Line Plots

Plots contianing lines generated from mathematical functions.

adjust.gle

adjust.gleadjust.gle adjust.zip zip file contains all files for this figure.

adjust.gle

 ! Demo about plot adjustments.
 ! Author: Francois Tonneau

 ! In this script, data from different phases will be obtained from a tab-
 ! delimited file. By default, GLE does not connect data points across missing
 ! values. So, we have used the trick of inserting missing values ('*') into
 ! the data file to create visual breaks across phases.

 size 10 8

 set font ss cap round join round

 begin graph

 xaxis min -2 max 68
 yaxis min -2 max 140 ftick 0 dticks 20

 ! We put custom tick labels ('xnames') at custom places along the x axis
 ! ('xplaces'):

 xplaces 1 10 24 34 44 55 65
 xnames 1 10 10 20 30 10 20

 x2axis off
 y2axis off
 side off
 subticks off

 small = 0.1
 xticks length -small
 yticks length small

 xtitle "Sessions" dist 0.3
 ytitle "Responses per minute" dist 0.3

 data "adjust.dat"

 ! Aside from named colors and the #RRGGBB notation, GLE lets us define hues
 ! with the rgb255() function. Each of its arguments is a number from 0 to
 ! 255, corresponding to the intensity of red, blue, and green.

 d1 line color rgb255(0,78,88) lwidth 0.03
 d2 line color rgb255(205,92,92) lwidth 0.03

 ! We create a custom dataset to plot a horizontal line starting at x = 15:

 base_level = 71
 let d3 = base_level from 15 to 68

 ! GLE plots graphical elements through successive layers, the layer for
 ! data lines being layer #700. Creating a new layer with a number < 700
 ! forces the horizontal line to lie behind the data:

 begin layer 600
 d3 line color #999999 lstyle 44 lwidth 0.025
 end layer

 end graph

 set lwidth 0.025

 ! The xg() and yg() functions transform axis-relative coordinates (e.g., x = 1)
 ! into actual centimeters. These functions are very useful for positioning an
 ! object on the plot, but they cannot be called directly from a graph block --
 ! so we call them once the graph block is over. Here we use them to add line
 ! segments to the x axis:

 amove xg(1) yg(-2)
 aline xg(14) yg(-2)

 amove xg(15) yg(-2)
 aline xg(45) yg(-2)

 amove xg(46) yg(-2)
 aline xg(68) yg(-2)

 amove xg(-2) yg(0)
 aline xg(-2) yg(140)

 set lwidth 0.02

 ! We define a custom subroutine to add special ticks to the x axis:

 sub add_tick place
 amove xg(place) yg(-2)
 rline 0 -small
 end sub

 add_tick 5

 add_tick 19
 add_tick 29
 add_tick 39

 add_tick 50
 add_tick 60

 ! We also add vertical dashed lines to separate phases from one another:

 set lstyle 12

 amove xg(14.5) yg(0)
 aline xg(14.5) yg(139)

 amove xg(45.5) yg(0)
 aline xg(45.5) yg(139)

 ! Finally, we add custom labels to the plot:

 amove 2 yg(140)
 write "S53"

 amove xg(22) yg(122)
 write "VI"

 amove xg(20) yg(10)
 write "Ext"

 ! Done. We have used layers as well as the xg() and yg() functions.

adphas.gle

adphas.gleadphas.gle adphas.zip zip file contains all files for this figure.

adphas.gle

 ! Nice example by Axel Rohde

 size 22 24
 set font texcmr hei 0.55
 x1 = -0.15; x2 = 0.6; xstep = 0.001

 sub f x a
 return pi+2*atn(a-sqrt(1-a^2)*tan(25*x*sqrt(1-a^2)/2))
 end sub

 sub do_label s$
 gsave
 set just cc
 amove 0.75 yg(ygmax)+1
 write s$; circle 0.4
 grestore
 end sub

 amove 0 14
 begin graph
 size 25 9
 title "Driven Van der Pol oscillator - Adler's equation"
 xtitle "Time/a.u."
 ytitle "Phase/radian"
 xaxis min 0 max 10
 yaxis min -0.3 max 2*pi+0.3 ftick 0 dticks pi/2 format "pi"
 key position tr
 let d1 = f(x,0.99) from x1 to x2 step xstep
 d1 line color green lstyle 9 xmin x1 xmax x2 key "\alpha,円= 0.99"
 let d2 = f(x,0.8) from x1 to x2 step xstep
 d2 line color blue lstyle 4 xmin x1 xmax x2 key "\alpha,円= 0.8"
 let d3 = f(x,0.5) from x1 to x2 step xstep
 d3 line color red lstyle 2 xmin x1 xmax x2 key "\alpha,円= 0.5"
 let d4 = f(x,0.3) from x1 to x2 step xstep
 d4 line color black lstyle 0 xmin x1 xmax x2 key "\alpha,円= 0.3"
 let d5 = f(x,0) from x1 to x2 step xstep
 d5 line color cyan lstyle 3 xmin x1 xmax x2 key "\alpha,円= 0"
 end graph

 do_label "a"

 amove xg(3) yg(3.14)
 write "fast"
 amove xg(1.5) yg(5.5)
 write "slow"

