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|
%% $Id: pst-func.tex 625 2012-01-15 20:56:13Z herbert $
%%
%% This is file `pst-func.tex',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pst-func.tex'
%%
%% Herbert Voss <hvoss@tug.org>
%%
%% This program can be redistributed and/or modified under the terms
%% of the LaTeX Project Public License Distributed from CTAN archives
%% in directory macros/latex/base/lppl.txt.
%%
%% DESCRIPTION:
%% `pst-func' is a PSTricks package to plot special functions
%%
%% For a ChangeLog go the the end
%%
\csname PSTfuncLoaded\endcsname
\let\PSTfuncLoaded\endinput
% Requires some PSTricks packages
\ifx\PSTricksLoaded\endinput\else \input pstricks.tex\fi
\ifx\PSTnodesLoaded\endinput\else \input pst-plot.tex\fi
\ifx\PSTmathLoaded\endinput \else \input pst-math.tex\fi
\ifx\PSTricksAddLoaded\endinput\else\input pstricks-add.tex\fi
\ifx\PSTXKeyLoaded\endinput\else \input pst-xkey.tex \fi
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
% interface to the `xkeyval' package
\pst@addfams{pst-func}
%
\def\fileversion{0.76}
\def\filedate{2012/01/13}
\message{`PST-func' v\fileversion, \filedate\space (hv)}
%
\pstheader{pst-func.pro}
%\pstheader{pst-math.pro}% for GAMMALN
%
% Shortcuts ....
\def\ChebyshevT{ tx@FuncDict begin ChebyshevT end }
\def\ChebyshevU{ tx@FuncDict begin ChebyshevU end }
%
\define@key[psset]{pst-func}{xShift}[0]{\def\psk@xShift{#1}}
\psset[pst-func]{xShift=0}
%
\define@key[psset]{pst-func}{cosCoeff}[0]{\def\psk@cosCoeff{#1}}
\define@key[psset]{pst-func}{sinCoeff}[1]{\def\psk@sinCoeff{#1}}
\psset[pst-func]{cosCoeff=0,sinCoeff=1} % coeff=a0 a1 a2 a3 ...
%
\def\psFourier{\@ifnextchar[{\psFourier@i}{\psFourier@i[]}}
\def\psFourier@i[#1]#2#3{{%
\pst@killglue
\psset{#1}
\psplot[algebraic=false]{#2}{#3}{%
/type (cos) def
/Fourier {
aload length /n exch def
n -1 roll 2 div n 1 roll % a0/2
n 1 sub -1 0 {
/i exch def
i x mul 180 mul 3.141592 div
type (sin) eq {sin}{cos} ifelse
mul n 1 roll
} for
n 1 sub -1 1 { pop add } for
} def
[\psk@cosCoeff] Fourier
/type (sin) def
[0 \psk@sinCoeff] Fourier add
}%
}\ignorespaces}
%
\define@key[psset]{pst-func}{coeff}[0 1]{\def\psk@coeff{#1}}
\define@key[psset]{pst-func}{Derivation}[0]{\def\psk@Derivation{#1}}
\define@boolkey[psset]{pst-func}[Pst@]{markZeros}[true]{}
\define@key[psset]{pst-func}{epsZero}[0.1]{\def\psk@epsZero{#1}}
\define@key[psset]{pst-func}{dZero}[0.1]{\def\psk@dZero{#1}}
\define@key[psset]{pst-func}{zeroLineTo}[-1]{\def\psk@zeroLineTo{#1}}
\define@key[psset]{pst-func}{zeroLineColor}[black]{\pst@getcolor{#1}\psk@zeroLineColor}
\newdimen\psk@zeroLineWidth
\define@key[psset]{pst-func}{zeroLineWidth}[0.5\pslinewidth]{\pssetlength\psk@zeroLineWidth{#1}}
\define@key[psset]{pst-func}{zeroLineStyle}[dashed]{%
\@ifundefined{psls@#1}%
{\@pstrickserr{Line style `#1' not defined}\@eha}%
{\edef\psk@zeroLineStyle{#1}}%
}
\psset[pst-func]{%
coeff=0 1, % coeff=a0 a1 a2 a3 ...
Derivation=0, % 0 is the original function
markZeros=false,% no dots for the zeros
epsZero=0.1, % the distance between two zero points
dZero=0.1, % the distance of the x value for scanning the function
zeroLineTo=-1, % a line to the value of the lineTo's Derivation (-1= none)
zeroLineStyle=dashed,%
zeroLineWidth=0.5\pslinewidth,%
zeroLineColor=black}%
%
\def\psPolynomial{\pst@object{psPolynomial}}
\def\psPolynomial@i#1#2{%
\pst@killglue%
\begingroup%
\use@par%
\@nameuse{beginplot@\psplotstyle}%
\gdef\psplot@init{}%
\@nameuse{testqp@\psplotstyle}%
\addto@pscode{%
tx@FuncDict begin
/coeff [ \psk@coeff ] def
/x0 #1 def /x1 #2 def
/dx x1 x0 sub \psk@plotpoints\space div def
/Derivation \psk@Derivation\space def
/x x0 def
\ifPst@markZeros
5 dict begin % hold all local!
