Version 19 of Fun with functions
Updated 2016-08-09 18:22:05 by jeenakhoyamailcom
Richard Suchenwirth 2001-05-28 - My teenage daughter hates math. In order to motivate her, I beefed up A little function plotter which before only took one function, in strict Tcl (expr) notation, from the command line. Now there's an entry widget, and the accepted language has also been enriched: beyond exprs rules, you can omit dollar and multiplication signs, like 2x+1, powers can be written as x3 instead of ($x*$x*$x); in simple cases you can omit parens round function arguments, like sin x2. Hitting <Return> in the entry widget displays the function's graph.
If you need some ideas, click on the "?" button to cycle through a set of demo functions, from boring to bizarre (e.g. if rand() is used). Besides default scaling, you can zoom in or out. Moving the mouse pointer over the canvas displays x and y coordinates, and the display changes to white if you're on a point on the curve.
The target was not reached: my daughter still hates math. But at least I had hours of Tcl (and function) fun again, surfing in the Cartesian plane... hope you enjoy it too!
A starkit version of this code is available on sdarchive.
package require Tk
proc main {} {
canvas .c -bg white -borderwidth 0
bind .c <Motion> {displayXY .info %x %y}
frame .f
label .f.1 -text "f(x) = "
entry .f.f -textvar ::function -width 40
bind .f.f <Return> {plotf .c $::function}
button .f.demo -text " ? " -pady 0 -command {demo .c}
label .f.2 -text " Zoom: "
entry .f.fac -textvar ::factor -width 4
set ::factor 32
bind .f.fac <Return> {zoom .c 1.0}
button .f.plus -text " + " -pady 0 -command {zoom .c 2.0}
button .f.minus -text " - " -pady 0 -command {zoom .c 0.5}
eval pack [winfo children .f] -side left -fill both
label .info -textvar ::info -just left
pack .info .f -fill x -side bottom
pack .c -fill both -expand 1
demo .c
}
set ::demos {
"cos x3" 2 1-x 0.5x2 x3/5 "sin x" "sin x2" 1/x sqrt(x)
"tan x/5" x+1/x x abs(x) "exp x" "log x" "log x2"
round(x) "int x%2" "x-int x" "0.2tan x+1/tan x" x*(rand()-0.5)
x2/5-1/(2x) "atan x" sqrt(1-x2) "abs(x-int(x*2))" (x-1)/(x+1)
"sin x-tan x" "sin x-tan x2" "x-abs(int x)" 0.5x-1/x
-0.5x3+x2+x-1 3*sin(2x) -0.05x4-0.2x3+1.5x2+2x-3 "9%int x"
0.5x2/(x3-3x2+4) "abs x2-3 int x" "int x%3"
}
proc displayXY {w cx cy} {
set x [expr {double($cx-$::dx)/$::factor}]
set y [expr {double(-$cy+$::dy)/$::factor}]
set ::info [format "x=%.2f y=%.2f" $x $y]
catch {
$w config -fg [expr {abs([expr $::fun]-$y)<0.01?"white":"black"}]
} ;# may divide by zero, or other illegal things
}
proc zoom {w howmuch} {
set ::factor [expr round($::factor*$howmuch)]
plotf $w $::function
}
proc plotf {w function} {
foreach {re subst} {
{([a-z]) +(x[0-9]?)} {\1(\2)} " " "" {([0-9])([a-z])} {\1*\2}
x2 x*x x3 x*x*x x4 x*x*x*x x \$x {e\$xp} exp
} {regsub -all $re $function $subst function}
set ::fun $function
set ::info "Tcl: expr $::fun"
set color [lpick {red blue purple brown green}]
plotline $w [fun2points $::fun] -fill $color
}
proc lpick L {lindex $L [expr {int(rand()*[llength $L])}]}
proc fun2points {fun args} {
array set opt {-from -10.0 -to 10.0 -step .01}
array set opt $args
set res "{"
for {set x $opt(-from)} {$x<= $opt(-to)} {set x [expr {$x+$opt(-step)}]} {
if {![catch {expr $fun} y]} {
if {[info exists lasty] && abs($y-$lasty)>100} {
append res "\} \{" ;# incontinuity
}
append res " $x $y"
set lasty $y
} else {append res "\} \{"}
}
append res "}"
}
proc plotline {w points args} {
$w delete all
foreach i $points {
if {[llength $i]>2} {eval $w create line $i $args -tags f}
}
set fac $::factor
$w scale all 0 0 $fac -$fac
$w create line -10000 0 10000 0 ;# X axis
$w create line 0 -10000 0 10000 ;# Y axis
$w create line $fac 0 $fac -3 ;# x=1 tick
$w create line -3 -$fac 0 -$fac ;# y=1 tick
set ::dx [expr {[$w cget -width]/2}]
set ::dy [expr {[$w cget -height]/2}]
$w move all $::dx $::dy
$w raise f
}
proc demo {w} {
set ::function [lindex $::demos 0] ;# cycle through...
