CCHEX(3F)CCHEX(3F)NAMECCHEX - CCHEX updates the Cholesky factorization
A = CTRANS(R)*R
of a positive definite matrix A of order P under diagonal permutations of
the form
TRANS(E)*A*E
where E is a permutation matrix. Specifically, given an upper triangular
matrix R and a permutation matrix E (which is specified by K, L, and
JOB), CCHEX determines a unitary matrix U such that
U*R*E = RR,
where RR is upper triangular. At the users option, the transformation U
will be multiplied into the array Z. If A = CTRANS(X)*X, so that R is
the triangular part of the QR factorization of X, then RR is the
triangular part of the QR factorization of X*E, i.e. X with its columns
permuted. For a less terse description of what CCHEX does and how it may
be applied, see the LINPACK Guide.
The matrix Q is determined as the product U(L-K)*...*U(1) of plane
rotations of the form
( C(I)S(I) )
( ) ,
( -CONJG(S(I)) C(I) )
where C(I) is real. The rows these rotations operate on are described
below.
There are two types of permutations, which are determined by the value of
JOB.
1. Right circular shift (JOB = 1).
The columns are rearranged in the following order.
1,...,K-1,L,K,K+1,...,L-1,L+1,...,P.
U is the product of L-K rotations U(I), where U(I)
acts in the (L-I,L-I+1)-plane.
2. Left circular shift (JOB = 2).
The columns are rearranged in the following order
1,...,K-1,K+1,K+2,...,L,K,L+1,...,P.
U is the product of L-K rotations U(I), where U(I)
acts in the (K+I-1,K+I)-plane.
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CCHEX(3F)CCHEX(3F)SYNOPSYS
SUBROUTINE CCHEX(R,LDR,P,K,L,Z,LDZ,NZ,C,S,JOB)
DESCRIPTION
On Entry
R COMPLEX(LDR,P), where LDR .GE. P.
R contains the upper triangular factor
that is to be updated. Elements of R
below the diagonal are not referenced.
LDR INTEGER.
LDR is the leading dimension of the array R.
P INTEGER.
P is the order of the matrix R.
K INTEGER.
K is the first column to be permuted.
L INTEGER.
L is the last column to be permuted.
L must be strictly greater than K.
Z COMPLEX(LDZ,NZ), where LDZ .GE. P.
Z is an array of NZ P-vectors into which the
transformation U is multiplied. Z is
not referenced if NZ = 0.
LDZ INTEGER.
LDZ is the leading dimension of the array Z.
NZ INTEGER.
NZ is the number of columns of the matrix Z.
JOB INTEGER.
JOB determines the type of permutation.
JOB = 1 right circular shift.
JOB = 2 left circular shift. On Return
R contains the updated factor.
Z contains the updated matrix Z.
C REAL(P).
C contains the cosines of the transforming rotations.
S COMPLEX(P).
S contains the sines of the transforming rotations. LINPACK. This
version dated 08/14/78 . Stewart, G. W., University of Maryland, Argonne
National Lab.
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CCHEX(3F)CCHEX(3F)CCHEX uses the following functions and subroutines. Extended BLAS CROTG
Fortran MIN0
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