%% $Id: pst-func.tex 697 2023-04-14 10:17:32Z herbert $ %% %% This is file `pst-func.tex', %% %% IMPORTANT NOTICE: %% %% Package `pst-func.tex' %% %% Herbert Voss %% %% 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\PSTtoolsLoaded\endinput \else \input pst-tools.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{1.02} \def\filedate{2023/04/14} \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}{epsilon}[1.e-08]{\def\psk@epsilon{#1 }} \psset[pst-func]{epsilon=1.e-08} \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}{% /psFtype (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 psFtype (sin) eq {sin}{cos} ifelse mul n 1 roll } for n 1 sub -1 1 { pop add } for } def [\psk@cosCoeff] Fourier /psFtype (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\psGetZeros{\pst@object{psGetZeros}} \def\psGetZeros@i(#1,#2)#3{% \pst@killglue \begin@SpecialObj \use@par \addto@pscode{ tx@FuncDict begin /xStart #1 def /xEnd #2 def /x xStart def /func { /x exch def \ifPst@algebraic (#3) AlgParser cvx exec \else #3 \fi } def #1 Steffensen \ifPst@markZeros \fi end }% \end@SpecialObj \ignorespaces } \iffalse /Steffensen {% the start value and the function must be on top of the stack /y0 exch def % the start value /Iter 0 def /MaxIter 200 def { y0 Function /F exch def F abs eps2 lt { exit } if y0 F sub /Phi exch def Phi Function /F2 exch def F2 abs eps2 le { exit }{ Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0 add Div /Diff exch def y0 Diff sub /y0 exch def Diff abs eps1 le { exit } if } ifelse /Iter Iter 1 add def Iter MaxIter gt { exit } if } loop y0 % the returned value ist the zero point 0 \tx@ScreenCoor pstack 3 0 360 arc gsave 0 0 1 setrgbcolor fill grestore 1 setlinewidth stroke } def \fi % \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,constI=1,constII=0}% \psset{#1,algebraic=false}% \pstVerb{ /toDegrees { 57.29577951 mul } def } \parametricplot{#3}{#4}{% /J1 0 def /xBessel t toDegrees def 0 0.1 180 { /tB exch toDegrees 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}{n}[1]{\def\psk@func@n{#1 }} \psset[pst-func]{n=0} % \def\psLaguerre{\@ifnextchar[\psLaguerre@i{\psLaguerre@i[]}}%% hv 20200111 \def\psLaguerre@i[#1](#2,#3){{%%% n \pst@killglue \psplot[#1]{#2}{#3}{% /L_n 1 def 0 1 \psk@func@n { /k_i ED -1 k_i exp k_i factorial div \psk@func@n k_i MoverN mul x k_i exp mul L_n add /L_n ED } for x \pst@number\psxunit mul L_n %dup == %\pst@number\psyunit div }% }\ignorespaces} % \def\psLaguerreC{\pst@object{psLaguerreC}}%% hv 20200612 \def\psLaguerreC@i(#1,#2)(#3,#4){{%%% n (xMin,xMax)(yMin,yMax) \pst@killglue \begin@SpecialObj \addto@pscode{% % 20 dict begin /yC #3 def /dx #2 #1 sub \psk@plotpoints div def /dy #4 #3 sub \psk@plotpoints div def /L_i { 5 userdict begin /X ED /n_i ED /L_n 0 def 0 1 n_i { /k_i ED -1 k_i exp k_i factorial div n_i k_i MoverN mul X k_i exp mul L_n add /L_n ED } for L_n % return L_n(x) end } def /n \psk@func@n def [ % start array of x/y values \psk@plotpoints { /xC #1 def \psk@plotpoints { /Re 0 def 0 1 \psk@func@n 2 div floor { /j ED % loop index /j2 j dup add def % 2j n j2 sub xC L_i % calculate L_{n-2j}(x) j2 exp % L_{n-2j}^{2j}(x) -1 j exp yC j2 exp mul % (-1^j)*y^(2j) j2 factorial % (2*j)! div mul Re add /Re ED } for /Im 0 def 0 1 \psk@func@n 1 sub 2 div floor { /j ED % loop index /j2 j dup add def % 2j n j2 sub 1 sub xC L_i % calculate L_{n-2j-1}(x) j2 1 add exp % L_{n-2j}^{2j+1}(x) -1 j 1 sub exp yC j2 1 add exp mul % (-1^j)*y^(2j+1) j2 1 add factorial % (2*j+1)! div mul Im add /Im ED } for Re Im 2 copy \tx@ScreenCoor % Re Im dup mul exch dup mul add sqrt dup 4 gt {pop 4} if 4 div setgray % xC yC \tx@ScreenCoor 0 360 2 arc gsave fill stroke grestore xC dx add /xC ED } repeat yC dy add /yC ED } repeat false \tx@NArray \psk@dotsize \@nameuse{psds@\psk@dotstyle} \tx@setStrokeTransparency newpath n { transform floor .5 add exch floor .5 add exch itransform Dot } repeat %% end }% \end@SpecialObj }\ignorespaces} % \def\psLaguerreCC{\pst@object{psLaguerreCC}}%% hv 20200612 \def\psLaguerreCC@i(#1,#2)(#3,#4){{%%% n (xMin,xMax)(yMin,yMax) \pst@killglue \begin@SpecialObj \addto@pscode{% % 20 dict begin gsave /yC #3 def /dx #2 #1 sub \psk@plotpoints div def /dy #4 #3 sub \psk@plotpoints div def /n \psk@func@n def [ % start array of x/y values \psk@plotpoints { /xC #1 def \psk@plotpoints { /z [xC yC ] def /L0 [1 0] def /L1 [1 z {-1 mul} forall 3 1 roll add exch] def n 1 le { n 0 eq {/L1 L0 def} if n 1 eq {/L1 L1 def} if }{ /m 1 def n 1 sub { /L2 1 m 1 add div [2 m mul 1 add z {-1 mul} forall 3 1 roll add exch] L1 cxmul L0 m neg cxrmul cxadd exch cxrmul def /L0 L1 def /L1 L2 def /m m 1 add def } repeat } ifelse L1 aload pop \tx@ScreenCoor xC dx add /xC ED } repeat yC dy add /yC ED } repeat false \tx@NArray \psk@dotsize \@nameuse{psds@\psk@dotstyle} \tx@setStrokeTransparency