gsave
\pst@number\psk@zeroLineWidth SLW
\pst@usecolor\psk@zeroLineColor
\psk@epsZero\space \psk@dZero\space FindZeros
aload length { % zero array is on stack
/xZero exch def
xZero \pst@number\psxunit mul /xPixel exch def
\psk@dotsize
\@nameuse{psds@\psk@dotstyle}%
xPixel 0 Dot
\psk@zeroLineTo\space 0 ge { % line to function \psk@lineTo
xPixel 0 moveto
xZero coeff \psk@zeroLineTo\space FuncValue
\pst@number\psyunit mul xPixel exch L
\@nameuse{psls@\psk@zeroLineStyle}
} if
} repeat
grestore
end
\fi
/xy {
x \psk@xShift\space sub coeff Derivation FuncValue \pst@number\psyunit mul
x \pst@number\psxunit mul exch
} def
xy moveto
}%
\if@pst% lines and dots
\psPolynomial@iii%
\else% curves
\psPolynomial@ii%
\fi%
\endgroup
\ignorespaces}
%
\def\psPolynomial@ii{%
\addto@pscode{%
xy \@nameuse{beginqp@\psplotstyle}
\psk@plotpoints {
xy \@nameuse{doqp@\psplotstyle}
/x x dx add def
} repeat
xy \@nameuse{doqp@\psplotstyle}
end
}%
\@nameuse{endqp@\psplotstyle}%
}
\def\psPolynomial@iii{% curves
\addto@pscode{%
mark
/n 2 def
\psk@plotpoints {
xy
n 2 roll
/n n 2 add def
/x x dx add def
} repeat
/x x1 def
xy
n 2 roll
end
}%
\@nameuse{endplot@\psplotstyle}%
}
%
% Bessel 2004-06-08
% Manuel Luque, Herbert Voss
% Look at the end for some more documentation about the algorithm
%
\define@key[psset]{pst-func}{constI}[1]{\def\psk@constI{#1 }}
\define@key[psset]{pst-func}{constII}[0]{\def\psk@constII{#1 }}
\psset{constI=1,constII=0}
%
\def\psBessel{\@ifnextchar[{\psBessel@i}{\psBessel@i[]}}
\def\psBessel@i[#1]#2#3#4{{%%% #2 = n
\pst@killglue
\psset{plotpoints=500}%
\psset{#1}%
\parametricplot{#3}{#4}{%
/J1 0 def
/k { 57.29577951 mul } def
/xBessel t k def
0 0.1 180 {
/tB exch k def
/J1 J1 0.1 xBessel
tB sin mul tB #2\space mul sub cos mul add def
} for
t J1 180 div \psk@constI mul \psk@constII add
}%
}\ignorespaces}
%
%
\def\psModBessel{\@ifnextchar[{\psModBessel@i}{\psModBessel@i[]}}%% hv 20111021
\def\psModBessel@i[#1]#2#3{{%%% #2 = n
\pst@killglue%
\psset{nue=0,#1}%
\psplot{#2}{#3}[ /nue \psk@nue def /epsilon 1e-20 def ]{%
/Sum 0 def
/Iter 0 def
{/Sum_Iter
x dup mul 4 div Iter exp % nominator
nue Iter add 1 add GAMMA Iter tx@AddMathFunc begin ! end mul % denominator
Div def
Sum_Iter abs epsilon lt { exit } if
/Sum Sum Sum_Iter add def
/Iter Iter 1 add def
} loop
x 0.5 mul nue exp Sum mul
}%
}\ignorespaces}
%
\define@key[psset]{pst-func}{sigma}[0.5]{\def\psk@sigma{#1 }}
\define@key[psset]{pst-func}{mue}[0]{\def\psk@mue{#1 }}
\define@key[psset]{pst-func}{nue}[1]{\def\psk@nue{#1 }}
\psset[pst-func]{sigma=0.5,mue=0,nue=1}
%
\def\psGauss{\@ifnextchar[{\psGauss@i}{\psGauss@i[]}}
\def\psGauss@i[#1]#2#3{{%
\pst@killglue%
\psset{plotpoints=200}%
\psset{#1}%
\psplot[algebraic=false]{#2}{#3}{%
Euler x \psk@mue sub dup mul 2 div \psk@sigma dup mul div neg exp
1.0 \psk@sigma div TwoPi sqrt div mul%
}%
}\ignorespaces}
%
\define@key[psset]{pst-func}{Simpson}[5]{\def\psk@Simpson{#1 }}
\psset[pst-func]{Simpson=5}
%
\def\psGaussI{\pst@object{psGaussI}}
\def\psGaussI@i#1#2{%
\addbefore@par{plotpoints=200,plotstyle=line}
\begin@OpenObj%
\addto@pscode{
/a #1 def
/dx #2 #1 sub \psk@plotpoints\space div def
/b a dx add def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
tx@FuncDict begin
/C 1 \psk@sigma div TwoPi sqrt div def
/SFunc {% x on Stack
Euler exch \psk@mue\space sub dup mul 2 div \psk@sigma\space dup mul div neg exp C mul
} def
end
% a scx 0 moveto
a scx 0 \@nameuse{beginqp@\psplotstyle}
\psk@plotpoints 1 sub {
a b \psk@Simpson % a b M on Stack
tx@FuncDict begin Simpson I end % y value on stack
scy b scx exch \@nameuse{doqp@\psplotstyle} %lineto
/b b dx add def
} repeat
% stroke
}%
\end@OpenObj%
}
%
\def\psSi{\pst@object{psSi}}
\def\psSi@i#1#2{%
\begin@OpenObj%
\addto@pscode{
/x #1 def
/dx #2 #1 sub \psk@plotpoints\space div def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
x scx x tx@FuncDict begin Si end scy moveto
\psk@plotpoints 1 sub {
x dup scx exch tx@FuncDict begin Si end scy lineto
/x x dx add def
} repeat
stroke
}%
\end@OpenObj%
}
\def\pssi{\pst@object{pssi}}
\def\pssi@i#1#2{%
\begin@OpenObj%
\addto@pscode{
/x #1 def
/dx #2 #1 sub \psk@plotpoints\space div def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
x scx x tx@FuncDict begin si end scy moveto
\psk@plotpoints 1 sub {
x dup scx exch tx@FuncDict begin si end scy lineto
/x x dx add def
} repeat
stroke
}%
\end@OpenObj%
}
%
\def\psCi{\pst@object{psCi}}
