path: root/Master/texmf-dist/tex/generic/pstricks-add/pstricks-add.tex

%%
%% This is file `pstricks-add.tex',
%%
%% IMPORTANT NOTICE:
%%
%% Package `pstricks-add.tex'
%%
%% Dominique Rodriguez <Dominique.Rodriguez _at_ waika9.fr>
%% Herbert Voss <Herbert.Voss _at_ pstricks.de>
%%
%% 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:
%%   `pstricks-add' is a PSTricks package for additionals to the standard
%%         pstricks package
%%
\csname PSTricksAddLoaded\endcsname
\let\PSTricksAddLoaded\endinput
%
% Requires some packages
\ifx\PSTricksLoaded\endinput\else\input pstricks \fi
\ifx\PSTplotLoaded\endinput\else\input pst-plot \fi
\ifx\PSTnodesLoaded\endinput\else\input pst-node \fi
\ifx\MultidoLoaded\endinput\else\input multido \fi
\ifx\PSTXKeyLoaded\endinput\else\input pst-xkey \fi
%
\def\fileversion{2.76b}
\def\filedate{2006/07/07}
\message{`pstricks-add' v\fileversion, \filedate\space (dr,hv)}
%
\edef\PstAtCode{\the\catcode`\@} \catcode`\@=11\relax
\SpecialCoor
\pst@addfams{pstricks-add}
%
%% prologue for postcript
\pstheader{pstricks-add.pro}%
%\pstheader{shfill_emulate.pro}%
%
%-------------------------------- pstricks ------------------------------------
%
%%%%%%% \begin{pspicture} %%%%%%%%%%%%%%%%%%%
\newdimen\pst@dimm%
\newdimen\pst@dimn%
\newdimen\pst@dimo%
\newdimen\pst@dimp%
\newcount\pst@cntm%
\newcount\pst@cntn%
\newcount\pst@cnto%
\newcount\pst@cntp%
%\psset{dx=0}%
%\psset{dy=0}%
\newcount\@zero\@zero=0\relax
%
\def\psPiFour{12.566371}
\def\psPiTwo{6.283185}
\def\psPi{3.14159265}
\def\psPiH{1.570796327}
\newdimen\pstRadUnit
\newdimen\pstRadUnitInv
\pstRadUnit=1.047198cm % this is pi/3
\pstRadUnitInv=0.95493cm % this is 3/pi
%
\def\pst@getdimdim#1 #2 #3\@nil{%
  \def\pst@tempA{#2}%
  \ifx\pst@tempA\@empty
    \pssetlength\pst@dimn{#1}%
    \pst@dimm=\z@%
  \else%
    \pssetlength\pst@dimm{#1}%
    \pssetlength\pst@dimn{#2}%
  \fi%
}
\def\pst@getxdimdim#1 #2 #3\@nil{%
  \def\pst@tempA{#2}%
  \ifx\pst@tempA\@empty
    \pssetxlength\pst@dimn{#1}%
    \pst@dimm=\z@
  \else%
    \pssetxlength\pst@dimm{#1}%
    \pssetxlength\pst@dimn{#2}%
  \fi%
}
\def\pst@getydimdim#1 #2 #3\@nil{%
  \def\pst@tempA{#2}
  \ifx\pst@tempA\@empty
    \pssetylength\pst@dimn{#1}
    \pst@dimm=\z@
  \else
    \pssetylength\pst@dimm{#1}%
    \pssetylength\pst@dimn{#2}%
  \fi%
}
%
% A modulo macro for integer values
% \pst@mod{34}{6}\value ==> \value is 4
%
\def\pst@mod#1#2#3{%
  \begingroup%
  \pst@cntm=#1\pst@cntn=#2\relax%
  \pst@cnto=\pst@cntm%
  \divide\pst@cntm by \pst@cntn%
  \multiply\pst@cntn by \pst@cntm%
  \advance\pst@cnto by -\pst@cntn%
  \edef\value{\endgroup\def\noexpand#3{\number\pst@cnto}}\value%
}
\def\pst@max#1#2#3{%
  \begingroup%
  \pst@cntm=#1\pst@cntn=#2\relax%
  \ifnum\pst@cntm<\pst@cntn\pst@cntm=\pst@cntn\fi
  \global#3=\the\pst@cntm%
  \endgroup%
}
\def\pst@maxdim#1#2#3{%
  \begingroup%
  \pst@dimm=#1\pst@dimn=#2\relax%
  \ifdim\pst@dimm<\pst@dimn\pst@dimm=\pst@dimn\fi
  \global#3=\the\pst@dimm%
  \endgroup%
}
\def\pst@abs#1#2{%
  \begingroup%
  \pst@cntm=#1\relax%
  \ifnum\pst@cntm<\z@\pst@cntm=-\pst@cntm\fi%
  \global#2=\the\pst@cntm
  \endgroup%
}
\def\pst@absdim#1#2{%
  \begingroup%
  \pst@dimm=#1\relax%
  \ifdim\pst@dimm<\z@\pst@dimm=-\pst@dimm\fi%
  \global#2=\the\pst@dimm%
  \endgroup%
}
%
%--------------------------------------- small stuff -------------------------------
\def\defineTColor{\@ifnextchar[{\defineTColor@i}{\defineTColor@i[]}}
\def\defineTColor@i[#1]#2#3{%     transparency "colors"
  \def\pst@tempA{#1}%
  \newpsstyle{#2}{%
     fillstyle=vlines,hatchwidth=0.1\pslinewidth,
     hatchsep=1\pslinewidth,hatchcolor=#3}%
  \ifx\pst@tempA\@empty\else\psset{#1}\fi%
}
\defineTColor{TRed}{red}
\defineTColor{TGreen}{green}
\defineTColor{TBlue}{blue}
%
\def\rmultiput{\def\pst@par{}\pst@ifstar{\@ifnextchar[{\rmultiput@i}{\rmultiput@i[]}}}
\def\rmultiput@i[#1]{\begingroup\psset{#1}\rmultiput@ii}
\def\rmultiput@ii#1{\def\@rmultiputArg{#1}%
  \@ifnextchar({\rmultiput@iii}{\rmultiput@iii(\z@,\z@)}}
\def\rmultiput@iii(#1){%
  \pst@killglue%
  \if@star\rput*(#1){\@rmultiputArg}
  \else\rput(#1){\@rmultiputArg}%
  \fi
  \@ifnextchar({\rmultiput@iii}{\endgroup}%
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%    \psrotation(x,y){a}{objet}    %%%
%%% construit l'image de <objet>     %%%
%%% par la rotation de centre (x,y)  %%%
%%% et d'angle a.                    %%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\psrotate{\pst@object{psrotate}} % idea from Jean-C���e Charpentier
\def\psrotate@i(#1,#2)#3#4{%
  \pst@killglue
  \begin@SpecialObj%
  \addto@pscode{%
    #1 \pst@number\psxunit mul #2 \pst@number\psyunit mul translate
    #3 rotate -1 -1 scale 
    #1 \pst@number\psxunit mul #2 \pst@number\psyunit mul translate
    -1 -1 scale
  }%
  #4% 
  \end@SpecialObj%
}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Begin patch TN; Date (YY-MM-DD): 04-07-17; first part
\define@key[psset]{}{dash}{%	defined in pstricks.tex
  \pst@expandafter\psset@@dash{#1}\@nil% Error handling for empty argument.
}
\define@key[psset]{pstricks-add}{maxdashes}{\def\psk@maxdashes{#1}}
%\psset{maxdashes=11}
\def\psset@@dash#1\@nil{%
 \def\psk@dash{}%
 % modification 04-08-07:
 \pst@cntm0
 \def\next##1 ##2\relax{%
   \expandafter\ifnum\psk@maxdashes>\pst@cntm\relax% 04-08-07
   \edef\@tempa{##1}%
   \ifx\@tempa\@empty\else% gobble leading spaces
   \pssetlength\pst@dimc{##1}%
       \advance\pst@cntm by 1
   \edef\psk@dash{\psk@dash\space\pst@number\pst@dimc}%
   \fi%
   \edef\@tempa{##2}%
   \ifx\@tempa\@empty\else% detect end
   \ifx\@tempa\space\else% gobble trailing spaces
     \next##2\relax%
   \fi\fi%
   \else% 04-08-07
     \@pstrickserr{Number of dashes > \psk@maxdashes. Increasing 
        'maxdashes' might work.}\@ehpa% 04-08-07
   \fi% 04-08-07
 }%
\expandafter\next#1 \relax}
%% End patch TN; Date (YY-MM-DD): 04-07-17; 1st part
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\psset{dash=5pt 3pt}% black white black white 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Begin patch TN; Date (YY-MM-DD): 04-07-17; 2nd part
\def\psls@dashed{%
  \ifpsdashadjust
    [ \psk@dash ] \pst@linetype\space \tx@DashLine
  \else
    [ \psk@dash ] 0 setdash stroke
  \fi}
%% End patch TN; Date (YY-MM-DD): 04-07-17; 2nd part
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%-----------------------------------------------------------------------------------
\pst@def{DashLine}<
    dup 0 gt
    { /a .5 def PathLength exch div }
    { pop /a 1 def PathLength } ifelse
    /b ED % pattern should fit evenly in b
    dup /X ED % pattern array
    0 get /y ED % length of first black segment
    /z 0 X {add} forall def % length of the full pattern
    %% Computation of the scaling factor as described by van Zandt:
    b a .5 sub 2 mul y mul sub z Div round
    z mul a .5 sub 2 mul y mul add b exch Div
    %%%% scaling factor on stack.
    /z ED %% now, z is the scaling factor
    false % for the length test below
    X { z mul } forall X astore %% modification TN 04-08-07
    %%% Checking whether at least one dash in X has positive length:
    {0 gt or} forall
    { X 1 a sub y mul }
    { [ 1 0 ] 0 }
    ifelse
    setdash stroke >
%% TN end patch; Date (YY-MM-DD): 04-07-17;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
\define@key[psset]{pstricks-add}{intSeparator}{\def\psk@intSeparator{#1}}
%\psset{intSeparator={,}}
%
\def\psFormatInt{\def\pst@par{}\pst@object{psFormatInt}}
\def\psFormatInt@i#1{{%
  \pst@killglue
  \use@par
  \count1=#1\count2=\count1
  \ifnum\count1=0 0\else
    \ifnum\count1>999999
    \count3=\count1
    \divide\count3 by 1000000
    \the\count3\psk@intSeparator\relax
    \multiply\count3 by 1000000
    \advance\count1 by -\count3 % modulo 1000000
  \fi%
  \ifnum\count2>999
    \count3=\count1
    \divide\count3 by 1000
    \ifnum\count2>99999
	\ifnum\count3<100 0\fi
	\ifnum\count3<10 0\fi
    \fi%
    \the\count3\psk@intSeparator\relax
    \multiply\count3 by 1000
    \advance\count1 by -\count3 %modulo 1000
  \fi%
  \ifnum\count2>999
    \ifnum\count1<100 0\fi
    \ifnum\count1<10 0\fi
  \fi%
  \the\count1
  \fi%
}\ignorespaces}
%
\newdimen\pst@braceWidth
\define@key[psset]{pstricks-add}{braceWidth}{\pssetlength\pst@braceWidth{#1}}
\define@key[psset]{pstricks-add}{bracePos}{\def\psk@bracePos{#1}}
%\psset{braceWidth=10pt,bracePos=0.5}
%
\def\@@rput@iv(#1){\pst@killglue\pst@makebox{\@@rput@v{#1}}}
\def\@@rput@v#1{%
  \begingroup
    \use@par
    \pst@makesmall\pst@hbox
    \pst@Verb{%
      Alpha 90 sub \pst@number\pst@braceWidth  0 lt {180 add} if
      \ifx\psk@rot\@empty\else\psk@rot add \fi
      /rotAngle exch def
    }%
    \setbox\pst@hbox=\hbox{%
      \pst@Verb{rotAngle \tx@RotBegin}%
      \box\pst@hbox\pst@Verb{\tx@RotEnd}%
    }%
    \psput@{#1}\pst@hbox
  \endgroup
  \ignorespaces%
}
%
\def\psbrace{\pst@object{psbrace}}
\def\psbrace@i(#1)(#2)#3{%
  \addbefore@par{ArrowInside=-,linearc=2mm,linewidth=1pt,%
    nodesepA=0pt,nodesepB=0pt,bracePos=0.5}% the default
  \begin@SpecialObj
  \use@par%
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pnode(!%
    /bW2 \pst@number\pst@braceWidth \pst@number\psyunit div 2.0 div def
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /Alpha YB YA sub XB XA sub atan def
    /xMid XB XA sub \psk@bracePos\space mul XA add def
    /yMid YB YA sub \psk@bracePos\space mul YA add def
    /@deltaX Alpha sin bW2 mul def
    /@deltaY Alpha cos bW2 mul def
    /@xTemp xMid @deltaX 2 mul add def
    /@yTemp yMid @deltaY 2 mul sub def
    @xTemp @yTemp){@tempNode}%
  \pst@getcoor{@tempNode}\pst@tempC%
  \@@rput@iv(! %
    \pst@tempC /Yc exch def
    /Xc exch def
    Xc \psk@nodesepA\space add \pst@number\psxunit div
    Yc \psk@nodesepB\space add \pst@number\psyunit div ){#3}
  \psline(#1)%
    (! XA @deltaX add YA @deltaY sub)%
    (! @xTemp @deltaX sub @yTemp @deltaY add)(@tempNode)%
  \psline(@tempNode)%
    (! @xTemp @deltaX sub @yTemp @deltaY add)%
    (! XB @deltaX add YB @deltaY sub)(#2)%
  \end@SpecialObj
  \ignorespaces}
%
% -------------- the arrow part -------------
%  the original table
% \def\pst@arrowtable{,<->,<<->>,>-<,>>-<<,(-),[-],)-(,]-[,|>-<|}
%
% HookLeft/RightArrow
\newdimen\pshooklength
\newdimen\pshookwidth
\define@key[psset]{pstricks-add}{hooklength}{\pssetlength\pshooklength{#1}}
\define@key[psset]{pstricks-add}{hookwidth}{\pssetlength\pshookwidth{#1}}
%\psset{hooklength=3mm,hookwidth=1mm}
%
\edef\pst@arrowtable{\pst@arrowtable,H-H,h-h} % add new arrow
\def\tx@RHook{RHook }         % PostScript name
\def\tx@Rhook{Rhook }         % PostScript name
\@namedef{psas@H}{%
  /RHook {
    /x ED                     % hook width
    /y ED                     % hook length 
    /z CLW 2 div def          % save it
    x y moveto                % goto first point
    x 0 0 0 0 y 
    curveto                   % draw Bezier
    stroke 
    0 y moveto                % define current point
  } def
  \pst@number\pshooklength
  \pst@number\pshookwidth
  \tx@RHook 
}
\@namedef{psas@h}{%
  /Rhook {
    CLW mul 			% size * CLW
    add dup 			% +length  size*CLW+length size*CLW+length 
    2 div /w ED	 		% (size*CLW+length)/2  -> w 
    mul dup /h ED mul 		% (size*CLW+length)
    /a ED  
    w neg h abs moveto 0 0 L 
    gsave 
    stroke grestore 
  } def
  0 \psk@arrowlength \psk@arrowsize \tx@Rhook 
}
% New parameter "arrowfill", with default as "true"
\define@boolkey[psset]{pstricks-add}[ps]{ArrowFill}[true]{}
%
% Modification of the PostScript macro Arrow to choose to fill or not the arrow
% (it require to restore the current linewidth, despite of the scaling)
\pst@def{Arrow}<{%
    CLW mul add dup 2 div
    /w ED mul dup
    /h ED mul
    /a ED { 0 h T 1 -1 scale } if
    gsave
    \ifpsArrowFill\else\pst@number\pslinewidth \pst@arrowscale\space div SLW \fi
    w neg h moveto
    0 0 L w h L w neg a neg rlineto
    \ifpsArrowFill gsave fill grestore \else gsave closepath stroke grestore \fi
    grestore
    0 h a sub moveto
}>
%
\define@key[psset]{pstricks-add}{nArrowsA}{\def\psk@nArrowsA{#1}}
\define@key[psset]{pstricks-add}{nArrowsB}{\def\psk@nArrowsB{#1}}
\define@key[psset]{pstricks-add}{nArrows}{\def\psk@nArrowsA{#1}\def\psk@nArrowsB{#1}}
%\psset{nArrows=2}
%
\@namedef{psas@>>}{%
    \psk@nArrowsA\space 1 sub {
      false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
      0 h a sub T
    } repeat
    gsave
    newpath
    false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
    CP
    grestore
    moveto
}
%
\@namedef{psas@<<}{%
    true \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
    0 h neg a add T
  \psk@nArrowsB\space 2 sub {
    false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
    0 h neg a add T
  } repeat
  false \psk@arrowinset \psk@arrowlength \psk@arrowsize \tx@Arrow
  0 h a 5 mul 2 div sub moveto
}
%
% DG addition begin - Dec. 18/19, 1997 and Oct. 11, 2002
% Adapted from \psset@arrows
  \def\psk@ArrowInside{}
  \define@key[psset]{pstricks-add}{ArrowInside}{%
  \def\pst@tempA{#1}%
  \ifx\pst@tempA\@empty \def\psk@ArrowInside{} %
  \else%
    \begingroup%
      \pst@activearrows%
      \xdef\pst@tempg{<#1}%
    \endgroup%
    \expandafter\psset@@ArrowInside\pst@tempg\@empty-\@empty\@nil%
    \if@pst\else\@pstrickserr{Bad intermediate arrow specification: #1}\@ehpa\fi%
  \fi%
}
% Adapted from \psset@@arrows
\def\psset@@ArrowInside#1-#2\@empty#3\@nil{%
  \@psttrue
  \def\next##1,#1-##2,##3\@nil{\def\pst@tempg{##2}}%
  \expandafter\next\pst@arrowtable,#1-#1,\@nil
  \@ifundefined{psas@#2}%
    {\@pstfalse\def\psk@ArrowInside{}}%
    {\def\psk@ArrowInside{#2}}%
}
% Default value empty
%\psset{ArrowInside={}}
% Modified version of \pst@addarrowdef
\def\pst@addarrowdef{%
  \addto@pscode{%
    /ArrowA {
      \ifx\psk@arrowA\@empty
        \pst@oplineto
      \else
	\pst@arrowdef{A}
	moveto
      \fi
    } def
    /ArrowB { 
      \ifx\psk@arrowB\@empty \else \pst@arrowdef{B} \fi 
    } def
% DG addition
    /ArrowInside { 
      \ifx\psk@ArrowInside\@empty \else \pst@arrowdefA{Inside} \fi 
    } def
  }%
}
% Adapted from \pst@arrowdef
\def\pst@arrowdefA#1{%
  \ifnum\pst@repeatarrowsflag>\z@ 
    /Arrow#1c [ 6 2 roll ] cvx def Arrow#1c 
  \fi   
  \tx@BeginArrow
  \psk@arrowscale
  \@nameuse{psas@\@nameuse{psk@Arrow#1}}
  \tx@EndArrow%
}
% ArrowInsidePos parameter (default value 0.5)
\define@key[psset]{pstricks-add}{ArrowInsidePos}{\pst@checknum{#1}\psk@ArrowInsidePos}%
%\psset{ArrowInsidePos=0.5}
%
% Modified version of \begin@ClosedObj
\def\begin@ClosedObj{%
    \leavevmode
    \pst@killglue
    \begingroup
	\use@par
	\solid@star
	\ifpsdoubleline \pst@setdoublesep \fi
	\pst@addarrowdef% DG addition
	\init@pscode%
}
%
% Redefinition of the PostScript /Line macro to print the intermediate
% arrow on each segment of the line
%
\define@key[psset]{pstricks-add}{ArrowInsideNo}{\pst@checknum{#1}\psk@ArrowInsideNo}% hv 20031001
\define@key[psset]{pstricks-add}{ArrowInsideOffset}{\pst@checknum{#1}\psk@ArrowInsideOffset}% hv 20031001
%\psset{ArrowInsideNo=1,ArrowInsideOffset=0}
%
\def\arrowType@H{H}
\pst@def{Line}<{%
  NArray n 0 eq not { n 1 eq { 0 0 /n 2 def } if
  (\psk@ArrowInside) length 0 gt {
    \ifx\psk@arrowA\arrowType@H   % do we have a Hook arrow at the beginning?