set ::demos [concat [lrange $::demos 1 end] [list $::function]]
set ::factor 32
plotf $w $::function
}
mainPT 13-May-2003: This is fantastic! I wish I'd had one of these when I was at school. Great job.
23-Oct-2011: I've created 2005 a version with little more GUI and "screen" management. It was very helpful when writing my diploma thesis, see tkFPlot.
RR 24Nov03: I had a similar idea because of a problem I had at work. Sometimes I get a set of x-y data. I can plot it, of course. There are ways to approximate the data with some polynomial or Fourier series. In some cases, however, that misses some (relatively) simple analytical formula which is actually a better fit to the data. So I built a little script that plots a file of (comma separated) x-y data. Then, using the same scales and intervals, plots a user-input formula (I ditched the '$' but still require Tcl syntax). Then, you can plot the difference. In practice, this has only been really useful a couple of times, but then it was quite useful!
# Function Analysis
#-----------------------------------------------defaults
set gwth 650
set ghght 250
set numtc 12
set nxtc 8
set pfnm [pwd]/pvt.csv
set flatc SystemButtonFace
#-----------------------------------------------globals
set gblst {cnvs gwth ghght minx maxx miny \
i numtc nxtc garr cgarr xscale yscale}
#-----------------------------------------------Main
wm title . "Functional Analysis"
wm deiconify .
foreach f1 {1 2 3 4 5} {
frame .$f1 -borderwidth 2 -relief groove
pack .$f1 -side top -pady 1
foreach f2 {1 2 3 4} {
frame .$f1.$f2 -borderwidth 4
pack .$f1.$f2 -side left
}
}
set w .1.2
button $w.filebut -text Plot\nFile -command {graph 0 $pfnm $gblst}
label $w.filelab -text "File: "
entry $w.filent -textvariable pfnm -width 38
label $w.txt -text "text file of x,y pairs"
pack $w.filebut $w.filelab -side left
pack $w.txt $w.filent -side top
bind $w.filent <Return> {graph 0 $pfnm $gblst}
bind $w.filent <F1> {
if [winfo exists .1.5] {
destroy .1.5
} else {
frame .1.5 -borderwidth 4
pack .1.5 -side top
label .1.5.text -text "File of the type: <x value>,<y value>"
pack .1.5.text
}
}
bind $w.filent <Button-3> {set pfnm [tk_getOpenFile]}
set w .4.2
set cnvs $w.gcvs1
frame $w.gp -borderwidth 4; pack $w.gp -side top
set w .4.2.gp
label $w.wdlab -text "Graph Width:"
entry $w.wdent -textvariable gwth -relief flat -bg $flatc -width 8
label $w.htlab -text "Graph Height:"
entry $w.htent -textvariable ghght -relief flat -bg $flatc -width 8
pack $w.wdlab $w.wdent $w.htlab $w.htent -side left
bind . <Escape> exit
#-----------------------------------------------Plot difference
proc diffPlt {gblst} {
set cmd "global"
foreach v $gblst {append cmd " $v"}
eval $cmd
for {set p 0} {$p < $i} {incr p} {
set garr($p,y3) [expr $garr($p,y)-$garr($p,y2)]