\def\psCi@i#1#2{%
\begin@OpenObj%
\addto@pscode{
/x #1 def
/dx #2 #1 sub \psk@plotpoints\space div def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
x scx x tx@FuncDict begin Ci end scy moveto
\psk@plotpoints 1 sub {
x dup scx exch tx@FuncDict begin Ci end scy lineto
/x x dx add def
} repeat
stroke
}%
\end@OpenObj%
}
\def\psci{\pst@object{psci}}
\def\psci@i#1#2{%
\begin@OpenObj%
\addto@pscode{
/x #1 def
/dx #2 #1 sub \psk@plotpoints\space div def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
x scx x tx@FuncDict begin ci end scy moveto
\psk@plotpoints 1 sub {
x dup scx exch tx@FuncDict begin ci end scy lineto
/x x dx add def
} repeat
stroke
}%
\end@OpenObj%
}
%
\define@key[psset]{pst-func}{PSfont}[Times-Roman]{\def\psk@PSfont{/#1 }}
\define@key[psset]{pst-func}{valuewidth}[10]{\pst@getint{#1}\psk@valuewidth }
\define@key[psset]{pst-func}{fontscale}[10]{\pst@checknum{#1}\psk@fontscale }
\define@key[psset]{pst-func}{decimals}[-1]{\pst@getint{#1}\psk@decimals }
\psset[pst-func]{PSfont=Times-Roman,fontscale=10,valuewidth=10,decimals=-1}
%
\def\psPrintValue{\pst@object{psPrintValue}}
\def\psPrintValue@i#1{\expandafter\psPrintValue@ii#1,,\@nil}
\def\psPrintValue@ii#1,#2,#3\@nil{% #1,#2 only for algebraic code
\begin@SpecialObj
\addto@pscode{
gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
\ifPst@algebraic
/x #1 def
/Func (#2) tx@AlgToPs begin AlgToPs end cvx def
Func
\else #1 \fi
\psk@decimals -1 gt { 10 \psk@decimals exp dup 3 1 roll mul cvi exch div } if
\psk@valuewidth string cvs %/Output exch def % save output
\ifPst@comma dot2comma \fi % do we have to change dot to comma
\psk@xShift\space 0 moveto %Output
show grestore
}%
\end@SpecialObj%
}
\define@boolkey[psset]{pst-func}[Pst@]{round}[true]{}%
\define@boolkey[psset]{pst-func}[Pst@]{science}[true]{%
\ifPst@science\def\psk@Scin{true }\else\def\psk@Scin{false }\fi}
\psset[pst-func]{science=false,round=false}
\def\psPrintValueNew{\pst@object{psPrintValueNew}}
\def\psPrintValueNew@i#1{\expandafter\psPrintValueNew@ii#1,,\@nil}
\def\psPrintValueNew@ii#1,#2,#3\@nil{% #1,#2 only for algebraic code
\begin@SpecialObj
\addto@pscode{ % thanks to Buddy Ledger
/mfont { \psk@PSfont findfont \psk@fontscale scalefont setfont } bind def
/mfontexp { \psk@PSfont findfont \psk@fontscale 1.2 div scalefont setfont } bind def
/s1 { /Symbol findfont \psk@fontscale scalefont setfont } bind def
\ifPst@algebraic
/x #1 def
/Func (#2) tx@AlgToPs begin AlgToPs end cvx def
Func
\else #1 \fi
/value ED
\psk@Scin {
value 0 ne { value log floor cvi /expon ED }{ /expon 0 def } ifelse
value 10 expon exp div
\psk@decimals -1 gt { 10 \psk@decimals exp dup 3 1 roll mul
\ifPst@round round \else cvi \fi exch div } if
\psk@decimals 0 eq { cvi } if /numb ED
expon \psk@valuewidth string cvs /expon exch def
numb \psk@valuewidth string cvs
\ifPst@comma dot2comma \fi % do we have to change dot to comma
/Output exch def
/txspc \psk@fontscale 4 div def
\psk@xShift\space 0 moveto mfont Output show
txspc 0 rmoveto s1 (\string\264) show
txspc 0 rmoveto mfont (10) show
txspc 2 div txspc 1.5 mul rmoveto mfontexp expon show }
{ value
\psk@decimals -1 gt { 10 \psk@decimals exp dup 3 1 roll mul
\ifPst@round round \else cvi \fi exch div } if
\psk@decimals 0 eq { cvi } if %inserted to handle decimals=0
\psk@valuewidth string cvs
\ifPst@comma dot2comma \fi % do we have to change dot to comma
\psk@xShift\space 0 moveto mfont %Output
show
} ifelse
}%
\end@SpecialObj%
}
%
% Integrals 2006-01-16
% Jose-Emilio Vila-Forcen, Herbert Voss
%
\def\psCumIntegral{\pst@object{psCumIntegral}}
\def\psCumIntegral@i#1#2#3{%
\begin@OpenObj%
\addto@pscode{
/a #1 def
/dx #2 #1 sub \psk@plotpoints\space div def
/b a dx add def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
tx@FuncDict begin /SFunc { #3 } def end
a scx 0 moveto
\psk@plotpoints 1 sub {
a b \psk@Simpson % a b M on Styack
tx@FuncDict begin Simpson I end % y value on stack
scy b scx exch lineto
/b b dx add def
} repeat
% stroke
}%
% \psk@fillstyle%
% \pst@stroke%
\end@OpenObj%
}
%
\def\psIntegral{\pst@object{psIntegral}}
\def\psIntegral@i#1#2(#3,#4)#5{%
\begin@OpenObj%
\addto@pscode{
/a #3 def
/dx #4 #3 sub \psk@plotpoints\space div def
/b #4 def
/aa #1 def
/dd #2 #1 sub \psk@plotpoints\space div def
/t aa dd add def
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
tx@FuncDict begin /SFunc { t #5 } def end