newpath n { transform floor .5 add exch floor .5 add exch itransform Dot } repeat grestore %% end }% \end@SpecialObj }\ignorespaces} % \def\psLaguerreCCC{\pst@object{psLaguerreCCC}}%% hv 20200612 \def\psLaguerreCCC@i(#1,#2)(#3,#4){{%%% n (xMin,xMax)(yMin,yMax) \pst@killglue \begin@SpecialObj \addto@pscode{% % 20 dict begin /yC #3 def /dx #2 #1 sub \psk@plotpoints div def /dy #4 #3 sub \psk@plotpoints div def [ % start array of x/y values \psk@plotpoints { /xC #1 def \psk@plotpoints { /Z [xC yC] def /L [1 0] def 0 1 \psk@func@n { /k ED \psk@func@n k MoverN -1 k exp k factorial div mul Z k tx@FuncDict begin cxexp exch cxrmul L cxadd end /L ED } for L aload pop \tx@ScreenCoor xC dx add /xC ED } repeat yC dy add /yC ED } repeat % ] aload length 3 1 roll moveto 2 div cvi 1 sub { lineto } repeat 1 0 0 setrgbcolor 0.1 setlinewidth stroke false \tx@NArray \psk@dotsize \@nameuse{psds@\psk@dotstyle} \tx@setStrokeTransparency newpath n { transform floor .5 add exch floor .5 add exch itransform Dot } repeat %% end }% \end@SpecialObj }\ignorespaces} % \def\psLaguerreCCCC{\pst@object{psLaguerreCCCC}}%% hv 20200612 \def\psLaguerreCCCC@i(#1,#2)(#3,#4){{%%% n (xMin,xMax)(yMin,yMax) \pst@killglue \begin@SpecialObj \addto@pscode{% % 20 dict begin /yC #3 def /dx #2 #1 sub \psk@plotpoints div def /dy #4 #3 sub \psk@plotpoints div def % start array of x/y values \psk@plotpoints { /xC #1 def [ \psk@plotpoints { /Z [xC yC] def /L [1 0] def 0 1 \psk@func@n { /k ED \psk@func@n k MoverN -1 k exp k factorial div mul Z k tx@FuncDict begin cxexp exch cxrmul L cxadd end /L ED } for L aload pop \tx@ScreenCoor xC dx add /xC ED } repeat ] aload length 3 1 roll moveto 2 div cvi 1 sub { lineto } repeat 1 0 0 setrgbcolor 0.1 setlinewidth stroke yC dy add /yC ED } repeat % ] aload length 3 1 roll moveto 2 div cvi 1 sub { lineto } repeat 1 0 0 setrgbcolor 0.1 setlinewidth stroke % false \tx@NArray % \psk@dotsize % \@nameuse{psds@\psk@dotstyle} % \tx@setStrokeTransparency % newpath % n { transform floor .5 add exch floor .5 add exch itransform Dot } repeat %% end }% \end@SpecialObj }\ignorespaces} % \def\psContourLaguerre{\pst@object{psContourLaguerre}}%% hv 20200612 \def\psContourLaguerre@i(#1,#2)(#3,#4){{%%% n (xMin,xMax)(yMin,yMax) \pst@killglue \begin@SpecialObj \addto@pscode{% /yC #3 def /dx #2 #1 sub \psk@plotpoints div def /dy #4 #3 sub \psk@plotpoints div def /contourdata [ % start array of x/y values \psk@plotpoints { /xC #1 def [ \psk@plotpoints { /Z [xC yC] def /L [1 0] def 0 1 \psk@func@n { /k ED \psk@func@n k MoverN -1 k exp k factorial div mul Z k tx@FuncDict begin cxexp exch cxrmul L cxadd end /L ED } for % L aload cxnorm exch pop xC yC L cxre exch pop xC dx add /xC ED } repeat ] yC dy add /yC ED } repeat ] def /zMax 0 def /zMin 0 def % lowest and highest value contourdata aload length /N ED % get the no of arrays N { % inside contourdata /data ED % save first inner array data aload length 3 div round cvi { % get the records \psk@colorOffset dup zMin lt % z n /nV exch def % der \"{u}bergebene Wert wird in nV abgespeichert /iV 1 def % Startwert ist iV=1 0 nV { iV log add /iV iV 1 add def } repeat % 0 + log(1) + log(2) + ... + log(n) Die Null ist dazu n\"{o}tig um die erste Addition machen zu k\"{o}nnen end } def /binomial_comb{ % log(N!) - log(k!) - log((n-k)!) = log[N!/(k!*(n-k)!)] 2 dict begin /nV exch def /NV exch def NV SumLog nV SumLog sub NV nV sub SumLog sub end } def /PnN { 3 dict begin /pV exch def /nV exch def /NV exch def 10 NV nV binomial_comb nV pV log mul NV nV sub 1 pV sub log mul add add exp end } def %%------------------------------------------------------------------------------------------------ %%------------------------------------------------------------------------------------------------ N ValueSwitch2Log gt { } { 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 } ifelse m 1 n {% % n-m+1 times /k exch def % save loop variable N ValueSwitch2Log gt { N k p PnN /Y exch def } { k 0 eq { /Y q N exp def } { /Y Y N k sub 1 add mul k div p mul q div def } ifelse } ifelse % recursive definition \ifx\psk@fillstylename\pst@alternateColors newpath kOld scx 0 moveto \fi 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 \ifx\psk@fillstylename\pst@alternateColors closepath gsave toggle {ColA}{ColB} ifelse \tx@setTransparency fill grestore /toggle toggle not def \fi \ifPst@printValue gsave \psk@PSfont\space findfont \psk@fontscale scalefont setfont \pst@usecolor\psk@LabelColor % Y \psFunc@PrintVLimit le { () } { Y \psk@valuewidth\space string cvs } ifelse \ifPst@comma dot2comma \fi k scx \psk@fontscale 2 div add \psFunc@xlabelsep scx add Y scy \pst@number\pslabelsep add moveto \psFunc@langle 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\space findfont \psk@fontscale scalefont setfont \pst@usecolor\psk@LabelColor % 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 \psFunc@xlabelsep scx add y scy \pst@number\pslabelsep add moveto \psFunc@langle 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\psBinomialF{\pst@object{psBinomialF}} \def\psBinomialF@i#1#2{\psBinomialF@ii#1,,,\@nil{#2}}% \def\psBinomialF@ii#1,#2,#3,#4\@nil#5{% \def\pst@tempA{#2}% \ifx\pst@tempA\@empty \psBinomialF@iii{0}{#1}{#1}{#5}% \else \def\pst@tempA{#3}% \ifx\pst@tempA\@empty\psBinomialF@iii{#1}{#2}{#2}{#5}% \else\psBinomialF@iii{#1}{#2}{#3}{#5}\fi \fi}% \def\psBinomialF@iii#1#2#3#4{% \addbefore@par{valuewidth=15}% \begin@OpenObj \addto@pscode{% /ValueSwitch2Log \psFunc@Switch2Log\space def /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 \ifPst@markZeros /kOld dx neg m add def \else /kOld m def \fi \psFunc@leftEnd 0 eq { } { kOld 0 eq { kOld \psFunc@leftEnd sub scx 0 moveto % starting point \ifPst@LineEnding kOld \psFunc@radiusout\pst@number\psxunit div sub scx 0 L stroke kOld scx 0 newpath \psFunc@radiusout 0 360 arc kOld scx 0 \psFunc@radiusinR 360 0 arcn closepath \pst@usecolor\psk@LineEndColorR fill \else kOld scx 0 L stroke \fi }{ } ifelse } ifelse kOld scx 0 moveto % starting point %%---------------------------------------------------------------------------------------------------------------------------------------------------------------- %%-------------------- Code, der bei gro{\ss}em N \"{u}ber den Logarithmus arbeitet von Manuel Luque --------------------------------------------- /SumLog {% log(1) + log(2) + ... + log(n) = log(n!) 2 dict begin % Erwartet die Eingabe eines Wertes, n\"{a}mlich bis zu welchem Wert addiert werden soll ---> n /nV exch def % der \"{u}bergebene Wert wird in nV abgespeichert /iV 1 def % Startwert ist iV=1 0 nV { iV log add /iV iV 1 add def } repeat % 0 + log(1) + log(2) + ... + log(n) Die Null ist dazu n\"{o}tig um die erste Addition machen zu k\"{o}nnen end } def /binomial_comb{ % log(N!) - log(k!) - log((n-k)!) = log[N!/(k!*(n-k)!)] 2 dict begin /nV exch def /NV exch def NV SumLog nV SumLog sub NV nV sub SumLog sub end } def /PnN { 3 dict begin /pV exch def /nV exch def /NV exch def 10 NV nV binomial_comb nV pV log mul NV nV sub 1 pV sub log mul add add exp end } def %%------------------------------------------------------------------------------------------------ %%------------------------------------------------------------------------------------------------ 0 1 m 1 sub { /k exch def % save loop variable N ValueSwitch2Log gt { k 0 eq { N k p PnN /Y exch def /F Y def } { N k p PnN /Y exch def /F F Y add def } ifelse }{ k 0 eq { /Y q N exp def /F Y def } { /Y Y N k sub 1 add mul k div p mul q div def /F F Y add def } ifelse } ifelse } for m 1 n { % n-m+1 times /k exch def % save loop variable N ValueSwitch2Log gt { k 0 eq { N k p PnN /Y exch def /F Y def } { N k p PnN /Y exch def /F F Y add def } ifelse } { k 0 eq { /Y q N exp def /F Y def } { /Y Y N k sub 1 add mul k div p mul q div def /F F Y add def } ifelse } ifelse % recursive definition F 1 gt { /F 1 def } if \ifPst@markZeros kOld scx F scy L k dx add scx F scy L k dx add scx 0 L kOld 1 add scx 0 L \else kOld scx F scy newpath \psFunc@radiusout 0 360 arc kOld scx F scy \psFunc@radiusinL 360 0 arcn closepath \pst@usecolor\psk@LineEndColorL fill kOld \ifPst@LineEnding\psFunc@radiusout\pst@number\psxunit div add \fi scx F scy moveto k 1 add \ifPst@LineEnding\psFunc@radiusout\pst@number\psxunit div sub \fi k N eq { \psFunc@rightEnd add } { } ifelse scx F scy L \pst@usecolor\pslinecolor [1 0] 0 setdash stroke \ifPst@LineEnding k N eq { } { k 1 add scx F scy newpath \psFunc@radiusout 0 360 arc k 1 add scx F scy \psFunc@radiusinR 360 0 arcn closepath \pst@usecolor\psk@LineEndColorR fill } ifelse \ifPst@VLines Y \psFunc@radiusout\pst@number\psyunit div 2 mul le { } { k scx F Y sub \psFunc@radiusout\pst@number\psyunit div add scy moveto k scx F \psFunc@radiusout\pst@number\psyunit div sub scy L \pst@usecolor\pslinecolor [3 2] 0 setdash stroke } ifelse \fi \else \ifPst@VLines Y \psFunc@radiusout\pst@number\psyunit div 0.1 mul le { } { k scx F Y sub scy moveto k scx F scy L \pst@usecolor\pslinecolor [3 2] 0 setdash stroke } ifelse \fi\fi\fi \ifPst@printValue gsave \psk@PSfont\space findfont \psk@fontscale scalefont setfont \pst@usecolor\psk@LabelColor % Y \psFunc@PrintVLimit le { () } { F \psk@valuewidth\space string cvs } ifelse \ifPst@comma dot2comma \fi k scx \psk@fontscale 2 div add \psFunc@xlabelsep scx add F scy \pst@number\pslabelsep add moveto \psFunc@langle rotate show grestore \fi /kOld kOld 1 add def } for }% \end@OpenObj% }% % \def\psBinomialFS{\pst@object{psBinomialFS}} \def\psBinomialFS@i#1#2{\psBinomialFS@ii#1,,,\@nil{#2}}% \def\psBinomialFS@ii#1,#2,#3,#4\@nil#5{% \def\pst@tempA{#2}% \ifx\pst@tempA\@empty \psBinomialFS@iii{0}{#1}{#1}{#5}% \else \def\pst@tempA{#3}% \ifx\pst@tempA\@empty\psBinomialFS@iii{#1}{#2}{#2}{#5}% \else\psBinomialFS@iii{#1}{#2}{#3}{#5}\fi \fi}% \def\psBinomialFS@iii#1#2#3#4{% \addbefore@par{valuewidth=15}% \begin@OpenObj \addto@pscode{% /ValueSwitch2Log \psFunc@Switch2Log\space def /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 \ifPst@markZeros /kOld dx neg m add def \else /kOld m def \fi kOld scx 0 moveto % starting point %%---------------------------------------------------------------------------------------------------------------------------------------------------------------- %%-------------------- Code, der bei gro{\ss}em N \"{u}ber den Logarithmus arbeitet von Manuel Luque --------------------------------------------- /SumLog {% log(1) + log(2) + ... + log(n) = log(n!) 2 dict begin % Erwartet die Eingabe eines Wertes, n\"{a}mlich bis zu welchem Wert addiert werden soll ---> n /nV exch def % der \"{u}bergebene Wert wird in nV abgespeichert /iV 1 def % Startwert ist iV=1 0 nV { iV log add /iV iV 1 add def } repeat % 0 + log(1) + log(2) + ... + log(n) Die Null ist dazu n\"{o}tig um die erste Addition machen zu k\"{o}nnen end } def /binomial_comb{ % log(N!) - log(k!) - log((n-k)!) = log[N!/(k!*(n-k)!)] 2 dict begin /nV exch def /NV exch def NV SumLog nV SumLog sub NV nV sub SumLog sub end } def /PnN { 3 dict begin /pV exch def /nV exch def /NV exch def 10 NV nV binomial_comb nV pV log mul NV nV sub 1 pV sub log mul add add exp end } def %%------------------------------------------------------------------------------------------------ 0 1 m 1 sub { /k exch def % save loop variable N ValueSwitch2Log gt { k 0 eq { N k p PnN /Y exch def /F Y def /FS 1 F sub def } { N k p PnN /Y exch def /F F Y add def /FS 1 F sub def } ifelse } { k 0 eq { /Y q N exp def /F Y def /FS 1 F sub def } { /Y Y N k sub 1 add mul k div p mul q div def /F F Y add def /FS 1 F sub def } ifelse } ifelse } for m 1 n { % n-m+1 times /k exch def % save loop variable N ValueSwitch2Log gt { k 0 eq { N k p PnN /Y exch def /F Y def /FS 1 F sub def } { N k p PnN /Y exch def /F F Y add def /FS 1 F sub def } ifelse } { k 0 eq { /Y q N exp def /F Y def /FS 1 F sub def } { /Y Y N k sub 1 add mul k div p mul q div def /F F Y add def /FS 1 F sub def } ifelse } ifelse % recursive definition FS 0 lt { /FS 0 def } if \ifPst@markZeros kOld scx FS scy L k dx add scx FS scy L k dx add scx 0 L kOld 1 add scx 0 L \else \ifPst@LineEnding k 0 eq { \psFunc@leftEnd neg scx 1 scy moveto \psFunc@radiusout neg 1 scy L gsave \pst@usecolor\pslinecolor stroke grestore } if k m eq {kOld scx \psFunc@radiusout add FS Y add scy moveto kOld scx FS Y add scy newpath \psFunc@radiusout 0 360 arc kOld scx FS Y add scy \psFunc@radiusinR 360 0 arcn closepath gsave \pst@usecolor\psk@LineEndColorR fill grestore } if kOld scx FS scy newpath \psFunc@radiusout 0 360 arc kOld scx FS scy \psFunc@radiusinL 360 0 arcn closepath \pst@usecolor\psk@LineEndColorL fill % } ifelse \fi kOld \ifPst@LineEnding\psFunc@radiusout\pst@number\psxunit div add \fi % k 0 eq % { \psFunc@leftEnd sub } % { } ifelse scx FS scy moveto k 1 add \ifPst@LineEnding\psFunc@radiusout\pst@number\psxunit div sub \fi k N eq { \psFunc@rightEnd add } { } ifelse scx FS scy L \pst@usecolor\pslinecolor [1 0] 0 setdash stroke \ifPst@LineEnding k N eq { } { k 1 add scx FS scy newpath \psFunc@radiusout 0 360 arc k 1 add scx FS scy \psFunc@radiusinR 360 0 arcn closepath \pst@usecolor\psk@LineEndColorR fill } ifelse \ifPst@VLines Y \psFunc@radiusout\pst@number\psyunit div 2 mul le { } { k scx FS Y add \psFunc@radiusout\pst@number\psyunit div sub scy moveto k scx FS \psFunc@radiusout\pst@number\psyunit div add scy L \pst@usecolor\pslinecolor [3 2] 0 setdash stroke } ifelse \fi \else \ifPst@VLines Y \psFunc@radiusout\pst@number\psyunit div 0.1 mul le { } { k scx FS Y add scy moveto k scx FS scy L \pst@usecolor\pslinecolor [3 2] 0 setdash stroke } ifelse \fi\fi\fi \ifPst@printValue gsave \psk@PSfont\space findfont \psk@fontscale scalefont setfont \pst@usecolor\psk@LabelColor % Y \psFunc@PrintVLimit le { () } { FS \psk@valuewidth\space string cvs } ifelse \ifPst@comma dot2comma \fi k 0.1 add scx \psk@fontscale 2 div add \psFunc@xlabelsep scx add FS scy \pst@number\pslabelsep add moveto \psFunc@langle rotate show grestore \fi /kOld kOld 1 add def } for }% \end@OpenObj }% % % \define@key[psset]{pst-func}{LeftClipX}[-1]{\def\psFunc@LeftClipX{#1 }} \define@key[psset]{pst-func}{RightClipX}[-1]{\def\psFunc@RightClipX{#1 }} \psset[pst-func]{LeftClipX=-1,RightClipX=1} \def\psBinomialC{\pst@object{psBinomialC}} \def\psBinomialC@i#1#2{% \leavevmode \pst@killglue \begingroup \use@par \begin{psclip}% {\psframe[linestyle=none,fillstyle=none](\psFunc@LeftClipX,-0.1)(!