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Thiele's interpolation formula: Difference between revisions
Added language PowerShell
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tan interpolation: 3.14826236377727
</pre>
=={{header|PowerShell}}==
<lang PowerShell>Function Reciprocal-Difference( [Double[][]] $function )
{
$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
}
Function Thiele-Interpolation ( [Double[][]] $function )
{
$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
}
$sint=@{}; 0..31 | ForEach-Object { $_ * 0.05 } | ForEach-Object { $sint[$_] = [Math]::sin($_) }
$cost=@{}; 0..31 | ForEach-Object { $_ * 0.05 } | ForEach-Object { $cost[$_] = [Math]::cos($_) }
$tant=@{}; 0..31 | ForEach-Object { $_ * 0.05 } | ForEach-Object { $tant[$_] = [Math]::tan($_) }
$asint=New-Object 'Double[][]' 32,2; $sint.GetEnumerator() | Sort-Object Value | ForEach-Object {$i=0}{ $asint[$i][0] = $_.Value; $asint[$i][1] = $_.Name; $i++ }
$acost=New-Object 'Double[][]' 32,2; $cost.GetEnumerator() | Sort-Object Value | ForEach-Object { $i=0 }{ $acost[$i][0] = $_.Value; $acost[$i][1] = $_.Name; $i++ }
$atant=New-Object 'Double[][]' 32,2; $tant.GetEnumerator() | Sort-Object Value | ForEach-Object {$i=0}{ $atant[$i][0] = $_.Value; $atant[$i][1] = $_.Name; $i++ }
$asin = (Thiele-Interpolation $asint)
#uncomment to see the function
#"{$asin}"
6*$asin.invoke(.5)[0]
$acos = (Thiele-Interpolation $acost)
#uncomment to see the function
#"{$acos}"
3*$acos.invoke(.5)[0]
$atan = (Thiele-Interpolation $atant)
#uncomment to see the function
#"{$atan}"
4*$atan.invoke(1)[0]</lang>
=={{header|Tcl}}==
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