a b \psk@Simpson % a b M on Stack
tx@FuncDict begin Simpson I end % y value on stack
scy t scx exch moveto
/t t dd add def
\psk@plotpoints 1 sub {
a b \psk@Simpson % a b M on Stack
tx@FuncDict begin Simpson I end % y value on stack
scy t scx exch lineto
/t t dd add def
} repeat
% stroke
}%
% \psk@fillstyle%
% \pst@stroke%
\end@OpenObj%
}
%
\def\psConv{\@ifnextchar[{\psConv@i}{\psConv@i[]}}
\def\psConv@i[#1]#2#3(#4,#5)#6#7{%
\psIntegral[#1]{#2}{#3}(#4,#5){pop pop x #6\space x t neg add #7\space mul}%
}%
%
\define@boolkey[psset]{pst-func}[Pst@]{printValue}[true]{}
\define@key[psset]{pst-func}{barwidth}[1]{\def\psFunc@barwidth{#1 }}% a factor, not a dimen
\psset[pst-func]{printValue=false,barwidth=1}
%
\def\psBinomial{\pst@object{psBinomial}}
\def\psBinomial@i#1#2{\psBinomial@ii#1,,,\@nil{#2}}%
\def\psBinomial@ii#1,#2,#3,#4\@nil#5{%
\def\pst@tempA{#2}%
\ifx\pst@tempA\@empty
\psBinomial@iii{0}{#1}{#1}{#5}%
\else
\def\pst@tempA{#3}%
\ifx\pst@tempA\@empty\psBinomial@iii{#1}{#2}{#2}{#5}%
\else\psBinomial@iii{#1}{#2}{#3}{#5}\fi
\fi}%
\def\psBinomial@iii#1#2#3#4{%
\begin@OpenObj%
\addto@pscode{
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
/m #1 def
/n #2 def
/N #3 def
/p #4 def
/dx \psFunc@barwidth 2 div def
/q 1 p sub def
/kOld dx neg m add def
kOld scx 0 moveto % starting point
0 1 m 1 sub {
/k exch def % save loop variable
k 0 eq
{ /Y q N exp def }
{ /Y Y N k sub 1 add mul k div p mul q div def }
ifelse
} for
m 1 n { % n-m+1 times
/k exch def % save loop variable
k 0 eq
{ /Y q N exp def }
{ /Y Y N k sub 1 add mul k div p mul q div def }
ifelse % recursive definition
kOld scx Y scy L k dx add scx Y scy L
\ifPst@markZeros k dx add scx 0 L kOld 1 add scx 0 L \fi
\ifPst@printValue
gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
Y \psk@valuewidth string cvs
\ifPst@comma dot2comma \fi
k scx \psk@fontscale 2 div add
Y scy \pst@number\pslabelsep add moveto
90 rotate show grestore
\fi
/kOld kOld 1 add def
} for
\ifPst@markZeros\else k dx add scx 0 L \fi % last line down to x-axis
}%
% \psk@fillstyle%
% \pst@stroke%
\end@OpenObj%
}%
%
\def\psBinomialN{\pst@object{psBinomialN}}
\def\psBinomialN@i#1#2{%
\leavevmode
\pst@killglue
\begingroup
\use@par
\init@pscode
\def\cplotstyle{curve}%
\ifx\psplotstyle\cplotstyle \@nameuse{beginplot@\psplotstyle} \fi%
\addto@pscode{
\ifx\psplotstyle\cplotstyle /Curve true def \else /Curve false def \fi
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
/N #1 def
/p #2 def % probability
/q 1 p sub def
/E N p mul def
/sigma E q mul sqrt def % variant
/dx 1.0 sigma div 2 div def
/xOld dx neg E sub sigma div def
/xEnd xOld neg dx add scx def
Curve
{ /Coors [xOld dx sub scx 0] def }% saves the coordinates for curve
{ xOld scx 0 moveto } % starting point
ifelse
0 1 N { % N times
/k exch def % save loop variable
k 0 eq
{ /Y q N exp def }
{ /Y Y N k sub 1 add mul k div p mul q div def }
ifelse % recursive definition
/x k E sub sigma div dx add def
/y Y sigma mul def % normalize
Curve
{ x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def}
{ xOld scx y scy L x scx y scy L
\ifPst@markZeros x scx 0 L \fi %
} ifelse
\ifPst@printValue
gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
y \psk@valuewidth string cvs %/Output exch def
\ifPst@comma dot2comma \fi % do we have to change dot to comma
x dx sub scx \psk@fontscale 2 div add
y scy \pst@number\pslabelsep add moveto
90 rotate show grestore
\fi
/xOld x def
} for
Curve { [ xEnd 0 Coors aload pop } if % showpoints on top of the stack
}%
\ifx\psplotstyle\cplotstyle\@nameuse{endplot@\psplotstyle}\else%
\psk@fillstyle%
\pst@stroke%
\fi%
\use@pscode%
\endgroup%
\ignorespaces%
}
%
\def\psPoisson{\pst@object{psPoisson}}% with contributions from Gerry Coombes
\def\psPoisson@i#1#2{\psPoisson@ii#1,,\@nil{#2}}%
\def\psPoisson@ii#1,#2,#3\@nil#4{%
\def\pst@tempA{#2}%
\ifx\pst@tempA\@empty\psPoisson@iii{0}{#1}{#4}\else
\psPoisson@iii{#1}{#2}{#4}\fi}%
\def\psPoisson@iii#1#2#3{% M N lambda
\begin@OpenObj%
\addto@pscode{
/scx { \pst@number\psxunit mul } def
/scy { \pst@number\psyunit mul } def
/M #1 def
/N #2 def
/lambda #3 def
/elambda Euler #3 neg exp def % e^-lambda
/dx \psFunc@barwidth 2 div def
/kOld dx neg M add def % addition of M here
kOld scx 0 moveto % starting point
/Y elambda def % start value
0 1 M 1 sub { % skip over first M-1 rectangles
/k exch def % whilst recursing probabilities
k 0 eq { /Y elambda def }{ /Y Y lambda mul k div def } ifelse
