # Same as cat -n from now x /^$/ s/^.*$/1/ G h s/^/ / s/^ *\(......\)\n/\1 /p x s/\n.*$// /^9*$/ s/^/0/ s/.9*$/x&/ h s/^.*x// y/0123456789/1234567890/ x s/x.*$// G s/\n// h
This script shows another way to do arithmetic with sed. In this case we have to add possibly large numbers, so implementing this by successive increments would not be feasible (and possibly even more complicated to contrive than this script).
The approach is to map numbers to letters, kind of an abacus implemented with sed. as are units, bs are tens and so on: we simply add the number of characters on the current line as units, and then propagate the carry to tens, hundreds, and so on.
As usual, running totals are kept in hold space.
On the last line, we convert the abacus form back to decimal.
For the sake of variety, this is done with a loop rather than
with some 80 s
commands9: first we
convert units, removing as from the number; then we
rotate letters so that tens become as, and so on
until no more letters remain.
#!/usr/bin/sed -nf # Add n+1 a's to hold space (+1 is for the newline) s/./a/g H x s/\n/a/ # Do the carry. The t's and b's are not necessary, # but they do speed up the thing t a : a; s/aaaaaaaaaa/b/g; t b; b done : b; s/bbbbbbbbbb/c/g; t c; b done : c; s/cccccccccc/d/g; t d; b done : d; s/dddddddddd/e/g; t e; b done : e; s/eeeeeeeeee/f/g; t f; b done : f; s/ffffffffff/g/g; t g; b done : g; s/gggggggggg/h/g; t h; b done : h; s/hhhhhhhhhh//g : done $! { h b } # On the last line, convert back to decimal : loop /a/! s/[b-h]*/&0/ s/aaaaaaaaa/9/ s/aaaaaaaa/8/ s/aaaaaaa/7/ s/aaaaaa/6/ s/aaaaa/5/ s/aaaa/4/ s/aaa/3/ s/aa/2/ s/a/1/ : next y/bcdefgh/abcdefg/ /[a-h]/ b loop p
This script is almost the same as the previous one, once each of the words on the line is converted to a single a (in the previous script each letter was changed to an a).
It is interesting that real wc programs have optimized loops for wc -c, so they are much slower at counting words rather than characters. This script's bottleneck, instead, is arithmetic, and hence the word-counting one is faster (it has to manage smaller numbers).
Again, the common parts are not commented to show the importance of commenting sed scripts.
#!/usr/bin/sed -nf # Convert words to a's s/[ tab][ tab]*/ /g s/^/ / s/ [^ ][^ ]*/a /g s/ //g # Append them to hold space H x s/\n// # From here on it is the same as in wc -c. /aaaaaaaaaa/! bx; s/aaaaaaaaaa/b/g /bbbbbbbbbb/! bx; s/bbbbbbbbbb/c/g /cccccccccc/! bx; s/cccccccccc/d/g /dddddddddd/! bx; s/dddddddddd/e/g /eeeeeeeeee/! bx; s/eeeeeeeeee/f/g /ffffffffff/! bx; s/ffffffffff/g/g /gggggggggg/! bx; s/gggggggggg/h/g s/hhhhhhhhhh//g :x $! { h; b; } :y /a/! s/[b-h]*/&0/ s/aaaaaaaaa/9/ s/aaaaaaaa/8/ s/aaaaaaa/7/ s/aaaaaa/6/ s/aaaaa/5/ s/aaaa/4/ s/aaa/3/ s/aa/2/ s/a/1/ y/bcdefgh/abcdefg/ /[a-h]/ by p
No strange things are done now, because sed gives us wc -l functionality for free!!! Look:
#!/usr/bin/sed -nf $=
This script is probably the simplest useful sed script.
It displays the first 10 lines of input; the number of displayed
lines is right before the q
command.
#!/usr/bin/sed -f 10q
Printing the last n lines rather than the first is more complex but indeed possible. n is encoded in the second line, before the bang character.
This script is similar to the tac script in that it keeps the final output in the hold space and prints it at the end:
#!/usr/bin/sed -nf 1! {; H; g; } 1,10 !s/[^\n]*\n// $p h
Mainly, the scripts keeps a window of 10 lines and slides it
by adding a line and deleting the oldest (the substitution command
on the second line works like a D
command but does not
restart the loop).
The “sliding window” technique is a very powerful way to write
efficient and complex sed scripts, because commands like
P
would require a lot of work if implemented manually.
To introduce the technique, which is fully demonstrated in the
rest of this chapter and is based on the N
, P
and D
commands, here is an implementation of tail
using a simple “sliding window.”
This looks complicated but in fact the working is the same as
the last script: after we have kicked in the appropriate number
of lines, however, we stop using the hold space to keep inter-line
state, and instead use N
and D
to slide pattern
space by one line:
#!/usr/bin/sed -f 1h 2,10 {; H; g; } $q 1,9d N D
Note how the first, second and fourth line are inactive after the first ten lines of input. After that, all the script does is: exiting on the last line of input, appending the next input line to pattern space, and removing the first line.
This is an example of the art of using the N
, P
and D
commands, probably the most difficult to master.
#!/usr/bin/sed -f
h
:b
# On the last line, print and exit
$b
N
/^\(.*\)\n\1$/ {
# The two lines are identical. Undo the effect of
# the n command.
g
bb
}
# If the N
command had added the last line, print and exit
$b
# The lines are different; print the first and go
# back working on the second.
P
D
As you can see, we mantain a 2-line window using P
and D
.
This technique is often used in advanced sed scripts.
This script prints only duplicated lines, like uniq -d.
#!/usr/bin/sed -nf $b N /^\(.*\)\n\1$/ { # Print the first of the duplicated lines s/.*\n// p # Loop until we get a different line :b $b N /^\(.*\)\n\1$/ { s/.*\n// bb } } # The last line cannot be followed by duplicates $b # Found a different one. Leave it alone in the pattern space # and go back to the top, hunting its duplicates D
This script prints only unique lines, like uniq -u.
#!/usr/bin/sed -f
# Search for a duplicate line --- until that, print what you find.
$b
N
/^\(.*\)\n\1$/ ! {
P
D
}
:c
# Got two equal lines in pattern space. At the
# end of the file we simply exit
$d
# Else, we keep reading lines with N
until we
# find a different one
s/.*\n//
N
/^\(.*\)\n\1$/ {
bc
}
# Remove the last instance of the duplicate line
# and go back to the top
D
As a final example, here are three scripts, of increasing complexity and speed, that implement the same function as cat -s, that is squeezing blank lines.