#1 \psFunc@RightClipX\space add 1)}% % \use@par \init@pscode \beginplot@cspline % \addto@pscode{/D {} def mark}% \addto@pscode{% /scx { \pst@number\psxunit mul } def /scy { \pst@number\psyunit mul } def /N #1 def /p #2 def % Wahrscheinlichkeit /q 1 p sub def % q = 1 - p /E N p mul def % Erwartungswert /sigma E q mul sqrt def % Varianz /dx 1.0 2 div def /xOld dx neg 3 sub def /xEnd 0 def /Coors [xOld dx sub scx 0] def % speichern der Koordinaten f\"{u}r den Spline %%---------------------------------------------------------------------------------------------------------------------------------------------------------------- %%-------------------- Code, der \"{u}ber den Logarithmus arbeitet von Manuel Luque --------------------------------------------- /SumLog {% log(1) + log(2) + ... + log(n) = log(n!) 2 dict begin % Erwartet die Eingabe eines Wertes, n\"{a}mlich bis zu welchem Wert addiert werden soll ---> n /nV exch def % der \"{u}bergebene Wert wird in nV abgespeichert /iV 1 def % Startwert ist iV=1 0 nV { iV log add /iV iV 1 add def } repeat % 0 + log(1) + log(2) + ... + log(n) %Die Null ist dazu n\"{o}tig um die erste Addition machen zu k\"{o}nnen end } def /binomial_comb{ % log(N!) - log(k!) - log((n-k)!) = log[N!/(k!*(n-k)!)] 2 dict begin /nV exch def /NV exch def NV SumLog nV SumLog sub NV nV sub SumLog sub end } def /PnN { 3 dict begin /pV exch def /nV exch def /NV exch def 10 NV nV binomial_comb nV pV log mul NV nV sub 1 pV sub log mul add add exp end } def %%------------------------------------------------------------------------------------------------ %%------------------------------------------------------------------------------------------------ %------------------------------- 3 Punkte um die Kurve links auf Null zu bringen mit dem weiter oben gew\"{a}hlten Startwert sind es also 4 ------------ /x -2 dx add def /y 0 def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def /x -0.65 dx add def /y N 0 p PnN 10 -1.3 exp mul def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def /x -0.375 dx add def /y N 0 p PnN 3 div def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def %---------------------------- Ende der 3 Punkte und Beginn eigentlicher Code ---------------- 0 1 N {% % Schleife geht von 0 bis N in 1-er Schritten /k exch def % save loop variable N k p PnN /Y exch def /x k dx add def /y Y def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def /xOld x def } for %--------------------------- Ende des eigentlichen Codes und Beginn von --- %------------------------------- 4 Punkte um die Kurve rechts auf Null zu bringen ----------- /x N 0.375 add dx add def /y Y 3 div def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def /x N 0.65 add dx add def /y Y 10 -1.3 exp mul def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def /x N 2 add dx add def /y 0 def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def /x N 3 add dx add def /y 0 def x dx sub scx y scy Coors aload length 2 add array astore /Coors exch def %---------------------------- Ende der 4 Punkte und Laden der Koordinaten des arrays ; L\"{o}schen (pop) von showpoints??---------------------- [ xEnd 1 add 0 Coors aload pop % showpoints on top of the stack }% \endplot@cspline \use@pscode \end{psclip}% \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\space 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 \begingroup \addbefore@par{plotpoints=200,alpha=1,beta=1}% \addto@par{algebraic=false}% % \begin@OpenObj \use@par \psplot{#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% \endgroup \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% } \define@key[psset]{pst-func}{lambda}[1]{\def\psk@lambda{#1 }} \psset[pst-func]{lambda=0.5} \def\psNonCentralTDist{\pst@object{psNonCentralTDist}} \def\psNonCentralTDist@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}{% P(x) = a ( b/c + d/e ) \psk@nue dup 2 div exp \psk@nue factorial mul % nominator of a 2 \psk@nue exp Euler \psk@lambda dup mul 2 div exp mul \psk@nue x dup mul add \psk@nue 2 div exp mul \psk@nue 2 div GAMMA mul % denominator of a div % a 2 sqrt \psk@lambda mul x mul \psk@nue 2 div 1 add 1.5 \psk@lambda dup mul x dup mul mul 2 div \psk@nue x dup mul add div tx@FuncDict begin ConfHyperFunc end % Confluent Hypergeometric Funtion of the First Kind mul % b \psk@nue x dup mul add \psk@nue 1 add 2 div GAMMA mul % c div % b/c \psk@nue 1 add 2 div 0.5 \psk@lambda dup mul x dup mul mul 2 div \psk@nue x dup mul add div tx@FuncDict begin ConfHyperFunc end % d \psk@nue x dup mul add sqrt \psk@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@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% } % \def\psNonCentralFDist{\pst@object{psNonCentralFDist}} \def\psNonCentralFDist@i#1#2{% \ifdim#1pt<\z@ \psframebox*{\color{red}!!!\#1 must be greater than 0!!!