2016 Update

Task/Cholesky-decomposition/PowerShell/cholesky-decomposition.psh

@@ -0,0 +1,56 @@
+function cholesky ($a) {
+    $l = @()
+    if ($a) {
+        $n = $a.count
+        $end = $n - 1
+        $l = @(0) * $n
+        foreach ($i  in 0..$end) {$l[$i] = @(0) * $n}
+        foreach ($k in 0..$end) {
+            $m = $k - 1
+            $sum = 0
+            if(0 -lt $k) {
+                foreach ($j in 0..$m) {$sum += $l[$k][$j]*$l[$k][$j]}
+            }
+            $l[$k][$k] = [Math]::Sqrt($a[$k][$k] - $sum)
+            if ($k -lt $end) {
+                foreach ($i in ($k+1)..$end) {
+                    $sum = 0
+                    if (0 -lt $k) {
+                        foreach ($j in 0..$m) {$sum += $l[$i][$j]*$l[$k][$j]}
+                    }
+                    $l[$i][$k] = ($a[$i][$k] - $sum)/$l[$k][$k]
+                }
+            }
+        }
+    }
+    $l
+}
+
+function show($a) {
+    if($a) {
+        0..($a.Count - 1) | foreach{ if($a[$_]){"$($a[$_])"}else{""} }
+    }
+}
+
+$a1 = @(
+@(25, 15, -5),
+@(15, 18, 0),
+@(-5, 0, 11)
+)
+"a1 ="
+show $a1
+""
+"l1 ="
+show (cholesky $a1)
+""
+$a2 = @(
+@(18, 22, 54, 42),
+@(22, 70, 86, 62),
+@(54, 86, 174, 134),
+@(42, 62, 134, 106)
+)
+"a2 ="
+show $a2
+""
+"l2 ="
+show (cholesky $a2)