The first leaves a blank line at the beginning and end if there are some already.
#!/usr/bin/sed -f # on empty lines, join with next # Note there is a star in the regexp :x /^\n*$/ { N bx } # now, squeeze all '\n', this can be also done by: # s/^\(\n\)*/\1/ s/\n*/\ /
This one is a bit more complex and removes all empty lines at the beginning. It does leave a single blank line at end if one was there.
#!/usr/bin/sed -f # delete all leading empty lines 1,/^./{ /./!d } # on an empty line we remove it and all the following # empty lines, but one :x /./!{ N s/^\n$// tx }
This removes leading and trailing blank lines. It is also the
fastest. Note that loops are completely done with n
and
b
, without relying on sed to restart the
the script automatically at the end of a line.
#!/usr/bin/sed -nf # delete all (leading) blanks /./!d # get here: so there is a non empty :x # print it p # get next n # got chars? print it again, etc... /./bx # no, don't have chars: got an empty line :z # get next, if last line we finish here so no trailing # empty lines are written n # also empty? then ignore it, and get next... this will # remove ALL empty lines /./!bz # all empty lines were deleted/ignored, but we have a non empty. As # what we want to do is to squeeze, insert a blank line artificially i\ bx
For those who want to write portable sed scripts,
be aware that some implementations have been known to
limit line lengths (for the pattern and hold spaces)
to be no more than 4000 bytes.
The posix standard specifies that conforming sed
implementations shall support at least 8192 byte line lengths.
GNU sed has no built-in limit on line length;
as long as it can malloc()
more (virtual) memory,
you can feed or construct lines as long as you like.
However, recursion is used to handle subpatterns and indefinite repetition. This means that the available stack space may limit the size of the buffer that can be processed by certain patterns.
In addition to several books that have been written about sed
(either specifically or as chapters in books which discuss
shell programming), one can find out more about sed
(including suggestions of a few books) from the FAQ
for the sed-users
mailing list, available from:
http://sed.sourceforge.net/sedfaq.html
Also of interest are http://www.student.northpark.edu/pemente/sed/index.htm and http://sed.sf.net/grabbag, which include sed tutorials and other sed-related goodies.
The sed-users
mailing list itself maintained by Sven Guckes.
To subscribe, visit http://groups.yahoo.com and search
for the sed-users
mailing list.
Email bug reports to<EMAIL_ADDRESS>Be sure to include the word “sed” somewhere in the Subject:
field.
Also, please include the output of sed --version in the body
of your report if at all possible.
Please do not send a bug report like this:
while building frobme-1.3.4
$ configure
error--> sed: file sedscr line 1: Unknown option to 's'
If GNU sed doesn't configure your favorite package, take a few extra minutes to identify the specific problem and make a stand-alone test case. Unlike other programs such as C compilers, making such test cases for sed is quite simple.
A stand-alone test case includes all the data necessary to perform the test, and the specific invocation of sed that causes the problem. The smaller a stand-alone test case is, the better. A test case should not involve something as far removed from sed as “try to configure frobme-1.3.4”. Yes, that is in principle enough information to look for the bug, but that is not a very practical prospect.
Here are a few commonly reported bugs that are not bugs.
N
command on the last lineFor example, the behavior of
sed N foo bar
would depend on whether foo has an even or an odd number of
lines10. Or, when writing a script to read the
next few lines following a pattern match, traditional
implementations of sed
would force you to write
something like
/foo/{ $!N; $!N; $!N; $!N; $!N; $!N; $!N; $!N; $!N }
instead of just
/foo/{ N;N;N;N;N;N;N;N;N; }
In any case, the simplest workaround is to use $d;N
in
scripts that rely on the traditional behavior, or to set
the POSIXLY_CORRECT
variable to a non-empty value.
\|
,
\+
, \?
, \`
, \'
, \<
,
\>
, \b
, \B
, \w
, and \W
.
As in all GNU programs that use posix basic regular
expressions, sed interprets these escape sequences as special
characters. So, x\+
matches one or more occurrences of x.
abc\|def
matches either abc or def.
This syntax may cause problems when running scripts written for other
seds. Some sed programs have been written with the
assumption that \|
and \+
match the literal characters
|
and +
. Such scripts must be modified by removing the
spurious backslashes if they are to be used with modern implementations
of sed, like
GNU sed.
On the other hand, some scripts use s|abc\|def||g to remove occurrences
of either abc
or def
. While this worked until
sed 4.0.x, newer versions interpret this as removing the
string abc|def
. This is again undefined behavior according to
POSIX, and this interpretation is arguably more robust: older
seds, for example, required that the regex matcher parsed
\/
as /
in the common case of escaping a slash, which is
again undefined behavior; the new behavior avoids this, and this is good
because the regex matcher is only partially under our control.
In addition, this version of sed supports several escape characters
(some of which are multi-character) to insert non-printable characters
in scripts (\a
, \c
, \d
, \o
, \r
,
\t
, \v
, \x
). These can cause similar problems
with scripts written for other seds.
The permissions on a file say what can happen to the data
in that file, while the permissions on a directory say what can
happen to the list of files in that directory. sed -i
will not ever open for writing a file that is already on disk.
Rather, it will work on a temporary file that is finally renamed
to the original name: if you rename or delete files, you're actually
modifying the contents of the directory, so the operation depends on
