apl>" <-APL2-------------------- sam319.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> '7Ox' graph 0,0,1,r,1  ,xpi     ,0   , 0.1,0 " tanhdata.tex

\begin{figure}[tbh]
\caption{Graph of y\#7Ox}
\begin{center}
\setlength{\unitlength}{ .716197in}
\begin{picture}(6.283185,8.37758)
%Draw a frame around the picture
 \put(0,0){\line(1,0){6.283185}}% bottom
 \put(0,0){\line(0,1){8.37758}}% left
 \put(0,8.37758){\line(1,0){6.283185}}% top
 \put(6.283185,0){\line(0,1){8.37758}}% right
%Draw the x axis
 \put(0,4.18879){\line(1,0){6.283185}}%x axis
  \put(  .785398 , 4.18879 ){\circle*{ .0286234}} 
  \put( 1.570796 , 4.18879 ){\circle*{ .0286234}} 
  \put( 2.356194 , 4.18879 ){\circle*{ .0286234}} 
  \put( 3.141593 , 4.18879 ){\circle*{ .0286234}} 
  \put(  3.92699 , 4.18879 ){\circle*{ .0286234}} 
  \put( 4.712389 , 4.18879 ){\circle*{ .0286234}} 
  \put( 5.497787 , 4.18879 ){\circle*{ .0286234}} 
%Draw the x axis marker values in pi
  \put(  .685398 , 3.993313 ){$ -\frac{3\pi}{4} $} 
  \put( 1.470796 , 3.993313 ){$  -\frac{\pi}{2} $} 
  \put( 2.256194 , 3.993313 ){$  -\frac{\pi}{4} $} 
  \put( 3.141593 , 3.993313 ){$               0 $} 
  \put(  3.92699 , 3.993313 ){$   \frac{\pi}{4} $} 
  \put( 4.712389 , 3.993313 ){$   \frac{\pi}{2} $} 
  \put( 5.497787 , 3.993313 ){$  \frac{3\pi}{4} $} 
%Draw the y axis
 \put(3.141593,0){\line(0,1){8.37758}}%y axis
%Draw the y axis markers
  \put( 3.141593 ,   .65704 ){\circle*{ .0286234}} 
  \put( 3.141593 , 1.049457 ){\circle*{ .0286234}} 
  \put( 3.141593 , 1.441874 ){\circle*{ .0286234}} 
  \put( 3.141593 ,  1.83429 ){\circle*{ .0286234}} 
  \put( 3.141593 , 2.226707 ){\circle*{ .0286234}} 
  \put( 3.141593 , 2.619124 ){\circle*{ .0286234}} 
  \put( 3.141593 ,  3.01154 ){\circle*{ .0286234}} 
  \put( 3.141593 , 3.403957 ){\circle*{ .0286234}} 
  \put( 3.141593 , 3.796374 ){\circle*{ .0286234}} 
  \put( 3.141593 , 4.581207 ){\circle*{ .0286234}} 
  \put( 3.141593 , 4.973624 ){\circle*{ .0286234}} 
  \put( 3.141593 ,  5.36604 ){\circle*{ .0286234}} 
  \put( 3.141593 , 5.758457 ){\circle*{ .0286234}} 
  \put( 3.141593 , 6.150873 ){\circle*{ .0286234}} 
  \put( 3.141593 ,  6.54329 ){\circle*{ .0286234}} 
  \put( 3.141593 , 6.935707 ){\circle*{ .0286234}} 
  \put( 3.141593 , 7.328123 ){\circle*{ .0286234}} 
  \put( 3.141593 ,  7.72054 ){\circle*{ .0286234}} 
%Draw the y axis marker values
  \put( 3.211406 ,  .631557 ){$ -0.9 $} 
  \put( 3.211406 , 1.023974 ){$ -0.8 $} 
  \put( 3.211406 ,  1.41639 ){$ -0.7 $} 
  \put( 3.211406 , 1.808807 ){$ -0.6 $} 
  \put( 3.211406 , 2.201224 ){$ -0.5 $} 
  \put( 3.211406 ,  2.59364 ){$ -0.4 $} 
  \put( 3.211406 , 2.986057 ){$ -0.3 $} 
  \put( 3.211406 , 3.378474 ){$ -0.2 $} 
  \put( 3.211406 ,  3.77089 ){$ -0.1 $} 
  \put( 3.211406 , 4.581207 ){$   .1 $} 
  \put( 3.211406 , 4.973624 ){$   .2 $} 
  \put( 3.211406 ,  5.36604 ){$   .3 $} 
  \put( 3.211406 , 5.758457 ){$   .4 $} 
  \put( 3.211406 , 6.150873 ){$   .5 $} 
  \put( 3.211406 ,  6.54329 ){$   .6 $} 
  \put( 3.211406 , 6.935707 ){$   .7 $} 
  \put( 3.211406 , 7.328123 ){$   .8 $} 
  \put( 3.211406 ,  7.72054 ){$   .9 $} 
%Draw the data points
  \put(  .03141593 , .28019946    ){\circle*{ .0286234}} 
  \put(  .06283185 , .28120737    ){\circle*{ .0286234}} 
  \put(  .09424778 , .28228037    ){\circle*{ .0286234}} 
  \put(   .1256637 , .28342262    ){\circle*{ .0286234}} 
  \put(  .15707963 , .28463859    ){\circle*{ .0286234}} 
  \put(  .18849556 , .28593298    ){\circle*{ .0286234}} 
  \put(  .21991149 , .28731085    ){\circle*{ .0286234}} 
  \put(  .25132741 , .28877753    ){\circle*{ .0286234}} 
  \put(  .28274334 , .29033872    ){\circle*{ .0286234}} 
  \put(  .31415927 , .29200047    ){\circle*{ .0286234}} 
  \put(  .34557519 ,  .2937692    ){\circle*{ .0286234}} 
  \put(  .37699112 , .29565175    ){\circle*{ .0286234}} 
  \put(  .40840704 , .29765538    ){\circle*{ .0286234}} 
  \put(  .43982297 , .29978782    ){\circle*{ .0286234}} 
