texlive[66750] Master/texmf-dist: pst-func (3apr23)
commits+karl at tug.org
commits+karl at tug.org
Mon Apr 3 23:32:33 CEST 2023
Revision: 66750
http://tug.org/svn/texlive?view=revision&revision=66750
Author: karl
Date: 2023-04-03 23:32:32 +0200 (Mon, 03 Apr 2023)
Log Message:
-----------
pst-func (3apr23)
Modified Paths:
--------------
trunk/Master/texmf-dist/doc/generic/pst-func/Changes
trunk/Master/texmf-dist/doc/generic/pst-func/README.md
trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib
trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
trunk/Master/texmf-dist/dvips/pst-func/pst-func.pro
trunk/Master/texmf-dist/tex/generic/pst-func/pst-func.tex
trunk/Master/texmf-dist/tex/latex/pst-func/pst-func.sty
Modified: trunk/Master/texmf-dist/doc/generic/pst-func/Changes
===================================================================
--- trunk/Master/texmf-dist/doc/generic/pst-func/Changes 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/doc/generic/pst-func/Changes 2023-04-03 21:32:32 UTC (rev 66750)
@@ -1,4 +1,7 @@
..... pst-func.tex
+1.01 2023-04-02 - added \psNonCentralTDist (noncentral Student's distribution)
+1.00 2022-09-11 - fix \psBessel: use toDeg instead of k
+ - set algebraic=false
0.99 2021-11-03 - fix for psLorenz (missing sort routine)
0.98 2021-10-30 - fix for Gini coefficiant
0.97 2021-10-29 - fix and extension for \psLorenz curve
@@ -119,6 +122,8 @@
..... pst-func.pro
+0.19 2023-04-02 - added /ConfHyperFunc { % Confluent Hypergeometric Function of the First Kind
+ needed by \psNonCentralTDist
0.18 2021-10-30 - added arraysum and arrayprod
0.17 2018-12-13 - allow algebraic mode for Simpson
0.16 2018-11-15 - new algorithm for Si/si/Ci/ci
Modified: trunk/Master/texmf-dist/doc/generic/pst-func/README.md
===================================================================
--- trunk/Master/texmf-dist/doc/generic/pst-func/README.md 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/doc/generic/pst-func/README.md 2023-04-03 21:32:32 UTC (rev 66750)
@@ -19,6 +19,7 @@
- psGammaDist
- psChiIIDist
- psTDist for Student's t-distribution
+- psNonCentralTDist for noncentral Student's t-distribution
- psBetaDist for Beta distribution
- psWeibull for Weibull distribution
- psLame (Lamé Curve - a superellipse)
@@ -43,8 +44,9 @@
PSTricks is PostScript Tricks, the documentation cannot be run
with pdftex, use lualatex or the sequence latex->dvips->ps2pdf or
-pdflatex with package auto-pst-pdf or xelatex.
+pdflatex with package auto-pst-pdf or xelatex or lualatex (preferred).
+
hvoss at tug.org
Modified: trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib
===================================================================
--- trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.bib 2023-04-03 21:32:32 UTC (rev 66750)
@@ -166,3 +166,11 @@
year = {2012},
url = {/graphics/pstricks/contrib/pst-tools}
}
+
+ at online{weisstein,
+ author = {Weisstein, Eric W.},
+ title = {Noncentral Student's t-Distribution},
+ subtitle = {From MathWorld--A Wolfram Web Resource},
+ url = {https://mathworld.wolfram.com/NoncentralStudentst-Distribution.html},
+ note = {Probability and Statistics; Statistical Distributions; Continuous Distributions }
+ }
Modified: trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
===================================================================
(Binary files differ)
Modified: trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
===================================================================
--- trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex 2023-04-03 21:32:32 UTC (rev 66750)
@@ -1,6 +1,6 @@
\RequirePackage{pdfmanagement-testphase}
\DeclareDocumentMetadata{}
-%% $Id: pst-func-doc.tex 306 2021-10-29 14:48:08Z herbert $
+%% $Id: pst-func-doc.tex 691 2023-04-03 10:51:04Z herbert $
\documentclass[fontsize=11pt,english,BCOR=10mm,DIV=12,bibliography=totoc,parskip=false,headings=small,
headinclude=false,footinclude=false,oneside]{pst-doc}
\usepackage{pst-func}
@@ -1158,7 +1158,7 @@
where \Lkeyword{constI} and \Lkeyword{constII} must be real PostScript expressions, e.g.