the permissions of the directory, not of the file. For this same
reason, sed does not let you use -i on a writeable file
in a read-only directory, and will break hard or symbolic links when
-i is used on such a file.
0a
does not work (gives an error)0,/
RE/
as active when the script starts: if
you write 1,/abc/d
and the first line includes the word abc,
then that match would be ignored because address ranges must span at least
two lines (barring the end of the file); but what you probably wanted is
to delete every line up to the first one including abc, and this
is obtained with 0,/abc/d
.
[a-z]
is case insensitive[a-z]
uses the current locale's collation order – in C parlance, that means using
strcoll(3)
instead of strcmp(3)
. Some locales have a
case-insensitive collation order, others don't.
Another problem is that [a-z]
tries to use collation symbols.
 In a Danish locale, for example,
the regular expression ^[a-z]$
matches the string aa,
because this is a single collating symbol that comes after a
and before b; ll behaves similarly in Spanish
locales, or ij in Dutch locales.
To work around these problems, which may cause bugs in shell scripts, set
the LC_COLLATE and LC_CTYPE environment variables to C.
s/.*//
does not clear pattern spaceTo work around these problems, which may cause bugs in shell scripts, set the LC_COLLATE and LC_CTYPE environment variables to C.
The only difference between basic and extended regular expressions is in the behavior of a few characters: ?, +, parentheses, and braces ({}). While basic regular expressions require these to be escaped if you want them to behave as special characters, when using extended regular expressions you must escape them if you want them to match a literal character.
Examples:
abc?
c\+
a\{3,\}
\(abc\)\{2,3\}
\(abc*\)\1
This is a general index of all issues discussed in this manual, with the exception of the sed commands and command-line options.
0
address: Reporting Bugss///
failed: Extended Commandss///
succeeded: Programming Commands0
address: Reporting Bugs0
address: Addressess///
failed: Extended Commandss
commands: The "s" Commandg
and number modifier interaction in s
command: The "s" CommandI
modifier: The "s" CommandI
modifier: AddressesL
command: Extended CommandsM
modifier: The "s" CommandR
command: Extended Commandsg
and number modifiers in the s
command: The "s" Command0
address: Reporting BugsN
command on the last line: Reporting BugsN
command on the last line: Reporting BugsPOSIXLY_CORRECT
behavior, bracket expressions: Regular ExpressionsPOSIXLY_CORRECT
behavior, enabling: Invoking sedPOSIXLY_CORRECT
behavior, escapes: EscapesPOSIXLY_CORRECT
behavior, N
command: Reporting BugsThis is an alphabetical list of all sed commands and command-line options.
# (comments)
: Common Commands--binary
: Invoking sed--expression
: Invoking sed--file
: Invoking sed--follow-symlinks
: Invoking sed--help
: Invoking sed--in-place
: Invoking sed--line-length
: Invoking sed--quiet
: Invoking sed--regexp-extended
: Invoking sed--silent
: Invoking sed--unbuffered
: Invoking sed--version
: Invoking sed-b
: Invoking sed-e
: Invoking sed-f
: Invoking sed-i
: Invoking sed-l
: Invoking sed-n
: Invoking sed-n, forcing from within a script
: Common Commands-r
: Invoking sed-u
: Invoking sed: (label) command
: Programming Commands= (print line number) command
: Other Commandsa (append text lines) command
: Other Commandsb (branch) command
: Programming Commandsc (change to text lines) command
: Other CommandsD (delete first line) command
: Other Commandsd (delete) command
: Common Commandse (evaluate) command
: Extended CommandsG (appending Get) command
: Other Commandsg (get) command
: Other CommandsH (append Hold) command
: Other Commandsh (hold) command
: Other Commandsi (insert text lines) command
: Other CommandsL (fLow paragraphs) command
: Extended Commandsl (list unambiguously) command
: Other CommandsN (append Next line) command
: Other Commandsn (next-line) command
: Common CommandsP (print first line) command
: Other Commandsp (print) command
: Common Commandsq (quit) command
: Common CommandsQ (silent Quit) command
: Extended Commandsr (read file) command
: Other CommandsR (read line) command
: Extended Commandss command, option flags
: The "s" CommandT (test and branch if failed) command
: Extended Commandst (test and branch if successful) command
: Programming Commandsv (version) command
: Extended Commandsw (write file) command
: Other CommandsW (write first line) command
: Extended Commandsx (eXchange) command
: Other Commandsy (transliterate) command
: Other Commandsz (Zap) command
: Extended Commands{} command grouping
: Common Commands[1] This applies to commands such as =
,
a
, c
, i
, l
, p
. You can
still write to the standard output by using the w
or W
commands together with the /dev/stdout
special file
[2] Note that GNU sed creates the backup file whether or not any output is actually changed.
[3] Actually, if sed prints a line without the terminating newline, it will nevertheless print the missing newline as soon as more text is sent to the same output stream, which gives the “least expected surprise” even though it does not make commands like sed -n p exactly identical to cat.
[4] This is equivalent to p
unless the -i
option is being used.
[5] This is equivalent to p
unless the -i
option is being used.
[6] All
the escapes introduced here are GNU
extensions, with the exception of \n
. In basic regular
expression mode, setting POSIXLY_CORRECT
disables them inside
bracket expressions.
[7] sed guru Greg Ubben wrote an implementation of the dc rpn calculator! It is distributed together with sed.
[8] This requires another script to pad the output of banner; for example
#! /bin/sh banner -w $1 $2 $3 $4 | sed -e :a -e '/^.\{0,'$1'\}$/ { s/$/ /; ba; }' | ~/sedscripts/reverseline.sed
[9] Some implementations have a limit of 199 commands per script
[10] which is the actual “bug” that prompted the change in behavior


