Arjen Markus (18 october 2004) I intend this page for recording various ways to implement algorithms to solve PDEs and their relative performance.
The first set of implementations concerns the creation and updating of a "matrix" (as a list of lists).
# testmatrix.tcl
# Test a variety of ways to create and update a matrix
# (implemented as a list of lists) and find out which is
# the fastest
#
proc buildup { norows nocols } {
#
# Use a nested for-loop to create and expand the lists
#
set newmat {}
for { set j 0 } { $j < $norows } { incr j } {
set newrow {}
for { set i 0 } { $i < $nocols } { incr i } {
lappend newrow [expr {rand()}]
}
lappend newmat $newrow
}
return $newmat
}
proc copy_and_update { matrix } {
#
# Use an existing matrix as a template, copy this and
# update the entries
#
set newmat $matrix
set r 0
foreach row $newmat {
set c 0
foreach col $row {
lset newmat $r $c [expr {rand()}]
incr c
}
incr r
}
return $newmat
}
proc template_and_buildup { matrix } {
#
# Use an existing matrix as a template and
# construct a new matrix via foreach-loops
#
set newmat {}
foreach row $matrix {
set newrow {}
foreach col $row {
lappend newrow [expr {rand()}]
}
lappend newmat $newrow
}
return $newmat
}
foreach size {10 20 50 100} times {10000 3000 1000 1000} {
puts "Size: $size"
puts "Build up: [time {buildup $size $size} $times]"
set matrix [buildup $size $size]
puts "Copy and update: [time {copy_and_update $matrix} $times]"
puts "Template and build up: [time {template_and_buildup $matrix} $times]"
}Here is the result with Tcl 8.4.5, on Windows XP, fairly fast hardware (but the relative speeds are more important):
Size: 10 Build up: 81 microseconds per iteration Copy and update: 103 microseconds per iteration Template and build up: 78 microseconds per iteration Size: 20 Build up: 273 microseconds per iteration Copy and update: 368 microseconds per iteration Template and build up: 260 microseconds per iteration Size: 50 Build up: 1534 microseconds per iteration Copy and update: 2279 microseconds per iteration Template and build up: 1499 microseconds per iteration Size: 100 Build up: 5936 microseconds per iteration Copy and update: 9262 microseconds per iteration Template and build up: 5781 microseconds per iteration
Conclusion from this (and another test, Tcl 8.4.1 on WIndows 98):