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|
# fourier.test --
# Test cases for the Fourier transforms in the
# ::math::fourier package
#
if {[lsearch [namespace children] ::tcltest] == -1} {
package require tcltest 2.1
namespace import ::tcltest::*
} else {
if {![package vsatisfies [package present tcltest] 2.0]} {
puts " Aborting tests for math::fourier."
puts " Requiring tcltest 2.1, have [package present tcltest]"
return
}
}
source [file join [file dirname [info script]] fourier.tcl]
namespace import ::math::fourier::*
proc matchComplex {expected actual} {
set match 1
foreach a $actual e $expected {
foreach {are aim} $a break
foreach {ere eim} $e break
if {abs($are-$ere) > 0.1e-8 ||
abs($aim-$eim) > 0.1e-8} {
set match 0
break
}
}
return $match
}
customMatch numbers matchComplex
test "dft-1.0" "Four numbers" \
-match numbers -body {
dft {1 2 3 4}
} -result {{10 0.0} {-2.0 2.0} {-2 0.0} {-2.0 -2.0}}
test "dft-1.1" "Five numbers" \
-match numbers -body {
dft {1 2 3 4 5}
} -result {{15.0 0.0} {-2.5 3.44095480118} {-2.5 0.812299240582} {-2.5 -0.812299240582} {-2.5 -3.44095480118}}
test "dft-1.2" "Four numbers - inverse" \
-match numbers -body {
inverse_dft {{10 0.0} {-2.0 2.0} {-2 0.0} {-2.0 -2.0}}
} -result {{1.0 0.0} {2.0 0.0} {3.0 0.0} {4.0 0.0}}
test "dft-1.3" "Five numbers - inverse" \
-match numbers -body {
inverse_dft {{15.0 0.0} {-2.5 3.44095480118} {-2.5 0.812299240582} {-2.5 -0.812299240582} {-2.5 -3.44095480118}}
} -result {{1.0 0.0} {2.0 8.881784197e-17} {3.0 4.4408920985e-17} {4.0 4.4408920985e-17} {5.0 -8.881784197e-17}}
# Testing to and from DFT
#
proc test_DFT {points {real 0} {iterations 20}} {
set in_dataL [list]
for {set k 0} {$k < $points} {incr k} {
if {$real} then {
lappend in_dataL [expr {2*rand()-1}]
} else {
lappend in_dataL [list [expr {2*rand()-1}] [expr {2*rand()-1}]]
}
}
set time1 [time {
set conv_dataL [dft $in_dataL]
} $iterations]
set time2 [time {
set out_dataL [inverse_dft $conv_dataL]
} $iterations]
set err 0.0
foreach iz $in_dataL oz $out_dataL {
if {$real} then {
foreach {o1 o2} $oz {break}
set err [expr {$err + ($i-$o1)*($i-$o1) + $o2*$o2}]
} else {
foreach i $iz o $oz {
set err [expr {$err + ($i-$o)*($i-$o)}]
}
}
}
return [list $time1 $time2 [expr {sqrt($err/$points)}]]
}
test "dft-2.1" "10 numbers - to and from" \
-body {
foreach {t1 t2 err} [test_DFT 10] break
set small_error [expr {$err < 1.0e-10}]
} -result 1
test "dft-2.2" "100 numbers - to and from" \
-body {
foreach {t1 t2 err} [test_DFT 100] break
set small_error [expr {$err < 1.0e-10}]
} -result 1
test "dft-2.3" "DFT versus FFT" \
-body {
foreach {dft1 dft2 err} [test_DFT 100] break
foreach {fft1 fft2 err} [test_DFT 128] break
set dft1 [lindex $dft1 0]
set dft2 [lindex $dft2 0]
set fft1 [lindex $fft1 0]
set fft2 [lindex $fft2 0]
# Expect a dramatic difference - at least factor 3!
set fft_used [expr {$dft1 > 3.0*$fft1 && $dft2 > 3.0*$fft2}]
} -result 1
test "dft-2.4" "1024 numbers - to and from" \
-body {
foreach {t1 t2 err} [test_DFT 1024 0 1] break
set small_error [expr {$err < 1.0e-10}]
} -result 1
# TODO: tests for lowpass and highpass filters
# End of test cases
tcltest::cleanupTests
|
