Thiele's interpolation formula: Difference between revisions

$rho=@()

$rho+=0

$funcl = $function.length

if( $funcl -gt 0 )

-2..($funcl-1) | ForEach-Object {

$i=$_

#Write-Host "$($i+1) - $($rho[$i+1]) - $($rho[$i+1].GetType())"

$rho[$i+2] = $( 0..($funcl-$i-1) | Where-Object {$_ -lt $funcl} | ForEach-Object {

$j=$_

switch ($i) {

{$_ -lt 0 } { 0 }

{$_ -eq 0 } { $function[$j][1] }

{$_ -gt 0 } { ( $function[$j][0] - $function[$j+$i][0] ) / ( $rho[$i+1][$j] - $rho[$i+1][$j+1] ) + $rho[$i][$j+1] }

if( $_ -lt $funcl )

$rho += 0

$rho

$funcl = $function.length

$invoke = "{`n`tparam([Double] `$x)`n"

if($funcl -gt 1)

$rho = Reciprocal-Difference $function

($funcl-1)..0 | ForEach-Object {

$invoke += "`t"

$invoke += '$x{0} = {1} - {2}' -f $_, @($rho[$_+2])[0], @($rho[$_])[0]

if($_ -lt ($funcl-1))

$invoke += ' + ( $x - {0} ) / $x{1} ' -f $function[$_][0], ($_+1)

$invoke += "`n"

$invoke+="`t`$x0`n}"

} else {

$invoke += "`t`$x`n}"

invoke-expression $invoke