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

Group: Linear Algebra
See also: svd eigsm ludecomp chol

Function: chold
Description: The function chold is calculating the triangularisation and the Cholesky decomposition

of x into matrices b and d, so that b'*d*b = x.


Usage: bd = chold(x,l)
Input:
x n x n matrix, the input matrix
l scalar, the number of lower non-zero subdiagonals including the diagonal, l<=dim(x)
Output:
bd n x n matrix, see note

Note:

Example:



randomize(0)

x = normal(3,3)

x = x*x'

x[1,3]=0

x[3,1]=0

x

chold(x,2)  ; since the third lower diagonal is zero                 

Result:



Contents of x

[1,]   1.9005   2.6997        0 

[2,]   2.6997   5.5519  -2.5479 

[3,]        0  -2.5479   4.3615 

Contents of chol

[1,]   1.9005   1.4205        0 

[2,]        0    1.717  -1.4839 

[3,]        0        0   0.5808 

Example:



randomize(0)

x = normal(3,3)

x = x*x'

x

bd = chold(x, 3)

d = diag(xdiag(bd))

b = bd -d + eye(rows(bd))

b'*d*b ; triangularisation

l = b'*sqrt(d) ; cholesky

l*l'      

Result:



Contents of x

[1,]   1.9005   2.6997  -1.2229 

[2,]   2.6997   5.5519  -2.5479 

[3,]  -1.2229  -2.5479   4.3615 

Contents of _tmp

[1,]   1.9005   2.6997  -1.2229 

[2,]   2.6997   5.5519  -2.5479 

[3,]  -1.2229  -2.5479   4.3615 

Contents of _tmp

[1,]   1.9005   2.6997  -1.2229 

[2,]   2.6997   5.5519  -2.5479 

[3,]  -1.2229  -2.5479   4.3615 


Group: Linear Algebra
See also: svd eigsm ludecomp chol

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

(C) MD*TECH Method and Data Technologies, 21.9.2000