2015-08-04: add example for cholesky decomposition.

add example for cholesky decomposition.

diff --git a/examples/cholesky.w b/examples/cholesky.w
new file mode 100644
--- /dev/null
+++ b/examples/cholesky.w
@@ -0,0 +1,50 @@
+#!/usr/bin/env sh
+# -*- wisp -*-
+exec guile -L $(dirname $(dirname $(realpath "$0"))) --language=wisp -e '(@@ (examples cholesky) main)' -s "$0" "$@"
+; !#
+
+;; Cholesky decomposition, following https://de.wikipedia.org/wiki/Cholesky-Zerlegung#Pseudocode
+
+define-module : examples cholesky
+              . #:exports : cholesky!
+
+use-modules : guildhall ext foof-loop
+
+define : matrrix-ref X u v
+  list-ref (list-ref X u) v
+
+define : matrrix-set! X u v val
+  list-set! (list-ref X u) v val
+
+
+define : cholesky! a
+   . "Modifies the square matirx a to contain the its cholesky decomposition.
+
+a is represented as list of lists."
+   let : : n : length a
+     loop
+       : for i : up-from 1 : to n
+       loop
+         : for j : up-from 1 : to i
+         let 
+           : sum : matrix-ref a i j
+           when (>= j 1)
+             loop
+               : for k : up-from 1 : to (- j 1)
+               set! sum 
+                 - sum 
+                   * (matrix-ref a i k) (matrix-ref a j k)
+           cond
+             : > i j ; lower triangle
+               matrix-set! a i j
+                 / sum : matrix-ref a j j
+               . a
+             : > sum 0 ; diagonal element
+               matrix-set! a i i : sqrt sum
+               . a
+             else
+               throw 'matrix-numerically-not-symmetric-positive-definite
+
+
+define : main args
+         display : cholesky! '((1 2)(3 4))