\begin{lstlisting}[style=syntax]
-\psset{constI=2.3,constII=t k sin 1.2 mul 0.37 add}
+\psset{constI=2.3,constII=t toDegrees sin 1.2 mul 0.37 add}
\end{lstlisting}
The Bessel function is plotted with the parametricplot macro, this is the
@@ -1174,13 +1174,11 @@
time consuming at this setting, it can be decreased in the usual
way, at the cost of some reduction in graphics resolution.
-\begin{LTXexample}
-{
+\begin{LTXexample}[pos=t]
\psset{xunit=0.25,yunit=5}
\begin{pspicture}(-13,-.85)(13,1.25)
\rput(13,0.8){%
- $\displaystyle J_n(x)=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt$%
-}
+ $\displaystyle J_n(x)=\frac{1}{\pi}\int_0^\pi\cos(x\sin t-nt)\dt$}
\psaxes[Dy=0.2,Dx=4]{->}(0,0)(-30,-.8)(30,1.2)
\psset{linewidth=1pt}
\psBessel[linecolor=red]{0}{-28}{28}%
@@ -1188,23 +1186,21 @@
\psBessel[linecolor=green]{2}{-28}{28}%
\psBessel[linecolor=magenta]{3}{-28}{28}%
\end{pspicture}
-}
\end{LTXexample}
-\begin{LTXexample}
-{
+
+\begin{LTXexample}[pos=t]
\psset{xunit=0.25,yunit=2.5}
\begin{pspicture}(-13,-1.5)(13,3)
\rput(13,0.8){%
- $\displaystyle f(t) = 2.3 \cdot J_0 + 1.2\cdot \sin t + 0.37$%
-}
+ $\displaystyle f(t) = 2.3 \cdot J_0 + 1.2\cdot \sin t + 0.37$}
\psaxes[Dy=0.8,dy=2cm,Dx=4]{->}(0,0)(-30,-1.5)(30,3)
\psset{linewidth=1pt}
-\psBessel[linecolor=red,constI=2.3,constII={t k sin 1.2 mul 0.37 add}]{0}{-28}{28}%
+\psBessel[linecolor=red,constI=2.3,constII={t toDegrees sin 1.2 mul 0.37 add}]{0}{-28}{28}%
\end{pspicture}
-}
\end{LTXexample}
+
%\clearpage
\subsection{Modfied Bessel function of first order}
The modified Bessel function of first order is defined as
@@ -1216,6 +1212,7 @@
%
\noindent The syntax of the macro is
+
\begin{BDef}
\Lcs{psModBessel}\OptArgs\Largb{xStart}\Largb{xEnd}
\end{BDef}
@@ -1223,6 +1220,11 @@
The only valid optional argument for the function is \Lkeyword{nue}, which
is preset to 0, it shows $I_0$.
+
+
+
+
+
\begin{LTXexample}
\begin{pspicture}(0,-0.5)(5,5)
\psaxes[ticksize=-5pt 0]{->}(5,5)
@@ -1909,6 +1911,70 @@
%The $t_\nu$-distribution has mode 0.