About Me
My curriculum vitae and contacts.
My curriculum vitae and contacts.
The collection of all notes for researches and study.
The list of my researches.
Codes (repositories) on Github.
Technical notes and some works for hobbies.
The main page of my laboratory in Dept. ECE, UH.
View all topics sorted by categories.
View all topics sorted by tags.


Random Geek comic was born out of my personal need to read geek comics at work! Instead of visiting multiple sites and hitting the random buttons over there, I though I'll whip up a little something that will take care of this!
Enjoy your dose of some of the best geek comics and more from the internet - new sources will be added as and when I can get back to this project!


jQuery Mobile has a rich theming system that gives you full control of how pages and forms are styled. By default all form elements inside a container will automatically adopt the same theme color swatch as their parent. This allows form elements to blend into their layouts with minimal work. The data-theme
attribute can be applied to any individual form element to apply any of the lettered theme color swatches to create contrast and emphasis in your designs.
All the form elements in the examples below use the same HTML code with no theme swatch specified on the individual form elements. The only difference between each example block code is a data-theme
swatch color assigned to each parent container. This illustrates the way form elements automatically adopt the theme swatch of their parent.


EasyHealth is your new health partner. It is fast, technologically advanced, responsive, scalable and reliable software which detects some of the major diseases with just in one eye scan.
EasyHealth is your new health partner. It is fast, technologically advanced, responsive, scalable and reliable software which detects some of the major diseases with just in one eye scan.
What all EasyHealth requires is a retina and iris scanner or a good quality camera.
Opticians
Small dispensaries
UIDAI
NGOs


The Wharton School also released the data in Table 9.8.1 on the distribution of student loan forgiveness benefits by income.
All Ages
Age \(25\)-\(35\)
Income Group
Percentage of benefit
Percentage of benefit
Bottom \(20\%\)
\(13.27\%\)
\(10.97\%\)
21st to 40th percentile
22.89%
24.56%
41st to 60th percentile
30.90%
30.62%
61st to 80th percentile
23.19%
23.03%
81st to 90th percentile
8.06%
10.39%
91st to 95th percentile
1.70%
0.43%


| 006:053 Khan | : |
Thus We have tried some of them with others, that they might say: "Is it these (poor believers) that Allah has favoured from amongst us?" Does not Allah know best those who are grateful? |
| 006:053 Maulana | : |
And thus do We try some of them by others so that they say: Are these they upon whom Allah has conferred benefit from among us? Does not Allah best know the grateful? |
| 006:053 Pickthal | : |
And even so do We try some of them by others, that they say: Are these they whom Allah favoureth among us? Is not Allah best Aware of the thanksgivers? |
| 006:053 Rashad | : |
We thus test the people by each other, to let them say (mockingly), "Are these the people among us who are blessed by GOD?" Is GOD not aware of the appreciative ones? |
| 006:053 Sarwar | : |
We test some of them by the conditions of the others so that the rich and proud ones (seeing your poor and humble followers) would say, "Are these the ones from among all of us whom God has chosen to favor?" Does not God know those who give thanks (much better than others do). |
| 006:053 Shakir | : |
And thus do We try some of them by others so that they say: Are these they upon whom Allah has conferred benefit from among us? Does not Allah best know the grateful? |
| 006:053 Sherali | : |
And in the like manner have WE tried some of them by others, that they may say, 'Is it these whom ALLAH has favoured from among us?' Does not ALLAH know best those who are grateful? |
| 006:053 Yusufali | : |
Thus did We try some of them by comparison with others, that they should say: "Is it these then that Allah hath favoured from amongst us?" Doth not Allah know best those who are grateful? |
Concepts/Themes Covered: أركان الإسلام > التوحيد > توحيد الله تعالي > صفات الله تعالى > أعلم Pillars of Islam> Islamic> Oneness of Allah> His Glory's Characteristics> The One who Knows Better أركان الإسلام > التوحيد > توحيد الله تعالي > علمه جلّ شأنه Pillars of Islam> Islamic> Oneness of Allah> His Glory's Knowledge الدعوة إلى الله > حدودها > التساهل مع المسالمين The Call for Allah> Its Limits> Lenient with the Peace-Loving الديانات > أهل الكتاب: ( اليهود و النصارى) > وجوب التساهل معهم(مع غير المحاربين) Religions> The People of the Book (the Jews and the Christians)> The Necessity to be Easy with them (with the Non-Fighters)
This tool uses eight English parallel translations for the Holy Quran imported from Mr. Clay Smith. You can also visit Qurany Concepts for browsing the Quran themes or topics. If you want to search the Holy Quran for keywords, please visit Qurany Keywords.


You recieved new message on {{date}} ✔
Name: {{name}} 🐴
Email: {{email}}
Phone: {{phone}}
Address: {{address}}
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The process itself took around an hour from the moment you arrive until you leave. The donation process itself usually took 10 to 15 minutes. There are few steps for the process which are:
Registration
1. You have to complete the registration form where you will need to fill in particular information about yourself like name, address, phone number and identification number.
Health History and Mini Physical
1. You will answer some confidential questionaire regarding your health history.
2. You will have your temperature, hemoglobin, blood pressure and pulse checked.
Donation
1.  This feels like a quick pinch and is over in seconds.
2.
Refreshments
1. Usually they will provide some refreshments for you.
2. After a few minutes taking the refreshments then you can leave.
After donating blood, take this precautions:
-Drink an extra four glasses (eight ounces each) of non-alcoholic liquids.
-Keep your bandage on and dry for the next five hours, and do not do heavy exercising or lifting.
-If the needle site starts to bleed, raise your arm straight up and press on the site until the bleeding stops.
-Because you could experience dizziness or loss of strength, use caution if you plan to do anything that could put you or others at risk of harm. For any hazardous occupation or hobby, follow applicable safety recommendations regarding your return to these activities following a blood donation.
-Eat healthy meals and consider adding iron-rich foods to your regular diet, or discuss taking an iron supplement with your health care provider, to replace the iron lost with blood donation.
-If you get a bruise: Apply ice to the area intermittently for 10-15 minutes during the first 24 hours. Thereafter, apply warm, moist heat to the area intermittently for 10-15 minutes. A rainbow of colors may occur for about 10 days.
-If you get dizzy or lightheaded: Stop what you are doing, lie down, and raise your feet until the feeling passes and you feel well enough to safely resume activities.
Only for a moment. Pinch the fleshy, soft underside of your arm. That pinch is similar to what you will feel when the needle is inserted.
The entire process takes about one hour and 15 minutes; the actual donation of a pint of whole blood unit takes eight to 10 minutes. However, the time varies slightly with each person depending on several factors including the donor’s health history and attendance at the blood drive.
The plasma from your donation is replaced within about 24 hours. Red cells need about four to six weeks for complete replacement. That’s why at least eight weeks are required between whole blood donations
You must wait at least eight weeks (56 days) between donations of whole blood and 16 weeks (112 days) between Power Red donations. Platelet apheresis donors may give every 7 days up to 24 times per year. Regulations are different for those giving blood for themselves (autologous donors).
In most states, donors must be age 17 or older. Some states allow donation by 16-year-olds with a signed parental consent form. Donors must weigh at least 110 pounds and be in good health. Additional eligibility criteria apply.
In almost all cases, medications will not disqualify you as a blood donor. Your eligibility will be based on the reason that the medication was prescribed. As long as the condition is under control and you are healthy, blood donation is usually permitted.
Persons who are pregnant are not eligible to donate. Wait 6 weeks after giving birth.
Wait 12 months after treatment for syphilis or gonorrhea.
Acceptable if it has been more than 12 months since you completed treatment for syphilis or gonorrhea.
Chlamydia, venereal warts (human papilloma virus), or genital herpes are not a cause for deferral if you are feeling healthy and well and meet all other eligibility requirements.