} for % nothing happens if M=0
M 1 N { % N-M+1 times
/k exch def % save loop variable
k 0 eq { /Y elambda def }{ /Y Y lambda mul k div def } ifelse
kOld scx Y scy L k dx add scx Y scy L
\ifPst@markZeros k dx add scx 0 L \fi
\ifPst@printValue
gsave \psk@PSfont findfont \psk@fontscale scalefont setfont
Y \psk@valuewidth string cvs %/Output exch def
\ifPst@comma dot2comma \fi % do we have to change dot to comma
k scx \psk@fontscale 2 div add
Y scy \pst@number\pslabelsep add moveto
90 rotate show grestore
\fi
/kOld kOld 1 add def
\ifPst@markZeros kOld scx 0 moveto \fi
} for
\ifPst@markZeros \else k dx add scx 0 L \fi % last line down to x-axis
}%
% \psk@fillstyle
% \pst@stroke
\end@OpenObj%
}
%
\define@key[psset]{pst-func}{alpha}[0.5]{\pst@checknum{#1}\psk@alpha }
\define@key[psset]{pst-func}{beta}[0.5]{\pst@checknum{#1}\psk@beta }
\psset[pst-func]{alpha=0.5,beta=0.5}
%
\def\psGammaDist{\pst@object{psGammaDist}}
\def\psGammaDist@i#1#2{%
\ifdim#1pt<\z@ \psframebox*{\color{red}!!!\#1 must be greater than 0!!!}
\else
\addbefore@par{plotpoints=500,alpha=0.5,beta=0.5}%
\begin@OpenObj
\psplot[algebraic=false]{#1}{#2}{
\psk@beta x mul \psk@alpha exp x div Euler \psk@beta neg x mul \psk@alpha GAMMALN sub exp mul}
\end@OpenObj%
\fi%
\ignorespaces%
}
%
\def\psBetaDist{\pst@object{psBetaDist}}
\def\psBetaDist@i#1#2{%
\ifdim#1pt<\z@ \psframebox*{\color{red}!!!\#1 must be greater than 0!!!}
\else
\addbefore@par{plotpoints=200,alpha=1,beta=1}%
\begin@OpenObj
\psplot[algebraic=false]{#1}{#2}{
\psk@beta \psk@alpha add GAMMA
\psk@beta GAMMA \psk@alpha GAMMA mul div
1 x sub \psk@beta 1.0 sub exp mul
x \psk@alpha 1.0 sub exp mul }
\end@OpenObj%
\fi%
\ignorespaces%
}
%
\def\psChiIIDist{\pst@object{psChiIIDist}}
\def\psChiIIDist@i#1#2{%
\addbefore@par{plotpoints=500,nue=1}%
\begin@OpenObj
% \ifdim\psk@nue pt<\z@ \psframebox*{\color{red}!!!nue must be greater than 0!!!}
% \else
\psplot[algebraic=false]{#1}{#2}{%
x 2 div \psk@nue 2 div exp x div Euler -0.5 x mul \psk@nue 2 div GAMMALN sub exp mul }%
% \fi%
\end@OpenObj%
\ignorespaces%
}
%
\def\psTDist{\pst@object{psTDist}}
\def\psTDist@i#1#2{%
\leavevmode
\pst@killglue
\begingroup
\addbefore@par{plotpoints=500}%
\use@par
\ifdim\psk@nue pt<\z@ \psframebox*{\color{red}!!!nue must be greater than 0!!!}
\else
\psplot[algebraic=false]{#1}{#2}{
1 x 2 exp \psk@nue div 1 add \psk@nue 1 add 2 div exp div
\psk@nue Pi mul sqrt div
Euler \psk@nue 1 add 2 div GAMMALN \psk@nue 2 div GAMMALN sub exp mul
}%
\fi%
\endgroup%
\ignorespaces%
}
%
\def\psFDist{\pst@object{psFDist}}
\def\psFDist@i#1#2{%
\ifdim#1pt<\z@ \psframebox*{\color{red}!!!\#1 must be greater than 0!!!}
\else
\leavevmode
\pst@killglue
\begingroup
\addbefore@par{plotpoints=500,mue=1}%
\use@par
\psplot[algebraic=false]{#1}{#2}{
x \psk@mue mul \psk@nue div dup \psk@mue 2 div exp x div
exch 1 add \psk@mue \psk@nue add 2 div exp div
Euler \psk@mue \psk@nue add 2 div GAMMALN
\psk@mue 2 div GAMMALN sub \psk@nue 2 div GAMMALN sub exp mul
}%
\endgroup%
\fi%
\ignorespaces%
}
%
\define@key[psset]{pst-func}{m}[0]{\def\psk@cauchy@m{#1 }}
\define@key[psset]{pst-func}{b}[1]{\def\psk@cauchy@b{#1 }}
\psset[pst-func]{m=0,b=1}
%
\def\psCauchy{\pst@object{psCauchy}}
\def\psCauchy@i#1#2{{%
\pst@killglue%
\addbefore@par{plotpoints=200}%
\use@par%
\psplot[algebraic=false]{#1}{#2}{
\psk@cauchy@b dup dup mul x \psk@cauchy@m sub dup mul add div Pi div
}%
}\ignorespaces}
%
\def\psCauchyI{\pst@object{psCauchyI}}
\def\psCauchyI@i#1#2{{%
\pst@killglue%
\addbefore@par{plotpoints=200}%
\use@par%
\psplot[algebraic=false]{#1}{#2}{
x \psk@cauchy@m sub \psk@cauchy@b div ATAN1 DegtoRad Pi div 0.5 add
}%
}\ignorespaces}
%
\def\psWeibull{\pst@object{psWeibull}}
\def\psWeibull@i#1#2{%
\addbefore@par{plotpoints=500,alpha=1,beta=1}%
\begin@OpenObj
\def\pst@tempA{#1}%
\ifdim#1pt<\z@ \psline(#1,0)(0,0)\def\pst@tempA{0}\fi
\psplot[algebraic=false]{\pst@tempA}{#2}{
\psk@alpha \psk@beta \psk@alpha neg exp mul % alpha*beta^(-alpha)
x \psk@alpha 1 sub exp % x^(alpha-1)
mul
Euler x \psk@beta div \psk@alpha exp neg exp % e^(-(x/beta)^alpha))
mul }
\end@OpenObj%
\ignorespaces%
}
\def\psWeibullI{\pst@object{psWeibullI}}
\def\psWeibullI@i#1#2{%
\addbefore@par{plotpoints=500,alpha=1,beta=1}%
\begin@OpenObj
\def\pst@tempA{#1}%
\ifdim#1pt<\z@ \psline(#1,0)(0,0)\def\pst@tempA{0}\fi
\psplot[algebraic=false]{\pst@tempA}{#2}{
1
