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Lagrange Interpolation in Powershell
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<# | |
Lagrange Interpolation Example | |
#> | |
function Point($x, $y) | |
{ | |
return [pscustomobject]@{ | |
PSTypeName = 'Point' | |
x = $x | |
y = $y | |
} | |
} | |
function Find-InterpolatedValue | |
{ | |
param | |
( | |
[parameter(Mandatory=$true)] | |
[array] | |
$Points, | |
[parameter(Mandatory=$true)] | |
[double] | |
$FindAt, | |
[parameter(Mandatory=$false)] | |
[array] | |
$Range = (0, $Points.Length) | |
) | |
# Expand Points to array | |
$x = $Points | select -ExpandProperty x | |
$y = $Points | select -ExpandProperty y | |
# Get Points in range | |
$_x = $x[$Range[0]..$Range[1]] | |
$_fx = $y[$Range[0]..$Range[1]] | |
$n = $_x.Length | |
$interpolatedValue = 0 | |
for ($i = 0; $i -lt $n; $i++) | |
{ | |
$lagrangian = 1.0 | |
for ($j = 0; $j -lt $n; $j++) | |
{ | |
if ($j -ne $i) | |
{ | |
$lagrangian *= ($FindAt - $_x[$j]) / ($_x[$i] - $_x[$j]); | |
} | |
} | |
$interpolatedValue += $lagrangian * $_fx[$i]; | |
} | |
return $interpolatedValue | |
} | |
cls | |
$points = @( | |
Point 0.3 0.404958 | |
Point 0.5 0.824361 | |
Point 0.7 1.40963 | |
Point 0.9 2.21364 | |
Point 1.1 3.30458 | |
) | |
$at = 0.6 | |
Find-InterpolatedValue -Points $points -Range (0,2) -FindAt $at | |
Find-InterpolatedValue -Points $points -Range (0,3) -FindAt $at | |
Find-InterpolatedValue -Points $points -Range (1,4) -FindAt $at | |
Find-InterpolatedValue -Points $points -Range (0,4) -FindAt $at |
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