      \pst@number\pshooklength  % yes 
    \else
      \psk@arrowsize\space CLW mul add dup \psk@arrowlength\space mul exch \psk@arrowinset mul neg add  
    \fi
    /arrowlength exch def 
    4 copy 				% copy all four values for the arrow line
    /y1 ED /x1 ED /y2 ED /x2 ED 	% save them
    /Alpha y2 y1 sub x2 x1 sub atan def % the gradient of the line
%    2 copy /y1 ED /x1 ED ArrowA x1 y1  
    ArrowA 				% draw arrowA
    x1 Alpha cos arrowlength mul add	% dx add
    y1 Alpha sin arrowlength mul add	% dy add, to get the current point at the end of the arrow tip
    /n n 1 sub def
    n {
      4 copy
      /y1 ED /x1 ED /y2 ED /x2 ED
      x1 y1
      \psk@ArrowInsidePos\space 1 gt {
        /Alpha y2 y1 sub x2 x1 sub atan def
        /ArrowPos \psk@ArrowInsideOffset\space def
        /Length x2 x1 sub y2 y1 sub Pyth def
        /dArrowPos \psk@ArrowInsidePos\space abs def
        {
          /ArrowPos ArrowPos dArrowPos add def
          ArrowPos Length gt { exit } if
          x1 Alpha cos ArrowPos mul add
          y1 Alpha sin ArrowPos mul add
          ArrowInside
          pop pop
        } loop
      }{
        /ArrowPos \psk@ArrowInsideOffset\space def
        /dArrowPos \psk@ArrowInsideNo 1 gt {%
          1.0 \psk@ArrowInsideNo 1.0 add div
        }{\psk@ArrowInsidePos } ifelse def
          \psk@ArrowInsideNo\space cvi {
            /ArrowPos ArrowPos dArrowPos add def
            x2 x1 sub ArrowPos mul x1 add
            y2 y1 sub ArrowPos mul y1 add
            ArrowInside
            pop pop
          } repeat
      } ifelse
      pop pop Lineto
    } repeat
  }{ ArrowA /n n 2 sub def n { Lineto } repeat } ifelse
  CP 4 2 roll ArrowB L pop pop } if%
}>
%
% Redefinition of the PostScript /Polygon macro to print the intermediate
% arrow on each segment of the line
\pst@def{Polygon}<{%
    NArray n 2 eq { 0 0 /n 3 def } if
    n 3 lt {
	n { pop pop } repeat
    }{
	n 3 gt { CheckClosed } if
	n 2 mul	-2 roll
	/y0 ED
	/x0 ED
    	/y1 ED
    	/x1 ED
    	/xx1 x1 def
    	/yy1 y1 def
    	x1 y1
    	/x1 x0 x1 add 2 div def
    	/y1 y0 y1 add 2 div def
    	x1 y1 moveto
    	/n n 2 sub def
	/drawArrows {
	    x11 y11
	    \psk@ArrowInsidePos\space 1 gt {
		/Alpha y12 y11 sub x12 x11 sub atan def
		/ArrowPos \psk@ArrowInsideOffset\space def
		/Length x12 x11 sub y12 y11 sub Pyth def
		/dArrowPos \psk@ArrowInsidePos\space abs def
		{
		    /ArrowPos ArrowPos dArrowPos add def
		    ArrowPos Length gt { exit } if
		    x11 Alpha cos ArrowPos mul add
		    y11 Alpha sin ArrowPos mul add
		    currentdict /ArrowInside known { ArrowInside } if
		    pop pop
		} loop
	    }{
		/ArrowPos \psk@ArrowInsideOffset\space def
		/dArrowPos \psk@ArrowInsideNo\space 1 gt {%
	    	    1.0 \psk@ArrowInsideNo\space 1.0 add div
		}{ \psk@ArrowInsidePos } ifelse def
		\psk@ArrowInsideNo\space cvi {
		    /ArrowPos ArrowPos dArrowPos add def
		    x12 x11 sub ArrowPos mul x11 add
		    y12 y11 sub ArrowPos mul y11 add
		    currentdict /ArrowInside known { ArrowInside } if
		    pop pop
		} repeat
	    } ifelse
	    pop pop Lineto
	} def
	n {
	    4 copy
	    /y11 ED /x11 ED /y12 ED /x12 ED
	    drawArrows
	} repeat
	x1 y1 x0 y0
	6 4 roll
	2 copy
	/y11 ED /x11 ED /y12 y0 def /x12 x0 def
	drawArrows
	/y11 y0 def /x11 x0 def /y12 yy1 def /x12 xx1 def
	drawArrows
	pop pop
    	closepath
    } ifelse %
}>
%
%
% Redefinition of the PostScript /OpenBezier macro to print the intermediate
% arrow
\pst@def{OpenBezier}<{%
  /dArrowPos \psk@ArrowInsideNo 1 gt {%
    1.0 \psk@ArrowInsideNo 1.0 add div
    }{ \psk@ArrowInsidePos } ifelse def
      BezierNArray
      n 1 eq { pop pop
      }{ 2 copy
        /y0 ED /x0 ED
        ArrowA
        n 4 sub 3 idiv { 6 2 roll 4 2 roll curveto } repeat
        6 2 roll
        4 2 roll
        ArrowB
        /y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED
        /cx x1 x0 sub 3 mul def
        /cy y1 y0 sub 3 mul def
        /bx x2 x1 sub 3 mul cx sub def
        /by y2 y1 sub 3 mul cy sub def
        /ax x3 x0 sub cx sub bx sub def
        /ay y3 y0 sub cy sub by sub def
        /getValues {
          ax t0 3 exp mul bx t0 t0 mul mul add cx t0 mul add x0 add
          ay t0 3 exp mul by t0 t0 mul mul add cy t0 mul add y0 add
          ax t 3 exp mul bx t t mul mul add cx t mul add x0 add
          ay t 3 exp mul by t t mul mul add cy t mul add y0 add
        } def
        /getdL {
          getValues
          3 -1 roll sub 3 1 roll sub Pyth
        } def
        /CurveLength {
          /u 0 def
          /du 0.01 def
          0 100 {
            /t0 u def
            /u u du add def
            /t u def
            getdL add
          } repeat } def
          /GetArrowPos {
            /ende \psk@ArrowInsidePos\space 1 gt
              {ArrowPos}
              {ArrowPos CurveLength mul} ifelse def
            /u 0 def
            /du 0.01 def
            /sum 0 def
            { /t0 u def
              /u u du add def
              /t u def
              /sum getdL sum add def
              sum ende gt {exit} if
            } loop u
          } def
          /ArrowPos \psk@ArrowInsideOffset\space def
          /loopNo \psk@ArrowInsidePos\space 1 gt {%
            CurveLength \psk@ArrowInsidePos\space div cvi
          }{ \psk@ArrowInsideNo } ifelse def
            loopNo cvi {
              /ArrowPos ArrowPos dArrowPos add def
              /t GetArrowPos def
              /t0 t 0.95 mul def
              getValues
              ArrowInside pop pop pop pop
            } repeat
            x1 y1 x2 y2 x3 y3 curveto
  } ifelse
}>
%
% Redefinition of the PostScript /NCLine macro to print the intermediate
% arrow of the line
\pst@def{NCLine}<{%
	NCCoor
	tx@Dict begin
	ArrowA CP 4 2 roll ArrowB
	4 copy
	/y2 ED /x2 ED /y1 ED /x1 ED
	x1 y1
	\psk@ArrowInsidePos\space 1 gt {
		/Alpha y2 y1 sub x2 x1 sub atan def
		/ArrowPos \psk@ArrowInsideOffset\space def
		/Length x2 x1 sub y2 y1 sub Pyth def
		/dArrowPos \psk@ArrowInsidePos\space abs def
		{%
			/ArrowPos ArrowPos dArrowPos add def
			ArrowPos Length gt { exit } if
			x1 Alpha cos ArrowPos mul add
			y1 Alpha sin ArrowPos mul add
			ArrowInside
			pop pop
		} loop
	}{%
		/ArrowPos \psk@ArrowInsideOffset\space def
		/dArrowPos \psk@ArrowInsideNo 1 gt {%
			1.0 \psk@ArrowInsideNo 1.0 add div
		}{ \psk@ArrowInsidePos } ifelse def
		\psk@ArrowInsideNo\space cvi {
			/ArrowPos ArrowPos dArrowPos add def
			x2 x1 sub ArrowPos mul x1 add
			y2 y1 sub ArrowPos mul y1 add
			ArrowInside
			pop pop
		} repeat
	} ifelse
	pop pop lineto pop pop
	end%
}>
%
\pst@def{NCCurve}<{%
	GetEdgeA GetEdgeB
	xA1 xB1 sub yA1 yB1 sub
	Pyth 2 div dup 3 -1 roll mul
	/ArmA ED
	mul
	/ArmB ED
	/ArmTypeA 0 def
	/ArmTypeB 0 def
	GetArmA GetArmB
	xA2 yA2 xA1 yA1
	2 copy
	/y0 ED /x0 ED
	tx@Dict begin
		ArrowA
	end
	xB2 yB2 xB1 yB1
	tx@Dict begin
		ArrowB
	end
	/y3 ED /x3 ED /y2 ED /x2 ED /y1 ED /x1 ED
	/cx x1 x0 sub 3 mul def
	/cy y1 y0 sub 3 mul def
	/bx x2 x1 sub 3 mul cx sub def
	/by y2 y1 sub 3 mul cy sub def
	/ax x3 x0 sub cx sub bx sub def
	/ay y3 y0 sub cy sub by sub def
	/getValues {
		ax t0 3 exp mul bx t0 t0 mul mul add cx t0 mul add x0 add
		ay t0 3 exp mul by t0 t0 mul mul add cy t0 mul add y0 add
		ax t 3 exp mul bx t t mul mul add cx t mul add x0 add
	ay t 3 exp mul by t t mul mul add cy t mul add y0 add
	} def
	/getdL {
		getValues
		3 -1 roll sub 3 1 roll sub Pyth
	} def
	/CurveLength {
		/u 0 def
		/du 0.01 def
		0 100 {
			/t0 u def
			/u u du add def
			/t u def
			getdL add
		} repeat } def
	/GetArrowPos {
		/ende \psk@ArrowInsidePos\space 1 gt {ArrowPos}{ArrowPos CurveLength mul} ifelse def
		/u 0 def
		/du 0.01 def
		/sum 0 def
		{
			/t0 u def
			/u u du add def
			/t u def
			/sum getdL sum add def
			sum ende gt {exit} if
		} loop u
	} def
	/dArrowPos \psk@ArrowInsideNo 1 gt {%
		1.0 \psk@ArrowInsideNo 1.0 add div
	}{ \psk@ArrowInsidePos } ifelse def
	/ArrowPos \psk@ArrowInsideOffset\space def
	/loopNo \psk@ArrowInsidePos\space 1 gt {%
		CurveLength \psk@ArrowInsidePos\space div cvi
		}{ \psk@ArrowInsideNo } ifelse def
	loopNo cvi {
		/ArrowPos ArrowPos dArrowPos add def
		/t GetArrowPos def
		/t0 t 0.95 mul def
		getValues
		ArrowInside pop pop pop pop
	} repeat
	x1 y1 x2 y2 x3 y3 curveto
	/LPutVar [ xA1 yA1 xA2 yA2 xB2 yB2 xB1 yB1 ] cvx def
	/LPutPos { t LPutVar BezierMidpoint } def
	/HPutPos { { HPutLines } HPutCurve } def
	/VPutPos { { VPutLines } HPutCurve } def
}>
%
%\def\psDashColorI{black}
%\def\psDashColorII{red}
\define@key[psset]{pstricks-add}{dashColorI}{\pst@getcolor{#1}\psDashColorI}
\define@key[psset]{pstricks-add}{dashColorII}{\pst@getcolor{#1}\psDashColorII}
\define@key[psset]{pstricks-add}{dashNo}{\def\psk@dashNo{#1}}
%
\define@key[psset]{pstricks-add}{linecap}{\def\psk@linecap{#1}}
%\psset{dashColorI=black,dashColorII=red,dashNo=0.2,linecap=0}
%
\pst@def{LineII}<{%
  NArray
  /n n 1 sub def
  /y1 ED /x1 ED x1 y1 ArrowA x1 y1 moveto
  \psk@linecap\space 3 gt
    {\psk@linecap\space 0 lt {0 setlinecap} if }
    {\psk@linecap\space setlinecap} ifelse
  n {
    /y2 ED /x2 ED
    /y0 y1 def /x0 x1 def
    /length x2 x1 sub y2 y1 sub Pyth def
    \psk@dashNo\space 1.0 lt
      {/cntMax 1.0 \psk@dashNo\space div .49 add cvi def}
      {/cntMax length \psk@dashNo\space div .49 add cvi def} ifelse
    x2 x1 sub cntMax div /dx ED
    y2 y1 sub cntMax div /dy ED
    /cnt 0 def
    cntMax {
      gsave
      /x1 x1 dx add def
      /y1 y1 dy add def
      x1 y1
      cnt 2 mod 0 eq
        { \pst@usecolor\psDashColorI }
	{ \pst@usecolor\psDashColorII } ifelse
      lineto stroke
      /cnt cnt 1 add def
      grestore
      x1 y1 moveto
    } repeat
    /y1 y2 def /x1 x2 def
  } repeat
  x0 y0 x2 y2 ArrowB L pop pop
}>
%
\def\pslineII{\pst@object{pslineII}}
\def\pslineII@i{%
    \pst@getarrows{%
        \begin@OpenObj
        \pst@getcoors[\pslineII@ii%
    }%
}
\def\pslineII@ii{%
  \addto@pscode{%
    \pst@cp
    \ifshowpoints true \else false \fi
    \tx@LineII
  }%
  \end@OpenObj%
}
%
\define@key[psset]{pstricks-add}{randomPoints}{\def\psk@randomPoints{#1}}
\define@boolkey[psset]{pstricks-add}[Pst@]{color}[true]{}
%\psset{randomPoints=1000,color=false}
%
\def\psRandom{\pst@object{psRandom}}%  hv  2004-11-12
\def\psRandom@i{\@ifnextchar({\psRandom@ii}{\psRandom@iii(0,0)(1,1)}}
\def\psRandom@ii(#1){\@ifnextchar({\psRandom@iii(#1)}{\psRandom@iii(0,0)(#1)}}
\def\psRandom@iii(#1)(#2)#3{%
  \def\pst@tempA{#3}%
  \ifx\pst@tempA\pst@empty\psclip{\psframe(#2)}\else\psclip{#3}\fi
  \pst@getcoor{#1}\pst@tempA 
  \pst@getcoor{#2}\pst@tempB 
  \begin@SpecialObj
  \addto@pscode{
    \pst@tempA\space /yMin exch def 
    /xMin exch def
    \pst@tempB\space /yMax exch def 
    /xMax exch def 
    /dy yMax yMin sub def
    /dx xMax xMin sub def
    rrand srand                 % initializes the random generator
    /getRandReal { rand 2147483647 div } def
    \psk@dotsize % defines /DS ... def
    \@nameuse{psds@\psk@dotstyle}
    \psk@randomPoints {
     \ifPst@color getRandReal getRandReal getRandReal setrgbcolor \fi
     getRandReal dx mul xMin add
     getRandReal dy mul yMin add
     Dot
     \ifx\psk@fillstyle\psfs@solid fill \fi stroke
    } repeat
  }%
  \end@SpecialObj
  \endpsclip
  \ignorespaces
}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%                pst-node                          %%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% This fixes a bug in pst-node, where the XY-direction is wrong