Git and Github
An Introduction
An Introduction
git
Image from PhD Comics
Commit = Snapshot of part of your project's state
Centralized (SVN, CVS) vs. Decentralized (Git, hg)
git, noun. Brit.informal. 1.  Git never forgets.
http://arstechnica.com/security/2013/01/psa-dont-upload-your-important-passwords-to-github/
First create a git repository!
$ mkdir my_python_app
$ cd my_python_app
$ git init
Git will do a one-time prompt for some basic information and then you have a Git Repository! All code in this code can be tracked by git as a single project.
Create and open a new file script.py
with the following command:
def f(x):
print(x**x)
if __name__ == "__main__":
f(5)
Save this file and leave the text editor and tell git to track this code.
$ git status
$ git add script.py
$ git commit -m "My first git commit!"
$ git status
$ git push origin master
$ git log
Git also allows you to clone
a remote repository to work on another
person's code. It's like downloading the entire project and it's git history.
$ cd ~
$ git clone git@github.com:DevOpsBootcamp/tinsy-flask-app.git
$ cd tinsy-flask-app
$ ls
You have successfully clone a remote repository and can start modifying the other person's code. Changes you make on your local version of this project will not affect the original version you modified (although you can push changes if you are allowed to do so by the original owner!)
Github allows you to 'branch' your codebase. This allows you to make changes on a separate track without modifying the original codebse in the same repository. Branches are preserved when you clone a remote repository.
$ git checkout broken
$ python myapp.py
Now you can see your webapp doesn't work correctly when you try to access it in the browser!
We can manually go in and fix it, or run a command to see what changed between this version and the version in the 'master' branch.
$ git diff master
Pull -> Work -> Add changes -> Commit -> Push
Larger projects have more complex workflows


[§286-216] Fines, fees and charges. All moneys collected under this part shall be paid into the state highway fund and shall be expended for the purpose of this part. [L Sp 1977 1st, c 20, pt of §1]


|
Calculates the index of the Array where item X should be placed, assuming the Array is sorted.
param: Array array The array containing the items. param: Number x The item that needs to be added to the array. param: Number low Inital Index that is used to start searching, optional. param: Number high The maximum Index that is used to stop searching, optional. returns: Number the index where item X should be placed
|
function bisection(array, x, low, high){
low || (low = 0);
high || (high = array.length);
var mid;
while(low < high){
mid = (low + high) >> 1;
if (x < array[mid]){
high = mid;
} else {
low = mid + 1;
}
}
return low;
};
|
|
Calculates the index of the Array where item X should be placed, assuming the Array is sorted.
##
param: Array array The array containing the items. param: number x The item that needs to be added to the array. param: number low Inital Index that is used to start searching, optional. param: number high The maximum Index that is used to stop searching, optional. return: number the index where item X should be placed
|
bisection.left = function left( array, x, low , high ){
low || (low = 0);
high || (high = array.length);
var mid;
while(low < high){
mid = (low + high) >> 1;
if(x < array[mid]){
low = mid + 1;
} else {
high = mid;
}
}
return low;
};
|


supersimplestocks.spark
Package¶
-
class
supersimplestocks.spark.
Spark
[source]¶ Bases:
object
-
compatible_trades
(trade_offer, trades)[source]¶ Get compatible trades (according to price, oposite type, have open quantities.
Parameters: - trade_offer – to get copmatible trades
- trades – to filter
Returns: list of compatible trades
-
gbce
(begin_datetime, trades)[source]¶ Calculate GBCE based on the realized trades since the given time for all stocks. Algorithm: geometric mean of all stock prices: RootN(Sp1*Sp2*...SpN).
Parameters: - begin_datetime – begin date since to analyze
- trades – to analyze
Returns: calculated value
-
last_dividend
(symbol, dividents)[source]¶ Get last dividend from the list based on given symbol.
Parameters: - symbol – symbol of stock
- dividents – to analyze
Returns: last dividend from the list or throw a ValueError if not exists
-
spark_context
¶ Get spark context if needed and initialize it on first run.
Returns: spark context
-
stock_price
(symbol, begin_datetime, trades)[source]¶ Get stock price based on the realized trades since the given time for given stock symbol. Algorithm: Sum(trade_price*trade_quantity) / Sum(trade_quantity).
Parameters: - symbol – symbol of stock
- begin_datetime – begin date since to analyze
- trades – to analyze
Returns: calculated value
-
-
supersimplestocks.spark.
map_stock_price
(trade)[source]¶ Spark Map function for calculating stock price.
Parameters: trade – for calculation Returns: calculated value
-
supersimplestocks.spark.
postfix_gbce
(count, p)[source]¶ Postfix function to calculate results from Spark reduce function for calculating GBCE.
Parameters: - p – to calculate
- count – to calculate
Returns: calculated value


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{% set scriptdir = '../../common/js/' %} {% set cssdir = '../../common/css/' %} {% extends "templates/base.tmpl" %} {% block pagetitle %}Draft Installation Tutorials and Guides{% endblock %} {% block title %} Documentation > Draft Installation Tutorials and Guides {% endblock %} {% block content %}
This is documentation in progress for the next release.
Documentation treated like code, powered by the community - interested?
How To Contribute


4 writes to TypeTable
System.Management.Automation (4)
engine\remoting\client\RemotingProtocol2.cs (1)
45
_transportManager.
TypeTable
= typeTable;
engine\remoting\fanin\OutOfProcTransportManager.cs (1)
2606
this.
TypeTable
= typeTableToUse;
engine\remoting\fanin\WSManPluginTransportManager.cs (1)
399
this.
TypeTable
= srvrTransportMgr.TypeTable;
engine\remoting\server\ServerRemotingProtocol2.cs (1)
296
set { _transportManager.
TypeTable
= value; }
5 references to TypeTable
System.Management.Automation (5)
engine\CommandCompletion\CommandCompletion.cs (1)
434
if (transportManager != null && transportManager.
TypeTable
== null)
engine\remoting\fanin\OutOfProcTransportManager.cs (1)
2539
powerShellCmdId, this.
TypeTable
, this.Fragmentor.FragmentSize, this.CryptoHelper);
engine\remoting\fanin\WSManPluginTransportManager.cs (1)
399
this.TypeTable = srvrTransportMgr.
TypeTable
;
engine\remoting\server\ServerRemotingProtocol2.cs (2)
216
Dbg.Assert(cmdTransportManager.
TypeTable
!= null, "This should be already set in managed C++ code");
294
get { return _transportManager.
TypeTable
; }


