DCHEX(3F)							     DCHEX(3F)

NAME
     DCHEX   - DCHEX updates the Cholesky factorization

	A = TRANS(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), DCHEX determines an orthogonal 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 = TRANS(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 DCHEX 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) )
	(		     ) ,
	(    -S(I)	C(I) )

     where C(I) is double precision.  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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DCHEX(3F)							     DCHEX(3F)

SYNOPSYS
      SUBROUTINE DCHEX(R,LDR,P,K,L,Z,LDZ,NZ,C,S,JOB)

DESCRIPTION
     On Entry

     R DOUBLE PRECISION(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 DOUBLE PRECISION(LDZ,N)Z), 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 DOUBLE PRECISION(P).
	C contains the cosines of the transforming rotations.

     S DOUBLE PRECISION(P).
	S contains the sines of the transforming rotations.  LINPACK.  This
     version dated 08/14/78 .  G. W. Stewart, University of Maryland, Argonne
     National Lab.

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DCHEX(3F)							     DCHEX(3F)

     DCHEX uses the following functions and subroutines. BLAS DROTG Fortran
     MIN0

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