} \else \leavevmode \pst@killglue \begingroup \addbefore@par{plotpoints=500,nue=1,mue=1,lambda=0}% \use@par \iffalse %\ifluatex for later use \luaexec{ require("pst-func") printDataPlotFileFDist(#1,#2,\psk@plotpoints,\psk@mue,\psk@nue,\psk@lambda,"\jobname-lua","true") }% \fileplot{\jobname-lua.data}% \else \psplot[algebraic=false]{#1}{#2}[/F_BETA \psk@mue 2 div \psk@nue 2 div tx@FuncDict begin BETA end def]{ /constA Euler \psk@lambda -2 div exp def /Sum constA F_BETA % \psk@nue 2 div \psk@mue 2 div tx@FuncDict begin BETA end div % first fraction \psk@mue \psk@nue div \psk@mue 2 div exp mul \psk@nue dup \psk@mue x mul add div \psk@mue \psk@nue add 2 div exp mul x \psk@mue 2 div 1 sub exp mul def /K 1 def { constA \psk@lambda 2 div K exp mul % nominator \psk@nue 2 div \psk@mue 2 div K add tx@FuncDict begin BETA end K factorial mul % denominator div % first fraction \psk@mue \psk@nue div \psk@mue 2 div K add exp mul \psk@nue dup \psk@mue x mul add div \psk@mue \psk@nue add 2 div K add exp mul x \psk@mue 2 div 1 sub K add exp mul dup abs 1e-5 lt { pop exit } { Sum add /Sum ED K 1 add /K ED } ifelse K 100 ge { (Error ConfHyperFunc: K=100) == exit } if } loop Sum }% \fi \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 Power mul % alpha*beta^(-alpha) x \psk@alpha 1 sub Power % x^(alpha-1) mul Euler x \psk@beta div \psk@alpha Power neg Power % 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 Power neg Power % 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{\def\pst@par{}\pst@object{psLorenz}} \def\psLorenz@i{\@ifnextchar<\psLorenz@ii{\psLorenz@ii<>}} \def\psLorenz@ii<#1>#2{% \if@star\addto@par{fillstyle=solid,fillcolor=\pslinecolor}\fi \begingroup \use@par \def\Lorenz@code{ 25 dict begin [ #2 ] dup length /nVal ED bubblesort /Yval ED Yval arraySum /Ysum ED Yval { Ysum div } forall nVal array astore /YvalRel ED % Pred dist \if$#1$ /temp {1 nVal div} bind def [ nVal { temp } repeat ] /XvalRel ED [ 1 1 nVal { nVal div } for ] /XvalRelCum ED %YvalRel bubblesort /YvalRel ED \else [ #1 ] /Xval ED Xval arraySum /Xsum ED Xval { Xsum div } forall nVal array astore /XvalRel ED % Freq dist /CumFreq 0 def [ 0 1 nVal 1 sub { XvalRel exch get CumFreq add dup /CumFreq ED } for ] /XvalRelCum ED % XvalRelCum == \fi /CumPred 0 def [ 0 1 nVal 1 sub { YvalRel exch get CumPred add dup /CumPred ED } for ] /YvalRelCum ED % YvalRelCum == % Xsum == Ysum == \ifPst@Gini [ 0 1 nVal 1 sub { /Index ED YvalRelCum Index get Index 0 eq { 0 }{ YvalRelCum Index 1 sub get } ifelse add 0.5 mul XvalRel Index get mul } for ] /Area ED % Area == Area arraySum /B ED 0.5 B sub dup B add div \psk@PSfont\space 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 0 % the start point 0 1 nVal 1 sub { dup XvalRelCum exch get exch YvalRelCum exch get } for % pstack \if@star 1 0 0 0 \fi % add values for the closed curve end }% filling the area under the curve. \if@star\listplot*{\Lorenz@code}\else\listplot{\Lorenz@code}% % \listplot[plotstyle=bezier,linecolor=red]{\Lorenz@code} \fi \endgroup \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} \define@key[psset]{pst-func}{endAngle}[0]{\pst@getangle{#1}\psk@endAngle} \psset[pst-func]{radiusA=1,radiusB=1,endAngle=0}% startAngle is defined in PSTricks % \def\psLame{\pst@object{psLame}} \def\psLame@i#1{% \leavevmode \pst@killglue \begingroup \addbefore@par{plotpoints=200,startAngle=0,endAngle=360,algebraic=false}% \use@par \parametricplot{\psk@startAngle}{\psk@endAngle}{% 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 } % \def\psWeierstrass{\pst@object{psWeierstrass}} \def\psWeierstrass@i(#1,#2){\@ifnextchar[{\psWeierstrass@ii(#1,#2)}{\psWeierstrass@iii(#1,#2)}} \def\psWeierstrass@ii(#1,#2)[#3]#4{% #1 xStart; #2 xEnd; #3 a; #4 b %% the original definition \addbefore@par{plotpoints=500}% \begin@SpecialObj \psplot{#1}{#2}[/ps@a #3 def /ps@b #4 def]{ /ps@n 0 def /ps@WS 0 def { ps@a ps@n exp ps@b ps@n exp Pi mul x mul RadtoDeg cos mul dup abs \psk@epsilon gt { ps@WS add /ps@WS ED }{ ps@WS add exit } ifelse ps@n 1 add /ps@n ED } loop }% \end@SpecialObj } \def\psWeierstrass@iii(#1,#2)#3{% #1 xStart; #2 xEnd; #3 a \addbefore@par{plotpoints=500}% \begin@SpecialObj \psplot{#1}{#2}[/ps@a #3 def]{ /ps@k 1 def /ps@WS 0 def { ps@k ps@a exp Pi mul dup x mul RadtoDeg sin exch div dup abs \psk@epsilon gt { ps@WS add /ps@WS ED }{ ps@WS add exit } ifelse ps@k 1 add /ps@k ED } loop }% \end@SpecialObj } % % 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[fillstyle=none]{#1}{#2}{#4}% original function \ifPst@algebraic \psplot[fillstyle=none]{#1}{#2}{-(#4)} \else \psplot[fillstyle=none]{#1}{#2}{#4 neg}% mirrored at the x-axis \fi \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 \ifPst@algebraic (#4) AlgParser cvx exec \else #4 \fi 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. \psellipse(#2,0)(!