apl>" <-APL2-------------------- sam320.txt ---------------------------->


apl>)run cap2/sample/graph.inc


apl>" <-APL2-------------------- graph.txt ----------------------------->


apl>" Legend describing various global values:


apl>"


apl>" World coordinates(wc) are those of the real data.


apl>" Graph coordinates(gc) are those of the graph.


apl>"


apl>" caption - Override to text for graph caption.  If null, a caption


apl>"           will be generated.  The graph function resets the global


apl>"           caption variable to null at the end of its processing.


apl>"


apl>" hk ------ Constant coefficient of input.  If xr=1 (see below) then


apl>"           hk becomes the constant imaginary coefficient for all


apl>"           values of x on the graph.  If xr=0, hk will be the constant


apl>"           real coefficient.


apl>"


apl>" htl ----- 0 = both, 1 = headers, 2 = trailers, 3 = neither.


apl>"


apl>" maxx ---- Maximum x axis value in world coordinates.


apl>"


apl>" maxy ---- Maximum y axis value in world coordinates.


apl>"


apl>" minx ---- Minimum x axis value in world coordinates.


apl>"


apl>" miny ---- Minimum y axis value in world coordinates.


apl>"


apl>" mgc ----- Vertical margin in graphic coordinates.


apl>"


apl>" n ------- Synonymous with hk (see above).  The x values to which


apl>"           the function is applied to obtain y values are derived


apl>"           by first creating xwc as a vector of integers uniformly


apl>"           distributed between minx and maxx inclusive.  Then, either


apl>"           'x#(nX0j1)+xwc' or 'x#n+0j1Xxwc' is evaluated.


apl>"


apl>" nlb ----- 1 = Label the curve with the n value.


apl>"


apl>" points -- Number of points to generate.


apl>"


apl>" xgc ----- Array of x values for data points in graph coordinates.


apl>"


apl>" xiv ----- x axis marker interval in world coordinates.


apl>"


apl>" xlin ---- Width of graph in inches.


apl>"


apl>" xpg ----- Divide xwc by xpg to get xgc.


apl>"


apl>" xpi ----- Array of three values for minx, maxx, and xiv, used when


apl>"           invoking the graph function and the array of x values


apl>"           spans -pi to +pi.


apl>"


apl>" xr ------ 1=vary real x coefficient, 0=vary imaginary coefficient,


apl>"           holding the other coefficient to the constant hk (see above.).


apl>"


apl>" xt ------ Used in a variety of places to temporarily generate


apl>"           graphics coordinates.


apl>"


apl>" xwc ----- Array of x values in world coordinates.


apl>"


apl>" yadj ---- Adjustment down to print text below a line.


apl>"


apl>" yabm ---- Maximum absolute value (|y) to appear on graph.


apl>"


apl>" ygc ----- Array of y values for data points in graph coordinates.


apl>"


apl>" ylin ---- Height of graph in inches.


apl>"


apl>" ymgn ---- Margin in inches at top and bottom of y axis.


apl>"


apl>" ypg ----- Divide ywc by ypg to get ygc.


apl>"


apl>" yt ------ Used in a variety of places to temporarily generate


apl>"           graphics coordinates.


apl>"


apl>" ywc ----- Array of y values for data points in world coordinates.


apl>"


apl>" Set global values. -------------------------------------------->


apl>"


apl>caption#'' " Empty caption causes one to be generated.


apl>i#11 " Circle function code to extract imag. coef. of complex number.


apl>points#200 " Number of data points to generate on graph.


apl>r#9 " Circle function code to extract real coef. of complex number.


apl>xlin#4.5 " Width of graph in inches.


apl>"  minx = -3.14159....


apl>"  |     maxx = 3.14159....


apl>"  |     |     xiv


apl>"  |     |     |


apl>"  V     V     V


apl>xpi#(O-1),(O1),O.25


apl>ylin#6 " Height of graph in inches.


apl>ymgn#.2 " Margin in inches at top and bottom of y axis.


apl>"


apl>" <----------------------------------------------------------------->


apl>" Generates the LaTeX \put statements for the data points to appear


apl>" on the graph.


apl>"


apl>Lex 'dodata'

1

apl>Gdodata


[1]       xgc#(xwc_minx)%xpg " xgc=x graphic coordinates for data points.


[2]       ygc#mgc+(ywc_miny)%ypg " ygc=y graphic coordinates for data points.


[3]       $bylabXI0=nlb " Branch if the curve is not to be labelled.


[4]       '%Label the curve'


[5]       xt#1Y(u=S/u#|ywc)/xgc " x coord where maximum/mininum occurs


[6]       yt#(_yadjX0>vs/ywc)+(vs#xt=xgc)/ygc " y coord of maximum/minimum


[7]       " Note: Calculation for yt works only if all minima occur below


[8]       " y axis, and all maxima occur above.


[9]       pcon,(xt,',',[1.5]yt),`Z'){n\#',(Fhk),'}'


[10]      bylab:'%Draw the data points'


[11]      pcon,((xgc#-1U1Uxgc),',',[1.5](ygc#-1U1Uygc)),circon


[12]      G


apl>" <----------------------------------------------------------------->


apl>" Generate xwc and ywc, the arrays of x/y coordinates for the data


apl>" points to appear on the graph.


apl>"


apl>Lex 'genxy'

1

apl>Ggenxy


[1]       xwc#minx+(xlwc#maxx_minx)X(-1+Ipoints+1)%points


[2]       $varyrealXIxr


[3]       x#hk+0j1Xxwc " real part is constant, imaginary varies.


[4]       $calcy " Branch to compute values of y for data points.


[5]       varyreal:x#(hkX0j1)+xwc " Imaginary is constant, real varies.


[6]       calcy:ywc#eOCfun " Compute values of y for data points


[7]       ywcm#yabm>|ywc " Mask of keepers, magnitudes of y < yabm.