+\subsection{Student's noncentral $t$-distribution}
+
+
+A generalization of Student's t-distribution known as the noncentral Student's t-distribution is given by
+
+\[
+ P(x)=\frac{\nu^{\nu/2}\nu!}{2^{\nu}e^{\lambda^2/2}(\nu+x^2)^{\nu/2}\Gamma(\frac12\nu)}
+ \left\{
+ \frac{\sqrt{2}\lambda x\, {}_1F_1\left(\frac12 \nu+1;\, \frac32; \,\frac{\lambda^2x^2}{2(\nu+x^2)}\right)}
+ {(\nu+x^2)\Gamma[\frac12(\nu+1)]}
+ + \frac{{}_1F_1\left(\frac12(\nu+1);\, \frac12; \, \frac{\lambda^2x^2}{2(\nu+x^2)}\right)}{\sqrt{\nu+x^2}\Gamma(\frac12\nu+1)}\right\}
+\]
+
+where $\Gamma(z)$ is the gamma function and ${}_1F_1(a;b;z)$ is a confluent hypergeometric function of the first kind.~\parencite{weisstein}
+
+
+\[ {}_1F_1(a;b;z) = 1+\frac ab z + \frac{a(a+1)}{b(b+1)} \frac{z^2}{2!}+ \cdots=\sum_{k=0}^\infty\frac{(a)_k}{(b)_k} \frac{z^k}{k!} \]
+
+
+%mu = lambdasqrt(n/2)(Gamma(1/2(n-1)))/(Gamma(1/2n))
+%sigma^2 = ((lambda^2+1)n)/(n-2)-(lambda^2n[Gamma(1/2(n-1))]^2)/(2[Gamma(1/2n)]^2).
+
+The macro has the same syntax as the centered Student's distribution:
+
+\begin{BDef}
+\Lcs{psNonCentralTDist}\OptArgs\Largb{x0}\Largb{x1}
+\end{BDef}
+
+
+There exists an additional optional parameter \Lkeyword{lambda}, which is preset to 0.5.
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=0.75cm,yunit=10cm}
+\begin{pspicture}(-6,-0.1)(11,.5)
+ \psaxes[Dy=0.1]{->}(0,0)(-4.5,0)(10,0.5)
+ \psset{linewidth=1pt,plotpoints=100}
+ \psNonCentralTDist[linecolor=red,lambda=0,nue=1]{-5}{10}% same as \psTDist
+ \psNonCentralTDist[linecolor=green,lambda=0,nue=4]{-5}{10}% dito
+ \psNonCentralTDist[linecolor=red,lambda=2,nue=1]{-5}{10}
+ \psNonCentralTDist[linecolor=green,lambda=2,nue=4]{-5}{10}
+\end{pspicture}
+\end{LTXexample}
+
+
+
+
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{xunit=1.25cm,yunit=10cm}
+\begin{pspicture}(-6,-0.1)(6,.5)
+ \psaxes[Dy=0.1]{->}(0,0)(-4.5,0)(5.5,0.5)
+ \psset{linewidth=1pt,plotpoints=100}
+ \psTDist[linecolor=blue]{-4}{4}
+ \psNonCentralTDist[linecolor=red]{-4}{5}
+ \psNonCentralTDist[linecolor=green,nue=4,lambda=2]{-4}{5}
+\end{pspicture}
+\end{LTXexample}
+
+
+
+
+
+
\clearpage
\subsection{$F$-distribution}
A continuous statistical distribution which arises in the testing of
@@ -2173,6 +2239,21 @@
\endpsgraph
\end{LTXexample}
+
+\begin{LTXexample}[pos=t,preset=\centering]
+\psset{lly=-13mm,llx=-5mm}
+\psgraph[Dx=0.2,Dy=0.2,axesstyle=frame](0,0)(1,1){6cm}{6cm}
+\psline[linestyle=dashed](1,1)
+\psLorenz[Gini,linecolor=red,linewidth=1.5pt]<.2 .2 .2 .2 .2>{.1 .1 .1 .35 .35 }
+\psLorenz[Gini,linecolor=blue,linestyle=dashed,linewidth=1.5pt]{.1 .1 .1 .35 .35 }
+\endpsgraph
+\end{LTXexample}
+
+
+
+
+
+
\clearpage
\subsection{\nxLcs{psLame} -- Lam\'e Curve, a superellipse}
A superellipse is a curve with Cartesian equation
Modified: trunk/Master/texmf-dist/dvips/pst-func/pst-func.pro