set cgarr($p,y3) [expr $ghght -($garr($p,y3)-$miny)*$yscale]
}
for {set p 1} {$p < $i} {incr p} {
set q [expr $p -1]
$cnvs create line $cgarr($q,x) $cgarr($q,y3) \
$cgarr($p,x) $cgarr($p,y3) -width 1 -fill #ff55aa
}
destroy .2.pfun .2.funlab .2.funent .2.difbut
}
#--------------------------------------------Plot file or function
proc graph {flg fun gblst} {
set cmd "global"
foreach v $gblst {append cmd " $v"}
eval $cmd
if {$flg == 0} {
destroy $cnvs
canvas $cnvs -width $gwth -height $ghght \
-borderwidth 2 -relief sunken -bg white
pack $cnvs -side bottom
set c0y $ghght
set c0x 0
set fid [open $fun r]
set pvtlst [split [read $fid] \n]
close $fid
foreach ptpr $pvtlst {
if {$ptpr != ""} {lappend pvtlst2 [split $ptpr ,]}
};#---------------------------------------note: comma delimited
set pvtlst [lsort -real -index 0 $pvtlst2];#----------------
set minx [lindex [lindex $pvtlst 0] 0]
set numelems [llength $pvtlst]
set lastelem [incr numelems -1]
set maxx [lindex [lindex $pvtlst $lastelem] 0]
# get all cartesian pairs to plot
set i 0
foreach ptpair $pvtlst {
set garr($i,x) [lindex $ptpair 0]
set garr($i,y) [lindex $ptpair 1]
incr i
}
#now "i" is the number of array elements since it starts w/ 0 and goes to i-1
# turn cartesian pairs into canvas coordinates
# first find ymax and ymin
set maxy $garr(0,y)
set miny $garr(0,y)
for {set p 1} {$p<$i} {incr p} {
if {$garr($p,y)<$miny} then {set miny $garr($p,y)}
if {$garr($p,y)>$maxy} then {set maxy $garr($p,y)}
}
set yscale [expr 1.00*$ghght/($maxy-$miny)]
set xscale [expr 1.00*$gwth/($maxx-$minx)]
for {set p 0} {$p < $i} {incr p} {
set cgarr($p,x) [expr $c0x +($garr($p,x)-$minx)*$xscale]
set cgarr($p,y) [expr $c0y -($garr($p,y)-$miny)*$yscale]
}
# create lines in canvas
set c $cnvs
# draw Yaxis
set xmd [expr $gwth/2]
set tcinc [expr $ghght/$numtc]
$c create line $xmd $c0y $xmd 0 -width 1 -fill white
for {set p 0} {$p<$numtc} {incr p} {
set tcy [expr $ghght - $tcinc*$p]
$c create line 0 $tcy $gwth $tcy -width 1 -fill grey
set yval [format "%3.2f" [expr $miny+$p*$tcinc/$yscale]]
$c create text $xmd $tcy -text $yval -fill grey
}
set xl [expr $gwth/($i*3)]
$c create text $xl $tcinc -text $minx -fill grey -anchor w
$c create text $gwth $tcinc -text $maxx -fill grey -anchor e
set ntx [expr $nxtc - 1]
set tcd [expr int($gwth/$ntx)]
set xdl [expr int($maxx-$minx)/$ntx]
incr ntx -1
for {set p 1} {$p<=$ntx} {incr p} {
incr xl $tcd
set xtx [expr {$minx+$p*$xdl}]
$c create text $xl $tcinc -text $xtx -fill grey
}
for {set p 1} {$p < $i} {incr p} {
set q [expr $p -1]
$c create line $cgarr($q,x) $cgarr($q,y) $cgarr($p,x) $cgarr($p,y) -width 1
}
set w .2.2
destroy $w.pfun $w.funlab $w.funent
button $w.pfun -text Plot\nFunction \
-command {graph 1 $funstr $gblst} -fg blue
label $w.funlab -text "enter function; tcl format; x is independent var."
