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Task/Thieles-interpolation-formula/PowerShell/thieles-interpolation-formula.psh

@@ -0,0 +1,69 @@
+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*$asin.InvokeReturnAsIs(.5)
+$acos = (Thiele-Interpolation $acost)
+#uncomment to see the function
+#"{$acos}"
+3*$acos.InvokeReturnAsIs(.5)
+$atan = (Thiele-Interpolation $atant)
+#uncomment to see the function
+#"{$atan}"
+4*$atan.InvokeReturnAsIs(1)