[8]       xwc#ywcm/xwc " Pick the keepers.


[9]       ywc#ywcm/ywc " Pick the keepers.


[10]      G


apl>"


apl>" <----------------------------------------------------------------->


apl>" Main graph routine.


apl>"


apl>Lex 'graph'

1

apl>Gfun graph a


[1]       "Graphs the imaginary or real coefficient of result of fun.


[2]       " fun = expression to evaluate.


[3]       (htl nlb xr e yabm minx maxx xiv hk yiv yca)#a


[4]       genxy " Generate the data points.


[5]       $dataXIhtl>1 " Branch if htl greater than 1.


[6]       scale " Calculate global scaling values.


[7]       headers " Generate LaTeX figure headers.


[8]       data:dodata " Process and graph data points.


[9]       trailers " Generate Latex figure trailers, maybe.


[10]      G


apl>"


apl>" <----------------------------------------------------------------->


apl>" Generates the LaTeX statements to begin the graph.


apl>"


apl>Lex 'headers'

1

apl>Gheaders


[1]       '\begin{figure}[tbh]'


[2]       $gencapXI0=Rcaption " Branch if no caption override.


[3]       '\caption{',caption,'}'


[4]       $begin


[5]       gencap:$realcapXI(xr=1)&hk=0 " Branch if x data are not complex.


[6]       $ncaptionXInlb=0 " Branch if curves are not labelled with n value.


[7]       '\caption{Graph of y\#',(Fe),'O',fun,'+nX0j1}'


[8]       $begin


[9]       ncaption:$cplxcapXIxr " Branch if varying real coefficient.


[10]      '\caption{Graph of y\#',(Fe),'O',(-1Ufun),(Fhk),'+xX0j1}'


[11]      $begin


[12]      cplxcap:'\caption{Graph of y\#',(Fe),'O',fun,'+(n\#',(Fhk),')X0j1}'


[13]      $begin


[14]      realcap:'\caption{Graph of y\#',fun,'}'


[15]      begin:'\begin{center}'


[16]      '\setlength{\unitlength}{',(Flin),'in}'


[17]      '\begin{picture}(',(Fxlin%lin),',',(Fylin%lin),')'


[18]      '%Draw a frame around the picture'


[19]      ' \put(0,0){\line(1,0){',(Fxlgc),'}}% bottom'


[20]      ' \put(0,0){\line(0,1){',(Fylgc),'}}% left'


[21]      ' \put(0,',(Fylgc),'){\line(1,0){',(Fxlgc),'}}% top'


[22]      ' \put(',(Fxlgc),',0){\line(0,1){',(Fylgc),'}}% right'


[23]      '%Draw the x axis'


[24]      ' \put(0,',(Fxax),'){\line(1,0){',(Fxlgc),'}}%x axis'


[25]      xt#xoff%xpg


[26]      pcon,((xt,[1.5]','),xax),circon " Draw the x axis markers.


[27]      xt#xt_xpgX.1Xxmk<0


[28]      yt#xax+((.05%lin)Xxax=mgc)_yadjXxax>mgc


[29]      $dopaxXIpix


[30]      '%Draw the x axis marker values'


[31]      pcon,xt,',',yt,econ,xmk,[1.5]scon


[32]      $doyax


[33]      dopax:'%Draw the x axis marker values in pi'


[34]      picon#(`Z'\frac{') ,`1 '\pi}{4}' '\pi}{2}' '3\pi}{4}'


[35]      picon#('-',`1`Rpicon),'0',picon


[36]      pcon,xt,',',yt,econ,picon,[1.5]scon


[37]      doyax:'%Draw the y axis'


[38]      $putymkXI(yax=0)


[39]      ' \put(',(Fyax),',0){\line(0,1){',(Fylgc),'}}%y axis'


[40]      putymk:'%Draw the y axis markers'


[41]      ymask#ymk^=0


[42]      yt#ymask/mgc+(ymk_miny)%ypg


[43]      pcon,yax,',',yt,[1.5]circon


[44]      '%Draw the y axis marker values'


[45]      xt#yax+.05%lin


[46]      yt#yt_ypgX.1X(ymask/ymk)<0


[47]      pcon,xt,',',yt,econ,(ymask/ymk),[1.5]scon


[48]      G


apl>"


apl>" <----------------------------------------------------------------->


apl>" Calculates a variety of values needed to produce the graph.


apl>"


apl>Lex 'scale'

1

apl>Gscale


[1]       $byyXIyca " Branch if ylwc, maxy, miny are precalculated.


[2]       ylwc#(maxy#S/ywc)_miny#D/ywc


[3]       byy:ylap#ylin_2Xymgn " ylap=height allowed for data points.


[4]       lin#(xlin%xlwc)Dylap%ylwc " unitlength in inches.


[5]       yadj#.14%lin " y graphic coordinate adjustment to print text below line.


[6]       mgc#ymgn%lin " Margin in graph coordinates.


[7]       xpg#xlwc%xlgc#xlin%lin " Divide xwc by xpg to get gc.


[8]       ypg#ylwc%(_2Xymgn%lin)+ylgc#ylin%lin " Divide ywc by ypg to get gc.


[9]       xax#(yz#(minyK0)&maxyZ0)Xmgc+(|miny)%ypg " xaxis in graph coordinates.


[10]      yax#(xz#(minx<0)&maxx>0)X(|minx)%xpg " yaxis in graph coordinates.


[11]      $piaxisXIpix#(minx=O-1)&maxx=O1 " branch if pi units on x axis.