entry $w.funent -textvariable funstr -width 50
pack $w.pfun -side left -padx 6
pack $w.funlab $w.funent -side top
bind $w.funent <Return> {graph 1 $funstr $gblst}
bind $w.funent <F1> {
if [winfo exists .5.5] {
destroy .5.5
} else {
frame .5.5 -borderwidth 4
pack .5.5 -side top
label .5.5.text -text {
FUNCTIONS
acos cos hypot sinh asin cosh log sqrt
atan exp log10 tan atan2 floor pow tanh
ceil fmod sin
OPERATORS
-,+,~,! *,/ +,-
<<,>> <,>,<=,>=
==,!=,&,^,|,&&,||,x?y:z
} -justify left
pack .5.5.text
}
}
} else {
for {set p 0} {$p<$i} {incr p} {
# Assume that input function uses "x" as independant variable
set fun2 [string map {x $garr($p,x)} $fun]
# make sure "exp" function not clobberd
set fun2 [string map {e$garr($p,x)p exp} $fun2]
set garr($p,y2) [expr $fun2]
}
for {set p 0} {$p < $i} {incr p} {
set cgarr($p,y2) [expr {$ghght -($garr($p,y2)-$miny)*$yscale}]
}
for {set p 1} {$p < $i} {incr p} {
set q [expr $p -1]
$cnvs create line $cgarr($q,x) $cgarr($q,y2) \
$cgarr($p,x) $cgarr($p,y2) -width 1 -fill blue
}
set w .2.2
destroy $w.difbut
button $w.difbut -text "Plot (file-minus-function)" \
-command {diffPlt $gblst} -fg red
pack $w.difbut -side bottom -pady 4
bind $w.difbut <Return> {diffPlt $gblst}
}
#bind . <Control-l> {exec wish83 protols.tcl $::pfnm}
bind . <Control-l> {set fid [open "| wish83 protols.tcl $::pfnm" r+]}
}See also A little graph plotter
jeenakhoyamailcom - 2016-08-09 18:22:05
Digital marketing training online marketing +96500-73658,digital marketing course http://www.helpforcareer.com/2016/06/digital-marketing-training-institute-in.html|digital marketing training|http://www.helpforcareer.com/2016/06/digital-marketing-training-institute-in.html,internet marketing,what is digital marketing,digital marketing agency,digital marketing company,digital marketing jobs,social media marketing strategy,digital marketing strategy,social media marketing companies,digital marketing course in delhi,web marketing,digital marketing services,digital marketing courses in mumbai,online marketing strategies,marketing tips,seo training,digital marketing ppt,digital marketing courses in bangalore,digital marketing training,online marketing courses,internet marketing strategies,digital marketing courses in pune,marketing courses,digital marketing certification,digital marketing trends,digital media marketing,digital marketing tools,digital marketing news,digital marketing blog,digital marketing manager,digital marketing definition,marketing certifications,social media marketing agency,online marketing agency,digital marketing institute,marketing classes,digital marketing course in hyderabad,online digital marketing courses,digital marketing course online +96500-73658,social media marketing courses,marketing program,internet marketing course,digital marketing certificate,learn digital marketing,digital marketing plan,digital marketing solutions,digital marketing specialist,digital marketing books,digital marketing expert,digital marketing course in kolkata,digital marketing conference,digital marketing courses online free,digital marketing course in chennai,digital marketing training in hyderabad,digital marketing online course,marketing training,social media marketing tips,digital marketing india,digital marketing campaign,digital marketing course fees,digital marketing strategist,digital marketing channels,free digital marketing courses,career in digital marketing,digital marketing career,internet marketing training,digital marketing classes,digital marketing training institute,best digital marketing courses,digital marketing degree,marketing certificate programs +96500-73658,internet marketing tips +96500-73658,online marketing tips,marketing certificate +96500-73658,website marketing strategy,digital marketing executive,digital marketing platform,digital market,internet marketing course in delhi,digital marketing techniques,why digital marketing,digital marketting,digital marketing training in bangalore,digital marketing course in noida,marketing courses online,online marketing certificate,online marketing classes,social media marketing classes,online marketing institute,automotive digital marketing,free online marketing courses,e marketing strategies,digital marketing plan template,digital marketing tips,digital marketing courses in india,about digital marketing,digital marketing course delhi,digital media courses,online marketing training,courses in digital marketing,social media marketing training,digital course,marketing education,online digital marketing,marketing analytics course,learn marketing,digital marketing case studies,digital marketing ideas,future of digital marketing,define digital marketing,school of digital marketing,digital marketing training in chennai +96500-73658,digital marketing institute in mumbai,marketing online courses,institute of digital marketing,digital marketing programs,internet marketing degree,digital marketing certificate program,digital marketing school,digital marketing for dummies,free marketing courses,digital marketing association,integrated digital marketing,digital marketing workshop,digital marketing course mumbai,best digital marketing courses in india,digital marketing training courses,digital marketing certificate online,diploma in digital marketing,courses on digital marketing,digital marketing course content,digital