Euler x \psk@beta div \psk@alpha exp neg exp % e^(-(x/beta)^alpha))
sub
}%
\end@OpenObj%
\ignorespaces%
}
%
\define@key[psset]{pst-func}{pd}[0.22]{\pst@checknum{#1}\psk@probability }
\define@key[psset]{pst-func}{R2}[0.11]{\pst@checknum{#1}\psk@portfolio }
\psset[pst-func]{pd=0.22,R2=0.11}
%
\def\psVasicek{\pst@object{psVasicek}}
\def\psVasicek@i#1#2{%
\addbefore@par{plotpoints=500}%
\begin@OpenObj
\psplot{#1}{#2}[/pd \psk@probability\space def /R2 \psk@portfolio\space def ]{x tx@FuncDict begin vasicek end}
\end@OpenObj%
\ignorespaces%
}
\define@boolkey[psset]{pst-func}[Pst@]{Gini}[true]{}
\psset[pst-func]{Gini=false}
%
\def\psLorenz{\pst@object{psLorenz}}
\def\psLorenz@i#1{{%
% \readdata{\L@Data}{#1}%
\if@star\addto@par{fillstyle=solid,fillcolor=\pslinecolor}\fi
\use@par%
\iffalse
\def\Lorenz@code{
/D {} def
[ \L@Data\space counttomark dup
1 sub /m ED 2 div cvi /n ED % m=0..n-1 n=number of pairs
] /xyValues ED
/Xval [] def /Yval [] def /Xmax 0 def
/Xsum 0 def /Ysum 0 def /XYsum 0 def
xyValues aload pop % [ x y x y x y ... ]
n { 2 copy mul XYsum add /XYsum ED
dup
Yval aload length 1 add array astore /Yval ED
Ysum add /Ysum ED
dup
Xval aload length 1 add array astore /Xval ED
dup Xsum add /Xsum ED
dup Xmax gt { /Xmax ED }{ pop } ifelse
} repeat
Xval bubblesort /Xval ED
Yval bubblesort /Yval ED
Xval { Xmax div } forall n array astore /XvalRelMax ED
Xval { Xsum div } forall n array astore /XvalRel ED
Yval { Ysum div } forall n array astore /YvalRel ED
0 1 n 1 sub {
cvi /Index ED
Xval Index get
Yval Index get
mul } for
n array astore /XmulY ED
XmulY aload length 1 sub { add } repeat
/XmulYsum ED
XmulY { XmulYsum div } forall
n array astore /XmulYdivXmulYsum ED
/X [0] def
/Y [0] def
/Xsum 0 def /Ysum 0 def
0 1 n 1 sub {
/Index ED
% XvalRel Index get Xsum add /Xsum ED
% X aload length 1 add Xsum exch array astore /X ED
X aload length 1 add XvalRelMax Index get exch array astore /X ED %%
XmulYdivXmulYsum Index get Ysum add /Ysum ED
Y aload length 1 add Ysum exch array astore /Y ED
} for
\ifPst@Gini
0 % start value for Gini
0 1 X length 2 sub {
/Index ED
Y Index get Y Index 1 add get add 2 div % yHeight=(y0+y1)/2
X Index 1 add get X Index get sub abs % xWidth=x1-x0
mul % x*y
add
} for
2 mul 1 sub neg % triangle area divided by the area under the polygon
\psk@PSfont findfont \psk@fontscale scalefont setfont
\psk@decimals -1 gt { 10 \psk@decimals exp dup 3 1 roll mul cvi exch div } if
\psk@valuewidth string cvs %/Output exch def % save output
\ifPst@comma dot2comma \fi % do we have to change dot to comma
/Output ED
\psk@xShift\space -30 moveto (Gini: ) show
Output show
\fi
0 1 n { dup X exch get exch Y exch get } for
\if@star 1 0 0 0 \fi % add values for the closed curve
}% filling the area under the curve.
\fi
%%%%%%%%%%%%%%%%%%%%%%5
\def\Lorenz@code{
[ #1 ] dup length /n ED
bubblesort /Yval ED
[ 1 1 n { } for ] /Xval ED
/Xsum n dup 1 add mul 2 div cvi def
/Ysum 0 def /XYsum 0 def
0 Yval { add } forall /Ysum ED
Xval { n div } forall n array astore /XvalRelMax ED
Xval { Xsum div } forall n array astore /XvalRel ED
Yval { Ysum div } forall n array astore /YvalRel ED
0 1 n 1 sub {
/Index ED
Xval Index get
Yval Index get
mul } for
n array astore /XmulY ED
XmulY aload length 1 sub { add } repeat
/XmulYsum ED
XmulY { XmulYsum div } forall
n array astore /XmulYdivXmulYsum ED
/X [0] def
/Y [0] def
/Xsum 0 def /Ysum 0 def
0 1 n 1 sub {
/Index ED
% XvalRel Index get Xsum add /Xsum ED
% X aload length 1 add Xsum exch array astore /X ED
X aload length 1 add XvalRelMax Index get exch array astore /X ED %%
XmulYdivXmulYsum Index get Ysum add /Ysum ED
Y aload length 1 add Ysum exch array astore /Y ED
} for
\ifPst@Gini
0 % start value for Gini
0 1 X length 2 sub {
/Index ED
Y Index get Y Index 1 add get add 2 div % yHeight=(y0+y1)/2
X Index 1 add get X Index get sub abs % xWidth=x1-x0
mul % x*y
add
} for
2 mul 1 sub neg % triangle area divided by the area under the polygon
\psk@PSfont findfont \psk@fontscale scalefont setfont
\psk@decimals -1 gt { 10 \psk@decimals exp dup 3 1 roll mul cvi exch div } if
\psk@valuewidth string cvs %/Output exch def % save output
\ifPst@comma dot2comma \fi % do we have to change dot to comma
/Output ED
\psk@xShift\space -30 moveto (Gini: ) show
Output show
\fi
0 1 n { dup X exch get exch Y exch get } for
\if@star 1 0 0 0 \fi % add values for the closed curve
}% filling the area under the curve.
