apl>" <-APL2-------------------- sam312.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> '5Ox' graph 1,1,1,i,5 ,xpi ,0.5 , 0 ,0 " sinhdatx.tex \begin{figure}[tbh] \caption{Graph of y\#11O5Ox+nX0j1} \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(0,0){\line(1,0){6.283185}}%x axis \put( .785398 , 0 ){\circle*{ .0286234}} \put( 1.570796 , 0 ){\circle*{ .0286234}} \put( 2.356194 , 0 ){\circle*{ .0286234}} \put( 3.141593 , 0 ){\circle*{ .0286234}} \put( 3.92699 , 0 ){\circle*{ .0286234}} \put( 4.712389 , 0 ){\circle*{ .0286234}} \put( 5.497787 , 0 ){\circle*{ .0286234}} %Draw the x axis marker values in pi \put( .685398 , 0 ){$ -\frac{3\pi}{4} $} \put( 1.470796 , 0 ){$ -\frac{\pi}{2} $} \put( 2.256194 , 0 ){$ -\frac{\pi}{4} $} \put( 3.141593 , 0 ){$ 0 $} \put( 3.92699 , 0 ){$ \frac{\pi}{4} $} \put( 4.712389 , 0 ){$ \frac{\pi}{2} $} \put( 5.497787 , 0 ){$ \frac{3\pi}{4} $} %Draw the y axis \put(3.141593,0){\line(0,1){8.37758}}%y axis %Draw the y axis markers \put( 3.141593 , 1.199247 ){\circle*{ .0286234}} \put( 3.141593 , 2.966514 ){\circle*{ .0286234}} \put( 3.141593 , 4.73378 ){\circle*{ .0286234}} \put( 3.141593 , 6.501047 ){\circle*{ .0286234}} %Draw the y axis marker values \put( 3.211406 , 1.199247 ){$ 1 $} \put( 3.211406 , 2.966514 ){$ 2 $} \put( 3.211406 , 4.73378 ){$ 3 $} \put( 3.211406 , 6.501047 ){$ 4 $} %Label the curve \put( .1256637 , 8.098328 ){n\# .5} %Draw the data points \put( .15707963 , 7.831603 ){\circle*{ .0286234}} \put( .18849556 , 7.573169 ){\circle*{ .0286234}} \put( .21991149 , 7.322771 ){\circle*{ .0286234}} \put( .25132741 , 7.080162 ){\circle*{ .0286234}} \put( .28274334 , 6.845101 ){\circle*{ .0286234}} \put( .31415927 , 6.617358 ){\circle*{ .0286234}} \put( .34557519 , 6.396706 ){\circle*{ .0286234}} \put( .37699112 , 6.182930 ){\circle*{ .0286234}} \put( .40840704 , 5.975816 ){\circle*{ .0286234}} \put( .43982297 , 5.775162 ){\circle*{ .0286234}} \put( .47123890 , 5.580769 ){\circle*{ .0286234}} \put( .502655 , 5.392445 ){\circle*{ .0286234}} \put( .53407 , 5.210004 ){\circle*{ .0286234}} \put( .565487 , 5.033266 ){\circle*{ .0286234}} \put( .596903 , 4.862057 ){\circle*{ .0286234}} \put( .628319 , 4.696208 ){\circle*{ .0286234}} \put( .659734 , 4.535554 ){\circle*{ .0286234}} \put( .69115 , 4.379938 ){\circle*{ .0286234}} \put( .722566 , 4.229206 ){\circle*{ .0286234}} \put( .753982 , 4.083209 ){\circle*{ .0286234}} \put( .785398 , 3.941803 ){\circle*{ .0286234}} \put( .816814 , 3.804849 ){\circle*{ .0286234}} \put( .84823 , 3.67221 ){\circle*{ .0286234}} \put( .879646 , 3.543757 ){\circle*{ .0286234}} \put( .911062 , 3.419363 ){\circle*{ .0286234}} \put( .942478 , 3.298904 ){\circle*{ .0286234}} \put( .973894 , 3.182261 ){\circle*{ .0286234}} \put( 1.005310 , 3.069321 ){\circle*{ .0286234}} \put( 1.036726 , 2.95997 ){\circle*{ .0286234}} \put( 1.068142 , 2.854103 ){\circle*{ .0286234}} \put( 1.099557 , 2.751613 ){\circle*{ .0286234}} \put( 1.130973 , 2.652399 ){\circle*{ .0286234}} \put( 1.162389 , 2.556364 ){\circle*{ .0286234}} \put( 1.193805 , 2.463413 ){\circle*{ .0286234}} \put( 1.225221 , 2.373454 ){\circle*{ .0286234}} \put( 1.256637 , 2.286399 ){\circle*{ .0286234}} \put( 1.288053 , 2.20216 ){\circle*{ .0286234}} \put( 1.319469 , 2.120657 ){\circle*{ .0286234}} \put( 1.350885 , 2.041807 ){\circle*{ .0286234}} \put( 1.3823 , 1.965533 ){\circle*{ .0286234}} \put( 1.413717 , 1.89176 ){\circle*{ .0286234}} \put( 1.445133 , 1.820415 ){\circle*{ .0286234}} \put( 1.476549 , 1.751427 ){\circle*{ .0286234}} \put( 1.507964 , 1.684728 ){\circle*{ .0286234}} \put( 1.53938 , 1.620254 ){\circle*{ .0286234}} \put( 1.570796 , 1.557939 ){\circle*{ .0286234}} \put( 1.602212 , 1.497722 ){\circle*{ .0286234}} \put( 1.633628 , 1.439545 ){\circle*{ .0286234}} \put( 1.665044 , 1.383349 ){\circle*{ .0286234}} \put( 1.69646 , 1.329079 ){\circle*{ .0286234}} \put( 1.727876 , 1.276681 ){\circle*{ .0286234}} \put( 1.759292 , 1.226105 ){\circle*{ .0286234}} \put( 1.790708 , 1.177299 ){\circle*{ .0286234}} \put( 1.822124 , 1.130216 ){\circle*{ .0286234}} \put( 1.853540 , 1.084809 ){\circle*{ .0286234}} \put( 1.884956 , 1.041034 ){\circle*{ .0286234}} \put( 1.916372 , .998847 ){\circle*{ .0286234}} \put( 1.947787 , .958206 ){\circle*{ .0286234}} \put( 1.979203 , .919072 ){\circle*{ .0286234}} \put( 2.010619 , .881405 ){\circle*{ .0286234}} \put( 2.042035 , .845170 ){\circle*{ .0286234}} \put( 2.073451 , .810329 ){\circle*{ .0286234}} \put( 2.104867 , .776848 ){\circle*{ .0286234}} \put( 2.136283 , .744696 ){\circle*{ .0286234}} \put( 2.167699 , .713838 ){\circle*{ .0286234}} \put( 2.199115 , .684246 ){\circle*{ .0286234}} \put( 2.23053 , .65589 ){\circle*{ .0286234}} \put( 2.261947 , .628743 ){\circle*{ .0286234}} \put( 2.293363 , .602776 ){\circle*{ .0286234}} \put( 2.324779 , .577965 ){\circle*{ .0286234}} \put( 2.356194 , .554285 ){\circle*{ .0286234}} \put( 2.38761 , .531713 ){\circle*{ .0286234}} \put( 2.419026 , .510226 ){\circle*{ .0286234}} \put( 2.450442 , .48980414 ){\circle*{ .0286234}} \put( 2.481858 , .47042593 ){\circle*{ .0286234}} \put( 2.513274 , .4520727 ){\circle*{ .0286234}} \put( 2.54469 , .43472635 ){\circle*{ .0286234}} \put( 2.576106 , .41836976 ){\circle*{ .0286234}} \put( 2.607522 , .40298677 ){\circle*{ .0286234}} \put( 2.638938 , .3885622 ){\circle*{ .0286234}} \put( 2.670354 , .37508182 ){\circle*{ .0286234}} \put( 2.701770 , .36253233 ){\circle*{ .0286234}} \put( 2.733186 , .35090132 ){\circle*{ .0286234}} \put( 2.764602 , .34017733 ){\circle*{ .0286234}} \put( 2.796017 , .33034977 ){\circle*{ .0286234}} \put( 2.827433 , .32140894 ){\circle*{ .0286234}} \put( 2.858849 , .31334601 ){\circle*{ .0286234}} \put( 2.890265 , .30615303 ){\circle*{ .0286234}} \put( 2.921681 , .29982289 ){\circle*{ .0286234}} \put( 2.953097 , .29434935 ){\circle*{ .0286234}} \put( 2.984513 , .289727 ){\circle*{ .0286234}} \put( 3.015929 , .28595129 ){\circle*{ .0286234}} \put( 3.047345 , .28301848 ){\circle*{ .0286234}} \put( 3.07876 , .28092568 ){\circle*{ .0286234}} \put( 3.110177 , .27967083 ){\circle*{ .0286234}} \put( 3.141593 , .27925268 ){\circle*{ .0286234}} \put( 3.173009 , .27967083 ){\circle*{ .0286234}} \put( 3.204425 , .28092568 ){\circle*{ .0286234}} \put( 3.23584 , .28301848 ){\circle*{ .0286234}} \put( 3.267256 , .28595129 ){\circle*{ .0286234}} \put( 3.298672 , .289727 ){\circle*{ .0286234}} \put( 3.330088 , .29434935 ){\circle*{ .0286234}} \put( 3.361504 , .29982289 ){\circle*{ .0286234}} \put( 3.39292 , .30615303 ){\circle*{ .0286234}} \put( 3.424336 , .31334601 ){\circle*{ .0286234}} \put( 3.455752 , .32140894 ){\circle*{ .0286234}} \put( 3.487168 , .33034977 ){\circle*{ .0286234}} \put( 3.518584 , .34017733 ){\circle*{ .0286234}} \put( 3.550000 , .35090132 ){\circle*{ .0286234}} \put( 3.581416 , .36253233 ){\circle*{ .0286234}} \put( 3.612832 , .37508182 ){\circle*{ .0286234}} \put( 3.644247 , .3885622 ){\circle*{ .0286234}} \put( 3.675663 , .40298677 ){\circle*{ .0286234}} \put( 3.707079 , .41836976 ){\circle*{ .0286234}} \put( 3.738495 , .43472635 ){\circle*{ .0286234}} \put( 3.769911 , .4520727 ){\circle*{ .0286234}} \put( 3.801327 , 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