% the types are changed 1<->2 between X<->Y
%
\define@key[psset]{}{XnodesepA}{%
    \pst@getlength{#1}\psk@nodesepA
    \def\psk@nodeseptypeA{2 }%
}
\define@key[psset]{}{XnodesepB}{%
    \pst@getlength{#1}\psk@nodesepB
    \def\psk@nodeseptypeB{2 }%
}
\define@key[psset]{}{Xnodesep}{%
    \pst@getlength{#1}\psk@nodesepA
    \let\psk@nodesepB\psk@nodesepA
    \def\psk@nodeseptypeA{2 }%
    \def\psk@nodeseptypeB{2 }%
}
\define@key[psset]{}{YnodesepA}{%
    \pst@getlength{#1}\psk@nodesepA
    \def\psk@nodeseptypeA{1 }%
}
\define@key[psset]{}{YnodesepB}{%
    \pst@getlength{#1}\psk@nodesepB
    \def\psk@nodeseptypeB{1 }%
}
\define@key[psset]{}{Ynodesep}{%
    \pst@getlength{#1}\psk@nodesepA
    \let\psk@nodesepB\psk@nodesepA
    \def\psk@nodeseptypeA{1 }%
    \def\psk@nodeseptypeB{1 }%
}
%
\pst@def{NCLineII}<{
  NCCoor
  /y1 ED /x1 ED x1 y1 ArrowA x1 y1 moveto
  /y2 ED /x2 ED
  /y0 y1 def /x0 x1 def
  /length x2 x1 sub y2 y1 sub Pyth def
  \psk@dashNo\space 1.0 lt
     {/cntMax 1.0 \psk@dashNo\space div .49 add cvi def}
     {/cntMax length \psk@dashNo\space div .49 add cvi def} ifelse
  x2 x1 sub cntMax div /dx ED
  y2 y1 sub cntMax div /dy ED
  /cnt 0 def
  cntMax {
    gsave
    /x1 x1 dx add def
    /y1 y1 dy add def
    x1 y1
    cnt 2 mod 0 eq
      { \pst@usecolor\psDashColorI }
      { \pst@usecolor\psDashColorII } ifelse
    lineto stroke
    /cnt cnt 1 add def
    grestore
    x1 y1 moveto
  } repeat
  x0 y0 x2 y2 ArrowB L pop pop%
}>
%
\def\nclineII{\pst@object{nclineII}}%
\def\nclineII@i{\check@arrow{\nclineII@ii}}%
\def\nclineII@ii#1#2{\nc@object{Open}{#1}{#2}{.5}%
    {\tx@NCLineII /LPutPos { xB yB xA yA \tx@LPutLine } def}%
}%
\def\pclineII{\pst@object{pclineII}}%
\def\pclineII@i{\pc@object\nclineII@ii}%
%
\define@key[psset]{pstricks-add}{lineAngle}{\psset{armB=0.5}\def\psk@lineAngle{#1}}%
%\psset{lineAngle=0}%
%
\pst@def{NCDiag}<{
  GetEdgeA GetEdgeB GetArmA GetArmB mark
  \psk@lineAngle\space abs 0 gt {
    /xTemp xA2 10 add def
    /yTemp yA2 \psk@lineAngle\space dup sin exch cos div 10 mul add def
    /dY1 yTemp yA2 sub def
    /dX1 xTemp xA2 sub def
    /dY2 yB2 yB1 sub def
    /dX2 xB2 xB1 sub def
    dX1 abs 0.01 lt {
      /m2 dY2 dX2 div def
      /xB2 xA2 def
      /yB2 xA2 xB1 sub m2 mul yB1 add def
    }{
      dX2 abs 0.01 lt {
        /m1 dY1 dX1 div def
        /xB2 xB1 def
        /yB2 xB1 xA2 sub m1 mul yA2 add def
      }{%
        /m1 dY1 dX1 div def
        /m2 dY2 dX2 div def
        /xB2 m1 xA2 mul m2 xB1 mul sub yA2 sub yB1 add m1 m2 sub div def
        /yB2 xB2 xA2 sub m1 mul yA2 add def
      } ifelse
    } ifelse
  } if
  ArmB 0 ne { xB1 yB1 } if
  xB2 yB2
  xA2 yA2
  ArmA 0 ne { xA1 yA1 } if
  tx@Dict begin false Line end
  /LPutVar [ xB1 yB1 xB2 yB2 xA2 yA2 xA1 yA1 ] cvx def
  /LPutPos { LPutLines } def
  /HPutPos { HPutLines } def
  /VPutPos { VPutLines } def
}>
% hv 2003-12-22
\pst@def{NCDiagg}<{
  GetEdgeA GetArmA \psk@lineAngle\space abs 0 gt { \psk@lineAngle\space }
    { yB yA2 sub xB xA2 sub Atan 180 add } ifelse /AngleB ED
  GetEdgeB mark
  \psk@lineAngle\space abs 0 gt {
    /dY2 yA2 yA1 sub def
    /dX2 xA2 xA1 sub def
    \psk@lineAngle\space abs 90 eq {
      /m2 dY2 dX2 div def
      /yA2 xB xA2 sub m2 mul yA2 add def
      /xA2 xB def
    }{
      /m1 \psk@lineAngle\space dup sin exch cos div def % tan alpha
      dX2 abs 0.01 lt {
        /yA2 xA1 xB sub m1 mul yB add def
        /xA2 xA1 def
      }{%
        /m2 dY2 dX2 div def
        /xA2 m1 xB mul m2 xA2 mul sub yA2 add yB sub m1 m2 sub div def
        /yA2 xA2 xB sub m1 mul yB add def
      } ifelse
    } ifelse
  } if
  xB1 yB1 xA2 yA2
  ArmA 0 ne { xA1 yA1 } if
  tx@Dict begin false Line end
  /LPutVar [ xB1 yB1 xA2 yA2 xA1 yA1 ] cvx def
  /LPutPos { LPutLines } def
  /HPutPos { HPutLines } def
  /VPutPos { VPutLines } def
}>
%
\def\ncbarr{\pst@object{ncbarr}}
\def\ncbarr@i#1#2{
  \begingroup
  \use@par%
  \psLNode(#1)(#2){0.5}{barr@tempNode}%
  \pst@dimm=\psk@angleA pt
  \pst@dimn=180pt
  % be sure, that angleA is 0 or 180. if not, we set it to 0
  \ifdim\pst@dimm=\z@\else\ifdim\pst@dimm=\pst@dimn\else\psset{angleA=0}\fi\fi
  \ncbar[arrows=-]{#1}{barr@tempNode}
  \ifdim\psk@angleA pt=\z@\relax
    \ncbar[angleA=180,angleB=180]{barr@tempNode}{#2}
  \else\ncbar[angleA=0,angleB=0]{barr@tempNode}{#2}\fi%
  \endgroup
}
%   #1-------#4----------------#2
% where #1#4= #3 * #1#2
%
\def\psLNode(#1)(#2)#3#4{%
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pnode(!%
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /dx XB XA sub def
    /dy YB YA sub def
    XA dx #3\space mul add YA dy #3\space mul add){#4}
}
%
% build the linear combination #2*#1+#4*#3=#5
\def\psLCNode(#1)#2(#3)#4#5{%
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#3}\pst@tempB%
  \pnode(!%
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    XA #2\space mul XB #4\space mul add
    YA #2\space mul YB #4\space mul add){#5}%
}
%
%
\define@boolkey[psset]{pstricks-add}[Pst@]{trueAngle}[true]{}
%\psset{trueAngle=false}
%
\def\psRelNode{\pst@object{psRelNode}}
\def\psRelNode@i(#1)(#2)#3#4{{% A - B - factor - node name
  \use@par
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pnode(!
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /AlphaStrich \psk@angleA\space def
    /unit \pst@number\psyunit \pst@number\psxunit div def % yunit/xunit
%            
    /dx XB XA sub  def
    /dy YB YA sub \ifPst@trueAngle\space unit mul \fi\space def
    /laenge dy dup mul dx dup mul add sqrt #3 mul def
    /Alpha dy dx atan def 
    /beta Alpha AlphaStrich add def
    laenge beta cos mul XA add
    laenge beta sin mul \ifPst@trueAngle\space unit div \fi\space YA add ){#4}%
}}
%
\def\psRelLine{\pst@object{psRelLine}}
\def\psRelLine@i{\@ifnextchar({\psRelLine@iii}{\psRelLine@ii}}
\def\psRelLine@ii#1{%
  \addto@par{arrows=#1}%
  \psRelLine@iii%
}
\def\psRelLine@iii(#1)(#2)#3#4{{
  \pst@killglue
  \use@par
  \psRelNode(#1)(#2){#3}{#4}
  \psline(#1)(#4)%
}\ignorespaces}
%
% #1 options
% draw a parallel line to #2 #3
%     #2---------#3
%         #4----------#5(new node)
% #5 length of the line
% #6 node name
\def\psParallelLine{\pst@object{psParallelLine}}
\def\psParallelLine@i{\@ifnextchar({\psParallelLine@iii}{\psParallelLine@ii}}
\def\psParallelLine@ii#1{%
  \addto@par{arrows=#1}%
  \psParallelLine@iii%
}
\def\psParallelLine@iii(#1)(#2)(#3)#4#5{{
  \pst@killglue
  \use@par
  \pst@getcoor{#1}\pst@tempA
  \pst@getcoor{#2}\pst@tempB
  \pst@getcoor{#3}\pst@tempC
%  \pst@getlength{#4}\pst@dima
  \pnode(!%
     \pst@tempA /YA exch \pst@number\psyunit div def
     /XA exch \pst@number\psxunit div def
     \pst@tempB /YB exch \pst@number\psyunit div def
     /XB exch \pst@number\psxunit div def
     \pst@tempC /YC exch \pst@number\psyunit div def
     /XC exch \pst@number\psxunit div def
%            
    /dx XB XA sub  def
    /dy YB YA sub  def
    /laenge dy dup mul dx dup mul add sqrt #4 mul def
    /Alpha dy dx atan def 
    laenge Alpha cos mul XC add
    laenge Alpha sin mul YC add ){#5}%
  \psline(#3)(#5)
}\ignorespaces}
%
\def\psIntersectionPoint(#1)(#2)(#3)(#4)#5{%
    \pst@getcoor{#1}\pst@tempA
    \pst@getcoor{#2}\pst@tempB
    \pst@getcoor{#3}\pst@tempC
    \pst@getcoor{#4}\pst@tempd
\pnode(!%
     \pst@tempA /YA exch \pst@number\psyunit div def
     /XA exch \pst@number\psxunit div def
     \pst@tempB /YB exch \pst@number\psyunit div def
     /XB exch \pst@number\psxunit div def
     \pst@tempC /YC exch \pst@number\psyunit div def
     /XC exch \pst@number\psxunit div def
     \pst@tempd /YD exch \pst@number\psyunit div def
     /XD exch \pst@number\psxunit div def
    /dY1 YB YA sub def
    /dX1 XB XA sub def
    /dY2 YD YC sub def
    /dX2 XD XC sub def
    dX1 abs 0.01 lt {
        /m2 dY2 dX2 div def
        XA dup XC sub m2 mul YC add
    }{
        dX2 abs 0.01 lt {
            /m1 dY1 dX1 div def
            XC dup XA sub m1 mul YA add
        }{%
            /m1 dY1 dX1 div def
            /m2 dY2 dX2 div def
            m1 XA mul m2 XC mul sub YA sub YC add m1 m2 sub div dup
            XA sub m1 mul YA add
        } ifelse
    } ifelse ){#5}%
}
%
\def\psLDNode(#1)(#2)#3#4{%  
% #1: node A  #2: node B  #3: dimen measured from A  #4: node name
  \pst@getcoor{#1}\pst@tempA%
  \pst@getcoor{#2}\pst@tempB%
  \pssetlength\pst@dima{#3}%
  \pnode(!%
    \pst@tempA /YA exch \pst@number\psyunit div def
    /XA exch \pst@number\psxunit div def
    \pst@tempB /YB exch \pst@number\psyunit div def
    /XB exch \pst@number\psxunit div def
    /dx XB XA sub def
    /dy YB YA sub def
    /angle dy dx Atan def
    /length \pst@number\pst@dima \pst@number\psunit div def
    XA length angle cos mul add YA length angle sin mul add ){#4}%
}
\def\nlput{\pst@object{nlput}}
\def\nlput@i(#1)(#2)#3#4{%
  \begin@SpecialObj
  \psLDNode(A)(B){#3}{@temp@lnput}
  \pcline[linestyle=none](#1)(@temp@lnput)%
  \ncput[npos=1]{#4}%
  \end@SpecialObj
} %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%                pst-plot                          %%%%%%%%%%
%%%%%%%%%%%                                                  %%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
\define@key[psset]{pstricks-add}{labelFontSize}{\def\psk@labelFontSize{#1}}%
\psset{labelFontSize={}}
\def\pshlabel#1{\psk@labelFontSize$#1$}%
\def\psvlabel#1{\psk@labelFontSize$#1$}
%
\define@boolkey[psset]{pstricks-add}[Pst@]{comma}[true]{}
%
\define@boolkey[psset]{pstricks-add}[Pst@]{xAxis}[true]{}
\define@boolkey[psset]{pstricks-add}[Pst@]{yAxis}[true]{}
%\define@boolkey[psset]{pstricks-add}[Pst@]{xAxis}[true]{\@nameuse{Pst@xAxis#1}}
%\define@boolkey[psset]{pstricks-add}[Pst@]{yAxis}[true]{\@nameuse{Pst@yAxis#1}}
\define@boolkey[psset]{pstricks-add}[Pst@]{xyAxes}[true]{%
    \@nameuse{Pst@xAxis#1}\@nameuse{Pst@yAxis#1}}%
%\psset{xyAxes=true}%
%
\define@key[psset]{pstricks-add}{xyDecimals}{\def\psk@xDecimals{#1}\def\psk@yDecimals{#1}}
\define@key[psset]{pstricks-add}{xDecimals}{\def\psk@xDecimals{#1}}
\define@key[psset]{pstricks-add}{yDecimals}{\def\psk@yDecimals{#1}}
%\psset{xyDecimals={}}%
%
\define@key[psset]{pstricks-add}{xlogBase}{\def\psk@xlogBase{#1}}
\define@key[psset]{pstricks-add}{ylogBase}{\def\psk@ylogBase{#1}}
\define@key[psset]{pstricks-add}{xylogBase}{\def\psk@xlogBase{#1}\def\psk@ylogBase{#1}}%
%\psset{xylogBase={}}%
%
\define@key[psset]{pstricks-add}{trigLabelBase}{\pst@getint{#1}{\psk@trigLabelBase}}
\psset{trigLabelBase=0}

\define@boolkey[psset]{pstricks-add}[Pst@]{trigLabels}[true]{%
  \ifPst@trigLabels
    \def\pst@@@hlabel##1{\pshlabel{##1}}
    \def\pshlabel##1{%
      \ifnum\psk@trigLabelBase<2
        \def\de@nominator{\@ne}\else\def\de@nominator{\psk@trigLabelBase}\fi
      \def\pst@tempA{##1} 
      \pst@abs{\pst@tempA}\pst@cntm 
      \pst@mod{\pst@cntm}{\de@nominator}\pst@cntp % cntb=##1 modulo trigLabelBase
      \ifnum\@ne>\pst@cntp                  % 1 > modulo -> then we have pi/x
        \pst@cnto=\pst@cntm \divide\pst@cnto by \de@nominator  
        \psk@labelFontSize
	\ifnum\pst@tempA<0 $-$\fi%
        \ifnum\pst@cnto=\@ne                % #1 = trigLabelBase
          $\pi$                             % print pi
        \else
          $\the\pst@cnto\pi$                % print \pst@cnto/\de@nominator pi
        \fi   
      \else
        \ifnum\pst@cntp=\@ne                % < 1 pi?
