| CHOLESKY-OF |
|
GENERIC FUNCTION |
Package
QUAIL
Description
If A is positive definite, A can be factored uniquely in the form A = tp ( R ) R, where R is an upper triangular matrix with positive diagonal elements. This is the Cholesky decomposition of A, and R is its Cholesky factor ( Linpack manual ) . Once calculated, the decomposition is cached on A so that it need not be recalculated on subsequent calls.
Lambda List
(A &KEY PIVOT INITIAL FINAL PROMPT-IF-FAIL?)
Returns
An instance of the class cholesky-decomposition.
See Also
Examples
:FILES
| Cholesky decomposition |
q:examples;arrays;matrices;decompositions;cholesky.lisp |
Argument Information
REQUIRED
a
KEY
pivot
Default Value: NIL
Pivot is non-null if pivoting is requested, null otherwise.
initial
Default Value: NIL
If pivot is non-NIL, then initial can be a list of the indices of those diagonal elements which are to be moved the leading positions of A during pivoting.If NIL, then there is no restriction on the initial columns.
final
Default Value: NIL
If pivot is non-NIL, then final can be a list of the indices of those diagonal elements which are to be moved to the trailing positions of A during pivoting. If NIL, then there is no restriction on the last columns.
prompt-if-fail?
Default Value: T
Only relevant if no pivoting is allowed. If the algorithm fails, should the user be offered the opportunity to continue? If NIL, it is assumed that continuation is preferred. Continuation will produce a cholesky-decomposition object containing only a partial decomposition together with the order of the leading submatrix found to not be positive definite and a vector z such that Az = 0 approx. These are stored as the slots info and null-vector, respectively.