 amove 0 0
 begin graph
 size 25 14
 title "Driven Van der Pol oscillator - numerical results"
 xtitle "Time/a.u."
 ytitle "Amplitude/a.u."
 xaxis min 83 max 210
 yaxis min -3 max 3
 data "adphas.dat"
 let d4 = d3*1.2
 key position tr
 d1 line smooth lstyle 1 color red key "Response"
 d4 line smooth lstyle 2 color blue key "Driver"
 end graph

 do_label "b"

 amove 9 yg(2.3)
 write "fast"
 amove 6 yg(2.3)
 write "slow"
 amove 5.5 2.5
 write "out of phase"
 amove 9.4 2.5
 write "in phase"

armand.gle

armand.glearmand.gle armand.zip zip file contains all files for this figure.

armand.gle

 size 21.5 13.5

 set font texcmr hei 0.5
 a = 0.9; t = asin(a); s = sqrt(1-a^2)

 amove 0.3 0.5
 begin graph
 size 12 8
 xtitle "side band frequency / \Omega_0"
 ytitle "log S(f)"
 xaxis min -10 max 2
 yaxis min 10^-2 max 1.5 log
 let d1 = tan(t/2) from 0 to s/2 step s
 let d2 = (1-tan(t/2)^2)*(tan(t/2)^(-x-1)) from -46*s to -s step s
 bar d1 width 0.05 color red fill red
 bar d2 width 0.05 color blue fill blue
 end graph

 begin key
 position tl
 text "\alpha\:=\:0.9"
 end key

 a = 0.1; t = asin(a); s = sqrt(1-a^2)

 amove 0.3 6.3
 begin graph
 size 12 8
 xlabels off
 ytitle "log S(f)"
 xaxis min -10 max 2
 yaxis min 10^-2 max 1.5 log
 let d1 = tan(t/2) from 0 to s/2 step s
 let d2 = (1-tan(t/2)^2)*(tan(t/2)^(-x-1)) from -100*s to -s step s
 bar d1 width 0.05 color red fill red
 bar d2 width 0.05 color blue fill blue
 end graph

 begin key
 position tl
 text "\alpha\:=\:0.1"
 end key

 amove xg(-0.3) yg(0.1)
 write "\omega_d"

 a = 0.9; omega = sqrt(1-a^2)

 amove 10.75 0.5
 begin graph
 size 12 8
 xtitle "time / 2\pi\Omega_0^{-1}"
 ytitle "\psi,円,円[rad]"
 xaxis min 0 max 4 dticks 1
 yaxis min -0.3-pi max pi+0.3 ftick -pi dticks pi format "pi"
 ysubticks off
 let d1 = 2*atn(a+sqrt(1-a^2)*tan(0.5*sqrt(1-a^2)*omega*2*pi*x)) step 0.001
 d1 line color blue
 end graph

 set lstyle 2
 amove xg(0) yg(-pi)
 aline xg(4) yg(-pi)
 amove xg(0) yg(pi)
 aline xg(4) yg(pi)
 set lstyle 0

 a = 0.1; omega = sqrt(1-a^2)

 amove 10.75 6.3
 begin graph
 size 12 8
 ytitle "\psi,円,円[rad]"
 xaxis min 0 max 4 dticks 1
 yaxis min -0.3-pi max pi+0.3 ftick -pi dticks pi format "pi"
 ysubticks off
 xlabels off
 let d1 = 2*atn(a+sqrt(1-a^2)*tan(0.5*sqrt(1-a^2)*omega*2*pi*x)) step 0.001
 d1 line color blue
 end graph

 set lstyle 2
 amove xg(0) yg(-pi)
 aline xg(4) yg(-pi)
 amove xg(0) yg(pi)
 aline xg(4) yg(pi)
 set lstyle 0

bspline.gle

bspline.glebspline.gle bspline.zip zip file contains all files for this figure.

bspline.gle

 size 10 8

 ! http://en.wikipedia.org/wiki/B-spline

 sub N j n x
 if n = 0 then
 if (x >= j) and (x < j+1) then return 1
 else return 0
 else
 return (x-j)/n*N(j,n-1,x) + (j+n+1-x)/n*N(j+1,n-1,x)
 end if
 end sub

 set texlabels 1
 begin graph
 scale auto
 title "B-Spline Basis Functions"
 xaxis min 0 max 5 dticks 1 grid
 xticks color gray10
 let d1 = N(0,2,x)
 let d2 = N(1,2,x)
 let d3 = N(2,2,x)
 key pos br
 d1 line color red key "$b_{0,2}$"
 d2 line color green key "$b_{1,2}$"
 d3 line color blue key "$b_{2,2}$"
 end graph

butterfly.gle

butterfly.glebutterfly.gle butterfly.zip zip file contains all files for this figure.

butterfly.gle

 size 9 7

 include "graphutil.gle"
 include "polarplot.gle"

 set font texcmr
 begin graph
 math
 title "Butterfly"
 xaxis min -4 max 6 dticks 2
 yaxis min -6 max 6 dticks 2
 labels off
 x0labels on
 y0labels on
 x2axis on
 y2axis on
 draw polar "exp(cos(t))-2*cos(4*t)+sin(t/12)^5" 0 12*pi fill yellow
 end graph

 set color black hei 0.33 just bl
 graph_textbox label "r(\theta) = exp(cos(\theta))-2cos(4\theta)+sin(\theta/12)^5"

compactkey.gle

compactkey.glecompactkey.gle compactkey.zip zip file contains all files for this figure.