          \if\pst@cntm=\@ne
            $\frac{\pi}{\de@nominator}$   % pi/x
          \else\ifnum\pst@tempA=-1 $\frac{-\pi}{\de@nominator}$
             \else \ifnum\pst@tempA=1 $\frac{\pi}{\de@nominator}$
                 \else$\frac{\pst@tempA\pi}{\de@nominator}$  % (x pi)/y
          \fi\fi\fi
        \else
          \ifnum\pst@tempA=1 $\frac{\pi}{\de@nominator}$
          \else\ifnum\pst@tempA=\de@nominator $\pi$
            \else$\frac{\pst@tempA\pi}{\de@nominator}$ 
      \fi\fi\fi\fi%
    }%
  \else
    \def\pst@@@hlabel##1{%
      \edef\@xyDecimals{\psk@xDecimals}%
      \ifnum\psk@ticks<\tw@ % ticks=all|x
        \ifx\psk@xlogBase\@empty
          \pshlabel{\psk@labelFontSize\expandafter\@LabelComma##1..\@nil\psk@xlabelFactor}%
        \else%
          \pshlabel{\psk@labelFontSize\psk@xlogBase\textsuperscript{\expandafter\@stripDecimals##1..\@nil }}
        \fi%
      \fi%
    }
    \def\pshlabel##1{\psk@labelFontSize$##1$}%
  \fi
}
\psset{trigLabels=false}
%
%logLines=all|x|y|none  (0,1,2,3)
\define@key[psset]{pstricks-add}{logLines}{\pst@expandafter\psset@@logLines{#1}\@nil\psk@logLines}
\def\psset@@logLines#1#2\@nil#3{%
  \ifx#1a\let#3\z@\else
    \ifx#1x\let#3\@ne\else
      \ifx#1y\let#3\tw@\else
        \ifx#1n\let#3\thr@@\else
          \@pstrickserr{Bad argument: `#1#2'}\@ehpa
  \fi\fi\fi\fi}
%\psset{logLines=none}%
%
% Define "ticklines" parameter (ticklines=all|x|y|none with default=none)
%\def\psset@ticklines#1{\pst@expandafter\psset@@ticklines{#1}\@nil\psk@ticklines}
%\psset@ticklines{none}
\define@key[psset]{pstricks-add}{ylabelFactor}{\def\psk@ylabelFactor{#1}}
\define@key[psset]{pstricks-add}{xlabelFactor}{\def\psk@xlabelFactor{#1}}
%\psset{xlabelFactor=\relax,ylabelFactor=\relax}%
% The parameter styles for the tick lines
% (default=arrows=-,linestyle=dotted,dotsep=5pt)
%\newpsstyle{ticklinesXStyle}{arrows=-,linestyle=dotted,dotsep=5pt}
%\newpsstyle{ticklinesYStyle}{arrows=-,linestyle=dotted,dotsep=5pt}
%
%
%% #1 integer
%% #2 decimals
%% #3 dot
\def\@stripDecimals#1.#2.#3\@nil{%
  \def\dummy{#1}%
  \ifx\dummy\@empty\the\@zero\else#1\fi% the integer part
}
%
\def\pst@@@vlabel#1{%
  \edef\@xyDecimals{\psk@yDecimals}%
%  \psk@yLabel%
  \ifodd\psk@ticks  % ticks=all||y (0,2)
  \else
    \ifx\psk@ylogBase\@empty
%      \ifPst@comma
       \psvlabel{\expandafter\@LabelComma#1..\@nil\psk@ylabelFactor}%
%      \else\psvlabel{#1\psk@ylabelFactor}\fi%
    \else%
      \psvlabel{\psk@ylogBase\textsuperscript{\expandafter\@stripDecimals#1..\@nil }}
    \fi%
  \fi%
}
\newcount\@digitcounter\@digitcounter=0\relax
\def\@inc@digitcounter{\global\advance\@digitcounter by 1\relax}
\def\@get@digitcounter{\the\@digitcounter\relax}
\def\@Reset@digitcounter{\global\@digitcounter=0\relax}
\def\@zeroFill{%
  \ifnum \@xyDecimals>\@get@digitcounter
    \bgroup
      0\@inc@digitcounter\@zeroFill
    \egroup%
  \fi%
}
% #1 the value, maybe empty
%
\def\@process@digits#1#2;{%
	\ifx *#1\@zeroFill\else#1\@inc@digitcounter\@process@digits#2;\fi%
}
\def\@writeDecimals#1{%
  \ifx\@xyDecimals\@empty% take value as is
    \def\@tempa{#1}% write only if not empty
    \ifx\@tempa\@empty% write nothing
    \else
      \ifPst@comma{,}\else.\fi%
      #1%
    \fi%
  \else% write only \xy@decimals
    \ifnum\@xyDecimals>\@zero
      \ifPst@comma{,}\else.\fi
        \@Reset@digitcounter
        \@process@digits#1*;
      \fi%
  \fi%
}
%% #1 integer
%% #2 decimals
%% #3 dot
\def\@LabelComma#1.#2.#3\@nil{%
  \def\pst@tempA{#1}%
  \ifx\pst@tempA\@empty\the\@zero\else#1\fi% the integer part
  \def\pst@tempA{#2}%
  \ifx\pst@tempA\@empty\@writeDecimals{}\else\@writeDecimals{#2}\fi%
}
%
\def\psxs@none{%
  \let\psk@arrowA\@empty%
  \let\psk@arrowB\@empty%
  \psxs@axes%
}
%\def\psxs@axes{%
%  \psxs@@axes\pst@dima\pst@dimc{}%
%  \psxs@@axes\pst@dimb\pst@dimd{exch}%
%}

%
\def\psxs@axes{{%
  \ifPst@xAxis\psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{}\fi%
  \ifPst@yAxis\psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{exch}\fi%
}}
\def\psaxes{\pst@object{psaxes}}
\def\psaxes@i{\pst@getarrows\psaxes@ii}
\def\psaxes@ii(#1){\@ifnextchar({\psaxes@iii(#1)}{\psaxes@iv(0,0)(0,0)(#1)}}
\def\psaxes@iii(#1)(#2){\@ifnextchar({\psaxes@iv(#1)(#2)}{\psaxes@iv(#1)(#1)(#2)}}
%
\def\psaxes@iv(#1,#2)(#3,#4)(#5,#6){%
  \pst@killglue%
  \begingroup%
  \setbox\pst@hbox=\hbox\bgroup%
  \use@par%
  \pssetxlength\pst@dimg{#1}% o-x
  \pssetylength\pst@dimh{#2}% o-y
  \pssetxlength\pst@dima{#3}% bl-x
  \pssetylength\pst@dimb{#4}% bl-y
  \pssetxlength\pst@dimc{#5}% ur-x
  \pssetylength\pst@dimd{#6}% ur-y
    % If minimum values are negative in log mode, we modify Ox
    % (respectively Oy) if this was not done by the user
    % X axis labels (\psk@log = 0 or 1)
%
% Whole thing will be translated to origin:
  \advance\pst@dima-\pst@dimg% Dist. from bl-x to o-x
  \advance\pst@dimb-\pst@dimh% Dist. from bl-y to o-y
  \advance\pst@dimc-\pst@dimg% Dist. from ur-x to o-x
  \advance\pst@dimd-\pst@dimh% Dist. from ur-y to o-y
% Make lines/arrows or frame:
  \@nameuse{psxs@\psk@axesstyle}%  \psxs@axes or \psxs@frame
  \ifPst@yAxis%
  \begingroup%
    \ifdim\pst@dima=\z@\else\showoriginfalse\fi%
    \ifnum\psk@dy=\z@%
      \pst@dimg=\psk@Dy\psyunit%
      \edef\psk@dy{\number\pst@dimg}%
    \fi%
    \ifPst@xAxis\else\showorigintrue\fi%
    \pst@vlabels{\pst@dimd}{\psk@arrowB}{#3}{#5}%
    \ifPst@xAxis\showoriginfalse\fi%
    \pst@vlabels{\pst@dimb}{\psk@arrowA}{#3}{#5}%
  \endgroup%
  \fi%
  \ifPst@xAxis%
  \begingroup%
    \ifdim\pst@dimb=\z@\else\showoriginfalse\fi%
    \ifnum\psk@dx=\z@%
      \pst@dimg=\psk@Dx\psxunit%
      \edef\psk@dx{\number\pst@dimg}%
    \fi%
    \ifPst@yAxis\else\showorigintrue\fi%
    \pst@hlabels{\pst@dimc}{\psk@arrowB}{#4}{#6}%
    \ifPst@yAxis\showoriginfalse\fi%
    \pst@hlabels{\pst@dima}{\psk@arrowA}{#4}{#6}%
  \endgroup%
  \fi%
% Now close "\pst@hbox" (which is 0-dimensional), and put it at the origin.
  \egroup%
  \pssetxlength\pst@dimg{#1}%
  \pssetylength\pst@dimh{#2}%
  \leavevmode\psput@cartesian\pst@hbox%
  \endgroup
  \ignorespaces%
}
%
\newdimen\psk@subticksize\psk@subticksize=\z@
\newdimen\pst@xticksizeA
\newdimen\pst@xticksizeB
\newdimen\pst@xticksizeC
\newdimen\pst@yticksizeA
\newdimen\pst@yticksizeB
\newdimen\pst@yticksizeC
%
\def\set@xticksize#1{%
  \pst@expandafter\pst@getydimdim{#1} {} {}\@nil % y-unit!!
  \pst@xticksizeA=\the\pst@dimm%
  \pst@xticksizeB=\the\pst@dimn%
  \edef\psk@xticksize{\pst@number\pst@xticksizeA \pst@number\pst@xticksizeB}%
  \ifdim\pst@dimm=\z@\relax
    \pst@xticksizeC=\z@
  \else%
    \pst@absdim{\pst@xticksizeA}\pst@dimm%
    \pst@absdim{\pst@xticksizeB}\pst@dimn%
    \pst@maxdim{\pst@dimm}{\pst@dimn}\pst@dimo%
    \pst@xticksizeC=\pst@dimo%
  \fi%
}
\def\set@yticksize#1{%
  \pst@expandafter\pst@getxdimdim{#1} {} {}\@nil % x-unit!
