f01mcf

Purpose

Synopsis

[al,d,ifail] = f01mcf(a,nrow<,ifail>)

Description

 
 This routine determines the unit lower triangular matrix L and 
                                                          T     
 the diagonal matrix D in the Cholesky factorization A=LDL  of a 
 symmetric positive-definite variable-bandwidth matrix A of order 
 n. (Such a matrix is sometimes called a 'sky-line' matrix.)
 
 The matrix A is represented by the elements lying within the 
 envelope of its lower triangular part, that is, between the first
 non-zero of each row and the diagonal. The width NROW(i) of the 
 ith row is the number of elements between the first non-zero 
 element and the element on the diagonal, inclusive. Although, of 
 course, any matrix possesses an envelope as defined, this routine 
 is primarily intended for the factorization of symmetric 
 positive-definite matrices with an average bandwidth which is 
 small compared with n.
 
 The method is based on the property that during Cholesky 
 factorization there is no fill-in outside the envelope.
 
 The determination of L and D is normally the first of two steps 
 in the solution of the system of equations Ax=b. The remaining 
                               T                            
 step, viz. the solution of LDL x=b may be carried out using 
 F04MCF.
 

Parameters

f01mcf

Required Input Arguments:

a (:)                                 real
nrow (:)                              integer

Optional Input Arguments:                       <Default>

ifail                                 integer  -1

Output Arguments:

al (:)                                real
d (:)                                 real
ifail                                 integer