compactkey.gle

 size 12 9

 set font texcmr
 begin graph
 scale auto
 title "``Compact'' key mode"
 yaxis dticks 0.5
 xaxis min 0 max 2*pi dticks pi/4 format "pi"
 let d1 = sin(x)
 let d2 = cos(x)
 key pos bl compact offset 0.2 0.2
 d1 line color red marker triangle mdist 1 key "Sine"
 d2 line color blue marker circle mdist 1 key "Cosine"
 end graph

diffeq.gle

diffeq.glediffeq.gle diffeq.zip zip file contains all files for this figure.

diffeq.gle

 size 10 8

 include "graphutil.gle"

 sub plotone x0 y0 cnt
 amove xg(x0) yg(y0)
 for i = 0 to cnt
 x0 = x0+y0*dt
 y0 = y0+(y0*(1-x0^2)-x0)*dt
 if (x0<-3) or (x0>3) or (y0<-3) or (y0>3) then
 i = cnt
 end if
 aline xg(x0) yg(y0)
 next i
 end sub

 sub plotall
 dt = 0.05
 set color gray40
 graph_line 0 -3 0 3
 graph_line -3 0 3 0
 set color rgb255(38,38,134)
 plotone -0.25 0 250
 plotone -0.1 0 250
 plotone 0.1 0 250
 plotone 0.25 0 250
 for j=0 to 3
 plotone -3 j 100
 plotone 3 -j 100
 next j
 for j=-3 to 3 step 0.25
 plotone -j 3 100
 plotone j -3 100
 next j
 end sub

 set texlabels 1
 begin graph
 scale auto
 title "2D differential equation"
 xtitle "$x$"
 ytitle "$y$"
 xaxis min -3 max +3
 yaxis min -3 max +3
 draw plotall
 end graph

 begin object key
 begin box add 0.1 fill white
 begin tex
 $\left\{ \begin{array}{l}
 \frac{dx}{dt}=y\vspace{0.2cm}\\
 \frac{dy}{dt}=-x+y(1-x^2)
 \end{array} \right.$
 end tex
 end box
 end object

 amove xg(xgmax) yg(ygmin)
 draw key.br

discontinuity.gle

discontinuity.glediscontinuity.gle discontinuity.zip zip file contains all files for this figure.

discontinuity.gle

 size 6 6

 set texlabels 1
 xmin = -4; xmax = 4

 sub floor x
 if x>=0 then
 return int(x)
 else if x=int(x) then
 return int(x)
 else
 return int(x)-1
 end if
 end sub

 begin graph
 math
 scale auto
 xaxis min xmin max xmax
 labels dist 0.15
 xaxis format "fix 0"
 yaxis format "fix 0"
 x2axis off
 y2axis off
 title "$\mathrm{floor}(x)$"
 discontinuity threshold 5
 let d1 = floor(x) step 0.1
 d1 line color red lwidth 0.05
 end graph

entropy.gle

entropy.gleentropy.gle entropy.zip zip file contains all files for this figure.

entropy.gle

 size 11 8

 sub entropy x
 return (-x)*log(x)/log(2)-(1-x)*log(1-x)/log(2)
 end sub

 set texlabels 1
 begin graph
 scale auto
 title "$E(D) = -p_\oplus \cdot \log_2 p_\oplus - (1-p_\oplus) \cdot \log_2 (1-p_\oplus)$"
 xtitle "$p_\oplus$"
 ytitle "Entropy $E(D)$"
 let d1 = entropy(x) from 0 to 1
 d1 line color red
 end graph

fill.gle

fill.glefill.gle fill.zip zip file contains all files for this figure.

fill.gle

 size 13 9

 set font texcmr
 begin graph
 title "Example of filling"
 xtitle "TRYPSIN activity"
 ytitle "Weight gain"
 data "test.dat"
 d1 line marker fcircle color red
 d2 line marker ftriangle color blue
 fill x1,d1 color gray50
 fill d1,d2 color gray20
 fill d2,x2 color gray5
 end graph

fill-ft.gle

fill-ft.glefill-ft.gle fill-ft.zip zip file contains all files for this figure.

fill-ft.gle

 ! Example of curve filling with semi-transparency.
 ! Author: Francois Tonneau

 ! *Because this figure involves semi-transparent elements, it must be compiled
 ! with the -cairo option:*

 ! gle -cairo -d pdf fill.gle

 ! Not including this option will result in compilation failure.

 size 12 9

 set font texcmr

 amove 1.5 1.5
 begin graph
 size 9 6
 fullsize
 xaxis min 1700 max 1780 dticks 20 hei 0.3 grid color gray20
 yaxis min 0 max 200 dticks 20 hei 0.3 grid color gray20
 side color gray70
 labels color black dist 0.2
 ylabels off
 y2labels on

 data "fill-ft.dat" d1=c1,c2 d2=c3,c4

 ! We plot our data sets with Savitsky-Golay smoothed curves ('svg_smooth')
 ! and semi-transparent hues. The rgba255() function accepts four channel
 ! values in the 0-255 range: red, green, blue, and alpha/transparency.

