apl>" <-APL2-------------------- sam302.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> points#300 apl> '3Ox' graph 1,1,1,r,1e6,xpi ,.15 , 0 ,0 " tandatx.tex \begin{figure}[tbh] \caption{Graph of y\#9O3Ox+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(0,4.18879){\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} $} %Draw the y axis \put(3.141593,0){\line(0,1){8.37758}}%y axis %Draw the y axis markers \put( 3.141593 , .617069 ){\circle*{ .0286234}} \put( 3.141593 , 1.807643 ){\circle*{ .0286234}} \put( 3.141593 , 2.998217 ){\circle*{ .0286234}} \put( 3.141593 , 5.379364 ){\circle*{ .0286234}} \put( 3.141593 , 6.569938 ){\circle*{ .0286234}} \put( 3.141593 , 7.760511 ){\circle*{ .0286234}} %Draw the y axis marker values \put( 3.211406 , .533076 ){$ -3 $} \put( 3.211406 , 1.723650 ){$ -2 $} \put( 3.211406 , 2.914223 ){$ -1 $} \put( 3.211406 , 5.379364 ){$ 1 $} \put( 3.211406 , 6.569938 ){$ 2 $} \put( 3.211406 , 7.760511 ){$ 3 $} %Label the curve \put( 1.424189 , 8.098328 ){n\# .15} %Draw the data points \put( .02094395 , 4.213176 ){\circle*{ .0286234}} \put( .0418879 , 4.237582 ){\circle*{ .0286234}} \put( .06283185 , 4.262028 ){\circle*{ .0286234}} \put( .0837758 , 4.286534 ){\circle*{ .0286234}} \put( .10471976 , 4.31112 ){\circle*{ .0286234}} \put( .1256637 , 4.335809 ){\circle*{ .0286234}} \put( .14660766 , 4.360619 ){\circle*{ .0286234}} \put( .1675516 , 4.385572 ){\circle*{ .0286234}} \put( .18849556 , 4.410691 ){\circle*{ .0286234}} \put( .20943951 , 4.435997 ){\circle*{ .0286234}} \put( .23038346 , 4.461514 ){\circle*{ .0286234}} \put( .25132741 , 4.487265 ){\circle*{ .0286234}} \put( .27227136 , 4.513275 ){\circle*{ .0286234}} \put( .29321531 , 4.539569 ){\circle*{ .0286234}} \put( .31415927 , 4.566173 ){\circle*{ .0286234}} \put( .33510322 , 4.593115 ){\circle*{ .0286234}} \put( .35604717 , 4.620422 ){\circle*{ .0286234}} \put( .37699112 , 4.648127 ){\circle*{ .0286234}} \put( .39793507 , 4.676258 ){\circle*{ .0286234}} \put( .41887902 , 4.70485 ){\circle*{ .0286234}} \put( .43982297 , 4.733937 ){\circle*{ .0286234}} \put( .46076692 , 4.763556 ){\circle*{ .0286234}} \put( .48171087 , 4.793745 ){\circle*{ .0286234}} \put( .502655 , 4.824546 ){\circle*{ .0286234}} \put( .523599 , 4.856001 ){\circle*{ .0286234}} \put( .544543 , 4.888158 ){\circle*{ .0286234}} \put( .565487 , 4.921066 ){\circle*{ .0286234}} \put( .58643 , 4.954776 ){\circle*{ .0286234}} \put( .607375 , 4.989346 ){\circle*{ .0286234}} \put( .628319 , 5.024836 ){\circle*{ .0286234}} \put( .649262 , 5.061310 ){\circle*{ .0286234}} \put( .670206 , 5.098837 ){\circle*{ .0286234}} \put( .69115 , 5.137493 ){\circle*{ .0286234}} \put( .712094 , 5.177359 ){\circle*{ .0286234}} \put( .733038 , 5.218519 ){\circle*{ .0286234}} \put( .753982 , 5.26107 ){\circle*{ .0286234}} \put( .774926 , 5.305112 ){\circle*{ .0286234}} \put( .79587 , 5.350755 ){\circle*{ .0286234}} \put( .816814 , 5.398120 ){\circle*{ .0286234}} \put( .837758 , 5.447335 ){\circle*{ .0286234}} \put( .858702 , 5.498542 ){\circle*{ .0286234}} \put( .879646 , 5.551895 ){\circle*{ .0286234}} \put( .900590 , 5.60756 ){\circle*{ .0286234}} \put( .921534 , 5.66572 ){\circle*{ .0286234}} \put( .942478 , 5.726573 ){\circle*{ .0286234}} \put( .963422 , 5.790336 ){\circle*{ .0286234}} \put( .984366 , 5.857242 ){\circle*{ .0286234}} \put( 1.005310 , 5.927548 ){\circle*{ .0286234}} \put( 1.026254 , 6.001528 ){\circle*{ .0286234}} \put( 1.047198 , 6.079482 ){\circle*{ .0286234}} \put( 1.068142 , 6.161727 ){\circle*{ .0286234}} \put( 1.089085 , 6.248603 ){\circle*{ .0286234}} \put( 1.110029 , 6.340464 ){\circle*{ .0286234}} \put( 1.130973 , 6.437675 ){\circle*{ .0286234}} \put( 1.151917 , 6.540598 ){\circle*{ .0286234}} \put( 1.172861 , 6.649575 ){\circle*{ .0286234}} \put( 1.193805 , 6.7649 ){\circle*{ .0286234}} \put( 1.214749 , 6.886772 ){\circle*{ .0286234}} \put( 1.235693 , 7.015223 ){\circle*{ .0286234}} \put( 1.256637 , 7.150017 ){\circle*{ .0286234}} \put( 1.277581 , 7.290484 ){\circle*{ .0286234}} \put( 1.298525 , 7.435279 ){\circle*{ .0286234}} \put( 1.319469 , 7.582016 ){\circle*{ .0286234}} \put( 1.340413 , 7.726733 ){\circle*{ .0286234}} \put( 1.361357 , 7.86311 ){\circle*{ .0286234}} \put( 1.3823 , 7.98138 ){\circle*{ .0286234}} \put( 1.403245 , 8.066877 ){\circle*{ .0286234}} \put( 1.424189 , 8.098328 ){\circle*{ .0286234}} \put( 1.445133 , 8.046288 ){\circle*{ .0286234}} \put( 1.466077 , 7.872833 ){\circle*{ .0286234}} \put( 1.48702 , 7.534631 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