===================================================================
--- trunk/Master/texmf-dist/dvips/pst-func/pst-func.pro 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/dvips/pst-func/pst-func.pro 2023-04-03 21:32:32 UTC (rev 66750)
@@ -1,4 +1,4 @@
-%% $Id: pst-func.pro 861 2018-12-13 20:40:06Z herbert $
+%% $Id: pst-func.pro 689 2023-04-03 06:46:27Z herbert $
%%
%% This is file `pst-func.pro',
%%
@@ -16,7 +16,7 @@
%% `pst-func' is a PSTricks package to plot special math functions
%%
%%
-%% version 0.17 / 2018-12-13 Herbert Voss
+%% version 0.19 / 2023-04-02 Herbert Voss
%
/tx at FuncDict 100 dict def
tx at FuncDict begin
@@ -289,13 +289,13 @@
/s1 0 def
/s2 0 def
1 1 M {
- /k exch def
- /xVal k 2 mul 1 sub h mul a add def
+ /simp_k exch def
+ /xVal simp_k 2 mul 1 sub h mul a add def
/s1 s1 xVal useX { /x exch def } if SFunc add def
} for
1 1 M 1 sub {
- /k exch def
- /xVal k 2 mul h mul a add def
+ /simp_k exch def
+ /xVal simp_k 2 mul h mul a add def
/s2 s2 xVal useX { /x exch def } if SFunc add def
} for
/I a useX { /x exch def } if SFunc b useX { /x exch def } if SFunc add s1 4 mul add s2 2 mul add 3 div h mul def
@@ -305,12 +305,12 @@
/LogGamma { 5 dict begin % z on stack
/z ED
/sum 0 def
- /k 1 def
+ /logGamma_k 1 def
{
- z k div dup 1 add ln sub dup
+ z logGamma_k div dup 1 add ln sub dup
abs eps8 lt { pop exit } if
sum add /sum exch def
- /k k 1 add def
+ /logGamma_k logGamma_k 1 add def
} loop
sum z ln sub CEuler z mul sub
end
@@ -321,10 +321,10 @@
/xtmp exch def
/n exch def
0 0 1 n .5 mul floor {
- /k exch def
- xtmp xtmp mul 1 sub k exp
- xtmp n 2 k mul sub exp mul
- n 2 k mul MoverN mul
+ /cheb_k exch def
+ xtmp xtmp mul 1 sub cheb_k exp
+ xtmp n 2 cheb_k mul sub exp mul
+ n 2 cheb_k mul MoverN mul
add
} for
end
@@ -335,10 +335,10 @@
/xtmp exch def
/n exch def
0 0 1 n .5 mul floor {
- /k exch def
- xtmp xtmp mul 1 sub k exp
- xtmp n 2 k mul sub exp mul
- n 1 add 2 k mul 1 add MoverN mul
+ /cheb_k exch def
+ xtmp xtmp mul 1 sub cheb_k exp
+ xtmp n 2 cheb_k mul sub exp mul
+ n 1 add 2 cheb_k mul 1 add MoverN mul
add
} for
end
@@ -368,6 +368,27 @@
} def
%end{vasicek density}
%
+% https://mathworld.wolfram.com/ConfluentHypergeometricFunctionoftheFirstKind.html
+/ConfHyperFunc { % Confluent Hypergeometric Funtion of the First Kind
+ % on stack must be a b z
+ 10 dict begin
+ /z ED /b ED /a ED
+ /sum 1 def
+ /k 0 def
+ /nom 1 def
+ /denom 1 def
+ {
+ nom a k add mul z mul /nom ED
+ denom b k add mul k 1 add mul /denom ED
+ nom denom div /diff ED
+ sum diff add /sum ED
+ diff 1e-5 lt { exit } { k 1 add /k ED } ifelse
+ k 1000 ge { (Error ConfHyperFunc: k =1000) == exit } if
+ } loop
+ sum
+ end
+} def
+%
end
%
/arraySum { % on stack the array
Modified: trunk/Master/texmf-dist/tex/generic/pst-func/pst-func.tex
===================================================================