 d1 svg_smooth line color rgba255(213,162,83,200) lwidth 0.05
 d2 svg_smooth line color rgba255(187,89,105,200) lwidth 0.05

 ! GLE can fill areas between an axis and a dataset or between different
 ! datasets. Also, filling can be clipped between minimal and maximal values.
 ! Here we add two semi-transparent fills to the plot, one to the left of
 ! x = 1754 and the other to the right; 1754 is where the curves of the
 ! d1 and d2 datasets cross.

 light$ = rgba255(247, 218, 215, 180)
 medium$ = rgba255(231, 217, 181, 180)

 fill d1,d2 color light$ xmin 1700 xmax 1754
 fill d1,d2 color medium$ xmin 1754 xmax 1780
 end graph

 ! We add labels to the plot:

 set font texcmti hei 0.325

 amove 4.4 4
 write "Balance against"

 ! Because the 'write' command cannot deal with multi-line labels, for our next
 ! label we employ a 'begin text ... end text' block:

 amove 8.80 5.35
 begin text
 Balance in
 favour of
 England.
 end text

 set font texcmb hei 0.3

 ! All the other labels are inserted in 'begin box ... end box' blocks to give
 ! the labels a rectangular white background. The 'add' option specifies the
 ! amount of padding between the text and the border of the box; 'nobox'
 ! means that the border will not be actually drawn:

 amove 3.6 4.7
 begin box add 0.05 nobox fill white
 write "Imports"
 end box

 amove 4.8 3.0
 begin box add 0.05 nobox fill white
 write "Exports"
 end box

 set font texcmb hei 0.3 just lc

 amove 1.9 7.2
 begin box add 0.05 nobox fill white
 write "Exports and Imports to and from"
 end box
 rmove 0 -0.3
 begin box add 0.05 nobox fill white
 write "DENMARK & NORWAY"
 end box
 rmove 0 -0.3
 begin box add 0.05 nobox fill white
 write "from 1700 to 1780."
 end box

 set font texcmr hei 0.25 just lc

 amove 3.4 1.8
 begin box add 0.10 nobox fill white
 write "Bottom line in years, right hand line divided into L10,000 each."
 end box

 ! Done. We have learned about curve filling, rgba255() transparency, 'begin
 ! text ... end text' blocks, and 'begin box ... end box' blocks.

hyperbola.gle

hyperbola.glehyperbola.gle hyperbola.zip zip file contains all files for this figure.

hyperbola.gle

 size 11 11

 set texlabels 1
 begin graph
 math
 scale auto
 title "Plot of $y(x) = \frac{1}{x}$"
 yaxis min -3 max 3
 let d1 = 1/x from -3 to 3
 d1 line color red
 end graph

let-multi-dim.gle

let-multi-dim.glelet-multi-dim.gle let-multi-dim.zip zip file contains all files for this figure.

let-multi-dim.gle

 size 11 8

 set texlabels 1
 begin graph
 scale auto
 title "Let modifies both $x$ and $y$ values"
 xaxis min -7 max 7
 yaxis min 0 max 4
 data "let-multi-dim.csv"
 let d2 = d1, x
 let d3 = d1+sin(6*pi*x), x from 0 step 0.02
 d2 line color blue
 d3 line color red
 end graph

line.gle

line.gleline.gle line.zip zip file contains all files for this figure.

line.gle

 ! Example of line plot.
 ! Author: Francois Tonneau

 include openline.gle

 size 18 9

 set lwidth 0.03

 amove 1.5 1
 begin graph
 size 16 8
 fullsize
 xaxis min 1966 max 1978 ftick 1967 dticks 1 nolast
 yaxis min 0 max 7 ftick 1
 side off
 ticks off
 labels color black font rm hei 0.5
 ynames $300 $320 $340 $360 $380 $400
 data "line.dat"
 d1 marker dot msize 0.35
 draw openline d1 0.3
 end graph

 set lstyle 22 lwidth 0.02
 amove 2 yg(5)
 rline 14.5 0
 amove 2 yg(6)
 rline 14.5 0

 set font rm hei 0.4 just cc
 amove xg(1977.1) yg(5.5)
 write "5%"

 set hei 0.35 just cr
 amove 15.5 3
 write "Per capita budget expanditures"
 amove xend() yend()
 rmove 0 -0.4
 write "in constant dollars"

linemode.gle

linemode.glelinemode.gle linemode.zip zip file contains all files for this figure.

linemode.gle

 size 18 8

 set font texcmr
 sub linemode xp yp type$
 amove xp*6 yp*4
 begin graph
 size 6 3.75
 data "test.dat"
 title "d1 line "+type$
 yaxis min 0 max 12 dticks 4
 xaxis min -0.5 max 5.5
 d1 line \expr{type$}
 d1 marker square msize 0.15 color red
 end graph
 end sub

 linemode 0 1 "impulses"
 linemode 1 1 "steps"
 linemode 0 0 "fsteps"
 linemode 1 0 "hist"
 linemode 2 1 "bar"

lines.gle

lines.glelines.gle lines.zip zip file contains all files for this figure.

