2016 Update

Task/Cholesky-decomposition/Haskell/cholesky-decomposition-2.hs

@@ -2,21 +2,17 @@ import Data.Array.IArray
 import Data.List
 import Cholesky
 
-takeDrop 0 xs = ([],xs)
-takeDrop _ [] = ([],[])
-takeDrop n (x:xs) = (x:a,b) where (a,b) = takeDrop (n-1) xs
-
 fm _ [] = ""
 fm _ [x] = fst x
 fm width ((a,b):xs) = a ++ (take (width - b) $ cycle " ") ++ (fm width xs)
 
 fmt width row (xs,[]) = fm width xs
-fmt width row (xs,ys) = fm width xs  ++ "\n" ++ fmt width row (takeDrop row ys)
+fmt width row (xs,ys) = fm width xs  ++ "\n" ++ fmt width row (splitAt row ys)
 
 showMatrice row xs   = ys where
   vs = map (\s -> let sh = show s in (sh,length sh)) xs
-  width = (maximum $ snd $ unzip vs) + 2
-  ys = fmt width row (takeDrop row vs)
+  width = (maximum $ snd $ unzip vs) + 1
+  ys = fmt width row (splitAt row vs)
 
 ex1, ex2 :: Arr
 ex1 = listArray ((0,0),(2,2)) [25, 15, -5,

Task/Cholesky-decomposition/PARI-GP/cholesky-decomposition.pari

@@ -0,0 +1,12 @@
+cholesky(M) =
+{
+  my (L = matrix(#M,#M));
+
+  for (i = 1, #M,
+    for (j = 1, i,
+      s = sum (k = 1, j-1, L[i,k] * L[j,k]);
+      L[i,j] = if (i == j, sqrt(M[i,i] - s), (M[i,j] - s) / L[j,j])
+    )
+  );
+  L
+}

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)

Task/Cholesky-decomposition/REXX/cholesky-decomposition.rexx

@@ -10,7 +10,7 @@ hexer =  18  22  54  42,                             /*define a  4x4  matrix. */
                            call Cholesky hexer
 exit                                   /*stick a fork in it,  we're all done. */
 /*────────────────────────────────────────────────────────────────────────────*/
-Cholesky: procedure;  parse arg mat;   say;   say;   call tell 'input array',mat
+Cholesky: procedure;  parse arg mat;   say;   say;   call tell 'input matrix',mat
              do    r=1  for ord
                 do c=1  for r; $=0;  do i=1  for c-1; $=$+!.r.i*!.c.i; end /*i*/
                 if r=c  then !.r.r=sqrt(!.r.r-$)

Task/Cholesky-decomposition/ZX-Spectrum-Basic/cholesky-decomposition.zx

@@ -0,0 +1,35 @@
+10 LET d=2000: GO SUB 1000: GO SUB 4000: GO SUB 5000
+20 LET d=3000: GO SUB 1000: GO SUB 4000: GO SUB 5000
+30 STOP
+1000 RESTORE d
+1010 READ a,b
+1020 DIM m(a,b)
+1040 FOR i=1 TO a
+1050 FOR j=1 TO b
+1060 READ m(i,j)
+1070 NEXT j
+1080 NEXT i
+1090 RETURN
+2000 DATA 3,3,25,15,-5,15,18,0,-5,0,11
+3000 DATA 4,4,18,22,54,42,22,70,86,62,54,86,174,134,42,62,134,106
+4000 REM Cholesky decomposition
+4005 DIM l(a,b)
+4010 FOR i=1 TO a
+4020 FOR j=1 TO i
+4030 LET s=0
+4050 FOR k=1 TO j-1
+4060 LET s=s+l(i,k)*l(j,k)
+4070 NEXT k
+4080 IF i=j THEN LET l(i,j)=SQR (m(i,i)-s): GO TO 4100
+4090 LET l(i,j)=(m(i,j)-s)/l(j,j)
+4100 NEXT j
+4110 NEXT i
+4120 RETURN
+5000 REM Print
+5010 FOR r=1 TO a
+5020 FOR c=1 TO b
+5030 PRINT l(r,c);" ";
+5040 NEXT c
+5050 PRINT
+5060 NEXT r
+5070 RETURN