--- trunk/Master/texmf-dist/tex/generic/pst-func/pst-func.tex 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/tex/generic/pst-func/pst-func.tex 2023-04-03 21:32:32 UTC (rev 66750)
@@ -1,4 +1,4 @@
-%% $Id: pst-func.tex 308 2021-10-30 14:11:45Z herbert $
+%% $Id: pst-func.tex 689 2023-04-03 06:46:27Z herbert $
%%
%% This is file `pst-func.tex',
%%
@@ -31,8 +31,8 @@
% interface to the `xkeyval' package
\pst at addfams{pst-func}
%
-\def\fileversion{0.99}
-\def\filedate{2021/11/03}
+\def\fileversion{1.01}
+\def\filedate{2023/04/02}
\message{`PST-func' v\fileversion, \filedate\space (hv)}
%
\pstheader{pst-func.pro}
@@ -233,14 +233,14 @@
\def\psBessel{\@ifnextchar[{\psBessel at i}{\psBessel at i[]}}
\def\psBessel at i[#1]#2#3#4{{%%% #2 = n
\pst at killglue
- \psset{plotpoints=500}%
- \psset{#1}%
+ \psset{plotpoints=500,constI=1,constII=0}%
+ \psset{#1,algebraic=false}%
+ \pstVerb{ /toDegrees { 57.29577951 mul } def }
\parametricplot{#3}{#4}{%
/J1 0 def
- /k { 57.29577951 mul } def
- /xBessel t k def
+ /xBessel t toDegrees def
0 0.1 180 {
- /tB exch k def
+ /tB exch toDegrees def
/J1 J1 0.1 xBessel
tB sin mul tB #2\space mul sub cos mul add def
} for
@@ -706,7 +706,9 @@
\def\psPrintValue{\pst at object{psPrintValue}}
\def\psPrintValue at i#1{\expandafter\psPrintValue at ii#1,,\@nil}
\def\psPrintValue at ii#1,#2,#3\@nil{% #1,#2 only for algebraic code
+ \addbefore at par{algebraic=false}%
\begin at SpecialObj
+ \use at par
\addto at pscode{
gsave \psk at PSfont\space findfont \psk at fontscale scalefont setfont
\ifPst at algebraic
@@ -1465,14 +1467,18 @@
\def\psBetaDist at i#1#2{%
\ifdim#1pt<\z@ \psframebox*{\color{red}!!!\#1 must be greater than 0!!!}
\else
+ \begingroup
\addbefore at par{plotpoints=200,alpha=1,beta=1}%
- \begin at OpenObj
- \psplot[algebraic=false]{#1}{#2}{
+ \addto at par{algebraic=false}%
+% \begin at OpenObj
+ \use at par
+ \psplot{#1}{#2}{
\psk at beta \psk at alpha add GAMMA
\psk at beta GAMMA \psk at alpha GAMMA mul div
1 x sub \psk at beta 1.0 sub exp mul
x \psk at alpha 1.0 sub exp mul }
- \end at OpenObj%
+% \end at OpenObj%
+ \endgroup
\fi%
\ignorespaces%
}
@@ -1508,6 +1514,44 @@
\endgroup%
\ignorespaces%
}
+
+\define at key[psset]{pst-func}{lambda}[1]{\def\psk at lambda{#1 }}
+\psset[pst-func]{lambda=0.5}
+
+\def\psNonCentralTDist{\pst at object{psNonCentralTDist}}
+\def\psNonCentralTDist at i#1#2{%
+ \leavevmode
+ \pst at killglue
+ \begingroup
+ \addbefore at par{plotpoints=500}%
+ \use at par
+ \ifdim\psk at nue pt<\z@ \psframebox*{\color{red}!!!nue must be greater than 0!!!}
+ \else
+ \psplot[algebraic=false]{#1}{#2}{% P(x) = a ( b/c + d/e )
+ \psk at nue dup 2 div exp \psk at nue factorial mul % nominator of a
+ 2 \psk at nue exp Euler \psk at lambda dup mul 2 div exp mul
+ \psk at nue x dup mul add \psk at nue 2 div exp mul