lines.gle

 ! Demo about line styles.
 ! Author: Francois Tonneau

 size 10 8

 set font ss

 ! We set line termination ('cap') to 'round' (other possible values are 'butt'
 ! and 'square'):

 set cap round

 begin graph

 ! In defining axis limits we use 'pi' (= 3.14...), which is a pre-declared
 ! variable in GLE. As usual, arithmetic expressions may not contain spaces:

 xaxis min 2*pi max 6*pi dticks 2*pi
 yaxis min -1 max 1 dticks 1

 ! We remove the axes and parts of axes (such as their spine or 'side') we
 ! don't want:

 x2axis off
 y2axis off
 xside off
 yside off
 subticks off

 ! We now define custom names for the x-axis ticks with the 'xnames' command.
 ! Quotes are not needed, any sequence of non-blank chars will be interpreted
 ! as a name. Each '\pi' expression (notice the backslash) will render as the
 ! Greek symbol, pi:

 xnames 2\pi 4\pi 6\pi

 ! A negative tick length makes the ticks face outward:

 ticks length -0.1

 ! In GLE, datasets d1, d2, ... can also be referred to as d[1], d[2], etc.
 ! The d[i] bracket notation for datasets is useful in scripts, especially
 ! when combined with loops, because the term inside [] can be any integer
 ! variable or expression. In this script we will use two 'for ... next'
 ! loops to define and plot 20 datasets in succession.

 ! First, we use a loop with the 'num' index to define and plot 10 blue
 ! curves. Because 'sin(x)' is divided by 'amplitude', the curves being
 ! drawn are progressively flatter:

 for num = 1 to 10
 amplitude = num
 let d[num] = sin(x)/amplitude
 d[num] line color cadetblue lwidth 0.03
 next num

 ! We then use another loop to define and plot 10 red curves. As in the
 ! previous loop, the curves being drawn are progressively flatter:

 for num = 11 to 20
 amplitude = num-10
 let d[num] = -sin(x)/amplitude
 d[num] line color indianred lwidth 0.03
 next num

 ! We finish the plot by adding two dashed lines. In GLE, a dash pattern is
 ! specified as a series of digits, each digit defining the length of a dash
 ! or a space (by default the pattern is '1', meaning a solid line):

 let d22 = sin(x/2)
 d22 line color seagreen lstyle 1241
 let d23 = -sin(x/2)
 d23 line color seagreen lstyle 11

 end graph

 ! Done. We have learned about the d[...] bracket notation, 'for ... next' loops,
 ! and dashes. We have used 23 datasets -- in GLE 4.2 one can use up to 1000.

lnx.gle

lnx.glelnx.gle lnx.zip zip file contains all files for this figure.

lnx.gle

 size 9 7

 include "shape.gle"
 include "graphutil.gle"

 a = 4

 ! draw graph
 set texlabels 1
 begin graph
 scale auto
 title "Natural Logarithm"
 xtitle "$x$"
 ytitle "$y$"
 xaxis min 0 max a+1
 yaxis min 0 max 1.2
 let d1 = 1/x
 let d2 = 1/x from 1 to a
 d1 line color red
 fill x1,d2 color moccasin
 end graph

 ! draw vertical red lines
 set color red
 graph_line 1 0 1 1
 graph_line a 0 a 1/a
 set color black

 ! draw integral equation
 set just cc
 amove xg(2.5) yg(0.18)
 tex "$\displaystyle\log a = \int_{1}^{a}{\textstyle \frac{1}{x},円dx}$"

 ! define subroutine to add labels to graph
 sub label_by_dist_angle xp yp label$ dist angle
 default dist 0.75
 default angle 90
 amove xg(xp) yg(yp); pmove dist angle
 set just bc; tex label$
 amove xg(xp) yg(yp); pmove dist-0.1 angle
 aline xg(xp) yg(yp) arrow end
 end sub

 ! draw "a" and "1/x"
 label_by_dist_angle a 1/a "$a$"
 label_by_dist_angle 1.75 1/1.75 "$y = \frac{1}{x}$" angle 40

math.gle

math.glemath.gle math.zip zip file contains all files for this figure.

math.gle

 ! Demo about plotting functions.
 ! Author: Francois Tonneau

 size 10 7

 set font ss

 ! We use a 'begin graph ... end graph' block to plot two simple mathematical
 ! functions.

 begin graph

 ! The effect of the 'math' command is that axes cross at point (0, 0) and
 ! that axis ticks extend on both sides of the axis.

 math

 ! Regardless of the 'math' command, there are many ways to customize axes
 ! in GLE. Here we specify the minimum, maximum, and numerical distance
 ! between ticks for the x axis. We also specify tick length and remove
 ! subticks from all axes. Anything about axes that is not customized
 ! assumes default values.

 xaxis min -3 max 3 dticks 1
 ticks length 0.08
 subticks off

 ! The 'let' command allows us to define datasets as mathematical functions
 ! (i.e., expressions of x) instead of values loaded from a data file. The
 ! defining expressions may include parentheses and usual math operators,
 ! but must be written without spaces.

