SCHUD(3F)							     SCHUD(3F)

NAME    [Toc]    [Back]

     SCHUD   - SCHUD updates an	augmented Cholesky decomposition of the
     triangular	part of	an augmented QR	decomposition.	Specifically, given an
     upper triangular matrix R of order	P, a row vector	X, a column vector Z,
     and a scalar Y, SCHUD determines a	unitary	matrix U and a scalar ZETA
     such that


	(R  Z)	   (RR	 ZZ )
	U  * (	  )  =	(	 ) ,
	(X  Y)	   ( 0	ZETA)

     where RR is upper triangular.  If R and Z have been obtained from the
     factorization of a	least squares problem, then RR and ZZ are the factors
     corresponding to the problem with the observation (X,Y) appended.	In
     this case,	if RHO is the norm of the residual vector, then	the norm of
     the residual vector of the	updated	problem	is SQRT(RHO**2 + ZETA**2).
     SCHUD will	simultaneously update several triplets (Z,Y,RHO).  For a less
     terse description of what SCHUD does and how it may be applied, see the
     LINPACK guide.

     The matrix	U is determined	as the product U(P)*...*U(1), where U(I) is a
     rotation in the (I,P+1) plane of the form

	(     C(I)	S(I) )
	(		     ) .
	(    -S(I)	C(I) )

     The rotations are chosen so that C(I) is real.

SYNOPSYS    [Toc]    [Back]

      SUBROUTINE SCHUD(R,LDR,P,X,Z,LDZ,NZ,Y,RHO,C,S)

DESCRIPTION    [Toc]    [Back]

     On	Entry

     R REAL(LDR,P), where LDR .GE. P.
	R contains the upper triangular	matrix
	that is	to be updated.	The part of R
	below the diagonal is not referenced.

     LDR INTEGER.
	LDR is the leading dimension of	the array R.

     P INTEGER.
	P is the order of the matrix R.

     X REAL(P).
	X contains the row to be added to R.  X	is
	not altered by SCHUD.




									Page 1






SCHUD(3F)							     SCHUD(3F)



     Z REAL(LDZ,NZ), where LDZ .GE. P.
	Z is an	array containing NZ P-vectors to
	be updated with	R.

     LDZ INTEGER.
	LDZ is the leading dimension of	the array Z.

     NZ	INTEGER.
	NZ is the number of vectors to be updated.
	NZ may be zero,	in which case Z, Y, and	RHO
	are not	referenced.

     Y REAL(NZ).
	Y contains the scalars for updating the	vectors
	Z.  Y is not altered by	SCHUD.

     RHO REAL(NZ).
	RHO contains the norms of the residual
	vectors	that are to be updated.	 If RHO(J)
	is negative, it	is left	unaltered.  On Return RC

     RHO contain the updated quantities.

     Z


     C REAL(P).
	C contains the cosines of the transforming
	rotations.

     S REAL(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.

     SCHUD uses	the following functions	and subroutines. Extended BLAS SROTG
     Fortran SQRT


									PPPPaaaaggggeeee 2222