\if@star\listplot*{\Lorenz@code}\else\listplot{\Lorenz@code}%
% \listplot[plotstyle=bezier,linecolor=red]{\Lorenz@code}
\fi%
}\ignorespaces}
%
% Superellipese / Lamefunction
\define@key[psset]{pst-func}{radiusA}[1]{\pst@getlength{#1}\pst@radiusA}
\define@key[psset]{pst-func}{radiusB}[1]{\pst@getlength{#1}\pst@radiusB}
\psset[pst-func]{radiusA=1,radiusB=1}
%
\def\psLame{\pst@object{psLame}}
\def\psLame@i#1{%
\leavevmode
\pst@killglue
\begingroup
\addbefore@par{plotpoints=200}%
\use@par
\parametricplot{0}{360}{%
t cos dup mul 1 #1\space div exp \pst@radiusA \pst@number\psxunit div mul
t 90 gt { t 270 lt { neg } if } if
t sin dup mul 1 #1\space div exp \pst@radiusB \pst@number\psyunit div mul
t 180 gt { neg } if }
\endgroup\ignorespaces}
%
% For polar plots
%\define@boolkey[psset]{pst-func}[PstAdd@]{polarplot}[true]{}
%\psset[pst-func]{polarplot=false}
%
%\define@boolkey[psset]{pstricks-add}[Pst@]{GetFinalState}[true]{}
%\define@key[psset]{pstricks-add}{filename}{\def\psk@filename{#1}}%
%\define@boolkey[psset]{pstricks-add}[Pst@]{saveData}[true]{} % \ifPst@saveData
%\psset[pstricks-add]{GetFinalState=false,saveData=false,filename=PSTdata}
%
\define@key[psset]{pst-func}{stepFactor}[0.67]{\pst@checknum{#1}\psk@stepFactor }
\psset[pst-func]{stepFactor=0.67}
%
\def\psplotImp{\pst@object{psplotImp}}% 20060420
\def\psplotImp@i(#1,#2)(#3,#4){%
\@ifnextchar[{\psplotImp@ii(#1,#2)(#3,#4)}{\psplotImp@ii(#1,#2)(#3,#4)[]}}
\def\psplotImp@ii(#1,#2)(#3,#4)[#5]#6{%
\addbefore@par{filename=\jobname.data}%
\begin@OpenObj%
\addto@pscode{
\ifPst@saveData /Pst@data (\psk@filename) (w) file def \fi
/xMin #1 def
/xMax #3 def
/yMin #2 def
/yMax #4 def
#5 % additional PS code
\ifPst@polarplot
/@PolarAlgPlot (#6) tx@addDict begin AlgParser end cvx def
/Func {
/phi y x atan def
/r x y Pyth def
\ifPst@algebraic @PolarAlgPlot \else #6 \fi } def
\else
/Func \ifPst@algebraic (#6) tx@addDict begin AlgParser end cvx \else { #6 } \fi def
\fi
/xPixel xMax xMin sub \pst@number\psxunit mul round cvi def
/yPixel yMax yMin sub \pst@number\psyunit mul round cvi def
/dx xMax xMin sub xPixel div def
/dy yMax yMin sub yPixel div def
/setpixel {
dy div exch
dx div exch
\ifPst@saveData
2 copy
\pst@number\psyunit div exch \pst@number\psxunit div
20 string cvs Pst@data exch writestring
Pst@data (\space) writestring
20 string cvs Pst@data exch writestring
% Pst@data (\string\]) writestring
Pst@data (\string\n) writestring
\fi
\pst@number\pslinewidth 2 div 0 360 arc fill } bind def
%
/VZ true def % suppose that F(x,y)>=0
/x xMin def /y yMin def Func 0.0 lt { /VZ false def } if % erster Wert
xMin dx \psk@stepFactor\space mul xMax {
/x exch def
\ifPst@saveData Pst@data ([\string\n) writestring \fi
yMin dy \psk@stepFactor\space mul yMax {
/y exch def
Func 0 lt
{ VZ { x y setpixel /VZ false def} if }
{ VZ {}{ x y setpixel /VZ true def } ifelse } ifelse
} for
\ifPst@saveData Pst@data (]\string\n) writestring \fi
} for
%% the same for the other way round without saving the data
/VZ true def % suppose that F(x,y)>=0
/x xMin def /y yMin def Func 0.0 lt { /VZ false def } if % erster Wert
yMin dy \psk@stepFactor\space mul yMax {
/y exch def
\ifPst@saveData Pst@data ([\string\n) writestring \fi
xMin dx \psk@stepFactor\space mul xMax {
/x exch def
Func 0 lt
{ VZ { x y setpixel /VZ false def} if }
{ VZ {}{ x y setpixel /VZ true def } ifelse } ifelse
} for
\ifPst@saveData Pst@data (]\string\n) writestring \fi
} for
%
\iffalse
/x xMin def /y yMin def Func 0.0 lt { /VZ false def } if % erster Wert
yMin dy \psk@stepFactor\space mul yMax {
/y exch def
xMin dx \psk@stepFactor\space mul xMax {
/x exch def
Func 0 lt
{ VZ { x y setpixel /VZ false def} if }
{ VZ {}{ x y setpixel /VZ true def } ifelse } ifelse
} for
} for
\fi
\ifPst@saveData Pst@data closefile \fi
}%
\end@OpenObj%
}
