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Ingy döt Net 2026-02-01 16:33:20 -08:00
parent 5150844a7d
commit 4bb20c9b71
7735 changed files with 38060 additions and 199180 deletions
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76
Task/Conjugate-transpose/PowerShell/conjugate-transpose.psh
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@ -1,76 +0,0 @@
function conjugate-transpose($a) {
$arr = @()
if($a) {
$n = $a.count - 1
if(0 -lt $n) {
$m = ($a | foreach {$_.count} | measure-object -Minimum).Minimum - 1
if( 0 -le $m) {
if (0 -lt $m) {
$arr =@(0)*($m+1)
foreach($i in 0..$m) {
$arr[$i] = foreach($j in 0..$n) {@([System.Numerics.complex]::Conjugate($a[$j][$i]))}
}
} else {$arr = foreach($row in $a) {[System.Numerics.complex]::Conjugate($row[0])}}
}
} else {$arr = foreach($row in $a) {[System.Numerics.complex]::Conjugate($row[0])}}
}
$arr
}
function multarrays-complex($a, $b) {
$c = @()
if($a -and $b) {
$n = $a.count - 1
$m = $b[0].count - 1
$c = @([System.Numerics.complex]::new(0,0))*($n+1)
foreach ($i in 0..$n) {
$c[$i] = foreach ($j in 0..$m) {
[System.Numerics.complex]$sum = [System.Numerics.complex]::new(0,0)
foreach ($k in 0..$n){$sum = [System.Numerics.complex]::Add($sum, ([System.Numerics.complex]::Multiply($a[$i][$k],$b[$k][$j])))}
$sum
}
}
}
$c
}
function identity-complex($n) {
if(0 -lt $n) {
$array = @(0) * $n
foreach ($i in 0..($n-1)) {
$array[$i] = @([System.Numerics.complex]::new(0,0)) * $n
$array[$i][$i] = [System.Numerics.complex]::new(1,0)
}
$array
} else { @() }
}
function are-eq ($a,$b) { -not (Compare-Object $a $b -SyncWindow 0)}
function show($a) {
if($a) {
0..($a.Count - 1) | foreach{ if($a[$_]){"$($a[$_])"}else{""} }
}
}
function complex($a,$b) {[System.Numerics.complex]::new($a,$b)}
$id2 = identity-complex 2
$m = @(@((complex 2 7), (complex 9 -5)),@((complex 3 4), (complex 8 -6)))
$hm = conjugate-transpose $m
$mhm = multarrays-complex $m $hm
$hmm = multarrays-complex $hm $m
"`$m ="
show $m
""
"`$hm = conjugate-transpose `$m ="
show $hm
""
"`$m * `$hm ="
show $mhm
""
"`$hm * `$m ="
show $hmm
""
"Hermitian? `$m = $(are-eq $m $hm)"
"Normal? `$m = $(are-eq $mhm $hmm)"
"Unitary? `$m = $((are-eq $id2 $hmm) -and (are-eq $id2 $mhm))"