[12]      xic#(yax=0)+Dxlwc%xiv


[13]      $doyiv


[14]      piaxis:xic#Dxlwc%xiv#O.25


[15]      doyiv:$doyicXIyiv^=0


[16]      yiv#10*D10@ylwc


[17]      doyic:yic#yic+0=2|yic#Dylwc%yiv


[18]      xoff#(I-1+xic)Xxiv " Offset from minx in world coord. of x markers.


[19]      yoff#(_yiv)+(Iyic)Xyiv " Offset from miny in world coord. of y markers.


[20]      $yoffplusXIminy>0


[21]      ymk#yoff+miny+yiv||miny


[22]      $yoffdone


[23]      yoffplus:ymk#yoff+miny_yiv|miny " y for y axis markers in world coord.


[24]      yoffdone:xmk#minx+xoff " x for x axis markers in world coord.


[25]      circon#`Z'){\circle*{',(F.0205%lin),'}}'


[26]      scon#`Z'$}'


[27]      econ#`Z'){$'


[28]      pcon#`Z' \put('


[29]      G


apl>"


apl>" <----------------------------------------------------------------->


apl>" Generates the LaTeX statements to finish the graph.


apl>"


apl>Lex 'trailers'

1

apl>Gtrailers


[1]       $epicXIhtl=0 " Branch if both headers and trailers.


[2]       $eojckXInlb " Branch if graph already labelled.


[3]       pcon,(1Yxgc+xpgX.1),',',(1Yygc),'){',fun,'}' " Label the graph.


[4]       eojck:$eojXI(htl=1)+htl=3 " br if headers only, or neither.


[5]       epic:'\end{picture}'


[6]       '\end{center}'


[7]       eoj:'%Finis.'


[8]       caption#'' " Reset global caption


[9]       G


apl>"            htl: 0=both, 1=headers, 2=trailers, 3=neither.


apl>"            | nlb 1 = Label the curve.


apl>"            | | xr = 1=vary real x coeff, 0=vary imaginary coeff.


apl>"            | | | e = i(11) or r(9) to select coefficient to graph.


apl>"            | | | | yabm = maximum |y printed on graph.


apl>"            | | | | |   minx = minimum value of x.


apl>"            | | | | |   |  maxx = maximum value of x.


apl>"            | | | | |   |  | xiv = x axis marker interval.


apl>"            | | | | |   |  | | hk = Constant coefficient of input.


apl>"            | | | | |   |  | | |   yiv = y axis marker interval, or 0.


apl>"            | | | | |   |  | | |   |    yca = ylwc, maxy, miny are precalculated.


