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#!/usr/bin/env tclsh
## -*- tcl -*-
#
# rosenbrock.demo3.test.tcl --
# Plot the contours of the Rosenbrock function with
# Tklib/Plotchart.
# Test with a small screen.
# Based on a modified Plotchart version, implementing
# contourlinesvalues with a helper function for
# the axis values.
#
# Copyright 2008-2009 Michael Baudin
#
package require Plotchart
package require cmdline
set width 500
set height 500
proc rosenbrock {x} {
set x1 [lindex $x 0]
set x2 [lindex $x 1]
set y [expr {100.0 * pow($x2 - $x1*$x1,2) + pow(1.0 - $x1,2)}]
return $y
}
#
# linspace --
# Generate a list of values in the given range.
# Arguments
# -min min : the minimum value in the range (default 0.0)
# -max max : the maximum value in the range (default (1.0)
# -step step : the step to use (default 0.1)
# -nb nb : the number of points in the range (default 10)
# -method method : the method to use to generate the points in the range (default "step")
# * if method is "step", the step is used to generate
# the list of values
# * if method is "nb", the nb parameter is used to compute a step
#
proc linspace {args} {
set opts {
{min.arg 0.0 "the minimum value in the range"}
{max.arg 1.0 "the maximum value in the range"}
{step.arg 0.1 "the step to use"}
{nb.arg 10 "the number of points in the range"}
{method.arg "step" "the method to compute the values"}
}
set usage ": plotcontours \[options] ...\noptions:"
array set params [::cmdline::getoptions args $opts $usage]
set min $params(min)
set max $params(max)
if {$min > $max} then {
error "The minimum value is $min but the maximum value is $max"
}
switch -- $params(method) {
"nb" {
set nb $params(nb)
set step [expr {($max-$min)/($nb-1)}]
}
"step" {
set step $params(step)
}
default {
error "Unknown method $params(method)"
}
}
set result {}
set current $min
while {1} {
lappend result $current
set current [expr {$current + $step}]
if {$current > $max} then {
break
}
}
return $result
}
#
# Direct use of the API
#
#set xvec {-2.0 -1.75 -1.5 -1.25 -1.0 -0.25 -0.5 -0.25 0.0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0}
#set yvec {-1.0 -0.25 -0.5 -0.25 0.0 0.25 0.5 0.75 1.0 1.25 1.5 1.75 2.0}
set xvec [linspace -min -2.0 -max 2.0 -step 0.05]
set yvec [linspace -min -1.0 -max 2.0 -step 0.05]
set fmat {}
foreach y $yvec {
set frow {}
foreach x $xvec {
lappend frow [rosenbrock [list $x $y]]
}
lappend fmat $frow
}
set contours { \
0.0 1.0 3.0 5.0 10 30 \
50 100 200 500 1000 2000 3000 \
}
set xlimits {-2.0 2.0 2.0}
set ylimits {-1.0 2.0 1.0}
wm title . "Rosenbrock contours"
::Plotchart::colorMap jet
set c [canvas .c -background white -width $width -height $height]
pack $c -fill both -side top
set chart1 [::Plotchart::createXYPlot $c $xlimits $ylimits]
$chart1 contourlinesfunctionvalues $xvec $yvec $fmat $contours
$chart1 saveplot "rosenbrock.demo3.png" -format png
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