{ #2 dup #1 sub #3 div 2 div sub /x ED \ifPst@algebraic (#4) AlgParser cvx exec \else #4 \fi dup 8 div exch}) % draw again the ellipse to get the borderline. \psset{plotstyle=line,linestyle=dashed, plotpoints=40,dotstyle=*,dotsize=0.5pt} \psplot[fillstyle=none]{#1}{#2}{#4} \ifPst@algebraic \psplot[fillstyle=none]{#1}{#2}{-(#4)} \else \psplot[fillstyle=none]{#1}{#2}{#4 neg}% mirrored at the x-axis \fi % 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 % save 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 pop 0 moveto lineto } if } if % 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} % \define@boolkey[psset]{pst-func}[Pst@]{xory}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{approx}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{Framed}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{Newton}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{PrintCoord}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{onlyNode}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{onlyYVal}[true]{} \define@boolkey[psset]{pst-func}[Pst@]{originV}[true]{} \define@key[psset]{pst-func}{PointName}[I]{\def\psk@func@PointName{#1}} \define@key[psset]{pst-func}{ydecimals}[2]{\pst@getint{#1}\psk@ydecimals } \define@key[psset]{pst-func}{labeldistance}[0]{\def\psk@ldistance{#1 }} \psset[pst-func]{originV=false,onlyNode=false,ydecimals=2,labeldistance=0, PrintCoord=false,onlyYVal=false,Newton=false,PointName=I,Framed=false,xory=false,approx=true} % %-------------------------------------------------------------------- %------------- calculate the value of an intersectionpoint ----------- %--------------------------------------------------------------------- % \def\psZero{\def\pst@par{}\pst@object{psZero}} \def\psZero@i(#1,#2)#3{\@ifnextchar[{\psZero@ii(#1,#2)#3}{\psZero@ii(#1,#2){#3}[0]}} \def\psZero@ii(#1,#2)#3[#4]#5{% % (#1,#2) Intervall f\"{u}r die Nullstelle, bzw #1 Startwert f\"{u}r Newton, #3 1. Funktion, #4 2. Funktion, #5 Knotenname \begingroup \pst@killglue \addbefore@par{labelangle=0,framesep=1pt}%fontscale=40,PSfont=NimbusRomNo9L-Regu}% % labelangle=0 -> take xShift and yShift into account, otherwise xShift=pslabelsep * cos(labelangle) % yShift=pslabelsep * sin(labelangle) \use@par \pst@Verb{ /FunctionA \ifPst@algebraic (#3) tx@AlgToPs begin AlgToPs end cvx \else {#3} \fi def /FunctionB \ifPst@algebraic (#4) tx@AlgToPs begin AlgToPs end cvx \else {#4} \fi def \ifPst@Newton % --------------------------- Newton-Verfahren --- TS 05.2014 /eps 1e-6 def % eps f\"{u}r (f(x+eps)-f(x))/eps /x0 #1 def % Startwert wird vorgegeben /Xend x0 def { /xe x0 eps add def % xe=x+eps /x x0 def % x nun x0 setzen, damit f(x0) berechnet werden kann /func0 FunctionA FunctionB sub def % func0=F(x0)-FB(x0) func0 0 eq {exit} if % wenn func0 = 0 -> exit /x xe def % x xe setzen /func1 FunctionA FunctionB sub def % func1=F(xe)-FB(xe) /Xend x0 func0 eps mul func1 func0 sub div sub def % Xend=x0-(func0*eps)/(func1-func0) /x Xend def % x wird nun Xend /funcend FunctionA FunctionB sub def % funcend=F(Xend)-FB(Xend) funcend abs 1e-6 le {exit} if % Wenn funcend < 1e-6 -> exit /x0 Xend def % sonst x0 = Xend und } loop % die Schleife beginnt mit x0 = Xend /xM Xend def \else % -------------------- Intervallhalbierungsverfahren von Manuel L. /Xinf #1 def % linker Wert des Intervalls, in dem die Nullstelle gesucht wird /Xsup #2 def % linker Wert des Intervalls, in dem die Nullstelle gesucht wird { /xM Xinf Xsup add 2 div def % Mittelwert -> Mitte des Intervalls ist xM2 /x Xinf def % Variable x wird als linker Wert festgelegt /F_1 FunctionA FunctionB sub def % Definition der Differenzfunktion F_1 an der Stelle x=Xinf2 /x xM def % Variable x wird als Mittelwert festgelegt /F_M FunctionA FunctionB sub def % Definition der Differenzfunktion F_M an der Stelle x=xM2 F_M 0 eq {exit} if % Ist F_M = 0 => fertig F_1 F_M mul 0 ge {/Xinf xM def} {/Xsup xM def} ifelse % F_1 * F_M > 0 (F_1 und F_M haben gleiches VZ) => neuer linker x-Wert = xM2 Xinf Xsup sub abs 1e-6 le {exit} if } loop % Die Schleife endet, wenn die Differenz von linkem und rechtem Wert < 10^-6 \fi /x xM def FunctionA /yM exch def % x wird Mittelwert und an dieser Stelle die Funktion berechnet und als yM definiert }% \pnode(! xM yM){#5}% \addto@pscode{% \iftrue %\psFunc@langle pt>\z@ /xShift \psFunc@langle cos \psk@ldistance mul def /yShift \psFunc@langle sin \psk@ldistance mul def \else /xShift \psk@xShift\space def /yShift \psk@yShift\space def \fi \ifPst@onlyNode\else /dec \psk@decimals\space def % Anzahl der Dezimahlen f\"{u}r x /ydec \psk@ydecimals\space def % Anzahl der Dezimalen f\"{u}r y /symb { /StandardSymL findfont \psk@fontscale\space scalefont setfont } bind def % Symbolschrift f\"{u}r Klammer und senkrechten Strich /schrift { \psk@PSfont\space findfont \psk@fontscale scalefont setfont } bind def % Schrift f\"{u}r die Ergebnisse /TiefSchrift { /StandardSymL