Polynomial regression: Difference between revisions
PowerShell added
(Scala contribution added.) |
(PowerShell added) |
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IupMainLoop()
IupClose()</lang>
=={{header|PowerShell}}==
<lang PowerShell>
function qr([double[][]]$A) {
$m,$n = $A.count, $A[0].count
$pm,$pn = ($m-1), ($n-1)
[double[][]]$Q = 0..($m-1) | foreach{$row = @(0) * $m; $row[$_] = 1; ,$row}
[double[][]]$R = $A | foreach{$row = $_; ,@(0..$pn | foreach{$row[$_]})}
foreach ($h in 0..$pn) {
[double[]]$u = $R[$h..$pm] | foreach{$_[$h]}
[double]$nu = $u | foreach {[double]$sq = 0} {$sq += $_*$_} {[Math]::Sqrt($sq)}
$u[0] -= if ($u[0] -lt 1) {$nu} else {-$nu}
[double]$nu = $u | foreach {$sq = 0} {$sq += $_*$_} {[Math]::Sqrt($sq)}
[double[]]$u = $u | foreach { $_/$nu}
[double[][]]$v = 0..($u.Count - 1) | foreach{$i = $_; ,($u | foreach{2*$u[$i]*$_})}
[double[][]]$CR = $R | foreach{$row = $_; ,@(0..$pn | foreach{$row[$_]})}
[double[][]]$CQ = $Q | foreach{$row = $_; ,@(0..$pm | foreach{$row[$_]})}
foreach ($i in $h..$pm) {
foreach ($j in $h..$pn) {
$R[$i][$j] -= $h..$pm | foreach {[double]$sum = 0} {$sum += $v[$i-$h][$_-$h]*$CR[$_][$j]} {$sum}
}
}
if (0 -eq $h) {
foreach ($i in $h..$pm) {
foreach ($j in $h..$pm) {
$Q[$i][$j] -= $h..$pm | foreach {$sum = 0} {$sum += $v[$i][$_]*$CQ[$_][$j]} {$sum}
}
}
} else {
$p = $h-1
foreach ($i in $h..$pm) {
foreach ($j in 0..$p) {
$Q[$i][$j] -= $h..$pm | foreach {$sum = 0} {$sum += $v[$i-$h][$_-$h]*$CQ[$_][$j]} {$sum}
}
foreach ($j in $h..$pm) {
$Q[$i][$j] -= $h..$pm | foreach {$sum = 0} {$sum += $v[$i-$h][$_-$h]*$CQ[$_][$j]} {$sum}
}
}
}
}
foreach ($i in 0..$pm) {
foreach ($j in $i..$pm) {$Q[$i][$j],$Q[$j][$i] = $Q[$j][$i],$Q[$i][$j]}
}
[PSCustomObject]@{"Q" = $Q; "R" = $R}
}
function leastsquares([Double[][]]$A,[Double[]]$y) {
$QR = qr $A
[Double[][]]$Q = $QR.Q
[Double[][]]$R = $QR.R
$m,$n = $A.count, $A[0].count
[Double[]]$z = foreach ($j in 0..($m-1)) {
0..($m-1) | foreach {$sum = 0} {$sum += $Q[$_][$j]*$y[$_]} {$sum}
}
[Double[]]$x = @(0)*$n
for ($i = $n-1; $i -ge 0; $i--) {
for ($j = $i+1; $j -lt $n; $j++) {
$z[$i] -= $x[$j]*$R[$i][$j]
}
$x[$i] = $z[$i]/$R[$i][$i]
}
$x
}
function polyfit([Double[]]$x,[Double[]]$y,$n) {
$m = $x.Count
[Double[][]]$A = 0..($m-1) | foreach{$row = @(1) * ($n+1); ,$row}
for ($i = 0; $i -lt $m; $i++) {
for ($j = $n-1; 0 -le $j; $j--) {
$A[$i][$j] = $A[$i][$j+1]*$x[$i]
}
}
leastsquares $A $y
}
function show($m) {$m | foreach {write-host "$_"}}
$A = @(@(12,-51,4), @(6,167,-68), @(-4,24,-41))
$x = @(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
$y = @(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
"polyfit "
"X^2 X constant"
"$(polyfit $x $y 2)"
</lang>
{{out}}
<pre>
polyfit
X^2 X constant
3 1.99999999999998 1.00000000000005
</pre>
=={{header|Python}}==
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