The foreign exchange market includes all aspects of buying, selling and exchanging currencies at current or determined prices. In terms of trading volume, it is by far the largest financially traded asset class in the world, with average daily turnover in excess of US$5 trillion. Currency markets are open 5 days a week, 24 hours a day. FX transactions are similar to other financial products in the regardless of ta bearish market there are still opportunities to make money. At Ruizean Markets we are on track to become one of the world's preferred foreign exchange providers, offering our customers a CFD & FX margin trading experience.
Market liquidity is an important indicator of whether the market is in a good condition. On occasion, due to high risk events or economic data releases, liquidity can be an issue. However, at Ruizean Markets we have direct access to a plethora of liquidity providers to ensure consistent pricing when our clients need it most.
The foreign exchange market operates 5 days a week, 24 hours a day. Trading is available from Sunday at 17:01 to Friday at 16:55 New York time.
Forex trading gives you greater flexibility, and in both a bear and a bull market there are plenty of trading opportunities. For example, assume that euro is going up against US dollar you purchase EUR and selling US dollar. If your expectation is correct, you will make a profit. If you assume that US dollar value will be increased against EURO, you sell EURO and purchase US dollar.
| Currency Pairs | Standard Account | Institutional Accounts |
| EUR / USD | 1.8 Pips | 0.3 Pips |
| GBP / USD | 2.2 Pips | 1.2 Pips |
| AUD / USD | 1.8 Pips | 0.8 Pips |
| USD / JPY | 1.8 Pips | 0.8 Pips |
| USD / CAD | 2.2 Pips | 1.2 Pips |
| USD / CHF | 2.4 Pips | 1.4 Pips |
*The above spreads are for informational purposes only. These are average figures during the European Trading Session.


Derek Eder
@derekeder
RT @emilyst: It’s odd how _Linus_ adds a code of conduct, and yet the vitriol gets aimed at _Coraline_, who had nothing to do with it and k…
9/20/2018, 9:40:59 AM
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Derek Eder
@derekeder
RT @emilyst: It’s odd how _Linus_ adds a code of conduct, and yet the vitriol gets aimed at _Coraline_, who had nothing to do with it and k…
9/20/2018, 9:40:59 AM
Favs: 0
Retweets: 0
link


Stpl.js
All exemple in this document will use following family object defined here:
Defining a template string
Using a script tag
To define a template string just create a
script tag with
type="text/stpl" and a template name in the rel attribute.
For example writing this:
define a template named "templateName" with "this is my template {{withVar}}" as the template String where withVar will be replaced by the content of the given withVar property of given datas
Using registerString method
You also can directly register a template string using the
registerString method
stpl.registerString('templateName', 'this is my template {{withVar}}');
Simple variable replacement
with this template defined
We can perform replacement and put it inside a div just like this:
document.getElementById('divFamilyDesc').innerHTML = stpl("familyDesc",family);
this will lead to the following result:
pointing dotted properties
Template defined:
Javascript replacement:
document.getElementById('divMotherAndDad').innerHTML = stpl("motherAndDad",family);
give the following result:
Looping through child elements
to get a listing of the family's childs we can perform as follow:
code in the page
Javascript replacement:
document.getElementById('childsList').innerHTML = stpl("childs",family);
give the following result:
pointing property of parents elements
modifying the previous example like this:
code in the page
Javascript replacement:
document.getElementById('childsList').innerHTML = stpl("childs",family);
give the following result:
Conditional


'Mandalorian': Cast, trailer, schedule, other things to know about Disney+ Star Wars series
by WABCThe Disney+ series "The Mandalorian" is the first live-action Star Wars series. Disney CEO Bob Iger described the series as "unlike anything audiences seen before on any platform," adding that it is "a strong indication of the quality in the storytelling that will define Disney+."
Here's what to know about the show, which is available now on Disney+.
"The Mandalorian" plot, cast
"After the stories of Jango and Boba Fett, another warrior emerges in the Star Wars universe. 'The Mandalorian' is set after the fall of the Empire and before the emergence of the First Order," Disney wrote in its official description of the series. "We follow the travails of a lone gunfighter in the outer reaches of the galaxy, far from the authority of the New Republic."
"The Mandalorian" stars Pedro Pascal, Carl Weathers, Gina Carano, Werner Herzog and Nick Nolte. Taika Waititi is also credited as a voice actor. Jon Favreau and Dave Filoni both serve as executive producers and writers.
"It's really, really great storytelling within a world we already know," Pascal told ABC7 Chicago about his work on the series, "and challenging that world with a bunch of originality and unexpected personality and some edge. All of the shady characters in the bar in the first movie we all saw come more to the forefront."
"The Mandalorian" premiere date, episode release schedule
Chapter 1 of "The Mandalorian" premiered on Disney+ when the streaming service launched on Nov. 12. Disney announced that Chapter 2 will release on Friday, Nov. 15, with Chapter 3 slated for a Friday, Nov. 22, premiere.
The remainder of the eight-episode season will presumably follow the Friday release pattern.
"The Mandalorian" trailer
On the eve of the Disney+ launch, Disney relesed a special look at "The Mandalorian" during Monday Night Football on ESPN:
A second special look followed Tuesday morning on "Good Morning America":
Disney dropped the first "Mandalorian" trailer in August during the company's D23 Expo fan event in Anaheim, California. Check out that trailer below or watch the second trailer released in October in the video player above.
Click here to learn more about Disney+.
The Walt Disney Company is the parent company of Lucasfilm and this station.