marketing course syllabus,digital marketing magazine,digital marketing course pdf,business marketing strategies,digital marketing forum,trends in digital marketing,definition of digital marketing,how to learn digital marketing,digital marketing course bangalore,free online digital marketing courses,digital marketing free online course,digital marketing institute in bangalore,learn online marketing,marketing training programs,marketing classes online,learn internet marketing,marketing certification courses,learn digital marketing online,web marketing agency,digital marketing events,digital marketing awards,digital marketing industry,certificate in marketing,digital marketing tactics,digital marketing online,digital marketing professional,digital training,free digital marketing courses online,learn digital marketing online free,marketing courses in india,digital marketing online course free,social media marketing courses in mumbai,digital marketing training in kolkata,digital marketing course hyderabad,digital media marketing courses,certificate in digital marketing,social media marketing online course,marketing certification programs,marketing certificate programs online,digital marketing certification courses,digital marketing academy,best digital marketing,digital marketing course india,digital marketing course free,marketing training courses,online marketing programs,online advertising courses,learn marketing online, +96500-73658online marketing certification,digital marketing education,best online marketing courses,online digital marketing certificate,social media marketing training courses,courses in marketing,marketing certificate online,certification in digital marketing,digital marketing certification online,digital marketing london,best digital marketing courses in the world,certification courses in marketing,understanding digital marketing,digital marketing degree online,digital marketing assistant,digital marketing group,digital online marketing,digital marketing course distance learning,digital marketing seminar,digital marketing case study,digital mark,digital marketing courses nyc,digital marketing training in mumbai,digital marketing courses in usa,digital marketing free course,what is the digital marketing,digital marketing courses in canada,digital marketing diploma,social media marketing courses online,
<internet marketing certificate Call ++96500-73658,internet marketing program,online marketing school,digital marketing online training,courses for digital marketing [L1 ]
online courses in digital marketing,online courses for digital marketing, [L2 ] online courses on digital marketing,courses for marketing,best online digital marketing courses,marketing certifications online,digital marketing classes online,certificate course in digital marketing,online education market,online marketing certificate programs,online social media marketing courses,digital analytics certification,digital marketing certificate course,best digital marketing certification,digital marketing training certification,online marketing courses free,digital marketing uk,digital marketing learning,digital marketing mix,digital marketing qualifications,best marketing certifications,|digital marketing training|marketing institute,digital marketing research,free internet marketing course,digital marketin,digital marketing communications,internet marketing course delhi,free social media marketing courses +96500-73658,digital marketing methods,online marketing courses in mumbai,how to digital marketing,+96500-73658 institute of digital marketing mumbai,digital marketing training hyderabad,digital marketing classes nyc,internet marketing certification,digital marketing training online,online digital marketing training,internet marketing courses online,best marketing courses,digital marketing certificate programs online,online marketing certifications,best digital marketing courses online,certified digital marketer,social media marketing classes online,certification in marketing,marketing strategy course,internet marketing certificate programs online,certifications in marketing,best online marketing certificate programs,marketing schools online,digital advertising courses,certificate courses in marketing,certifications for marketing,free internet marketing training,digital marketing trainer,digital marketing institute ireland,global digital marketing,product marketing training,social media marketing certificate,digital marketing masters degree online,marketing in the digital age,digital marketing media,digital internet marketing,digital marketing system,internet marketing course online free,online digital marketing courses in india,free online marketing classes,digital marketing training bangalore,digital marketing training mumbai,free digital marketing,online marketing training in bangalore,digital marketing institute in india,digital marketing training institute in mumbai,digital marketing training in india,digital marketing training institute mumbai,internet marketing school,e marketing course,digital media courses online,online courses marketing,online course digital marketing,best internet marketing course,digital strategy course,internet marketing class,msc digital marketing,digital marketing online certificate,digital marketing courses distance learning,digital courses online, >