  \pst@yticksizeA=\the\pst@dimm%
  \pst@yticksizeB=\the\pst@dimn%
  \edef\psk@yticksize{\pst@number\pst@yticksizeA \pst@number\pst@yticksizeB}%
  \ifdim\pst@dimm=\z@\relax
    \pst@yticksizeC=\z@
  \else%
    \pst@absdim{\pst@yticksizeA}\pst@dimm%
    \pst@absdim{\pst@yticksizeB}\pst@dimn%
    \pst@maxdim{\pst@dimm}{\pst@dimn}\pst@dimo%
    \pst@yticksizeC=\pst@dimo%
  \fi%
}
\define@key[psset]{}{ticksize}{\set@xticksize{#1}\set@yticksize{#1}}
\define@key[psset]{pstricks-add}{xticksize}{\set@xticksize{#1}}
\define@key[psset]{pstricks-add}{yticksize}{\set@yticksize{#1}}%  overwrites the definition in pstricks
%\psset{ticksize=-4pt 4pt}
%
% full= 0, top=1, bottom=-1
\define@key[psset]{}{tickstyle}{%
  \pst@expandafter\psset@@tickstyle{#1}\@nil%
  \pst@cnta=\psk@tickstyle
  \advance\pst@cnta by 1
  \ifcase\pst@cnta% bottom
    \pst@xticksizeB=\z@
    \pst@yticksizeB=\z@
  \or% full
  \or% top
    \pst@xticksizeA=\z@
    \pst@yticksizeA=\z@
  \fi
}
%\psset{tickstyle=full}%
%
%
\define@key[psset]{pstricks-add}{subticks}{\def\psk@xsubticks{#1}\def\psk@ysubticks{#1}}
\define@key[psset]{pstricks-add}{xsubticks}{\def\psk@xsubticks{#1}}
\define@key[psset]{pstricks-add}{ysubticks}{\def\psk@ysubticks{#1}}
%
\define@key[psset]{pstricks-add}{subticksize}{\def\psk@xsubticksize{#1}\def\psk@ysubticksize{#1}}
\define@key[psset]{pstricks-add}{xsubticksize}{\def\psk@xsubticksize{#1}}
\define@key[psset]{pstricks-add}{ysubticksize}{\def\psk@ysubticksize{#1}}
%
\define@key[psset]{pstricks-add}{tickwidth}{%
  \pst@getlength{#1}\psk@xtickwidth%
  \pst@getlength{#1}\psk@ytickwidth}
\define@key[psset]{pstricks-add}{xtickwidth}{\pst@getlength{#1}\psk@xtickwidth}
\define@key[psset]{pstricks-add}{ytickwidth}{\pst@getlength{#1}\psk@ytickwidth}
\define@key[psset]{pstricks-add}{subtickwidth}{%
  \pst@getlength{#1}\psk@xsubtickwidth%
  \pst@getlength{#1}\psk@ysubtickwidth}
\define@key[psset]{pstricks-add}{xsubtickwidth}{\pst@getlength{#1}\psk@xsubtickwidth}
\define@key[psset]{pstricks-add}{ysubtickwidth}{\pst@getlength{#1}\psk@ysubtickwidth}
%
\define@key[psset]{pstricks-add}{tickcolor}{\def\psk@xtickcolor{#1}\def\psk@ytickcolor{#1}}
\define@key[psset]{pstricks-add}{xtickcolor}{\def\psk@xtickcolor{#1}}
\define@key[psset]{pstricks-add}{ytickcolor}{\def\psk@ytickcolor{#1}}
\define@key[psset]{pstricks-add}{subtickcolor}{%
  \pst@getcolor{#1}\psk@xsubtickcolor%
  \pst@getcolor{#1}\psk@ysubtickcolor}
\define@key[psset]{pstricks-add}{xsubtickcolor}{\pst@getcolor{#1}\psk@xsubtickcolor}
\define@key[psset]{pstricks-add}{ysubtickcolor}{\pst@getcolor{#1}\psk@ysubtickcolor}
%
\define@key[psset]{pstricks-add}{xticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxticklinestyle{#1}}}
\define@key[psset]{pstricks-add}{xsubticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxsubticklinestyle{#1}}}
\define@key[psset]{pstricks-add}{yticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psyticklinestyle{#1}}}
\define@key[psset]{pstricks-add}{ysubticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psysubticklinestyle{#1}}}
\define@key[psset]{pstricks-add}{ticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxticklinestyle{#1}\def\psyticklinestyle{#1}}}
\define@key[psset]{pstricks-add}{subticklinestyle}{%
  \@ifundefined{psls@#1}%
    {\@pstrickserr{Line style `#1' not defined}\@eha}%
    {\def\psxsubticklinestyle{#1}\def\psysubticklinestyle{#1}}}
%
\define@key[psset]{pstricks-add}{ticklinestyle}{\psset{xticklinestyle=#1,yticklinestyle=#1}}
\define@key[psset]{pstricks-add}{subticklinestyle}{\psset{xsubticklinestyle=#1,ysubticklinestyle=#1}}
%\psset{subticksize=0.75,subticks=1,tickcolor=black,ticklinestyle=solid,%
%  subticklinestyle=solid,%
%  subtickcolor=gray,%
%  tickwidth=0.5\pslinewidth,%
%  subtickwidth=0.25\pslinewidth}
%
\newif\ifis@yAxis%
%
\def\psxs@@axes#1#2#3#4#5{% llx,lly,urx,ury,exch,arrowA,arrowB
  \pst@killglue%
  \begin@SpecialObj%
    \def\pst@tempA{#5}%
    \ifx\pst@tempA\@empty\relax%
      \is@yAxisfalse%
      \ifnum\psk@dx=\z@%
        \pst@dimg=\psk@Dx\psxunit%
        \def\psk@dx{\number\pst@dimg}%
      \fi%
    \else%
      \is@yAxistrue%
      \ifnum\psk@dy=\z@%
        \pst@dimg=\psk@Dy\psyunit% 
        \def\psk@dy{\number\pst@dimg}%
      \fi%
    \fi% 
    \let\pst@linetype\pst@arrowtype%
    \def\pst@tempA{none}%
    \pst@addarrowdef%
    \addto@pscode{
      \ifis@yAxis 0 \pst@number#4 \else \pst@number#3 0 \fi
      \ifis@yAxis 0 \pst@number#2 \else \pst@number#1 0 \fi
      ArrowA
      CP 4 2 roll
      ArrowB 
      /yEnd exch def /xEnd exch def
      xEnd yEnd 
      \ifx\psk@axesstyle\pst@tempA
        pop pop % axesstyle = none (only ticks)
      \else
        L                                  % the line with arrows 
      \fi
      /yStart exch def
      /xStart exch def
      \@nameuse{psls@\pslinestyle}                 % linestyle for the axes
      stroke                                       % draw the main line
%     \psk@ticks: all=0; x=1; y=2; none=3
      \number\psk@ticks\space dup 2 mod 0 eq \ifis@yAxis true \else false \fi and 
      exch 2 lt \ifis@yAxis false \else true \fi and or {
      /viceversa 
        \ifis@yAxis\pst@number#2 \pst@number#4 \else\pst@number#1 \pst@number#3 \fi
         gt { true }{ false } ifelse def           % other way round
      /epsilon 0.01 def                            % rounding errors
      /minTickline \ifis@yAxis \pst@number#1 \else \pst@number#2 \fi def
      /maxTickline \ifis@yAxis \pst@number#3 \else \pst@number#4 \fi def
      /dT \ifis@yAxis \psk@dy \else \psk@dx \fi\space abs  % added abs 2006-07-07
        65536 div viceversa { neg } if def                 % div to get pt instead of sp
      /subTNo \ifis@yAxis\psk@ysubticks\else\psk@xsubticks\fi \space def
      subTNo 0 gt { /dsubT dT subTNo div def}{ /dsubT 0 def } ifelse  % deltaSubTick
      \ifis@yAxis \psk@yticksize \else \psk@xticksize \fi
      /tickend exch def /tickstart exch def
      /Twidth \ifis@yAxis \psk@ytickwidth \else \psk@xtickwidth \fi\space def
      /subTwidth \ifis@yAxis \psk@ysubtickwidth \else \psk@xsubtickwidth \fi\space def
      /STsize \ifis@yAxis \psk@ysubticksize \else \psk@xsubticksize \fi\space def
      /TColor {
        \ifis@yAxis\pst@usecolor\psk@ytickcolor
        \else\pst@usecolor\psk@xtickcolor\fi\space } def
      /subTColor {
        \ifis@yAxis\pst@usecolor\psk@ysubtickcolor
        \else\pst@usecolor\psk@xsubtickcolor\fi\space } def
      /MinValue { \ifis@yAxis yStart \else xStart \fi
        \ifx\psk@arrowA\@empty\else 
          \psk@arrowsize\space CLW mul add \psk@arrowlength\space mul 
           viceversa { sub epsilon add } { add epsilon sub } ifelse \fi } def
      /MaxValue { \ifis@yAxis yEnd \else xEnd \fi
        \ifx\psk@arrowB\@empty\else
          \psk@arrowsize\space CLW mul add \psk@arrowlength\space mul 
           viceversa { add epsilon sub } { sub epsilon add } ifelse \fi } def
      /logLines {
        \ifnum\psk@logLines=\z@ true \else         % all axes
          \ifnum\psk@logLines<\tw@                 % x axis
            \ifis@yAxis false \else true \fi       % do we have x or y axis
          \else
            \ifnum\psk@logLines<\thr@@             % y axis
              \ifis@yAxis true \else false \fi     % do we have x or y axis
            \else 
              false                                % no one
            \fi
          \fi
        \fi
      } def
      /LSstroke {                                  % set linestyle and stroke
        \ifis@yAxis\@nameuse{psls@\psyticklinestyle}
        \else\@nameuse{psls@\psxticklinestyle}\fi } def
      /subLSstroke {                               % set sublinestyle and stroke
        \ifis@yAxis\@nameuse{psls@\psysubticklinestyle}
        \else\@nameuse{psls@\psxsubticklinestyle}\fi } def
%\iffalse
% start ticks ---------------------------------------------------------
      0 dT MaxValue {                              % the positive part of the axes
        /cntTick exch def                          % the index
        logLines {                                 % log lines?
          gsave
          1 10 subTNo div 9.99 {                   % do not write a line for 1
            /dx exch def                           % save index
            /x cntTick dT dx log mul add def       %
            x abs MaxValue abs le {                % out of range?
              x minTickline #5\space moveto
              x maxTickline #5\space lineto
            } if
          } for
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
          grestore                                 % restore main tick status
          stroke
          /dsubT 0 def                             % no other subticks
        } if
        dsubT abs 0 gt {                           % du we have subticks?
          gsave                                    % save graphic state
% start subticks ----------------------------------------------------------
            /cntsubTick cntTick dsubT add def
            subTNo 1 sub {
            cntsubTick abs MaxValue abs le {       % out of range?
              cntsubTick tickstart STsize mul #5\space moveto
              cntsubTick tickend STsize mul #5\space lineto
            }{ exit }  ifelse
            /cntsubTick cntsubTick dsubT add def
          } repeat 
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
% end subticks ----------------------------------------------------------
          grestore                                 % restore tick status
        } if
        gsave
        cntTick tickstart #5\space moveto          % line begin main Tick
        cntTick tickend #5\space lineto            % lineto tick end
        Twidth SLW TColor                          % set line width and tick color
        LSstroke
        grestore
      } for
% end ticks ----------------------------------------------------------
%\fi
%\iffalse
% ================================================ % the other side 
      /dT dT neg def                               % the other side of the axis
      /dsubT dsubT neg def
% start ticks ----------------------------------------------------------
      0 dT MinValue epsilon viceversa { add }{ sub } ifelse {
        /cntTick exch def
        logLines {                                 % log lines?
          gsave
          1 10 subTNo div 9.99 {                   % do not write a line for 1
            /dx exch def                           % save index
            /x cntTick dT dx log mul add def       %
            x abs MinValue abs le {                % out of range?
              x minTickline #5\space moveto
              x maxTickline #5\space lineto
            } if
          } for
          /dsubT 0 def 
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
          grestore
        }
        dsubT abs 0 gt {                           % do we have subticks?
          gsave                                    % save main state
% start subticks ----------------------------------------------------------
          /cntsubTick cntTick dsubT add def
          subTNo 1 sub {
            cntsubTick abs MinValue abs le {       % out of range?
              cntsubTick tickstart STsize mul #5\space moveto
              cntsubTick tickend STsize mul #5\space lineto
            }{ exit } ifelse
            /cntsubTick cntsubTick dsubT add def
          } repeat % for
% end subticks ----------------------------------------------------------
          subTwidth SLW subTColor                  % set line width and subtick color
          subLSstroke
          grestore                                 % restore main state
        } if
        gsave
        cntTick tickstart #5\space moveto         % line begin main Tick
        cntTick tickend #5\space lineto           % lineto tick end
        Twidth SLW TColor                         % set line width and tick color
        LSstroke
        grestore
      } for
% end ticks ----------------------------------------------------------
%\fi    
    } if%
   }%  
  \end@SpecialObj%
  \ignorespaces%
}%
%
\def\psxs@frame{%
  \begin@SpecialObj%
    \addto@pscode{%
      \pst@number\pst@dima \pst@number\pst@dimb moveto \pst@number\pst@dimc \pst@number\pst@dimb L
      \pst@number\pst@dimc \pst@number\pst@dimd L \pst@number\pst@dima \pst@number\pst@dimd L 
      closepath}%
    \pst@stroke%
    \psk@fillstyle%
  \end@SpecialObj%
  \let\psk@arrowA\@empty%
  \let\psk@arrowB\@empty%
%  \pst@dima=0pt\pst@dimb=0pt%
%  \psset{xticksize=0 \pst@dimd,yticksize=0 \pst@dimc}%
  \pst@xticksizeC=\z@\pst@yticksizeC=\z@%
  \psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{}%
  \psxs@@axes\pst@dima\pst@dimb\pst@dimc\pst@dimd{exch}%
}
%
% #1:Max/Min in pt from origin; #2:arrow; #3:min; #4:max
\def\pst@hlabels#1#2#3#4{%
  \ifdim#1=\z@\else%                   % start from 0 ?
    \ifx#2\empty\else\advance#1\ifdim#1>\z@-\fi7\pslinewidth\fi%
    \pst@cnta=#1\relax%                % Distance (in sp) to end.
    \divide\pst@cnta\psk@dx\relax%     % Number of ticks/labels
    \ifnum\pst@cnta=\z@\else%
      \pst@dimb=\psk@dx sp%            % Space between ticks.
%        \ifPst@yAxis\else\showorigintrue\fi%
        \ifnum\psk@labels<\tw@ \ifPst@xAxis\pst@@hlabels\fi\fi%
        \showoriginfalse%
    \fi%
  \fi%
}
% Knows \pst@dimb and \pst@cnta
\def\pst@@hlabels{%
  \pst@dimm=\pst@xticksizeC\advance\pst@dimm by \pslabelsep%
  \vbox to\z@{%
    \ifdim\pst@dimd>\z@\vskip\pst@dimm\else\vss\fi%
    \ifnum\pst@cnta<\z@\pst@dimb=-\pst@dimb\fi%
    \hbox to\z@{%
      \ifshoworigin\hbox to \z@{\hss\pst@@@hlabel{\psk@Ox}\hss}\fi%
      \mmultido{\n=\psk@Ox+\psk@Dx}{\pst@cnta}{%
        \hskip\pst@dimb\hbox to \z@{\hss\pst@@@hlabel{\n}\hss}%
      }\hss%
    }%
    \ifdim\pst@dimd>\z@\vss\else\vskip\pst@dimm\fi%
}}%

% #1:Max/Min in pt from origin; #2:arrow; #3:min; #4:max
% \psk@labels 0:all; 1:x; 2:y; 3:none
\def\pst@vlabels#1#2#3#4{%
  \ifdim#1=\z@\else%
    \ifx#2\empty\else\advance#1\ifdim#1>\z@-\fi7\pslinewidth\fi%
    \pst@cnta=#1\relax          %      % Distance (in sp) to end.
    \divide\pst@cnta\psk@dy\relax  %   % Number of ticks/labels
    \ifnum\pst@cnta=\z@\else%
      \pst@dima=\psk@dy sp%            % Space between ticks.
%      \ifPst@xAxis\else\showorigintrue\fi%
      \ifodd\number\psk@labels\else\ifPst@yAxis\pst@@vlabels\fi\fi%
      \showoriginfalse%
    \fi%
  \fi%
}
% \pst@dima: the width between two labels in pt
% \pst@dimc: the coordinate of the origin in pt
% \pst@cnta: the lowest label
\def\pst@@vlabels{%
  \pst@dimm=\pst@yticksizeC%
  \advance\pst@dimm by \pslabelsep%
  \vbox to\z@{%
    \ifnum\pst@cnta>\z@\pst@dima=-\pst@dima\fi%
    \offinterlineskip%
    \ifshoworigin
      \vbox to \z@{\vss\hbox to\z@{%
        \ifdim\pst@dimc>\z@\hss\else\hskip\pst@dimm\fi
        \pst@@@vlabel{\psk@Oy}%
        \ifdim\pst@dimc>\z@\hskip\pst@dimm\else\hss\fi}\vss}%
    \fi%
    \mmultido{\n=\psk@Oy+\psk@Dy}{\pst@cnta}{%
      \vbox to\pst@dima{\vss}
      \vbox to \z@{%
        \vss\hbox to\z@{%
          \ifdim\pst@dimc>\z@%
            \hss\pst@@@vlabel{\n}\hskip\pst@dimm%
          \else%
            \hskip\pst@dimm\pst@@@vlabel{\n}\hss%
          \fi
        }\vss%
    }}%
    \vss%
}}
%
\define@key[psset]{pstricks-add}{nStep}{\def\psk@nStep{#1}}
\define@key[psset]{pstricks-add}{nStart}{\def\psk@nStart{#1}}
\define@key[psset]{pstricks-add}{nEnd}{\def\psk@nEnd{#1}}
\define@key[psset]{pstricks-add}{xStep}{\def\psk@xStep{#1}}
\define@key[psset]{pstricks-add}{yStep}{\def\psk@yStep{#1}}
%
\define@key[psset]{pstricks-add}{xStart}{\def\psk@xStart{#1}}
\define@key[psset]{pstricks-add}{xEnd}{\def\psk@xEnd{#1}}
\define@key[psset]{pstricks-add}{yStart}{\def\psk@yStart{#1}}
\define@key[psset]{pstricks-add}{yEnd}{\def\psk@yEnd{#1}}
%
\define@key[psset]{pstricks-add}{plotNo}{\def\psk@plotNo{#1}}
\define@key[psset]{pstricks-add}{plotNoMax}{\def\psk@plotNoMax{#1}}
%
%\psset{nStep=1, nStart=0, nEnd={},%
%  xStep=0, yStep=0, xStart={}, xEnd={},  yStart={}, yEnd={}, comma=false,%
%  plotNo=1,plotNoMax=1}%
%
\def\pstScalePoints(#1,#2)#3#4{%
%  xScale | yScale | xOperator | yOperator  
% the operators can be any Postscript code
  \pst@def{ScalePoints}<%
    /y ED /x ED
    counttomark dup dup cvi eq not { exch pop } if
    /m exch def /n m 2 div cvi def
    n {
      #4\space y mul #2\space mul m 1 roll
      #3\space x mul #1\space mul m 1 roll
      /m m 2 sub
      def } repeat>
}
%\pstScalePoints(1,1){}{}% the default -> no special operators
%
\def\listplot@ii#1{%
  \@nameuse{beginplot@\psplotstyle}%
  \addto@pscode{/D {} def mark}%
  #1%
  \addto@pscode{%
    \tx@PreparePoints
    \pst@number\psxunit
    \pst@number\psyunit
    \tx@ScalePoints%
  }%
  \@nameuse{endplot@\psplotstyle}%
}
%
\define@boolkey[psset]{pstricks-add}[Pst@]{ChangeOrder}[true]{}
\pst@def{PreparePoints}<{%
  counttomark /m exch def
  \ifPst@ChangeOrder
    /m0 m def
    m \psk@plotNoMax\space 1 add div 1 sub cvi {
      m0 \psk@plotNoMax\space 1 add roll /m0 m0 \psk@plotNoMax\space 1 add sub def
    } repeat
  \fi
  /n m \psk@plotNoMax\space 1 add div cvi def
  \psk@plotNoMax\space 1 gt {% multiple data files?
    n {
      \psk@plotNoMax\space \psk@plotNo\space 1 sub neg roll % x yNo y y y ...