apl>"            | | | | |   |  | | |   |    |


apl>"            V V V V V   V  V V V   V    V


apl>ylwc#(maxy#1.5)_miny#-1.5


apl> '7Ox' graph 1,1,1,r,1.5,-4,4,1,0.5,.5  ,1 " tanhdatx.tex

\begin{figure}[tbh]
\caption{Graph of y\#9O7Ox+nX0j1}
\begin{center}
\setlength{\unitlength}{ .5625in}
\begin{picture}(8,10.66667)
%Draw a frame around the picture
 \put(0,0){\line(1,0){8}}% bottom
 \put(0,0){\line(0,1){10.66667}}% left
 \put(0,10.66667){\line(1,0){8}}% top
 \put(8,0){\line(0,1){10.66667}}% right
%Draw the x axis
 \put(0,5.333333){\line(1,0){8}}%x axis
  \put( 1 , 5.333333 ){\circle*{ .03644444}} 
  \put( 2 , 5.333333 ){\circle*{ .03644444}} 
  \put( 3 , 5.333333 ){\circle*{ .03644444}} 
  \put( 4 , 5.333333 ){\circle*{ .03644444}} 
  \put( 5 , 5.333333 ){\circle*{ .03644444}} 
  \put( 6 , 5.333333 ){\circle*{ .03644444}} 
  \put( 7 , 5.333333 ){\circle*{ .03644444}} 
%Draw the x axis marker values
  \put(  .9 , 5.084444 ){$ -3 $} 
  \put( 1.9 , 5.084444 ){$ -2 $} 
  \put( 2.9 , 5.084444 ){$ -1 $} 
  \put(   4 , 5.084444 ){$  0 $} 
  \put(   5 , 5.084444 ){$  1 $} 
  \put(   6 , 5.084444 ){$  2 $} 
  \put(   7 , 5.084444 ){$  3 $} 
%Draw the y axis
 \put(4,0){\line(0,1){10.66667}}%y axis
%Draw the y axis markers
  \put( 4 ,  .35555556 ){\circle*{ .03644444}} 
  \put( 4 ,   2.014815 ){\circle*{ .03644444}} 
  \put( 4 ,   3.674074 ){\circle*{ .03644444}} 
  \put( 4 ,   6.992593 ){\circle*{ .03644444}} 
  \put( 4 ,   8.651852 ){\circle*{ .03644444}} 
  \put( 4 ,   10.31111 ){\circle*{ .03644444}} 
%Draw the y axis marker values
  \put( 4.088889 ,  .32542163 ){$ -1.5 $} 
  \put( 4.088889 ,    1.98468 ){$   -1 $} 
  \put( 4.088889 ,    3.64394 ){$ -0.5 $} 
  \put( 4.088889 ,   6.992593 ){$   .5 $} 
  \put( 4.088889 ,   8.651852 ){$    1 $} 
  \put( 4.088889 ,   10.31111 ){$  1.5 $} 
%Label the curve
  \put( 0 , 1.767129   ){n\# .5} 
%Draw the data points
  \put(  .04 , 2.016118   ){\circle*{ .03644444}} 
  \put(  .08 , 2.016227   ){\circle*{ .03644444}} 
  \put(  .12 , 2.016345   ){\circle*{ .03644444}} 
  \put(  .16 , 2.016472   ){\circle*{ .03644444}} 
  \put(   .2 ,  2.01661   ){\circle*{ .03644444}} 
  \put(  .24 , 2.016760   ){\circle*{ .03644444}} 
  \put(  .28 , 2.016922   ){\circle*{ .03644444}} 
  \put(  .32 , 2.017097   ){\circle*{ .03644444}} 
  \put(  .36 , 2.017288   ){\circle*{ .03644444}} 
  \put(   .4 , 2.017494   ){\circle*{ .03644444}} 
  \put(  .44 , 2.017717   ){\circle*{ .03644444}} 
  \put(  .48 , 2.017959   ){\circle*{ .03644444}} 
  \put(  .52 ,  2.01822   ){\circle*{ .03644444}} 
  \put(  .56 , 2.018505   ){\circle*{ .03644444}} 
  \put(   .6 , 2.018812   ){\circle*{ .03644444}} 
  \put(  .64 , 2.019145   ){\circle*{ .03644444}} 
  \put(  .68 , 2.019507   ){\circle*{ .03644444}} 
  \put(  .72 , 2.019898   ){\circle*{ .03644444}} 
  \put(  .76 , 2.020322   ){\circle*{ .03644444}} 
  \put(   .8 ,  2.02078   ){\circle*{ .03644444}} 
  \put(  .84 , 2.021278   ){\circle*{ .03644444}} 
  \put(  .88 , 2.021817   ){\circle*{ .03644444}} 
  \put(  .92 , 2.022402   ){\circle*{ .03644444}} 
  \put(  .96 , 2.023035   ){\circle*{ .03644444}} 
  \put(    1 ,  2.02372   ){\circle*{ .03644444}} 
  \put( 1.04 , 2.024464   ){\circle*{ .03644444}} 
  \put( 1.08 , 2.025269   ){\circle*{ .03644444}} 
  \put( 1.12 , 2.026142   ){\circle*{ .03644444}} 
  \put( 1.16 , 2.027088   ){\circle*{ .03644444}} 
  \put(  1.2 , 2.028113   ){\circle*{ .03644444}} 
  \put( 1.24 , 2.029224   ){\circle*{ .03644444}} 
  \put( 1.28 , 2.030428   ){\circle*{ .03644444}} 
  \put( 1.32 , 2.031733   ){\circle*{ .03644444}} 
  \put( 1.36 , 2.033147   ){\circle*{ .03644444}} 
  \put(  1.4 ,  2.03468   ){\circle*{ .03644444}} 
  \put( 1.44 , 2.036342   ){\circle*{ .03644444}} 
  \put( 1.48 , 2.038144   ){\circle*{ .03644444}} 
  \put( 1.52 , 2.040097   ){\circle*{ .03644444}} 
  \put( 1.56 , 2.042214   ){\circle*{ .03644444}} 
  \put(  1.6 ,  2.04451   ){\circle*{ .03644444}} 
  \put( 1.64 , 2.047000   ){\circle*{ .03644444}} 
  \put( 1.68 , 2.049699   ){\circle*{ .03644444}} 
  \put( 1.72 , 2.052627   ){\circle*{ .03644444}} 
  \put( 1.76 , 2.055802   ){\circle*{ .03644444}} 
  \put(  1.8 , 2.059246   ){\circle*{ .03644444}} 
  \put( 1.84 , 2.062982   ){\circle*{ .03644444}} 
  \put( 1.88 , 2.067034   ){\circle*{ .03644444}} 
  \put( 1.92 , 2.071432   ){\circle*{ .03644444}} 
  \put( 1.96 , 2.076203   ){\circle*{ .03644444}} 
  \put(    2 , 2.081381   ){\circle*{ .03644444}} 
  \put( 2.04 , 2.087002   ){\circle*{ .03644444}} 
  \put( 2.08 , 2.093103   ){\circle*{ .03644444}} 
  \put( 2.12 , 2.099726   ){\circle*{ .03644444}} 
  \put( 2.16 , 2.106918   ){\circle*{ .03644444}} 
  \put(  2.2 , 2.114728   ){\circle*{ .03644444}} 
  \put( 2.24 , 2.123211   ){\circle*{ .03644444}} 
  \put( 2.28 , 2.132427   ){\circle*{ .03644444}} 
  \put( 2.32 , 2.142439   ){\circle*{ .03644444}} 
  \put( 2.36 , 2.153319   ){\circle*{ .03644444}} 
  \put(  2.4 , 2.165145   ){\circle*{ .03644444}} 
  \put( 2.44 , 2.177999   ){\circle*{ .03644444}} 
  \put( 2.48 , 2.191975   ){\circle*{ .03644444}} 
  \put( 2.52 , 2.207172   ){\circle*{ .03644444}} 
  \put( 2.56 , 2.223699   ){\circle*{ .03644444}} 
  \put(  2.6 , 2.241677   ){\circle*{ .03644444}} 
  \put( 2.64 , 2.261233   ){\circle*{ .03644444}} 
  \put( 2.68 , 2.282509   ){\circle*{ .03644444}} 
  \put( 2.72 , 2.305659   ){\circle*{ .03644444}} 
  \put( 2.76 , 2.330848   ){\circle*{ .03644444}} 
  \put(  2.8 , 2.358257   ){\circle*{ .03644444}} 
  \put( 2.84 , 2.388079   ){\circle*{ .03644444}} 
  \put( 2.88 , 2.420525   ){\circle*{ .03644444}} 