 let d1 = (1/4)*(x^2)
 let d2 = 3*sin(x)

 ! Now we can plot our previously defined datasets:

 d1 line color cadetblue lwidth 0.03
 d2 line color indianred lwidth 0.03

 end graph

 ! We add descriptions of our functions to the plot. GLE has a variety of text
 ! formatting operators, such as the '^{...}' operator to produce superscript:

 amove 0.6 5.6
 write "y = 0.25 x^{2}"

 amove 6 6.25
 write "y = 3 sin(x)"

 ! Done. We have learned about function plotting and about the math mode of axis
 ! customization.

quantilescale.gle

quantilescale.glequantilescale.gle quantilescale.zip zip file contains all files for this figure.

quantilescale.gle

 size 12 9

 set font texcmr
 begin graph
 math
 scale auto
 title "Complex quantile scale example"
 xaxis min -4.5 max 4.5
 yaxis scale quantile
 let d1 = sin(x)
 d1 line color red
 let d2 = x
 d2 line color 0.2
 let d3 = x-x^3/6
 d3 line color 0.4
 let d4 = x-x^3/6+x^5/120
 d4 line color 0.6
 let d5 = x-x^3/6+x^5/120-x^7/5040
 d5 line color 0.8
 end graph

rt-y-is-x.gle

rt-y-is-x.glert-y-is-x.gle rt-y-is-x.zip zip file contains all files for this figure.

rt-y-is-x.gle

 size 12 10

 set font texcmr hei 0.26
 include "simpletree.gle"

 ! Draw the main graph (RMSE versus number of nodes in regression tree)
 amove 1 6.5
 begin graph
 size 6 3
 fullsize
 title "Regression trees approximating y = x"
 data "rt-y-is-x-labels.dat"
 xtitle "Size (nodes)"
 ytitle "RMSE"
 xplaces 1 2 3 4 5 6
 xnames 1 3 7 20 50 250
 xaxis min 1 max 6
 yaxis max 0.3
 d3 line color red marker square
 end graph

 ! Draw an example regression tree with 7 nodes
 ! x > 0.496
 ! +--yes: x > 0.738
 ! | +--yes: 0.861
 ! | +--no: 0.617
 ! +--no: x > 0.248
 ! +--yes: 0.377
 ! +--no: 0.124

 gsave
 set just bc
 amove (xg(6)+pagewidth())/2 pageheight()-0.9
 write "Tree with 7 nodes"
 binrootnode xpos() ypos()-0.3 "x > 0.496" "yes" "no" 1
 binnode "r1" "x > 0.738" "yes" "no" 0.5
 leaf "r11" "0.861"
 leaf "r12" "0.617"
 binnode "r2" "x > 0.248" "yes" "no" 0.5
 leaf "r21" "0.377"
 leaf "r22" "0.124"
 grestore

 sub bluediagonal
 set color rgb255(100,100,255)
 amove xg(0) yg(0); aline xg(1) yg(1)
 set color black
 end sub

 ! Draw one of the small graphs (make sure the red goes over the blue)
 sub plot x y n nodes
 amove x*3.9+1 y*2.9+0.4
 begin graph
 size 3.1 2.1
 fullsize
 data "rt-y-is-x.dat"
 d[n] line color red
 title "\expr{nodes} nodes"
 xaxis min 0 max 1 dticks 0.25
 yaxis min 0 max 1 dticks 0.25
 draw bluediagonal
 end graph
 end sub

 ! Loop to draw the 6 small graphs
 number = 1
 fopen "rt-y-is-x-labels.dat" f1 read
 for y = 1 to 0 step -1
 for x = 0 to 2
 fread f1 idx nodes mse rmse
 plot x y number nodes
 number = number+1
 next x
 next y
 fclose f1

saddle-contour.gle

saddle-contour.glesaddle-contour.gle saddle-contour.zip zip file contains all files for this figure.

saddle-contour.gle

 size 9 6

 include "contour.gle"

 set font texcmr

 begin letz
 data "saddle.z"
 z = 3/2*(cos(3/5*(y-1))+5/4)/(1+(((x-4)/3)^2))
 x from 0 to 20 step 0.5
 y from 0 to 20 step 0.5
 end letz

 begin contour
 data "saddle.z"
 values 0.5 1 1.5 2 3
 end contour

 begin graph
 scale 0.85 0.75 center
 title "Saddle Plot Contour Lines" hei 0.35
 data "saddle-cdata.dat"
 xaxis min -0.75 max 11.75
 yaxis min -1.5 max 21.5
 d1 line color blue
 end graph

 contour_labels "saddle-clabels.dat" "fix 1"

semitrans.gle

semitrans.glesemitrans.gle semitrans.zip zip file contains all files for this figure.