 When the man's deadbeat half-brother takes them all out for a boat ride, the film suddenly switches gears, and turns into an all-out battle of self-discovery and survival.
CRITIQUE: People will be divided on this film. On the one hand, it is a wonderfully photographed picture set in a lush environment not often caught on film, Alaska, with genuine performances from all of its main leads, interesting characters and an ending that might have you appreciating its fresh unconventionality. On the other hand, it's basically a movie featuring an Alaskan fisherman who falls for an over-the-hill folkie singer with a messed up daughter, that runs a little over 125 minutes, moves at a slow pace, and might have many people screaming "foul" after its anti-Hollywood ending. I personally reside somewhere in between these two views (I guess you could say that I'm in "limbo" over my opinion....hehe....sorry, but I had to!), with heavy kudos to Vanessa Martinez, who played the daughter, John Sayles for executing an interesting character study inside an unexciting environment (for me, at least), and the ending, which initially left me feeling betrayed, but ultimately challenged me to think about the deeper meaning of this film's message.
The actual goal of the film wasn't to tidy things up nice and cozy, it was to present us with the lives of various characters interacting amongst one another under different life experiences, motivations and vulnerabilities. In the end, I felt as though many of their innermost fears had been conquered and they were ready to take on the world/or disappear from it. If you are the type of person who does not like films with open-ended finishes, you will probably HATE this movie! I personally found it to be a little long for my taste (I think they could have cut some parts of the daughter reading endlessly out of the diary), a little boring in others, but overall, it didn't dull me as much as I thought it would. The screenwriter and actors should be commended for that, since it was their characters who sparked that subtle interest within me. All in all, think character study meets THE EDGE (7.5/10) with an ending that nobody can agree on.
Little Known Facts about this film and its stars: John Sayles has been nominated for an Oscar on two occasions for Best Screenplay, one for PASSION FISH and the other for LONE STAR. He is also well known to support himself as a Hollywood script doctor, and has written numerous scripts for other directors including THE CHALLENGE for John Frankenheimer and BREAKING IN for director Bill Forsyth. Mary Elizabeth Mastrantonio made her big-screen debut in Martin Scorsese's THE KING OF COMEDY (8/10) and followed that up with her infamous role of Al Pacino's younger sister in SCARFACE (8.5/10). She also starred in a film called THE JANUARY MAN, directed by her husband Pat O'Connor, with whom she now resides in London, with their two kids. David Strathairn began his acting career in John Sayles' RETURN OF THE SECAUCUS SEVEN. He also starred in six other Sayles movies, including this one. The San Francisco-born actor graduated from Williams College and earned another degree from the Ringling Brothers Clown College before turning his talents to film and stage. Kris Kristofferson has eight Grammy nominations and the Best Song Grammy Award for "Help Me Make It Through The Night". In 1970, he won Song of the Year and Songwriter of the Year awards from the Country Music Association. The part of Noelle was written for 19-year old Vanessa Martinez, who had a small but pivotal role in Sayles' LONE STAR, her feature film debut.
Review Date: June 8, 1999 Director: John Sayles Writer: John Sayles Producer: Maggie Renzi Actors: Mary Elizabeth Mastrantonio as Donna De Angelo David Strathairn as Joe Gastineau Vanessa Martinez as Noelle De Angelo Genre: Drama Year of Release: 1999 --------------------------------------- JoBlo's Movie Emporium http://www.joblo.com --------------------------------------- (c) 1999 Berge Garabedian
The review above was posted to the
rec.arts.movies.reviews newsgroup (de.rec.film.kritiken for German reviews).
The Internet Movie Database accepts no responsibility for the contents of the
review and has no editorial control. Unless stated otherwise, the copyright
belongs to the author.
Please direct comments/criticisms of the review to relevant newsgroups.
Broken URLs inthe reviews are the responsibility of the author.
The formatting of the review is likely to differ from the original due
to ASCII to HTML conversion.
Related links: index of all rec.arts.movies.reviews reviews


Tests the goodness-of-fit to the Normal distribution for the errors of an ARMA model.
| Version: | 1.0.2 |
| Depends: | R (≥ 2.10.0), astsa |
| Published: | 2017-04-14 |
| Author: | Pierre Duchesne and Pierre Lafaye de Micheaux |
| Maintainer: | Pierre Lafaye de Micheaux <lafaye at unsw.edu.au> |
| License: | GPL (> 2) |
| NeedsCompilation: | yes |
| Citation: | nortestARMA citation info |
| CRAN checks: | nortestARMA results |
| Reference manual: | nortestARMA.pdf |
| Package source: | nortestARMA_1.0.2.tar.gz |
| Windows binaries: | r-devel: nortestARMA_1.0.2.zip, r-release: nortestARMA_1.0.2.zip, r-oldrel: nortestARMA_1.0.2.zip |
| OS X binaries: | r-release: nortestARMA_1.0.2.tgz, r-oldrel: nortestARMA_1.0.2.tgz |
| Old sources: | nortestARMA archive |
Please use the canonical form https://CRAN.R-project.org/package=nortestARMA to link to this page.