  \put( 2.92 , 2.455820   ){\circle*{ .03644444}} 
  \put( 2.96 , 2.494204   ){\circle*{ .03644444}} 
  \put(    3 , 2.535934   ){\circle*{ .03644444}} 
  \put( 3.04 , 2.581284   ){\circle*{ .03644444}} 
  \put( 3.08 ,  2.63054   ){\circle*{ .03644444}} 
  \put( 3.12 , 2.684003   ){\circle*{ .03644444}} 
  \put( 3.16 , 2.741984   ){\circle*{ .03644444}} 
  \put(  3.2 , 2.804804   ){\circle*{ .03644444}} 
  \put( 3.24 , 2.872785   ){\circle*{ .03644444}} 
  \put( 3.28 ,  2.94625   ){\circle*{ .03644444}} 
  \put( 3.32 , 3.025518   ){\circle*{ .03644444}} 
  \put( 3.36 , 3.110888   ){\circle*{ .03644444}} 
  \put(  3.4 , 3.202638   ){\circle*{ .03644444}} 
  \put( 3.44 , 3.301012   ){\circle*{ .03644444}} 
  \put( 3.48 , 3.406209   ){\circle*{ .03644444}} 
  \put( 3.52 ,  3.51837   ){\circle*{ .03644444}} 
  \put( 3.56 , 3.637567   ){\circle*{ .03644444}} 
  \put(  3.6 , 3.763787   ){\circle*{ .03644444}} 
  \put( 3.64 , 3.896923   ){\circle*{ .03644444}} 
  \put( 3.68 , 4.036762   ){\circle*{ .03644444}} 
  \put( 3.72 , 4.182977   ){\circle*{ .03644444}} 
  \put( 3.76 , 4.335123   ){\circle*{ .03644444}} 
  \put(  3.8 , 4.492634   ){\circle*{ .03644444}} 
  \put( 3.84 , 4.654827   ){\circle*{ .03644444}} 
  \put( 3.88 , 4.820912   ){\circle*{ .03644444}} 
  \put( 3.92 , 4.990006   ){\circle*{ .03644444}} 
  \put( 3.96 ,  5.16115   ){\circle*{ .03644444}} 
  \put(    4 , 5.333333   ){\circle*{ .03644444}} 
  \put( 4.04 , 5.505516   ){\circle*{ .03644444}} 
  \put( 4.08 ,  5.67666   ){\circle*{ .03644444}} 
  \put( 4.12 , 5.845755   ){\circle*{ .03644444}} 
  \put( 4.16 ,  6.01184   ){\circle*{ .03644444}} 
  \put(  4.2 , 6.174033   ){\circle*{ .03644444}} 
  \put( 4.24 , 6.331544   ){\circle*{ .03644444}} 
  \put( 4.28 , 6.483690   ){\circle*{ .03644444}} 
  \put( 4.32 , 6.629905   ){\circle*{ .03644444}} 
  \put( 4.36 , 6.769744   ){\circle*{ .03644444}} 
  \put(  4.4 ,  6.90288   ){\circle*{ .03644444}} 
  \put( 4.44 , 7.029100   ){\circle*{ .03644444}} 
  \put( 4.48 , 7.148296   ){\circle*{ .03644444}} 
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  \put( 4.56 , 7.365655   ){\circle*{ .03644444}} 
  \put(  4.6 , 7.464029   ){\circle*{ .03644444}} 
  \put( 4.64 , 7.555779   ){\circle*{ .03644444}} 
  \put( 4.68 , 7.641149   ){\circle*{ .03644444}} 
  \put( 4.72 , 7.720416   ){\circle*{ .03644444}} 
  \put( 4.76 , 7.793882   ){\circle*{ .03644444}} 
  \put(  4.8 , 7.861863   ){\circle*{ .03644444}} 
  \put( 4.84 , 7.924682   ){\circle*{ .03644444}} 
  \put( 4.88 , 7.982663   ){\circle*{ .03644444}} 
  \put( 4.92 , 8.036126   ){\circle*{ .03644444}} 
  \put( 4.96 , 8.085382   ){\circle*{ .03644444}} 
  \put(    5 , 8.130732   ){\circle*{ .03644444}} 
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  \put( 5.08 , 8.210847   ){\circle*{ .03644444}} 
  \put( 5.12 , 8.246142   ){\circle*{ .03644444}} 
  \put( 5.16 , 8.278587   ){\circle*{ .03644444}} 
  \put(  5.2 , 8.308410   ){\circle*{ .03644444}} 
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  \put(  5.4 ,  8.42499   ){\circle*{ .03644444}} 
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  \put(  5.8 , 8.551938   ){\circle*{ .03644444}} 
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  \put(    6 , 8.585285   ){\circle*{ .03644444}} 
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  \put( 6.08 , 8.595235   ){\circle*{ .03644444}} 
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  \put(  6.2 , 8.607421   ){\circle*{ .03644444}} 
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  \put( 6.32 , 8.616968   ){\circle*{ .03644444}} 
  \put( 6.36 , 8.619667   ){\circle*{ .03644444}} 
  \put(  6.4 , 8.622157   ){\circle*{ .03644444}} 
  \put( 6.44 , 8.624452   ){\circle*{ .03644444}} 
  \put( 6.48 , 8.626570   ){\circle*{ .03644444}} 
  \put( 6.52 , 8.628523   ){\circle*{ .03644444}} 
  \put( 6.56 , 8.630325   ){\circle*{ .03644444}} 
  \put(  6.6 , 8.631986   ){\circle*{ .03644444}} 
  \put( 6.64 , 8.633520   ){\circle*{ .03644444}} 
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  \put( 6.76 , 8.637443   ){\circle*{ .03644444}} 
  \put(  6.8 , 8.638554   ){\circle*{ .03644444}} 
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  \put( 6.92 , 8.641398   ){\circle*{ .03644444}} 
  \put( 6.96 , 8.642203   ){\circle*{ .03644444}} 
  \put(    7 , 8.642946   ){\circle*{ .03644444}} 
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  \put( 7.08 , 8.644265   ){\circle*{ .03644444}} 
  \put( 7.12 , 8.644849   ){\circle*{ .03644444}} 
  \put( 7.16 , 8.645388   ){\circle*{ .03644444}} 
  \put(  7.2 , 8.645886   ){\circle*{ .03644444}} 
  \put( 7.24 , 8.646345   ){\circle*{ .03644444}} 
  \put( 7.28 , 8.646769   ){\circle*{ .03644444}} 
  \put( 7.32 ,  8.64716   ){\circle*{ .03644444}} 
  \put( 7.36 , 8.647521   ){\circle*{ .03644444}} 
  \put(  7.4 , 8.647854   ){\circle*{ .03644444}} 
  \put( 7.44 , 8.648162   ){\circle*{ .03644444}} 
  \put( 7.48 , 8.648446   ){\circle*{ .03644444}} 
  \put( 7.52 , 8.648708   ){\circle*{ .03644444}} 
  \put( 7.56 , 8.648950   ){\circle*{ .03644444}} 
  \put(  7.6 , 8.649173   ){\circle*{ .03644444}} 
  \put( 7.64 , 8.649379   ){\circle*{ .03644444}} 
  \put( 7.68 , 8.649569   ){\circle*{ .03644444}} 
  \put( 7.72 , 8.649745   ){\circle*{ .03644444}} 
  \put( 7.76 , 8.649907   ){\circle*{ .03644444}} 
  \put(  7.8 , 8.650057   ){\circle*{ .03644444}} 
  \put( 7.84 , 8.650195   ){\circle*{ .03644444}} 
  \put( 7.88 , 8.650322   ){\circle*{ .03644444}} 
  \put( 7.92 , 8.650440   ){\circle*{ .03644444}} 
  \put( 7.96 , 8.650548   ){\circle*{ .03644444}} 
%Finis.