findfont \psk@fontscale 1.8 div scalefont setfont } bind def % Schrift f\"{u}r tiefergestellte Buchstaben /spdx \psk@fontscale 4 div def % Abstand, der mit der Schriftg\"{o}{\ss}e skaliert ist /spdy \psk@fontscale 15 div def % Abstand, der mit der Schriftg\"{o}{\ss}e skaliert ist /Wert { dec -1 le { /dec 15 def } if 10 dec exp mul round 10 dec exp div dec 0 eq { cvi 15 string cvs } { 15 string cvs } ifelse % x-Wert runden und als string ablegen \ifPst@comma dot2comma \fi show } def % gegebenenfalls Komma statt Punkt und Ergebnis anzeigen /yWert { 10 ydec exp mul round 10 ydec exp div ydec 0 eq { cvi 15 string cvs } { 15 string cvs } ifelse % y-Wert runden und als string ablegen \ifPst@comma dot2comma \fi show } def % gegebenenfalls Komma statt Punkt und Ergebnis anzeigen /FunctionA \ifPst@algebraic (#3) tx@AlgToPs begin AlgToPs end cvx \else {#3} \fi def /FunctionB \ifPst@algebraic (#4) tx@AlgToPs begin AlgToPs end cvx \else {#4} \fi def /frs \pst@number\psframesep def \ifPst@Newton /eps 1e-6 def /x0 #1 def /Xend x0 def { /xe x0 eps add def /x x0 def /func0 FunctionA FunctionB sub def func0 0 eq {exit} if /x xe def /func1 FunctionA FunctionB sub def /Xend x0 func0 eps mul func1 func0 sub div sub def /x Xend def /funcend FunctionA FunctionB sub def funcend abs 1e-6 le {exit} if /x0 Xend def } loop /xM Xend def \else /Xinf #1 def /Xsup #2 def { /xM Xinf Xsup add 2 div def /x Xinf def /F_1 FunctionA FunctionB sub def /x Xsup def /F_2 FunctionA FunctionB sub def /x xM def /F_M FunctionA FunctionB sub def F_M 0 eq {exit} if F_1 F_M mul 0 ge {/Xinf xM def} {/Xsup xM def} ifelse Xinf Xsup sub abs 1e-6 le {exit} if } loop \fi /x xM def FunctionA /yM exch def \ifPst@originV 0 0 \else xM xShift add \pst@number\psxunit mul yM yShift add \pst@number\psyunit mul \fi \pst@usecolor\pslinecolor \ifPst@PrintCoord /xytext { moveto schrift (\psk@func@PointName) show 0 spdy 2 mul neg rmoveto TiefSchrift (\psk@postString) show 0 spdy 3 mul rmoveto symb (\string\050) show 0 spdy neg rmoveto schrift xM Wert spdx 3 div spdy rmoveto symb (\string\174) show spdx 3 div spdy neg rmoveto schrift yM yWert 0 spdy rmoveto symb (\string\051) show } bind def xytext 0 spdy neg rmoveto % ------------------------------------------------------------------------------ TS 03.2017 \ifPst@Framed frs \psk@fontscale 0.15 mul frs add neg rmoveto 0 \psk@fontscale 0.9 mul frs 2 mul add rlineto \ifPst@originV frs neg \psk@fontscale 0.75 mul frs add L \else xM xShift add \pst@number\psxunit mul frs sub yM yShift add \pst@number\psyunit mul \psk@fontscale 0.75 mul add frs add L \fi 0 \psk@fontscale 0.9 mul frs 2 mul add neg rlineto closepath gsave \pst@usecolor\psfillcolor \tx@setTransparency fill grestore \ifx\pslinestyle\@none\else \pst@number\pslinewidth SLW \pst@usecolor\pslinecolor \tx@setStrokeTransparency \@nameuse{psls@\pslinestyle} stroke \fi \ifPst@originV 0 0 \else xM xShift add \pst@number\psxunit mul yM yShift add \pst@number\psyunit mul \fi xytext 0 spdy neg rmoveto \fi %------------------------------ Wenn nicht die Form P(a|b) sondern x = a oder y = b oder nur a oder nur b ------------------- \else \ifPst@originV 0 0 \else xM xShift add \pst@number\psxunit mul yM yShift add \pst@number\psyunit mul \fi /xorytext { moveto schrift \ifPst@onlyYVal% nur der y-Wert \ifPst@xory% in Form von y=b (\psk@func@PointName) show spdx 5 div neg spdy 2.2 mul neg rmoveto TiefSchrift (\psk@postString) show spdx 1.5 div spdy 2 mul rmoveto symb(\ifPst@approx \string \273 \else \string = \fi) show spdx 1.5 div neg 0 rmoveto schrift yM yWert \else schrift yM yWert \fi \else \ifPst@xory% in Form x = a (\psk@func@PointName) show spdx 7 div neg spdy 2.2 mul neg rmoveto TiefSchrift (\psk@postString) show spdx 1.5 div spdy 2 mul rmoveto symb (\ifPst@approx \string \273 \else \string = \fi) show spdx 1.5 div neg 0 rmoveto schrift xM Wert \else schrift xM Wert \fi \fi } bind def xorytext \ifPst@Framed%------------------------------ Rahmenbeginn ------------------------------ frs \psk@fontscale 0.14 mul frs add neg rmoveto 0 \psk@fontscale 0.9 mul frs 2 mul add rlineto \ifPst@originV frs neg \psk@fontscale 0.75 mul frs add L \else xM xShift add \pst@number\psxunit mul frs sub yM yShift add \pst@number\psyunit mul \psk@fontscale 0.75 mul add frs add L \fi 0 \psk@fontscale 0.9 mul frs 2 mul add neg rlineto closepath gsave \pst@usecolor\psfillcolor \tx@setTransparency fill grestore \ifx\pslinestyle\@none\else \pst@number\pslinewidth SLW \pst@usecolor\pslinecolor \tx@setStrokeTransparency \@nameuse{psls@\pslinestyle} stroke \fi \ifPst@originV 0 0 \else xM xShift add \pst@number\psxunit mul yM yShift add \pst@number\psyunit mul \fi xorytext \fi \fi \fi}% \ifPst@markZeros\psdot(#5)\fi \endgroup\use@pscode\ignorespaces }% % \catcode`\@=\PstAtCode\relax % %% END: pst-func.tex \endinput %