      \psk@plotNoMax\space 1 sub { pop } repeat % x yNo
      /m m \psk@plotNoMax\space 1 sub sub def
      m 2 roll
    } repeat
  } if % no multiple data files
%	counttomark /m exch def
%	/n m 2 div cvi def
  /xMax -99999 def /yMax -99999 def
  /xP 0 def /yP 0 def
  m copy
  n {
    /y exch def /x exch def
    xMax x lt { /xMax x def } if
    yMax y lt {/yMax y def } if
    xP x gt { /xP x def } if
    yP y gt { /yP y def } if
  } repeat
%	m 2 roll
  \psk@xStep\space 0 gt \psk@yStep\space 0 gt or (\psk@xStart) length 0 gt or
  (\psk@yStart) length 0 gt or (\psk@xEnd) length 0 gt or (\psk@yEnd) length 0 gt or {
%
    (\psk@xStart) length 0 gt {\psk@xStart\space }{ xP } ifelse /xStart exch def
    (\psk@yStart) length 0 gt {\psk@yStart\space }{ yP } ifelse /yStart exch def
    (\psk@xEnd) length 0 gt { \psk@xEnd\space }{ xMax } ifelse /xEnd exch def
    (\psk@yEnd) length 0 gt { \psk@yEnd\space }{ yMax } ifelse /yEnd exch def
    n {
      m -2 roll
      2 copy /yVal exch def /xVal exch def
      xVal xP ge
      yVal yP ge and
      xVal xEnd le and
      yVal yEnd le and
      xVal xStart ge and
      yVal yStart ge and {
        /xP xP \psk@xStep\space add def
        /yP yP \psk@yStep\space add def
      }{%
        pop pop
        /m m 2 sub def
      } ifelse
    } repeat
  }{%
    /ncount 0 def
    (\psk@nEnd) length 0 gt { \psk@nEnd\space }{ m } ifelse 
    /nEnd exch def
    n {
      m -2 roll
      \psk@nStep\space 1 gt {
        ncount \psk@nStart\space sub \psk@nStep\space mod 0 eq }{ true } ifelse
        ncount nEnd le and
        ncount \psk@nStart\space ge and not {
          pop pop
          /m m 2 sub def
        } if
        /ncount ncount 1 add def
      } repeat
  } ifelse
}>
%
%
\define@key[psset]{pstricks-add}{xAxisLabel}{\def\psk@xAxisLabel{#1}}
\define@key[psset]{pstricks-add}{yAxisLabel}{\def\psk@yAxisLabel{#1}}
%\psset{xAxisLabel=x,yAxisLabel=y}
\define@key[psset]{pstricks-add}{xAxisLabelPos}{\def\psk@xAxisLabelPos{#1}}
\define@key[psset]{pstricks-add}{yAxisLabelPos}{\def\psk@yAxisLabelPos{#1}}
%\psset{yAxisLabelPos={},xAxisLabelPos={}}
%
\newdimen\psk@llx
\newdimen\psk@lly
\newdimen\psk@urx
\newdimen\psk@ury
\define@key[psset]{pstricks-add}{llx}{\pssetxlength\psk@llx{#1}}
\define@key[psset]{pstricks-add}{lly}{\pssetylength\psk@lly{#1}}
\define@key[psset]{pstricks-add}{urx}{\pssetxlength\psk@urx{#1}}
\define@key[psset]{pstricks-add}{ury}{\pssetylength\psk@ury{#1}}
%\psset{llx=\z@, lly=\z@, urx=\z@, ury=\z@}% prevents rounding errors 
\newif\ifPst@plot@box
\define@key[psset]{pstricks-add}{box}[true]{\@nameuse{Pst@plot@box#1}}
%
\newdimen\pst@xunit
\newdimen\pst@yunit
%
\def\psgraph{\def\pst@par{}\pst@object{psgraph}}
\def\psgraph@i{\pst@getarrows\psgraph@ii}
\def\psgraph@ii(#1,#2){\@ifnextchar({\psgraph@iii(#1,#2)}{\psgraph@iv(0,0)(#1,#2)}}
\def\psgraph@iii(#1,#2)(#3,#4){\@ifnextchar({\psgraph@v(#1,#2)(#3,#4)}{\psgraph@iv(#1,#2)(#3,#4)}}
%
\def\psgraph@iv(#1,#2)(#3,#4)#5#6{%  no special origin defined
% minX | minY | maxX | maxY | Length x-axis | length y-axis%  
  \pst@killglue
  \begingroup
  \pst@dimo=#3\p@\advance\pst@dimo by -#1\p@ % delta x
  \pst@divide{#5}{\pst@dimo}\pst@tempA
  \pst@xunit=\pst@tempA\p@%
  \pst@dimo=#4\p@\advance\pst@dimo by -#2\p@ % delta y
  \pst@dima=#6
  \pst@divide\pst@dima{\pst@dimo}\pst@tempA%
  \pst@yunit=\pst@tempA\p@%
  %
  \pst@dima=#1\pst@xunit \advance\pst@dima by \psk@llx%
  \pst@dimb=#2\pst@yunit \advance\pst@dimb by \psk@lly%
  \pst@dimc=#3\pst@xunit \advance\pst@dimc by \psk@urx%
  \pst@dimd=#4\pst@yunit \advance\pst@dimd by \psk@ury%
  \if@star\pspicture*(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\else
    \pspicture(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\fi
  \psset{xunit=\pst@xunit,yunit=\pst@yunit}%
  \bgroup
  \use@par
  \psaxes(#1,#2)(#3,#4)
  \egroup
  \psgraph@vi(#1,#2)(#3,#4)%
}
\def\psgraph@v(#1,#2)(#3,#4)(#5,#6)#7#8{%  with special origin
% Xorig | yorig | minX | minY | maxX | maxY | Length x-axis | length y-axis%  
  \pst@killglue
  \begingroup
  \pst@dimo=#5\p@\advance\pst@dimo by -#3\p@ % delta x
  \pst@divide{#7}{\pst@dimo}\pst@tempA
  \pst@xunit=\pst@tempA\p@%
  \pst@dimo=#6\p@\advance\pst@dimo by -#4\p@ % delta y
  \pst@dima=#8
  \pst@divide\pst@dima{\pst@dimo}\pst@tempA%
  \pst@yunit=\pst@tempA\p@%
  %
  \pst@dima=#3\pst@xunit \advance\pst@dima by \psk@llx%
  \pst@dimb=#4\pst@yunit \advance\pst@dimb by \psk@lly%
  \pst@dimc=#5\pst@xunit \advance\pst@dimc by \psk@urx%
  \pst@dimd=#6\pst@yunit \advance\pst@dimd by \psk@ury%
  \if@star\pspicture*(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\else
    \pspicture(\pst@dima,\pst@dimb)(\pst@dimc,\pst@dimd)\fi
  \psset{xunit=\pst@xunit,yunit=\pst@yunit}%
  \bgroup
  \use@par
  \psaxes(#1,#2)(#3,#4)(#5,#6)
  \egroup
  \psgraph@vi(#1,#2)(#5,#6)%
}
\def\psgraph@vi(#1,#2)(#3,#4){%
  \ifx\psk@xAxisLabel\@empty\else%
    \ifx\psk@xAxisLabelPos\@empty\uput[0](#3,#2){\psk@xAxisLabel}%
    \else\rput(\psk@xAxisLabelPos){\psk@xAxisLabel}%
    \fi%
  \fi%
  \ifx\psk@yAxisLabel\@empty\else%
    \ifx\psk@yAxisLabelPos\@empty\uput[90](#1,#4){\psk@yAxisLabel}%
    \else\rput{90}(\psk@yAxisLabelPos){\psk@yAxisLabel}%
    \fi%
  \fi%
  \ignorespaces%
}
\def\endpsgraph{%
  \pst@killglue
  \endpspicture%
  \endgroup%
}
\@namedef{psgraph*}{\psgraph*}
\@namedef{endpsgraph*}{\endpsgraph}
%
\define@key[psset]{pstricks-add}{ignoreLines}{\def\psk@ignoreLines{#1}}

\newcount\linecnt
\begingroup
\catcode`\,=13
\catcode`\_=13
\gdef\savedata@#1[#2]{%
  \xdef\pst@tempg{#2_}%
  \endgroup
  \let#1\pst@tempg
  \global\let\pst@tempg\relax
  \ignorespaces}
\gdef\readdata@{%
  \read1 to \pst@tempA
  \ifnum\linecnt=\psk@nStep
    \global\linecnt=0
    \expandafter\readdata@@\pst@tempA_\@nil
  \fi
  \global\advance\linecnt by 1
  \ifeof1\else\expandafter\readdata@\fi}
\gdef\pst@@readfile#1#2\@nil{\addto@pscode{,#1#2}}%
\gdef\readdata@@#1#2\@nil{\xdef\pst@tempg{\pst@tempg,#1#2}}%
\endgroup

\def\readdata{\@ifnextchar[{\readdata@i}{\readdata@i[]}}
\def\readdata@i[#1]#2#3{%
  \def\pst@tempA{#1}%
  \ifx\pst@tempA\@empty\else\psset{#1}\fi
  \openin1=#3
  \begingroup
  \def\pst@tempg{}%
  \ifeof1
    \@pstrickserr{Data file `#3' not found.}\@ehpa
  \else
    \pst@datadelimiters
    \catcode`\[=1
    \catcode`\]=2
    \pst@cnta=0
    \loop \ifnum\the\pst@cnta<\psk@ignoreLines
      \advance\pst@cnta by 1\relax
      \read1 to \pst@tempA
    \repeat
    \ifnum\Pst@Debug>0 \typeout{>>> ignored \the\pst@cnta\space data lines}\fi%
    \global\linecnt=\psk@nStep%
    \readdata@%
  \fi%
  \endgroup%
  \global\let#2\pst@tempg%
  \global\let\pst@tempg\relax%
\ignorespaces}
%
% D.G. addition - Jun.  9, 1998 - Polar plots using the \psplot macro
% Code added according the way suggested by Ulrich Dirr <udirr@das-team.com>
% For polar plots
\define@boolkey[psset]{pstricks-add}[Pst@]{polarplot}[true]{}
%\psset{polarplot=false}
%
\define@boolkey[psset]{pstricks-add}[Pst@]{algebraic}[true]{}%
%\psset{dimen=middle}% remark of ML
\define@key[psset]{pstricks-add}{method}{\def\psk@method{#1}}%     	   adams - rk4
\define@key[psset]{pstricks-add}{whichabs}{\def\psk@whichabs{#1}}%
\define@key[psset]{pstricks-add}{whichord}{\def\psk@whichord{#1}}%
\define@key[psset]{pstricks-add}{plotfuncx}{\def\psk@plotfuncx{#1}}%
\define@key[psset]{pstricks-add}{plotfuncy}{\def\psk@plotfuncy{#1}}%
\define@key[psset]{pstricks-add}{expression}{\def\psk@expression{#1}}%
\define@boolkey[psset]{pstricks-add}[Pst@]{buildvector}[true]{}%
\def\@rkiv{rk4}%		Runge-Kutta 4  method
\def\@adams{adams}%		Adams method
\def\@default{default}%		Adams method
%
\define@boolkey[psset]{pstricks-add}[Pst@]{VarStep}[true]{}
\define@key[psset]{pstricks-add}{PlotDerivative}{\def\psk@PlotDerivative{#1}}%
\define@key[psset]{pstricks-add}{VarStepEpsilon}{\def\psk@VarStepEpsilon{#1}}%
\define@key[psset]{pstricks-add}{varsteptol}{\def\psk@varsteptol{#1}}%     	    adams - rk4
\define@key[psset]{pstricks-add}{adamsorder}{\def\psk@adamsorder{#1}}%     	    adams - rk4
%\define@key[psset]{pstricks-add}{varstepincrease}{\def\psk@varstepincrease{#1}}% varrk4
%
\def\psplot@i#1#2#3{%
  \pst@killglue
  \begingroup
    \use@par
    \@nameuse{beginplot@\psplotstyle}%
% D.G. modification begin - Jun.  9, 1998
    \ifPst@polarplot
      \addto@pscode{%
        \psplot@init
        /x #1 def
        /x1 #2 def
        /dx x1 x sub \psk@plotpoints div def
        /F@pstplot \ifPst@algebraic (#3)
                    \ifx\psk@PlotDerivative\@none\else
                      \psk@PlotDerivative\space { (x) tx@Derive begin Derive end } repeat
                    \fi\space
                    tx@AlgToPs begin AlgToPs end cvx
                 \else { #3 } \fi  def
        \ifPst@VarStep
          /StillZero 0 def /LastNonZeroStep dx def
          /F2@pstplot tx@Derive begin (#3) (x) Derive (x) Derive end
                     \ifx\psk@PlotDerivative\@none\else
                       \psk@PlotDerivative\space { (x) tx@Derive begin Derive end } repeat
                     \fi\space
                    tx@AlgToPs begin AlgToPs end cvx def
          %% computation of the tolerance defined by plotpoints
          /epsilon12 \ifx\psk@VarStepEpsilon\@default tx@Derive begin F2@pstplot end dx 3 exp abs mul abs
                    \else\psk@VarStepEpsilon\space 12 mul \fi def
          /ComputeStep {
            dup 1e-4 lt
            { pop StillZero 2 ge { LastNonZeroStep 2 mul } { LastNonZeroStep } ifelse /StillZero StillZero 1 add def }
            { epsilon12 exch div 1 3 div exp /StillZero 0 def }
            ifelse } bind def
        \fi
        /xy {% Adapted from \parametricplot@i
          F@pstplot x \ifPst@algebraic RadtoDeg \fi PtoC
%          #3 dup x cos mul exch x sin mul
          \pst@number\psyunit mul exch
          \pst@number\psxunit mul exch
        } def}%
    \else
% D.G. modification end
    \addto@pscode{%
      \psplot@init
      /x #1 def
      /x1 #2 def
      /dx x1 x sub \psk@plotpoints div def
      /F@pstplot \ifPst@algebraic (#3)
                    \ifx\psk@PlotDerivative\@none\else
                      \psk@PlotDerivative\space { (x) tx@Derive begin Derive end } repeat
                    \fi\space
                    tx@AlgToPs begin AlgToPs end cvx
                 \else { #3 } \fi  def
      \ifPst@VarStep
         /StillZero 0 def /LastNonZeroStep dx def
         /F2@pstplot tx@Derive begin (#3) (x) Derive (x) Derive end
                     \ifx\psk@PlotDerivative\@none\else
                       \psk@PlotDerivative\space { (x) tx@Derive begin Derive end } repeat
                     \fi\space
                    tx@AlgToPs begin AlgToPs end cvx def
         %% computation of the tolerance defined by plotpoints
         /epsilon12 \ifx\psk@VarStepEpsilon\@default tx@Derive begin F2@pstplot end dx 3 exp abs mul abs
                    \else\psk@VarStepEpsilon\space 12 mul \fi def
         /ComputeStep {
           dup 1e-4 lt
           { pop StillZero 2 ge { LastNonZeroStep 2 mul } { LastNonZeroStep } ifelse /StillZero StillZero 1 add def }
           { epsilon12 exch div 1 3 div exp /StillZero 0 def }
           ifelse } bind def
      \fi
      /xy {
        x \pst@number\psxunit mul F@pstplot \pst@number\psyunit mul
%       \ifPst@algebraic F@pstplot \else #3 \fi \pst@number\psyunit mul
      } def}%
    \fi
    \gdef\psplot@init{}%
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if@pst
      \psplot@ii
    \else
      \psplot@iii
    \fi
  \endgroup
  \ignorespaces}
%
\def\psplot@ii{%
  \ifPst@VarStep
    \addto@pscode{%
      mark xy \@nameuse{beginqp@\psplotstyle}
      { F2@pstplot abs ComputeStep
        x 2 copy add dup x1 gt {pop x1} if /x exch def F2@pstplot abs ComputeStep
        /x 3 -1 roll def 2 copy gt { exch } if pop
        /x x 3 -1 roll add dup x1 gt {pop x1} if def
        xy \@nameuse{doqp@\psplotstyle}
        x x1 eq { exit } if} loop}%
  \else\pst@killglue%
    \addto@pscode{%