apl> '7Ox' graph 3,1,1,r,1.5,-4,4,1,2  ,.5  ,1 " tanhdatx.tex

%Label the curve
  \put( 3.52 , .700922    ){n\#2} 
%Draw the data points
  \put(  .04 , 2.013238   ){\circle*{ .03644444}} 
  \put(  .08 , 2.013107   ){\circle*{ .03644444}} 
  \put(  .12 , 2.012965   ){\circle*{ .03644444}} 
  \put(  .16 ,  2.01281   ){\circle*{ .03644444}} 
  \put(   .2 , 2.012644   ){\circle*{ .03644444}} 
  \put(  .24 , 2.012463   ){\circle*{ .03644444}} 
  \put(  .28 , 2.012267   ){\circle*{ .03644444}} 
  \put(  .32 , 2.012055   ){\circle*{ .03644444}} 
  \put(  .36 , 2.011825   ){\circle*{ .03644444}} 
  \put(   .4 , 2.011576   ){\circle*{ .03644444}} 
  \put(  .44 , 2.011307   ){\circle*{ .03644444}} 
  \put(  .48 , 2.011015   ){\circle*{ .03644444}} 
  \put(  .52 , 2.010698   ){\circle*{ .03644444}} 
  \put(  .56 , 2.010355   ){\circle*{ .03644444}} 
  \put(   .6 , 2.009984   ){\circle*{ .03644444}} 
  \put(  .64 , 2.009582   ){\circle*{ .03644444}} 
  \put(  .68 , 2.009146   ){\circle*{ .03644444}} 
  \put(  .72 , 2.008674   ){\circle*{ .03644444}} 
  \put(  .76 , 2.008163   ){\circle*{ .03644444}} 
  \put(   .8 , 2.007609   ){\circle*{ .03644444}} 
  \put(  .84 , 2.007009   ){\circle*{ .03644444}} 
  \put(  .88 , 2.006360   ){\circle*{ .03644444}} 
  \put(  .92 , 2.005656   ){\circle*{ .03644444}} 
  \put(  .96 , 2.004893   ){\circle*{ .03644444}} 
  \put(    1 , 2.004067   ){\circle*{ .03644444}} 
  \put( 1.04 , 2.003173   ){\circle*{ .03644444}} 
  \put( 1.08 , 2.002204   ){\circle*{ .03644444}} 
  \put( 1.12 , 2.001154   ){\circle*{ .03644444}} 
  \put( 1.16 , 2.000017   ){\circle*{ .03644444}} 
  \put(  1.2 , 1.998786   ){\circle*{ .03644444}} 
  \put( 1.24 , 1.997452   ){\circle*{ .03644444}} 
  \put( 1.28 , 1.996008   ){\circle*{ .03644444}} 
  \put( 1.32 , 1.994443   ){\circle*{ .03644444}} 
  \put( 1.36 , 1.992748   ){\circle*{ .03644444}} 
  \put(  1.4 , 1.990913   ){\circle*{ .03644444}} 
  \put( 1.44 , 1.988925   ){\circle*{ .03644444}} 
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  \put( 1.52 ,  1.98444   ){\circle*{ .03644444}} 
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  \put(  1.6 ,  1.97918   ){\circle*{ .03644444}} 
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  \put( 1.68 , 1.973012   ){\circle*{ .03644444}} 
  \put( 1.72 ,  1.96954   ){\circle*{ .03644444}} 
  \put( 1.76 , 1.965780   ){\circle*{ .03644444}} 
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  \put( 1.92 , 1.947362   ){\circle*{ .03644444}} 
  \put( 1.96 , 1.941770   ){\circle*{ .03644444}} 
  \put(    2 , 1.935716   ){\circle*{ .03644444}} 
  \put( 2.04 , 1.929164   ){\circle*{ .03644444}} 
  \put( 2.08 , 1.922073   ){\circle*{ .03644444}} 
  \put( 2.12 ,   1.9144   ){\circle*{ .03644444}} 
  \put( 2.16 , 1.906098   ){\circle*{ .03644444}} 
  \put(  2.2 , 1.897116   ){\circle*{ .03644444}} 
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  \put( 2.32 , 1.865534   ){\circle*{ .03644444}} 
  \put( 2.36 , 1.853252   ){\circle*{ .03644444}} 
  \put(  2.4 , 1.839980   ){\circle*{ .03644444}} 
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  \put( 2.72 , 1.688039   ){\circle*{ .03644444}} 
  \put( 2.76 , 1.661899   ){\circle*{ .03644444}} 
  \put(  2.8 , 1.633831   ){\circle*{ .03644444}} 
  \put( 2.84 , 1.603735   ){\circle*{ .03644444}} 
  \put( 2.88 ,  1.57152   ){\circle*{ .03644444}} 
  \put( 2.92 , 1.537110   ){\circle*{ .03644444}} 
  \put( 2.96 , 1.500445   ){\circle*{ .03644444}} 
  \put(    3 , 1.461497   ){\circle*{ .03644444}} 
  \put( 3.04 , 1.420282   ){\circle*{ .03644444}} 
  \put( 3.08 ,  1.37687   ){\circle*{ .03644444}} 
  \put( 3.12 , 1.331416   ){\circle*{ .03644444}} 
  \put( 3.16 , 1.284179   ){\circle*{ .03644444}} 
  \put(  3.2 , 1.235568   ){\circle*{ .03644444}} 
  \put( 3.24 , 1.186184   ){\circle*{ .03644444}} 
  \put( 3.28 ,  1.13689   ){\circle*{ .03644444}} 
  \put( 3.32 , 1.088887   ){\circle*{ .03644444}} 
  \put( 3.36 , 1.043824   ){\circle*{ .03644444}} 
  \put(  3.4 , 1.003926   ){\circle*{ .03644444}} 
  \put( 3.44 , .972163    ){\circle*{ .03644444}} 
  \put( 3.48 , .952438    ){\circle*{ .03644444}} 
  \put( 3.52 , .949811    ){\circle*{ .03644444}} 
  \put( 3.56 , .970734    ){\circle*{ .03644444}} 
  \put(  3.6 , 1.023252   ){\circle*{ .03644444}} 
  \put( 3.64 , 1.117120   ){\circle*{ .03644444}} 
  \put( 3.68 ,  1.26371   ){\circle*{ .03644444}} 
  \put( 3.72 , 1.475564   ){\circle*{ .03644444}} 
  \put( 3.76 , 1.765380   ){\circle*{ .03644444}} 
  \put(  3.8 , 2.144289   ){\circle*{ .03644444}} 
  \put( 3.84 , 2.619372   ){\circle*{ .03644444}} 
  \put( 3.88 , 3.190719   ){\circle*{ .03644444}} 
  \put( 3.92 , 3.848769   ){\circle*{ .03644444}} 
  \put( 3.96 , 4.573046   ){\circle*{ .03644444}} 