%
\def\psVolume{\pst@object{psVolume}}% 2007-06-23
\def\psVolume@i(#1,#2)#3#4{%
\leavevmode
\pst@killglue
\begingroup
\use@par
\psplot[algebraic=false,fillstyle=none]{#1}{#2}{#4}% original function
\psplot[algebraic=false,fillstyle=none]{#1}{#2}{#4 neg}% mirrored at the x-axis
\multido{\iA=1+1}{#3}{% run it #3 times with increment \A
\pscustom{% to get a closed filled ellipse
\code{ % the PS code
/dX #2 #1 sub #3 div def % delta x, the step
/Start dX \iA\space 1 sub mul #1 add def % xStart
/End Start dX add def % xEnd=xStart+dX
/Height End Start add 2 div /x ED #4 def } % height=f(x)
% x is the mean between Start+End
\psellipticarc(!Start 0)(! Height 8 div Height){90}{270}
% draw the first falf of the ellipse
\rlineto(! dX 0)% draw a line in x-direction
\psellipticarc(!End 0)(! Height 8 div Height){270}{90}
% draw the other half of the ellipse
\rlineto(!dX neg 0)}}% draw a line in negative x-direction
\psset{fillstyle=none}
\psellipse(#2,0)(!#2 dup #1 sub #3 div 2 div sub /x ED #4 dup
8 div exch)% draw again the ellipse to get the borderline.
\psset{plotstyle=line,linestyle=dashed,
plotpoints=40,dotstyle=*,dotsize=0.5pt}
\psplot[algebraic=false]{#1}{#2}{#4}\psplot{#1}{#2}{#4 neg}
% draw again the curves to get the borderline
\endgroup%
\ignorespaces%
}
\def\txFunc@BezierCurve{ tx@FuncDict begin BezierCurve Points end }
\def\txFunc@BezierShowPoints{ tx@Dict begin /Points ED BezierShowPoints end }
\def\pst@BezierType{2 } % the default
%
\def\psBezier#1{% % allowed order is 1 ... 9
\ifnum#1>0 \ifnum#1<10 \def\pst@BezierType{#1 }\fi\fi%
\pst@object{psBezier}}
\def\psBezier@i{%
\pst@getarrows{%
\addbefore@par{plotpoints=200}%
\begin@OpenObj
\pst@getcoors[\psBezier@ii%
}}
\def\psBezier@ii{%
\addto@pscode{%
\psk@plotpoints % step for Bezier T=0,0+epsilon,0+i*epsilon,...,1
\pst@BezierType % type of the Bezier curve 2,3,4,...
\txFunc@BezierCurve
\ifshowpoints \txFunc@BezierShowPoints \else pop \fi
}%
\end@OpenObj}
%
\def\tx@Bernstein{ tx@FuncDict begin Bernstein end }
\define@boolkey[psset]{pst-func}[Pst@]{envelope}[true]{}
\psset[pst-func]{envelope=false}
%
\def\psBernstein{\pst@object{psBernstein}}% \psBernstein[options](t1,t2)(i,n)
\def\psBernstein@i(#1,#2){%
\@ifnextchar({\psBernstein@ii(#1,#2)}{\psBernstein@ii(0,1)(#1,#2)}}
%
\def\psBernstein@ii(#1,#2)(#3,#4){% (tStart,tEnd)(i,n)
\addbefore@par{plotpoints=200}%
\begin@OpenObj
\addto@pscode{%
/ScreenCoor { \tx@ScreenCoor } def
#1\space #2\space
1.0 \psk@plotpoints\space div % step=1/plotpoints
#3\space #4\space
% on stack we have tStart tEnd epsilon i n
\ifPst@envelope true \else false \fi
\tx@Bernstein
}%
\end@OpenObj}
%
\def\psThomae{\pst@object{psThomae}}
\def\psThomae@i(#1,#2)#3{%
\addbefore@par{dotsize=1pt}
\begin@ClosedObj
\addto@pscode{
1 1 #3 {
dup
/ipSave ED % save loop value
/ip ED % dito
1 1 #3 {
dup
/iqSave ED % sabve loop value
/iq ED % dito
{
iq 0 le { exit } if
ip iq mod
/ip iq def
/iq ED
} loop
ip 1 eq {
/xVal ipSave iqSave div def
xVal #1 ge { xVal #2 le {
\psk@dotsize
\@nameuse{psds@\psk@dotstyle}
\pst@usecolor\pslinecolor xVal 1 iqSave div \tx@ScreenCoor
2 copy moveto Dot } if } if
} if
} for
} for
}%
\end@ClosedObj%
}
%
\def\psCplot{\def\pst@par{}\pst@object{psCplot}}
\def\psCplot@i#1#2#3#4{% start | end | complex variables | function
\pst@killglue
\begingroup
\use@par
\@nameuse{beginplot@\psplotstyle}%
\addto@pscode{%
\psplot@init
/x #1 def
/x1 #2 def
/dx x1 x sub \psk@plotpoints div def
#3
/xy {
% x
tx@FuncDict begin
#4 aload pop \pst@number\psyunit mul exch \pst@number\psxunit mul exch
end
} def}%
\gdef\psplot@init{}%
\@pstfalse
\@nameuse{testqp@\psplotstyle}%
\if@pst
\psplot@ii
\else
\psplot@iii
\fi
\endgroup
\ignorespaces}
%
\catcode`\@=\PstAtCode\relax
%
%% END: pst-func.tex
\endinput
%
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