+ \psk at nue 2 div GAMMA mul % denominator of a
+ div % a
+ 2 sqrt \psk at lambda mul x mul
+ \psk at nue 2 div 1 add
+ 1.5
+ \psk at lambda dup mul x dup mul mul 2 div \psk at nue x dup mul add div
+ tx at FuncDict begin ConfHyperFunc end % Confluent Hypergeometric Funtion of the First Kind
+ mul % b
+ \psk at nue x dup mul add \psk at nue 1 add 2 div GAMMA mul % c
+ div % b/c
+ \psk at nue 1 add 2 div 0.5 \psk at lambda dup mul x dup mul mul 2 div \psk at nue x dup mul add div
+ tx at FuncDict begin ConfHyperFunc end % d
+ \psk at nue x dup mul add sqrt \psk at nue 2 div 1 add GAMMA mul % e
+ div % d/e
+ add % b/c + d/e
+ mul % (b/c + d/e) * a
+ }%
+ \fi
+ \endgroup
+ \ignorespaces
+}
%
\def\psFDist{\pst at object{psFDist}}
\def\psFDist at i#1#2{%
@@ -1656,6 +1700,7 @@
\fi
0 0 % the start point
0 1 nVal 1 sub { dup XvalRelCum exch get exch YvalRelCum exch get } for
+% pstack
\if at star 1 0 0 0 \fi % add values for the closed curve
end
}% filling the area under the curve.
@@ -1676,7 +1721,7 @@
\leavevmode
\pst at killglue
\begingroup
- \addbefore at par{plotpoints=200,startAngle=0,endAngle=360}%
+ \addbefore at par{plotpoints=200,startAngle=0,endAngle=360,algebraic=false}%
\use at par
\parametricplot{\psk at startAngle}{\psk at endAngle}{%
t cos dup mul 1 #1\space div exp \pst at radiusA \pst at number\psxunit div mul
@@ -1683,7 +1728,9 @@
t 90 gt { t 270 lt { neg } if } if
t sin dup mul 1 #1\space div exp \pst at radiusB \pst at number\psyunit div mul
t 180 gt { neg } if }
- \endgroup\ignorespaces}
+ \endgroup
+ \ignorespaces
+}
%
\def\psWeierstrass{\pst at object{psWeierstrass}}
\def\psWeierstrass at i(#1,#2){\@ifnextchar[{\psWeierstrass at ii(#1,#2)}{\psWeierstrass at iii(#1,#2)}}
Modified: trunk/Master/texmf-dist/tex/latex/pst-func/pst-func.sty
===================================================================
--- trunk/Master/texmf-dist/tex/latex/pst-func/pst-func.sty 2023-04-03 21:32:12 UTC (rev 66749)
+++ trunk/Master/texmf-dist/tex/latex/pst-func/pst-func.sty 2023-04-03 21:32:32 UTC (rev 66750)
@@ -1,5 +1,5 @@
\RequirePackage{pstricks}
-\ProvidesPackage{pst-func}[2018/12/13 package wrapper for pst-func.tex (hv)]
+\ProvidesPackage{pst-func}[2021/10/30 package wrapper for pst-func.tex (hv)]
\RequirePackage{pst-plot}
\RequirePackage{pst-math}
\RequirePackage{pst-tools}
@@ -10,7 +10,7 @@
\ProvidesFile{pst-func.tex}
[\filedate\space v\fileversion\space `PST-func' (hv)]
\IfFileExists{pst-func.pro}{%
- \ProvidesFile{pst-func.pro}[2018/12/13 v. 0.17, PostScript prologue file (hv)]
+ \ProvidesFile{pst-func.pro}[2023/04/02 v. 0.19, PostScript prologue file (hv)]
\@addtofilelist{pst-func.pro}}{}%
\endinput
-%% $Id: pst-func.sty 306 2021-10-29 14:48:08Z herbert $
+%% $Id: pst-func.sty 693 2023-04-03 10:56:01Z herbert $
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