  \put(    4 , 5.333333   ){\circle*{ .03644444}} 
  \put( 4.04 , 6.093621   ){\circle*{ .03644444}} 
  \put( 4.08 , 6.817898   ){\circle*{ .03644444}} 
  \put( 4.12 , 7.475948   ){\circle*{ .03644444}} 
  \put( 4.16 , 8.047295   ){\circle*{ .03644444}} 
  \put(  4.2 , 8.522378   ){\circle*{ .03644444}} 
  \put( 4.24 , 8.901287   ){\circle*{ .03644444}} 
  \put( 4.28 , 9.191103   ){\circle*{ .03644444}} 
  \put( 4.32 , 9.402956   ){\circle*{ .03644444}} 
  \put( 4.36 , 9.54955    ){\circle*{ .03644444}} 
  \put(  4.4 , 9.64341    ){\circle*{ .03644444}} 
  \put( 4.44 , 9.69593    ){\circle*{ .03644444}} 
  \put( 4.48 , 9.71686    ){\circle*{ .03644444}} 
  \put( 4.52 , 9.71423    ){\circle*{ .03644444}} 
  \put( 4.56 ,  9.6945    ){\circle*{ .03644444}} 
  \put(  4.6 , 9.66274    ){\circle*{ .03644444}} 
  \put( 4.64 , 9.62284    ){\circle*{ .03644444}} 
  \put( 4.68 , 9.57778    ){\circle*{ .03644444}} 
  \put( 4.72 , 9.52978    ){\circle*{ .03644444}} 
  \put( 4.76 , 9.480482   ){\circle*{ .03644444}} 
  \put(  4.8 , 9.431099   ){\circle*{ .03644444}} 
  \put( 4.84 , 9.382487   ){\circle*{ .03644444}} 
  \put( 4.88 ,  9.33525   ){\circle*{ .03644444}} 
  \put( 4.92 , 9.289796   ){\circle*{ .03644444}} 
  \put( 4.96 , 9.246385   ){\circle*{ .03644444}} 
  \put(    5 , 9.205169   ){\circle*{ .03644444}} 
  \put( 5.04 , 9.166222   ){\circle*{ .03644444}} 
  \put( 5.08 , 9.129557   ){\circle*{ .03644444}} 
  \put( 5.12 , 9.095146   ){\circle*{ .03644444}} 
  \put( 5.16 , 9.062931   ){\circle*{ .03644444}} 
  \put(  5.2 , 9.032836   ){\circle*{ .03644444}} 
  \put( 5.24 , 9.004767   ){\circle*{ .03644444}} 
  \put( 5.28 , 8.978628   ){\circle*{ .03644444}} 
  \put( 5.32 , 8.954313   ){\circle*{ .03644444}} 
  \put( 5.36 , 8.931719   ){\circle*{ .03644444}} 
  \put(  5.4 , 8.910742   ){\circle*{ .03644444}} 
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  \put(  5.8 ,  8.76955   ){\circle*{ .03644444}} 
  \put( 5.84 , 8.760569   ){\circle*{ .03644444}} 
  \put( 5.88 , 8.752267   ){\circle*{ .03644444}} 
  \put( 5.92 , 8.744594   ){\circle*{ .03644444}} 
  \put( 5.96 , 8.737503   ){\circle*{ .03644444}} 
  \put(    6 ,  8.73095   ){\circle*{ .03644444}} 
  \put( 6.04 , 8.724897   ){\circle*{ .03644444}} 
  \put( 6.08 , 8.719305   ){\circle*{ .03644444}} 
  \put( 6.12 , 8.714138   ){\circle*{ .03644444}} 
  \put( 6.16 , 8.709366   ){\circle*{ .03644444}} 
  \put(  6.2 , 8.704958   ){\circle*{ .03644444}} 
  \put( 6.24 , 8.700887   ){\circle*{ .03644444}} 
  \put( 6.28 , 8.697127   ){\circle*{ .03644444}} 
  \put( 6.32 , 8.693654   ){\circle*{ .03644444}} 
  \put( 6.36 , 8.690447   ){\circle*{ .03644444}} 
  \put(  6.4 , 8.687486   ){\circle*{ .03644444}} 
  \put( 6.44 , 8.684751   ){\circle*{ .03644444}} 
  \put( 6.48 , 8.682226   ){\circle*{ .03644444}} 
  \put( 6.52 , 8.679895   ){\circle*{ .03644444}} 
  \put( 6.56 , 8.677742   ){\circle*{ .03644444}} 
  \put(  6.6 , 8.675754   ){\circle*{ .03644444}} 
  \put( 6.64 , 8.673918   ){\circle*{ .03644444}} 
  \put( 6.68 , 8.672224   ){\circle*{ .03644444}} 
  \put( 6.72 , 8.670659   ){\circle*{ .03644444}} 
  \put( 6.76 , 8.669214   ){\circle*{ .03644444}} 
  \put(  6.8 ,  8.66788   ){\circle*{ .03644444}} 
  \put( 6.84 , 8.666649   ){\circle*{ .03644444}} 
  \put( 6.88 , 8.665512   ){\circle*{ .03644444}} 
  \put( 6.92 , 8.664463   ){\circle*{ .03644444}} 
  \put( 6.96 , 8.663494   ){\circle*{ .03644444}} 
  \put(    7 , 8.662599   ){\circle*{ .03644444}} 
  \put( 7.04 , 8.661773   ){\circle*{ .03644444}} 
  \put( 7.08 , 8.661011   ){\circle*{ .03644444}} 
  \put( 7.12 , 8.660307   ){\circle*{ .03644444}} 
  \put( 7.16 , 8.659657   ){\circle*{ .03644444}} 
  \put(  7.2 , 8.659057   ){\circle*{ .03644444}} 
  \put( 7.24 , 8.658504   ){\circle*{ .03644444}} 
  \put( 7.28 , 8.657992   ){\circle*{ .03644444}} 
  \put( 7.32 ,  8.65752   ){\circle*{ .03644444}} 
  \put( 7.36 , 8.657085   ){\circle*{ .03644444}} 
  \put(  7.4 , 8.656682   ){\circle*{ .03644444}} 
  \put( 7.44 , 8.656311   ){\circle*{ .03644444}} 
  \put( 7.48 , 8.655968   ){\circle*{ .03644444}} 
  \put( 7.52 , 8.655652   ){\circle*{ .03644444}} 
  \put( 7.56 , 8.655360   ){\circle*{ .03644444}} 
  \put(  7.6 ,  8.65509   ){\circle*{ .03644444}} 
  \put( 7.64 , 8.654841   ){\circle*{ .03644444}} 
  \put( 7.68 , 8.654611   ){\circle*{ .03644444}} 
  \put( 7.72 , 8.654399   ){\circle*{ .03644444}} 
  \put( 7.76 , 8.654203   ){\circle*{ .03644444}} 
  \put(  7.8 , 8.654023   ){\circle*{ .03644444}} 
  \put( 7.84 , 8.653856   ){\circle*{ .03644444}} 
  \put( 7.88 , 8.653702   ){\circle*{ .03644444}} 
  \put( 7.92 , 8.653560   ){\circle*{ .03644444}} 
  \put( 7.96 , 8.653428   ){\circle*{ .03644444}} 
%Finis.

