Lagrange Interpolation in Powershell

PoshLagrange.ps1

<#
    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