semitrans.gle

 size 10 7
 set font texcmss
 set texlabels 1

 begin graph
 scale auto
 title "Semi-Transparent Fills"
 xtitle "Time"
 ytitle "Output"
 xaxis min 0 max 9
 yaxis min 0 max 6 dticks 1
 let d1 = sin(x)*1.5+1.5 from 0 to 10
 let d2 = 1/x from 0.01 to 10
 let d3 = 10*(1/sqrt(2*pi))*exp(-2*(sqr(x-4)/sqr(2))) from 0 to 10
 key background gray5
 begin layer 300
 fill x1,d1 color rgba255(255,0,0,80)
 d1 line color red key "1ドル.5\sin(x)+1.5$"
 end layer
 begin layer 301
 fill x1,d2 color rgba255(0,128,0,80)
 d2 line color green key "1ドル/x$"
 end layer
 begin layer 302
 fill x1,d3 color rgba255(0,0,255,80)
 d3 line color blue key "$\frac{10}{\sqrt{2\pi}}\exp\left(\frac{-2(x-4)^2}{2^2}\right)$"
 end layer
 end graph

shadow.gle

shadow.gleshadow.gle shadow.zip zip file contains all files for this figure.

shadow.gle

 size 12 8

 include "graphutil.gle"

 set font texcmr

 amove 0 0.3
 begin graph
 title "Chart 1"
 x2axis off
 y2axis off
 yside off
 yaxis grid
 yticks color gray
 xside color gray
 ysubticks off
 xaxis min 0 max 2
 xnoticks 2
 let d1 = x^2
 let d2 = x^2/2
 key pos bc compact offset 0 -0.6 nobox
 d1 line marker wdiamond mdist 1 color steelblue lwidth 0.05 key "Method 1"
 key separator
 d2 line marker wcircle msize 0.3 mdist 1 color green lwidth 0.05 key "Method 2" 
 begin layer 150
 draw graph_shaded_background from 0.7 to 1.0
 end layer
 end graph

sin.gle

sin.glesin.gle sin.zip zip file contains all files for this figure.

sin.gle

 size 12 10

 set font texcmr
 begin graph
 math
 title "f(x) = sin(x)"
 xaxis min -2*pi max 2*pi ftick -2*pi dticks pi/2 format "pi"
 yaxis dticks 0.25 format "frac"
 let d1 = sin(x)
 d1 line color red
 end graph

sine-approx.gle

sine-approx.glesine-approx.gle sine-approx.zip zip file contains all files for this figure.

sine-approx.gle

 size 11 8

 ! Based on example by Pascal B.

 include "graphutil.gle"

 set texlabels 1
 begin graph
 scale auto
 title "Sine Function Approximation"
 xtitle "$x$"
 xaxis min 0 max 10
 yaxis min -3 max 3
 ytitle "$f(x)$"
 key pos tr hei 0.25
 let d100 = sin(x)
 let d101 = x
 d100 line color autocolor(1) key "$\sin(x)$" 
 d101 line color autocolor(2) key "order = 1ドル$"
 let d1 = x
 factorial = 1
 for order = 2 to 5
 n = order-1
 factorial = factorial*(2*n)*(2*n+1)
 let d[order] = d[order-1]+(-1)^(n)*(x^(2*n+1))/factorial
 d[order] line color autocolor(order+1) key "order = $"+num$(order)+"$"
 next order 
 end graph

sqroot.gle

sqroot.glesqroot.gle sqroot.zip zip file contains all files for this figure.

sqroot.gle

 size 11 8

 set texlabels 1
 begin graph
 scale auto
 title "Square Root Function"
 xtitle "$x$"
 ytitle "$\sqrt{\alpha x}$"
 key pos tl hei 0.25
 for alpha = 1 to 10
 let d[alpha] = sqrt(alpha*x) from 0 to 10
 d[alpha] line color rgb(alpha/10,0,0) key "$\alpha = "+num$(alpha)+"$"
 next alpha
 end graph

square.gle

square.glesquare.gle square.zip zip file contains all files for this figure.

square.gle

 ! Example of combining datasets

 size 10 7

 set font texcmr
 begin graph
 scale auto
 title "Synthesis of a square wave"
 yaxis min -1.1 max 1.1
 xaxis min 0 max 5*pi dticks pi format "pi"
 xsubticks off
 let d1 = sin(x) step 0.02 ! The fundamental sine wave
 let d2 = sin(3*x) step 0.02 ! Various harmonics over
 let d3 = sin(5*x) step 0.02 ! the fundamental
 let d4 = sin(7*x) step 0.02
 let d5 = sin(9*x) step 0.02
 let d20 = sgn(d1) ! The square wave
 let d10 = d1+(1/3)*d2 ! We take linear combinations
 let d11 = d10+(1/5)*d3 ! of the various frequencies
 let d12 = d11+(1/7)*d4
 let d13 = d12+(1/9)*d5
 d1 line color gray10 ! These could also be plotted
 d10 line color gray20 ! in different colors or line
 d11 line color gray40 ! styles to make the difference
 d12 line color gray60 ! clearer. A key may also help
 d13 line color gray80
 d20 line color red lstyle 2
 end graph

steps.gle

steps.glesteps.gle steps.zip zip file contains all files for this figure.

steps.gle

 ! Demo about line steps.
 ! Author: Francois Tonneau

 size 17 12

 set font ss hei 0.6

 ! GLE lets us define subroutines that work like procedures or functions. Here we
 ! will use a subroutine to create a panel with a triangle, a title, and a line
 ! drawn in a given style. Our 'panel' procedure will have three parameters: two
 ! numeric ('left' and 'bottom') and one string ('style$'). In GLE, the name of
 ! a string parameter or variable must end with a dollar sign.