apl> '7Ox' graph 2,1,1,r,1.5,-4,4,1,4  ,.5  ,1 " tanhdatx.tex

%Label the curve
  \put( 2.68 , 1.730253   ){n\#4} 
%Draw the data points
  \put(  .04 , 2.014465   ){\circle*{ .03644444}} 
  \put(  .08 , 2.014436   ){\circle*{ .03644444}} 
  \put(  .12 , 2.014404   ){\circle*{ .03644444}} 
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  \put(  .28 , 2.014250   ){\circle*{ .03644444}} 
  \put(  .32 , 2.014203   ){\circle*{ .03644444}} 
  \put(  .36 , 2.014152   ){\circle*{ .03644444}} 
  \put(   .4 , 2.014097   ){\circle*{ .03644444}} 
  \put(  .44 , 2.014038   ){\circle*{ .03644444}} 
  \put(  .48 , 2.013974   ){\circle*{ .03644444}} 
  \put(  .52 , 2.013904   ){\circle*{ .03644444}} 
  \put(  .56 , 2.013829   ){\circle*{ .03644444}} 
  \put(   .6 , 2.013747   ){\circle*{ .03644444}} 
  \put(  .64 , 2.013659   ){\circle*{ .03644444}} 
  \put(  .68 , 2.013563   ){\circle*{ .03644444}} 
  \put(  .72 ,  2.01346   ){\circle*{ .03644444}} 
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  \put(  .96 , 2.012638   ){\circle*{ .03644444}} 
  \put(    1 ,  2.01246   ){\circle*{ .03644444}} 
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%Finis.

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