Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 Function: ludecomp Description: computes the LU decomposition of a square matrix, ; where L represents the lower ; and U the upper triangular matrix.

 Usage: z = ludecomp (x) Input: x p x p matrix of user-defined data which should be decomposed Output: z.l p x p lower triangular matrix z.u p x p upper triangular matrix z.index p x 1 indexvector, defining the order of the z.l*z.u matrix

Note:
!! Be careful: x must be a square matrix. !!

z.index is needed to restore the original matrix x from z.l ; and z.u. To rebuild x use index(z.l*z.u, z.index).

Keep in mind that the LU decomposition is not unique.

Example:
```x = #(1, 2, 3)~#(2, 3, 4)~#(3, 4, 5)
z = ludecomp(x)
z
index(z.l*z.u, z.index)

```
Result:
```Contents of z.l
[1,]        1        0        0
[2,]  0.33333        1        0
[3,]  0.66667      0.5        1
Contents of z.u
[1,]        3        4        5
[2,]        0  0.66667   1.3333
[3,]        0        0  1.1102e-16
Contents of z.index
[1,]        2
[2,]        3
[3,]        1
Contents of index
[1,]        1        2        3
[2,]        2        3        4
[3,]        3        4        5
```

(C) MD*TECH Method and Data Technologies, 05.02.2006