      xy \@nameuse{beginqp@\psplotstyle}
      \ifx\psk@method\@varrkiv\else\psk@plotpoints 1 sub \fi {
        /x x dx add \ifx\psk@method\@varrkiv  dup x1 gt { pop x1 } if \fi def
        xy \@nameuse{doqp@\psplotstyle}
        \ifx\psk@method\@varrkiv  x x1 eq { exit } if \fi
      } \ifx\psk@method\@varrkiv loop\else repeat\fi
      /x x1 def
      xy \@nameuse{doqp@\psplotstyle}}%
  \fi%
  \@nameuse{endqp@\psplotstyle}}
\def\psplot@iii{%
  \ifPst@VarStep
    \addto@pscode{%
      /n 2 def
      mark
      { xy n 2 roll F2@pstplot abs
        ComputeStep x 2 copy add dup x1 gt {pop x1} if
        /x exch def F2@pstplot abs ComputeStep
        /x 3 -1 roll def 2 copy gt { exch } if pop
        /x x 3 -1 roll dup /LastNonZeroStep exch def add dup x1 gt {pop x1} if def /n n 2 add def
        x x1 eq { exit } if } loop
      xy n 2 roll}%
  \else\pst@killglue%
    \addto@pscode{%
      mark
      /n 2 def
      \ifx\psk@method\@varrkiv\else\psk@plotpoints\fi {
        xy
        n 2 roll
        /n n 2 add def
        /x x dx add \ifx\psk@method\@varrkiv  dup x1 gt { pop x1 } if \fi def
        \ifx\psk@method\@varrkiv  x x1 eq { exit } if \fi
      } \ifx\psk@method\@varrkiv loop\else repeat\fi
      /x x1 def
      xy
      n 2 roll}%
  \fi%
  \@nameuse{endplot@\psplotstyle}}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\parametricplot@i#1#2#3{%
  \pst@killglue%
  \begingroup
    \use@par
    \@nameuse{beginplot@\psplotstyle}%
    \addto@pscode{%
      \psplot@init
      /t #1 def
      /t1 #2 def
      /dt t1 t sub \psk@plotpoints div def
      /F@pstplot \ifPst@algebraic (#3)
                    \ifx\psk@PlotDerivative\@none\else
                      \psk@PlotDerivative\space { (t) tx@Derive begin Derive end } repeat
                    \fi\space
                    tx@AlgToPs begin AlgToPs end cvx
                 \else { #3 } \fi  def
      \ifPst@VarStep
         /StillZero 0 def /LastNonZeroStep dt def
         /F2@pstplot tx@Derive begin (#3) (t) Derive (t) Derive end
                     \ifx\psk@PlotDerivative\@none\else
                       \psk@PlotDerivative\space { (t) tx@Derive begin Derive end } repeat
                     \fi\space
                    tx@AlgToPs begin AlgToPs end cvx def
         %% computation of the tolerance defined by plotpoints
         /epsilon12 \ifx\psk@VarStepEpsilon\@default
                       tx@Derive begin F2@pstplot end Pyth
                       dt 3 exp abs mul
                    \else\psk@VarStepEpsilon\space 12 mul \fi def
         /ComputeStep {
           dup 1e-4 lt
           { pop StillZero 2 ge { LastNonZeroStep 2 mul } { LastNonZeroStep } ifelse /StillZero StillZero 1 add def }
           { epsilon12 exch div 1 3 div exp /StillZero 0 def }
           ifelse } bind def
      \fi
      /xy {
        \ifPst@algebraic F@pstplot \else #3 \fi
        \pst@number\psyunit mul exch
        \pst@number\psxunit mul exch
      } def}%
    \gdef\psplot@init{}%
    \@pstfalse
    \@nameuse{testqp@\psplotstyle}%
    \if@pst
      \parametricplot@ii
    \else
      \parametricplot@iii
    \fi
  \endgroup
  \ignorespaces}
\def\parametricplot@ii{%
  \ifPst@VarStep
    \addto@pscode{%
      mark xy \@nameuse{beginqp@\psplotstyle}
      { F2@pstplot Pyth ComputeStep
        t 2 copy add dup t1 gt {pop t1} if /t exch def F2@pstplot Pyth ComputeStep
        /t 3 -1 roll def 2 copy gt { exch } if pop
        /t t 3 -1 roll add dup t1 gt {pop t1} if def
        xy \@nameuse{doqp@\psplotstyle}
        t t1 eq { exit } if } loop}%
  \else\pst@killglue%
    \addto@pscode{%
      xy \@nameuse{beginqp@\psplotstyle}
      \psk@plotpoints 1 sub {
        /t t dt add def
        xy \@nameuse{doqp@\psplotstyle}
      } repeat
      /t t1 def
      xy \@nameuse{doqp@\psplotstyle}}%
  \fi%
  \@nameuse{endqp@\psplotstyle}}
\def\parametricplot@iii{%
  \ifPst@VarStep
    \addto@pscode{%
      /n 2 def
      mark
      { xy n 2 roll F2@pstplot Pyth
        ComputeStep t 2 copy add dup t1 gt {pop t1} if
        /t exch def F2@pstplot Pyth ComputeStep
        /t 3 -1 roll def 2 copy gt { exch } if pop
        /t t 3 -1 roll dup /LastNonZeroStep exch def add dup t1 gt {pop t1} if def /n n 2 add def
        t t1 eq { exit } if } loop
      xy n 2 roll}%
  \else\pst@killglue%
    \addto@pscode{%
      mark
      /n 2 def
      \psk@plotpoints {
        xy
        n 2 roll
        /n n 2 add def
        /t t dt add def
      } repeat
      /t t1 def
      xy
      n 2 roll}%
  \fi%
  \@nameuse{endplot@\psplotstyle}}
%
\define@key[psset]{pstricks-add}{barwidth}{\pst@getlength{#1}\psk@barwidth}
%\psset{barwidth=0.25cm}
%
\def\psbar@ii{\addto@pscode{false \tx@NArray \psbar@iii}}
\def\psbar@iii{%
  newpath
  n { 
    /Yval exch def /Xval exch def 
    Xval \number\psk@barwidth 0.5 mul sub 0 moveto 
    0 Yval rlineto \number\psk@barwidth 0 rlineto 
    0 Yval neg rlineto \number\psk@barwidth neg 0 rlineto
  } repeat
}%
\def\beginplot@bar{\begin@SpecialObj}
\def\endplot@bar{%
  \psbar@ii\psk@fillstyle\ifpsshadow\pst@closedshadow\fi%
  \pst@stroke
  \end@SpecialObj%
}
%
\define@key[psset]{pstricks-add}{StepType}{\pst@expandafter\psset@@StepType{#1}\@nil}%
\def\psset@@StepType#1#2\@nil{%
  \ifx#1u\let\psk@StepType\@ne
  \else\ifx#1l\let\psk@StepType\z@\else\let\psk@StepType\tw@\fi\fi}
\psset{StepType=lower} %               alternative StepType=upper StepType=Riemann
%
\def\psStep{\pst@object{psStep}}
\def\psStep@i(#1,#2)#3#4{%
  \begin@ClosedObj%
  \addto@pscode{
    \ifPst@algebraic /Func (#4) tx@addDict begin AlgParser end cvx def \fi 
    /x #1  def
    /dx #2 #1 sub #3 div def
    /scx { \pst@number\psxunit mul } def 
    /scy { \pst@number\psyunit mul } def
    \ifcase\psk@StepType % 0->lower
      x scx 0 moveto 
      #3 {
        \ifPst@algebraic Func \else #4 \fi scy dup x scx exch lineto 
        /x x dx add def
        x scx exch lineto x scx 0 lineto
      } repeat
    \or % 1-> upper
      x scx 0 moveto 
      #3 {
        /x x dx add def
        \ifPst@algebraic Func \else #4 \fi scy dup x dx sub scx exch lineto 
        x scx exch lineto x scx 0 lineto
      } repeat
    \or % 2-> Riemann
      /eps3 100 def
      /xMinMax [] def
      /AMax [] def
      /AMin [] def
      /dt dx eps3 div def
      #3 {
        /Max \ifPst@algebraic Func \else #4 \fi def 
        /Min Max def 
	/t x def % save x value
	eps3 {
	  \ifPst@algebraic Func \else #4 \fi 
	  dup
	  Max lt { /Max exch def } { dup Min gt { /Min exch def }{ pop } ifelse } ifelse
	  /x x dt add def
	} repeat 
	/x t def  % restore
	x scx Min scy Max scy xMinMax aload length 3 add array astore /xMinMax exch def
        /x x dx add def
      } repeat
      /dx dx scx def
      xMinMax aload length 3 div cvi { 
        /yMax ED /yMin ED /x ED 
	x yMin moveto dx 0 rlineto x dx add yMax lineto 
	dx neg 0 rlineto x yMin lineto } repeat
    \fi
  }%
  \psk@fillstyle
  \pst@stroke
  \end@ClosedObj%
}
%
\define@key[psset]{pstricks-add}{Derive}{\def\psk@Derive{#1}}%
\def\@NOTEMPTY{NOT@EMPTY}%%dr 0606
%
%% #1 : x value
%% #2 : delta x
%% #3 : function
\def\psplotTangent{\pst@object{psplotTangent}}%  idea from Dominique Rodriguez
\def\psplotTangent@i#1#2#3{%
  \begin@OpenObj%
%  \let\pst@linetype\pst@arrowtype%
%  \pst@addarrowdef%
  \ifx\psk@Derive\@empty\ifPst@algebraic\psset{Derive=NOT@EMPTY}\fi\fi%%dr 0606
  \addto@pscode{
    gsave % save current state
    /F@pstplot \ifPst@algebraic (#3) tx@addDict begin AlgParser end cvx \else { #3 } \fi def % define function
    \ifx\psk@Derive\@empty\else
    \ifx\psk@Derive\@NOTEMPTY\else%%dr 0606
      /FDer@pstplot % do we have a derivation defined?
        \ifPst@algebraic (\psk@Derive) tx@addDict begin AlgParser end cvx \else { \psk@Derive } \fi def % define derivation
    \fi%%dr 0606
    \fi
    /@parametric false def %%dr 0606
    % first we calculate the origin
    #1 dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot 
      %%{ /y ED /x ED } % if yes, then we have 2 values
      { /y ED /x ED /@parametric true def } % if yes, then we have 2 values%%dr 0606
      { \ifPst@polarplot x \ifPst@algebraic RadtoDeg \fi PtoC /y ED /x ED \else /y ED \fi } ifelse 
    cleartomark 
    \ifx\psk@Derive\@NOTEMPTY%%begin dr 0606
        %% algebraic we can use the derivative machine
        /FDer@pstplot (#3) @parametric { (t) } { (x) } ifelse
        tx@Derive begin Derive end tx@addDict begin AlgParser end cvx def
    \fi%%end dr 0606
    x \pst@number\psxunit mul y \pst@number\psyunit mul 
    translate % define the temporary origin
    % now we calculate the slope of the tangent 
    \ifx\psk@Derive\@empty% de we have a derivation defined?
    #1 abs 1.0e-6 lt % no, we choose secant for the tangent 
      { #1 0.0005 add dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot
        { /y2 ED /x2 ED }  % we have 2 values
        { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi 
	  cos mul /x2 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x2 x def \fi /y2 ED } ifelse
        cleartomark % delete the mark
        #1 0.0005 sub dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot
          { /y1 ED /x1 ED }
	  { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi 
	    cos mul /x1 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x1 x def \fi /y1 ED } ifelse
         cleartomark 
        y2 y1 sub x2 x1 sub } % dy dx
      {  % > 1.0e-06
        #1 1.0005 mul dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot 
          { /y2 ED /x2 ED } % we have 2 values
          { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi 
	    cos mul /x2 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x2 x def \fi /y2 ED } ifelse
	cleartomark 
        #1 .9995 mul dup /x ED /t ED tx@addDict begin mark F@pstplot end counttomark 1 gt % test, if we have parametricplot 
          { /y1 ED /x1 ED } % we have 2 values 
          { \ifPst@polarplot dup x \ifPst@algebraic RadtoDeg \fi 
	    cos mul /x1 ED x \ifPst@algebraic RadtoDeg \fi sin mul \else /x1 x def \fi /y1 ED } ifelse
	cleartomark 
        y2 y1 sub \pst@number\psyunit mul x2 x1 sub \pst@number\psxunit mul } ifelse 
      atan %  atan(dy dx), we have the slope angle of the secant
    \else % there is a derivation defined
    #1 dup /x ED /t ED tx@addDict begin mark FDer@pstplot end counttomark 1 gt % test, if we have parametricplot 
      { /y ED /x ED }
      { \ifPst@polarplot /Fphi ED % the value F'(phi) 
           tx@addDict begin F@pstplot end x \ifPst@algebraic RadtoDeg \fi PtoC /y0 ED /x0 ED % the x y values
           x \ifPst@algebraic RadtoDeg \fi sin Fphi mul x0 add /y ED 
           x \ifPst@algebraic RadtoDeg \fi cos Fphi mul y0 sub /x ED 
      \else /y ED /x 1 def \fi } ifelse
    cleartomark 
    y \pst@number\psyunit mul x \pst@number\psxunit mul Atan 
%    y ATAN1  % we have the slope angle of the tangent. ATAN is defined int the pstricks.pro, patch 6
    \fi
    rotate 					% rotate, depending to the origin
    /Lineto /lineto load def
    [
    -#2 \pst@number\psxunit mul 0 		% moveto
     #2 \pst@number\psxunit mul 0 		% lineto
    \pst@cp					% kill the currentpoint, if any
    false					% don't show the points
    \tx@Line
%      ArrowA CP 4 2 roll ArrowB L          	% the line with arrows L is defined in pstricks.pro
%     \pst@number\pslinewidth SLW		% set linewidth in pt
%     \@nameuse{psls@\pslinestyle}           	% linestyle
%     \pst@usecolor\pslinecolor			% linecolor
    stroke					% stroke everything
    \ifshowpoints 				% show the points?
      \psk@dotsize
      \@nameuse{psds@\psk@dotstyle}%
      0 0 Dot
    \fi
    grestore					% restore old graphics state
   }%
  \use@pscode					% part of \end@OpenObj
  \endgroup%					% part of \end@OpenObj
  \ignorespaces%				% part of \end@OpenObj
}%
%
\def\@varrkiv{varrkiv}%		Runge-Kutta 4 with an adaptive step method
%% #1-#2 x range
%% #3 initial value of y (which is a vector) y(0) y'(0) y''(0) ...