  \put(  .47123890 , .30205726    ){\circle*{ .0286234}} 
  \put(    .502655 , .30447242    ){\circle*{ .0286234}} 
  \put(     .53407 , .30704255    ){\circle*{ .0286234}} 
  \put(    .565487 , .30977749    ){\circle*{ .0286234}} 
  \put(    .596903 , .31268768    ){\circle*{ .0286234}} 
  \put(    .628319 , .31578421    ){\circle*{ .0286234}} 
  \put(    .659734 , .31907884    ){\circle*{ .0286234}} 
  \put(     .69115 , .32258405    ){\circle*{ .0286234}} 
  \put(    .722566 , .32631311    ){\circle*{ .0286234}} 
  \put(    .753982 , .33028007    ){\circle*{ .0286234}} 
  \put(    .785398 , .33449983    ){\circle*{ .0286234}} 
  \put(    .816814 ,  .3389882    ){\circle*{ .0286234}} 
  \put(     .84823 , .34376195    ){\circle*{ .0286234}} 
  \put(    .879646 , .34883883    ){\circle*{ .0286234}} 
  \put(    .911062 , .35423763    ){\circle*{ .0286234}} 
  \put(    .942478 , .35997829    ){\circle*{ .0286234}} 
  \put(    .973894 , .36608189    ){\circle*{ .0286234}} 
  \put(   1.005310 , .37257074    ){\circle*{ .0286234}} 
  \put(   1.036726 , .37946843    ){\circle*{ .0286234}} 
  \put(   1.068142 , .38679992    ){\circle*{ .0286234}} 
  \put(   1.099557 , .39459157    ){\circle*{ .0286234}} 
  \put(   1.130973 , .40287124    ){\circle*{ .0286234}} 
  \put(   1.162389 , .41166832    ){\circle*{ .0286234}} 
  \put(   1.193805 , .42101383    ){\circle*{ .0286234}} 
  \put(   1.225221 , .43094047    ){\circle*{ .0286234}} 
  \put(   1.256637 , .44148270    ){\circle*{ .0286234}} 
  \put(   1.288053 ,  .4526768    ){\circle*{ .0286234}} 
  \put(   1.319469 , .46456097    ){\circle*{ .0286234}} 
  \put(   1.350885 , .47717532    ){\circle*{ .0286234}} 
  \put(     1.3823 , .49056202    ){\circle*{ .0286234}} 
  \put(   1.413717 ,   .504765    ){\circle*{ .0286234}} 
  \put(   1.445133 ,   .519832    ){\circle*{ .0286234}} 
  \put(   1.476549 ,   .535809    ){\circle*{ .0286234}} 
  \put(   1.507964 ,   .552750    ){\circle*{ .0286234}} 
  \put(    1.53938 ,   .570705    ){\circle*{ .0286234}} 
  \put(   1.570796 ,   .589732    ){\circle*{ .0286234}} 
  \put(   1.602212 ,   .609887    ){\circle*{ .0286234}} 
  \put(   1.633628 ,    .63123    ){\circle*{ .0286234}} 
  \put(   1.665044 ,   .653825    ){\circle*{ .0286234}} 
  \put(    1.69646 ,   .677736    ){\circle*{ .0286234}} 
  \put(   1.727876 ,   .703028    ){\circle*{ .0286234}} 
  \put(   1.759292 ,   .729773    ){\circle*{ .0286234}} 
  \put(   1.790708 ,    .75804    ){\circle*{ .0286234}} 
  \put(   1.822124 ,   .787904    ){\circle*{ .0286234}} 
  \put(   1.853540 ,   .819439    ){\circle*{ .0286234}} 
  \put(   1.884956 ,   .852722    ){\circle*{ .0286234}} 
  \put(   1.916372 ,    .88783    ){\circle*{ .0286234}} 
  \put(   1.947787 ,   .924844    ){\circle*{ .0286234}} 
  \put(   1.979203 ,   .963843    ){\circle*{ .0286234}} 
  \put(   2.010619 ,   1.004909   ){\circle*{ .0286234}} 
  \put(   2.042035 ,   1.048123   ){\circle*{ .0286234}} 
  \put(   2.073451 ,   1.093565   ){\circle*{ .0286234}} 
  \put(   2.104867 ,   1.141315   ){\circle*{ .0286234}} 
  \put(   2.136283 ,   1.191453   ){\circle*{ .0286234}} 
  \put(   2.167699 ,   1.244055   ){\circle*{ .0286234}} 
  \put(   2.199115 ,   1.299196   ){\circle*{ .0286234}} 
  \put(    2.23053 ,   1.356949   ){\circle*{ .0286234}} 
  \put(   2.261947 ,   1.417379   ){\circle*{ .0286234}} 
  \put(   2.293363 ,   1.480552   ){\circle*{ .0286234}} 
  \put(   2.324779 ,   1.546523   ){\circle*{ .0286234}} 
  \put(   2.356194 ,   1.615345   ){\circle*{ .0286234}} 
  \put(    2.38761 ,    1.68706   ){\circle*{ .0286234}} 
  \put(   2.419026 ,   1.761707   ){\circle*{ .0286234}} 
  \put(   2.450442 ,   1.839311   ){\circle*{ .0286234}} 
  \put(   2.481858 ,   1.919889   ){\circle*{ .0286234}} 
  \put(   2.513274 ,   2.003448   ){\circle*{ .0286234}} 
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%Finis.

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