 sub panel left bottom style$
 amove left bottom
 begin origin
 set color #d5d5d5
 set lwidth 0.03
 box 4 4

 ! A 'begin path ... end path' block allows us to draw and/or fill an
 ! arbitrary closed region. Here the region will be a triangle filled
 ! with the #d5d5d5 color. We only need to define two sides of the
 ! triangle, as GLE automatically connects the beginning and end of a
 ! path when doing the filling. If we had wanted a filled triangle with
 ! a visible contour, however, we should have added 'stroke' after 'fill'
 ! ('begin path fill #d5d5d5 stroke'), and we should have closed the path
 ! explicity with the 'closepath' command.

 amove 0 0
 begin path fill #d5d5d5
 rline 4 4
 rline 0 -4
 end path

 ! Using GLE's string concatenation operator ('+'), we compose the title
 ! of our panel from "line " and the style$ parameter:

 amove 0 4.5
 set color #2c2c2c
 write "line "+style$

 ! We use a graph block with hidden axes ('axis off') to draw a line
 ! inside the panel. 'fullsize' means that the plot will take up its
 ! full assigned area; ticks and labels, if any, will lie outside.

 amove 0 0
 begin graph
 size 4 4
 fullsize
 xaxis min 0.5 max 4.5
 yaxis min 0.5 max 4.5
 axis off

 ! To plot the line, we define a custom dataset with the 'let dn =
 ! x-expression from ... to ... step ...' syntax:

 let d1 = x from 1 to 4 step 1

 ! We use the 'if ... then ... else if ... end if' syntax to plot
 ! our custom dataset. The drawing command differs, depending on
 ! the value of style$:

 d1 color #004e58 lwidth 0.05 marker square msize 0.35
 if style$ = "" then
 d1 line
 else if style$ = "steps" then
 d1 line steps
 else if style$ = "hist" then
 d1 line hist
 else if style$ = "impulses" then
 d1 line impulses
 else if style$ = "fsteps" then
 d1 line fsteps
 else if style$ = "bar" then
 d1 line bar
 end if
 end graph

 end origin
 end sub

 ! Now is the time to use our 'panel' subroutine:

 panel 0.5 6.5 ""
 panel 6.5 6.5 "steps"
 panel 12.5 6.5 "hist"
 panel 0.5 0.5 "impulses"
 panel 6.5 0.5 "fsteps"
 panel 12.5 0.5 "bar"

 ! Done. We have learned about line/step styles in GLE, 'begin path ... end
 ! path' blocks, subroutines, and if-then-else control flow.

super-ellipse.gle

super-ellipse.glesuper-ellipse.gle super-ellipse.zip zip file contains all files for this figure.

super-ellipse.gle

 ! Graphical representation of Piet Hein's superellipse

 size 8 10.5

 set cap round just tc hei 0.5 font rm

 amove 4 5 
 begin origin ! Sets the origin of the ellipse at (10,9) 
 a = 3.75; b = 4.75 ! a and b represent the excentricity of the ellipse
 begin clip
 amove -a -b ! Draws the box that represents the limit as n tends to 
 begin path clip stroke
 box 2*a 2*b ! infinity
 end path 
 for n=0.5 to 5 step 0.25 ! n is the exponent of the ellipse 
 for i=0 to 360 ! Calculates the radial distance from the x and y
 ang = torad(i)
 c = abs(cos(ang))
 s = abs(sin(ang))
 ax = (c/a)^n ! ax is the projection of the radial coordinate along the x axis
 ay = (s/b)^n ! ay is the same along the y axis
 z = 1/(ax+ay)^(1/n) 
 if i = 0 then 
 amove z*cos(ang) z*sin(ang) 
 else 
 aline z*cos(ang) z*sin(ang)
 end if 
 next i 
 next n
 end clip
 end origin

 amove pagewidth()/2 pageheight()-0.15
 write "Piet Hein's superellipse"

 set just cc
 amove pagewidth()/2 5
 tex "\large $|\frac{x}{a}|^n + |\frac{y}{b}|^n = 1$"

texgraph.gle

texgraph.gletexgraph.gle texgraph.zip zip file contains all files for this figure.

texgraph.gle

 size 10 7

 set texlabels 1 titlescale 1
 begin graph
 title "Plot of $f(x) = \frac{x-\sqrt{5}}{(x-1)\cdot(x-4)}$"
 ytitle "$y = f(x)$"
 x0title "$x$"
 xaxis min 0 max 5 dticks 1 offset 0 symticks
 yaxis min -6 max 6
 let d1 = (x-sqrt(5))/((x-1)*(x-4)) from 0 to 5
 d1 line color red
 xlabels off
 x0labels on
 x0axis on symticks off
 x2axis on symticks off 
 end graph

 set just bc
 amove xg(sqrt(5)) yg(2.5)
 tex "$\sqrt{5}$" add 0.1 name sq5b

 amove pointx(sq5b.bc) pointy(sq5b.bc)
 aline xg(sqrt(5)) yg(0) arrow end