%% #4 value of the derivative (y and t can be used)
%
\def\psplotDiffEqn{\pst@object{psplotDiffEqn}}% initial code by Dominique 2005-05-21
\def\psplotDiffEqn@i#1#2#3#4{%
  \pst@killglue%
  \begingroup%
  \use@par%
  \@nameuse{beginplot@\psplotstyle}%
  \addto@pscode{%
    /x #1 def				% first value
    /x1 #2 def				% last value
    /y [ #3 ] def			% values for t=0
    /ylength y length def		% number of elements in #3
    /addvect {
      1 1 ylength {
        /i exch def
	ylength i sub 2 add -1 roll add ylength 2 mul i sub 1 roll
      } for
    } def
    /dx x1 x sub \psk@plotpoints\space div def
    /mulvect {
      ylength exch
      1 index {
        dup 4 -1 roll mul 2 index 2 add 1 roll
      } repeat
      pop pop } def
    /divvect { ylength exch 1 index { dup 4 -1 roll exch div 2 index 2 add 1 roll } repeat pop pop } def
    /k0 0 def /k1 0 def /k2 0 def /k3 0 def
    \ifPst@algebraic /F@pstplot (#4) tx@addDict begin AlgParser end cvx def \fi
    /Func {
      \ifPst@algebraic F@pstplot ylength array astore
      \else
        \ifPst@buildvector\else y aload pop \fi #4
        \ifPst@buildvector\else ylength array astore \fi
      \fi
    } def
    \ifx\psk@method\@adams /F1 0 def /F2 0 def /F3 0 def /F4 0 def /F5 0 def /F6 0 def /INIT 1 def \fi
    \ifx\psk@method\@empty\else
      \ifx\psk@method\@varrkiv	%% RUNGE-KUTTA method with var step algorithm
        /VarStep false def /VarStepRatio 1 def
        /RK {
           /k0 Func { dx mul } forall ylength array astore def 				%% y
           dup aload pop k0 { 2 div } forall addvect ylength array astore /y exch def %
           x dup dx 2 div add /x exch def 						%% y x
           /k1 Func { dx mul } forall ylength array astore def 				%% y x
           exch dup aload pop k1 { 2 div } forall addvect y astore pop 			%% x y
           /k2 Func { dx mul } forall ylength array astore def 				%% x y
           dup aload pop k2 aload pop addvect y astore pop exch dup dx add /x exch def 	%% y x
           /k3 Func { dx mul } forall ylength array astore def %% y x
           /x exch def 									%% y
           dup aload pop k0 aload pop k1 aload pop k2 aload pop addvect
           2 mulvect addvect k3 aload pop addvect
           6 divvect addvect y astore
        } def
        /VARRK {
          VarStep
          %{ /dx dx \psk@varstepincrease\space mul def /VarStep false def } if
          { /dx dx VarStepRatio mul def /VarStep false def } if
          x dx add x1 gt { /dx x1 x sub def } if
          %{ /dx dx \psk@varstepdecrease\space div def } ifelse
          %% we compute y(x+dx) from y(x) using RK4
          RK %% y(x) y(x+dx)
          exch /y exch def /dx dx 2 div def
          { %% we compute y(x+dx/2) from y(x) using RK4
            y RK %% y(x+dx) y(x+dx/2)
            %% then y(x+dx) from y(x+dx/2) using RK4
            /y exch def y RK %% y(x+dx) y(x) y(x+dx/2) y(x+dx)
            dup aload pop 4 ylength add -1 roll
            { -1 mul } forall addvect 0 ylength { exch abs 2 copy lt { exch } if pop } repeat
            0 3 -1 roll {abs 2 copy lt { exch } if pop } forall
            dup 1e-6 lt { pop } { div } ifelse
            /dx dx 2 mul def
            dup \psk@varsteptol\space lt
            %{ \psk@varsteptol\space div .1 lt { /VarStep true def } if pop exit } if
            %pop /dx dx 4 div def exch /y exch def } loop
            { .001 div dup .1 lt
              { dup 1e-6 lt { pop 3 } { log neg } ifelse /VarStepRatio exch def /VarStep true def }
              { pop } ifelse pop exit } if
            pop /dx dx 4 div def exch /y exch def } loop
        } def
      \else			%% RUNGE-KUTTA & ADAMS  methods
        /RK {
           /k0 Func { dx mul } forall ylength array astore def 				%% y
           dup aload pop k0 { 2 div } forall addvect ylength array astore /y exch def %
           x dup dx 2 div add /x exch def 						%% y x
           /k1 Func { dx mul } forall ylength array astore def 				%% y x
           exch dup aload pop k1 { 2 div } forall addvect y astore pop 			%% x y
           /k2 Func { dx mul } forall ylength array astore def 				%% x y
           dup aload pop k2 aload pop addvect y astore pop exch dup dx add /x exch def 	%% y x
           /k3 Func { dx mul } forall ylength array astore def %% y x
           /x exch def 									%% y
           dup aload pop k0 aload pop k1 aload pop k2 aload pop addvect
           2 mulvect addvect k3 aload pop addvect
           6 divvect addvect y astore pop
        } def
        \ifx\psk@method\@adams
           /ADAMS {
             \ifcase\psk@adamsorder
                \errmessage{pstricks-add error: no order 0th for adams method (see user's manual)}
             \or\errmessage{pstricks-add error: no order 1st for adams method (see user's manual)}
             \or\errmessage{pstricks-add error: no order 2nd for adams method (see user's manual)}
             \or\errmessage{pstricks-add error: no order 3rd for adams method (see user's manual)}
             \or
             %% ORDRE 4
               F4 aload pop  55 mulvect
               F3 aload pop -59 mulvect addvect
               F2 aload pop  37 mulvect addvect
               F1 aload pop  -9 mulvect addvect
               dx mulvect 24 divvect
             \or
             %% ORDRE 5
               F5 aload pop  1901 mulvect
               F4 aload pop -2774 mulvect addvect
               F3 aload pop  2616 mulvect addvect
               F2 aload pop -1274 mulvect addvect
               F1 aload pop   251 mulvect addvect
               dx mulvect 720 divvect
             \or
             %% ORDRE 6
               F6 aload pop  4277 mulvect
               F5 aload pop -7923 mulvect addvect
               F4 aload pop  9982 mulvect addvect
               F3 aload pop -7298 mulvect addvect
               F2 aload pop  2877 mulvect addvect
               F1 aload pop  -475 mulvect addvect
               dx mulvect 1440 divvect
             \fi
             y aload pop addvect ylength array astore /y exch def } def
        \fi
      \fi
    \fi
    /xy {
      \ifx\psk@plotfuncx\@empty
        \ifx\psk@whichabs\@empty x \else y \psk@whichabs\space get \fi
      \else \psk@plotfuncx\space \fi
      \pst@number\psxunit mul y
      \ifx\psk@method\@empty							%% EULER method
        /y Func { dx mul } forall y aload pop addvect ylength array astore def
      \else%
        \ifx\psk@method\@varrkiv						%% RUNGE-KUTTA method
	  VARRK
        \else\ifx\psk@method\@rkiv						%% RUNGE-KUTTA method
	  RK
        \else
          /F1 F2 def /F2 F3 def /F3 F4 def /F4 				        %% ADAMS method
          \ifcase\psk@adamsorder\or\or\or\or
           %% ORDRE 4
           Func def
           \or
           %% ORDRE 5
           F5 def /F5 Func def
           \or
           %% ORDRE 6
           F5 def /F5 F6 def /F6 Func def
          \fi
           INIT \psk@adamsorder\space lt
           { RK /INIT INIT 1 add def }
           { ADAMS } ifelse
        \fi\fi
      \fi
      \ifx\psk@plotfuncy\@empty
        \ifx\psk@whichord\@empty 0 \else \psk@whichord\space \fi  get %
      \else \psk@plotfuncy\space \fi
      \pst@number\psyunit mul
    } def
  }%
  \gdef\psplot@init{}%
  \@pstfalse
  \@nameuse{testqp@\psplotstyle}%
  \if@pst\psplot@ii\else\psplot@iii\fi
  \endgroup%
  \ignorespaces%
}
%
%
\def\psGTriangle{\pst@object{psGTriangle}}
\def\psGTriangle@i(#1)(#2)(#3)#4#5#6{{%
  \def\solid@star{}%
  \begin@ClosedObj
  \pst@getcoor{#1}\pst@tempA%   A: "rgb xr xg xb" or "gray xg"
  \pst@getcoor{#2}\pst@tempB%   B
  \pst@getcoor{#3}\pst@tempC%   C
  \pst@getcolor{#4}\pst@colorA
  \pst@getcolor{#5}\pst@colorB
  \pst@getcolor{#6}\pst@colorC
  \addto@pscode{%
    \pst@tempC		    % C
    \pst@tempB		    % B
    \psk@gangle             %   rotating angle
    \pst@tempA 		    % A, temporary origin
    /rgb {} def
    /gray {} def
    [ \pst@colorC ] aload length 1 eq { dup dup } if 3 array astore % gray -> rgb
    [ \pst@colorB ] aload length 1 eq { dup dup } if 3 array astore
    [ \pst@colorA ] aload length 1 eq { dup dup } if 3 array astore
    tx@addDict begin GTriangle end % PS part
  }%
  \if@star\pspolygon(#1)(#2)(#3)\fi%	draw borderline
  \def\pst@linetype{2}%
  \end@ClosedObj%
}}
%
\define@key[psset]{pstricks-add}{dicescale}{\def\psk@dicescale{#1}}
\def\psdice{\pst@object{psdice}}
\def\psdice@i#1{{%
  \pst@killglue
  \psset{framearc=0.3,linewidth=1pt,dicescale=1.0}%
  \use@par%
  \psscalebox{\psk@dicescale}{%
  \psframe(-0.5,-0.5)(0.5,0.5)%
  \ifcase#1%
    \or\qdisk(0,0){3pt}%
    \or\qdisk(-0.3,-0.3){3pt}\qdisk(0.3,0.3){3pt}%
    \or\psdice@i{1}\psdice@i{2}%
    \or\qdisk(-0.3,0.3){3pt}\qdisk(-0.3,-0.3){3pt}%
       \qdisk(0.3,0.3){3pt}\qdisk(0.3,-0.3){3pt}%
    \or\psdice@i{1}\psdice@i{4}%
    \or\psdice@i{4}\qdisk(-0.3,0){3pt}\qdisk(0.3,0){3pt}%
  \fi}%
  \ignorespaces%
}}
%
% the datafile must be a matrix with
% /dotmatrix [
%   .....
%   .....
% ] def
%
\def\psMatrixPlot{\pst@object{psMatrixPlot}}
\def\psMatrixPlot@i#1#2#3{%
  \pst@killglue
  \begingroup
  \begin@SpecialObj%
  \addto@pscode{
    (#3) run   		% load the data file
    \psk@dotsize
    \@nameuse{psds@\psk@dotstyle} % 
    /n 0 def   		% index for element
    1 1 #1 {		% the y loop (outer one)
      /y exch def	% save y
      1 1 #2 {		% the x loop (inner one)
        /x exch def	% save x
	dotmatrix n get % get value from matrix 
	dup 0 gt { 	% test if > 0
	  x \pst@number\psxunit mul 
	  \ifPst@ChangeOrder #1 y sub 1 add \else y \fi \pst@number\psyunit mul Dot%
	} { pop } ifelse
	/n n 1 add def
      } for 
    } for
  }%
  \end@SpecialObj%
  \endgroup%
  \ignorespaces%
}
%
\def\resetOptions{%
  \@zero=0%
  \def\pst@linetype{0}%
  \psset{%
%%%% pstricks %%%%%%%%
  unit=1cm,%
  swapaxes=false,%
  showpoints=false,%
  border=0pt, bordercolor=white,%
  doubleline=false, doublesep=1.25\pslinewidth,%
  doublecolor=white,%
  shadow=false, shadowsize=3pt, shadowangle=-45, shadowcolor=darkgray,%
  linewidth=.8pt,%
  linecolor=black,%
  maxdashes=11, dash=5pt 3pt, dashadjust=true, %
  dotsep=3pt,%
  linestyle=solid,%
  fillcolor=white,%
  hatchwidth=.8pt, hatchsep=4pt, hatchcolor=black, hatchangle=45,%
  hatchsepinc=0pt,hatchwidthinc=0pt,%
  fillstyle=none,%
  nArrows=2,%
  arrows=-, arrowscale=1, arrowsize=1.5pt 2, arrowlength=1.4, arrowinset=.4,%
  tbarsize=2pt 5,%
  bracketlength=.15, rbracketlength=.15,%
  hooklength=3mm,hookwidth=1mm,
  ArrowFill=true,%
  ArrowInside={},ArrowInsidePos=0.5,%
  ArrowInsideNo=1,ArrowInsideOffset=0,%
  liftpen=0, linetype=0,%
  gangle=0,%
  curvature=1 .1 0,%
  dotsize=2pt 2,%
  dotangle=0, dotscale=1, dotstyle=*,%
  linearc=0pt,%
  framearc=0,%
  cornersize=relative,%
  dimen=middle,%
  gridwidth=.8pt, griddots=0, gridcolor=black,%
  subgridwidth=.4pt, subgridcolor=gray, subgriddots=0, subgriddiv=5,%
  gridlabels=10pt, gridlabelcolor=black,%
  framesep=3pt, boxsep=true,%
  trimode=U,%
  arcsep=0,radius=.25cm,%
  ref=c,rot=0,labelsep=5pt,refangle=0,%
  intSeparator={,},%
  dicescale=1.0,%
%%%%%%%%% pst-plot %%%%%%%%%%%%%
  labelFontSize={},%
  StepType=lower, % alternative SumType=upper
  plotstyle=line,plotpoints=50,%
  ticksize=-4pt 4pt, 
  tickstyle=full, ticks=all,%
  subticksize=0.75,subticks=1,tickcolor=black,%
  ticklinestyle=solid,subticklinestyle=solid,%
  subtickcolor=gray,%
  tickwidth=0.5\pslinewidth,subtickwidth=0.25\pslinewidth,%
  labels=all,Ox=0,Dx=1,dx=0,Oy=0,Dy=1,dy=0,%
  xlabelFactor=\relax,ylabelFactor=\relax,%
  showorigin=true,%
  axesstyle=axes,%
  ChangeOrder=false,%
  braceWidth=0.35,bracePos=0.5,%
  arrowscale=1,%
  dashColorI=black,dashColorII=red,dashNo=0.2,linecap=0,%
  xyAxes=true,%
  trigLabels=false,trigLabelBase=0,%
  xDecimals={},yDecimals={},%
  xlogBase={},ylogBase={},%
  logLines=none,%
  ignoreLines=0,%
  nStep=1,nStart=0,nEnd={},%
  xStep=0,yStep=0,xStart={},xEnd={},yStart={},yEnd={},comma=false,%
  plotNo=1,plotNoMax=1,%
  xAxisLabel=x,yAxisLabel=y,%
  yAxisLabelPos={},xAxisLabelPos={},%
  llx=\z@, lly=\z@, urx=\z@, ury=\z@,% prevents rounding errors 
  randomPoints=1000,color=false,%
  method={},whichabs={},whichord={},%
  plotfuncx={},plotfuncy={},buildvector=false,algebraic=false,
  Derive={},adamsorder=4,%
  VarStep=false, PlotDerivative=none, VarStepEpsilon=default,%
  varsteptol=.001,%
  %%%%%%%%% pst-node %%%%%%%%%%
  lineAngle=0,%
  nodealign=false,%
  href=0,%
  vref=.7ex,%
  framesize=10pt,%
  nodesep=0pt,%
  arm=10pt,%
  offset=0pt,%
  angle=0,%
  arcangle=8,%
  ncurv=.67,%
  loopsize=1cm,%
  boxsize=.4cm,%
  nrot=0,%
  npos=,%
  tpos=0.5,%
  shortput=none,%
  colsep=1.5cm,%
  rowsep=1.5cm,%
  mcol=c,%
  mnode=R,%
  emnode=none
}}
%
\resetOptions
%
\catcode`\@=\PstAtCode\relax
%
%% END: pstricks-add.tex
\endinput