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# plotspecial.tcl --
# Facilities to draw specialised plots in a dedicated canvas
#
# Note:
# It is a companion of "plotchart.tcl"
#
# DrawTargetData --
# Compute the coordinates for the symbol representing the skill and draw it
#
# Arguments:
# w Name of the canvas
# series Name of the series of symbols
# xvalues List of model results
# yvalues List of measurements to which the model results are compared
# Result:
# None
#
# Side effects:
# Symbol drawn
#
# Note:
# The lists of model data and measurements must have the same length
# Missing data can be represented as {}. Only pairs that have both x and
# y values are used in the computations.
#
proc ::Plotchart::DrawTargetData { w series xvalues yvalues } {
variable data_series
if { [llength $xvalues] != [llength $yvalues] } {
return -code error "Lists of model data and measurements should have the same length"
}
set xn {}
set yn {}
set xmean 0.0
set ymean 0.0
set count 0
foreach x $xvalues y $yvalues {
if { $x != {} && $y != {} } {
lappend xn $x
lappend yn $y
set xmean [expr {$xmean + $x}]
set ymean [expr {$ymean + $y}]
incr count
}
}
if { $count <= 1 } {
return
}
set xmean [expr {$xmean/double($count)}]
set ymean [expr {$ymean/double($count)}]
set sumx2 0.0
set sumy2 0.0
set sumxy 0.0
foreach x $xn y $yn {
set sumx2 [expr {$sumx2 + ($x-$xmean)*($x-$xmean)}]
set sumy2 [expr {$sumy2 + ($y-$ymean)*($y-$ymean)}]
set sumxy [expr {$sumxy + ($x-$xmean)*($y-$ymean)}]
}
set stdevx [expr {sqrt($sumx2 / double($count-1))}]
set stdevy [expr {sqrt($sumy2 / double($count-1))}]
set corrxy [expr {$sumxy / $stdevx / $stdevy / double($count-1)}]
set bstar [expr {($xmean-$ymean) / $stdevy}]
set sstar2 [expr {$sumx2 / $sumy2}]
set rmsd [expr {sqrt(1.0 + $sstar2 - 2.0 * sqrt($sstar2) * $corrxy)}]
DataConfig $w $series -type symbol
DrawData $w $series $rmsd $bstar
}
# DrawPerformanceData --
# Compute the coordinates for the performance profiles and draw the lines
#
# Arguments:
# w Name of the canvas
# profiledata Names and data for each profiled item
# Result:
# None
#
# Side effects:
# Symbol drawn
#
# Note:
# The lists of model data and measurements must have the same length
# Missing data can be represented as {}. Only pairs that have both x and
# y values are used in the computations.
#
proc ::Plotchart::DrawPerformanceData { w profiledata } {
variable data_series
variable scaling
#
# Determine the minima per solved problem - they function as scale factors
#
set scale {}
set values [lindex $profiledata 1]
set number [llength $values]
foreach v $values {
lappend scale {}
}
foreach {series values} $profiledata {
set idx 0
foreach s $scale v $values {
if { $s == {} || $s > $v } {
lset scale $idx $v
}
incr idx
}
}
#
# Scale the data (remove the missing values)
# and draw the series
#
set plotdata {}
foreach {series values} $profiledata {
set newvalues {}
foreach s $scale v $values {
if { $s != {} && $v != {} && $s != 0.0 } {
lappend newvalues [expr {$v / $s}]
}
}
set newvalues [lsort -real $newvalues]
set count 1
set yprev {}
foreach v $newvalues vn [concat [lrange $newvalues 1 end] 1.0e20] {
set y [expr {$count/double($number)}]
#
# Construct the staircase
#
if { $v != $vn } {
if { $yprev == {} } {
DrawData $w $series 1.0 $y
} else {
DrawData $w $series $v $yprev
}
DrawData $w $series $v $y
set yprev $y
}
incr count
}
}
}
# DrawDataNormalPlot --
# Compute the coordinates for the empirical distribution and draw the series
# in a normal distribution plot
#
# Arguments:
# w Name of the canvas
# series Name of the series
# mean Estimated mean
# stdev Estimated standard deviation
# data Actual data
# Result:
# None
#
# Note:
# The value of "a" is adopted from the corresponding Wikipedia page,
# which in turn adopted it from the R "stats" package (qqnorm function)
#
proc ::Plotchart::DrawDataNormalPlot { w series mean stdev data } {
set n [llength $data]
set a 0.375
if { $n > 10 } {
set a 0.5
}
set idx 1
foreach x [lsort -real -increasing $data] {
if { $x != {} } {
set xn [expr {($x - $mean) / $stdev}]
set pn [expr {($idx - $a) / ($n + 1 - 2.0 * $a)}]
set yn [::math::statistics::Inverse-cdf-normal 0.0 1.0 $pn]
DrawData $w $series $xn $yn
} else {
DrawData $w $series {} {}
}
incr idx
}
}
# DrawDiagonalNormalPlot --
# Draw the diagonal line in a normal distribution plot
#
# Arguments:
# w Name of the canvas
# Result:
# None
#
# Note:
# You can use the "diagonal" series to configure its colour
#
proc ::Plotchart::DrawDiagonalNormalPlot { w } {
variable scaling
DrawData $w diagonal $scaling($w,xmin) $scaling($w,ymin)
DrawData $w diagonal $scaling($w,xmax) $scaling($w,ymax)
}
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