--- title: "Stirglin's approximation [sic]" author: "Einar" date: 2021-05-13 #categories: ["R"] tags: ["Stirling's approximation", "bad at maths"] math: true editor_options: chunk_output_type: console ---
If you have read any introductory probability material, which I have lately, you have seen Stirling’s approximation to the factorial \[n! = n\cdot(n-1)\cdot(n-2)\cdot\ldots\cdot2\cdot1.\] It seems to be standard material and looks like \[ n! \approx n^ne^{-n}\sqrt{2\pi n} = \hat n!. \]
I introduce the probably nonstandard \(\hat n!\) as a shorthand for this approximation. At the intro to probability level \(\hat n!\) is usually presented without comment. There are various proofs/derivations that show that for large \(n\) the ratio \(\frac{\hat n!}{n!}\) tends to unity, but they mostly look pretty tricky to me.
I saw a somewhat informal derivation in The Art of Doing Science and Engineering by Richard Hamming, which was quite understandable as far as it went. It went as far as \[ n! \approx Cn^ne^{-n}\sqrt n, \] and then moved on, stating simply that \(C=\sqrt{2\pi}\) is the approximation error as \(n\to\infty\).
 And if not (see previous), how close could I get?
The basic steps aren’t too bad. Usually when we have a huge product of things that we would rather break up into smaller, possibly more tractable things, we take \(\log\)s: \[ \log(n!) = \sum_{x=1}^n \log x. \] Fine. Knowing that a sum is basically a bumpy integral I suppose it could make sense to say that \[ \sum_{x=1}^n \log x \approx \int_1^n \log x~\mathrm dx. \] This is, after all, the Riemann sum of that integral with unit-size steps. The integral comes out as \[ \left. \int_1^n \log x~\mathrm dx = x\log x - x \right\rvert_1^n = n\log n -n + 1. \] So that’s the approximation sorted. Simply undo the \(\log\)s by taking the exponential and arrive at my latest invention, Stirglin’s approximation:1 \[ n! \stackrel{?}{\approx} n^n e^{-n}e = {{\hat n??}}. \] Here I have expanded the standard notation for the factorial to include chess annotation. At this point it’s usual to present a table of values for the factorial and the approximation. I’ll instead show a plot of \(\frac{\hat{n}!}{n!}\) and \(\frac{\hat n??}{n!}\) for various \(n\). The horizontal line is \(1 = \frac{n!}{n!}\), the perfect approximation.
stirling <- function(n) {
(n^n)*exp(-n)*sqrt(2*pi*n)
}
stirglin <- function(n) {
(n^n)*exp(1-n)
}
Although \(\hat n ??\) is exact for \(n=1\) it seems less useful for larger \(n\). What do we do?
We already know what’s wrong by inspecting \(\hat n!\). Thanks for the help Stirling; shoulders of giants and all that. The factor \(\sqrt{2\pi}\) is not that important, it’s roughly the same as our factor \(e\): What’s crucially missing is the factor \(\sqrt n\).
Where does it come from though? Hamming observes in his derivation that the trapezoidal rule approximation to an integral, which is more accurate than the Riemann sum, is \[ \begin{align} \frac{1}{2} \log 1 + \sum_{x=2}^{n-1} \log x + \frac{1}{2}\log n &\approx \int_1^n \log x~\mathrm dx \\&= n\log n -n + 1. \end{align} \] Notice that \(\log 1 = 0,\) so its coefficient doesn’t matter. Notice also that we’re missing half a \(\log n\) to make up the sum we want; if we add this on both sides of the equation we get \[ \sum_{x=1}^n \log x \approx n \log n - n + 1 + \frac{1}{2}\log n. \] This is the missing \(\sqrt n\). But I could not have known this beforehand, so let’s pretend we don’t. I suppose I would have known about the existence of the trapezoid rule but I would not have thought about using it. I would have thought about doing computations and plots.
I don’t know much about Stirling but probably he did not have a 2018 MacBook Pro. With this device it is not much work to multiply or sum a bunch of numbers, or even take \(\log\)s. What opulence. It certainly isn’t hard for me to compare \(\sum_{x=1}^n \log x\) with \(\log \hat n?? = n\log n -n + 1\) up to a very large \(n\) indeed.
Above I show the \(\log\) error in \(\hat n??\) all the way up to \(n=10^6\). The number \(10^6!\) has at the very least four and a half millions digits.2 You’d never want to look at that number itself, but you may want to use \(n!\) or an easier-to-deal-with approximation to derive other quantities (such as probabilities) supposing \(n\) quite large.
What we’re looking for is a function of \(n\) that we can multiply with \(\hat n??\) so that \(\frac{f(n)\hat n??}{n!} \approx 1\) as \(n\) increases.3 Or, equivalently, we’re looking for a function that that we can subtract on the \(\log\) scale to make the error zero. Then it’s just a matter of fitting the curve above.
It’s clear from the figure that the error is a non-linear function of \(n\). It would be nicest for the look of our approximation if the function could be made very simple. It would not be very satisfying with, say, a neural network function approximation.
In Exploratory Data Analysis, Tukey advocates trying a simple ladder of transformations, fitting curves of the form \(y = \beta_0 + \beta_1 f(x)\) with \(f(x)\) climbing the ladder \[ \frac{1}{x^2}, \frac{1}{x}, \frac{1}{\sqrt{x}}, \log x, \sqrt x, x, x^2. \] Our suspect is in this lineup, but we’re pretending to be me so we don’t know that. But we know that the curve is bendy downard, as they say in the technical language, and so the rungs below \(x\) are the transformations likely to make the relationship less bendy. They all stretch out smaller numbers and pack larger numbers closer together, if you think about it.
Look at that straight \(\log n\) line. Majestic! If we fit this straight line so that we have \(\mathrm{error} \approx \beta_0 + \beta_1\log n\) we can simply subtract it to get an error \(\approx\) zero.
lm_fit = lm(ratio~log(Ns))
coef(lm_fit)
## (Intercept) log(Ns)
## 0.08096557 -0.49999261
So we reckon \(\mathrm{error} \approx 0.08 - 0.5\log n\) and are in a position to formulate Stirglin’s approximation of order II: \[ \begin{align} \log n! &\approx \log \hat n!? \\ &= \log \hat n?? - (0.08 - 0.5\log n) \\ &= n\log n - n + 0.92 + 0.5\log n,\\ \mathrm{and\ so,}\\ \hat n!? &= n^ne^{-n}e^{0.92}\sqrt n \end{align} \]
Notice that we also got slightly closer to the \(\sqrt{2\pi}\) factor going from \(e\) to \(e^{0.92}\) The new comparison plot looks as follows:
stirglin_2 <- function(n) {
(n^n)*exp(.92-n)*sqrt(n)
}
The slightly larger grey points show Stirling’s approximation for comparison. We are very close! As with Stirling, Stirglin II looks good even for quite small \(n\). Let’s look at the error for large \(n\). I will go from \(n=100\,000\) to \(n=5\,000\,000\).
We very slightly overestimate. For my money that’s as good as very slightly underestimating. I believe the jigglyness toward the higher \(n\)s has to do with rounding error in floating point operations.
So empirically we get roughly what the theory dictates, which is always reassuring, but we’re pretending to not have the theory and to be too bad at maths to derive it. Stirglin’s second-order approximation gives us a decent approximation for quite large \(n\). If we need to know its error for an even larger but still reasonable \(n\) we can always check. What we don’t get is guarantees about its behavior as \(n\to\infty\).4 In other words it’s quite accurate for applied work, but you can’t use it for proofs.
I was thinking about doing a whole bit about Stirling’s less talented brother Stirglin, his manuscripts recently discovered in some attic, but it would have made this text insufferable.↩
Take everything above \(100\,000\) as \(100\,000\) exactly and drop what’s below for a smaller but easier-to-deal-with number. This will have \(\log_{10} 100\,000^{900\,000} = 900\,000\cdot5 = 4\,500\,000\) digits.↩
No point focussing on getting a good approximation for small \(n\), there we can just use \(n!\) directly.↩
Because I don’t know how. But I can offer a consolation prize type guarantee: If you know that for some \(n - 1\) the error is \(\mathrm{err}(n-1) = C - 0.5\log (n-1)\) you can show by some algebra tricks (nothing crazy but tedious to type out in full) that the error for \(n\) is \[C - 0.5\log(n) - 1 + (n - 0.5)\log\frac{n}{n-1} \\ = \mathrm{err}(n) - 1 + (n - 0.5)\log\frac{n}{n-1}.\] This last term goes toward unity quite quickly and it is the case that \(\lim_{n\to\infty} (n - 0.5)\log\frac{n}{n-1} = 1,\) according to SymPy, which I used to check that limit. It’s not an ironbound proof or anything, but it’s promising.↩


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