CLAED8 man page on IRIX

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CLAED8(3F)							    CLAED8(3F)

NAME
     CLAED8 - merge the two sets of eigenvalues together into a single sorted
     set

SYNOPSIS
     SUBROUTINE CLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, Z, DLAMDA, Q2,
			LDQ2, W, INDXP, INDX, INDXQ, PERM, GIVPTR, GIVCOL,
			GIVNUM, INFO )

	 INTEGER	CUTPNT, GIVPTR, INFO, K, LDQ, LDQ2, N, QSIZ

	 REAL		RHO

	 INTEGER	GIVCOL( 2, * ), INDX( * ), INDXP( * ), INDXQ( * ),
			PERM( * )

	 REAL		D( * ), DLAMDA( * ), GIVNUM( 2, * ), W( * ), Z( * )

	 COMPLEX	Q( LDQ, * ), Q2( LDQ2, * )

PURPOSE
     CLAED8 merges the two sets of eigenvalues together into a single sorted
     set.  Then it tries to deflate the size of the problem.  There are two
     ways in which deflation can occur:	 when two or more eigenvalues are
     close together or if there is a tiny element in the Z vector.  For each
     such occurrence the order of the related secular equation problem is
     reduced by one.

ARGUMENTS
     K	    (output) INTEGER
	    Contains the number of non-deflated eigenvalues.  This is the
	    order of the related secular equation.

     N	    (input) INTEGER
	    The dimension of the symmetric tridiagonal matrix.	N >= 0.

     QSIZ   (input) INTEGER
	    The dimension of the unitary matrix used to reduce the dense or
	    band matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

     Q	    (input/output) COMPLEX array, dimension (LDQ,N)
	    On entry, Q contains the eigenvectors of the partially solved
	    system which has been previously updated in matrix multiplies with
	    other partially solved eigensystems.  On exit, Q contains the
	    trailing (N-K) updated eigenvectors (those which were deflated) in
	    its last N-K columns.

     LDQ    (input) INTEGER
	    The leading dimension of the array Q.  LDQ >= max( 1, N ).

									Page 1

CLAED8(3F)							    CLAED8(3F)

     D	    (input/output) REAL array, dimension (N)
	    On entry, D contains the eigenvalues of the two submatrices to be
	    combined.  On exit, D contains the trailing (N-K) updated
	    eigenvalues (those which were deflated) sorted into increasing
	    order.

     RHO    (input/output) REAL
	    Contains the off diagonal element associated with the rank-1 cut
	    which originally split the two submatrices which are now being
	    recombined. RHO is modified during the computation to the value
	    required by SLAED3.

	    CUTPNT (input) INTEGER Contains the location of the last
	    eigenvalue in the leading sub-matrix.  MIN(1,N) <= CUTPNT <= N.

     Z	    (input) REAL array, dimension (N)
	    On input this vector contains the updating vector (the last row of
	    the first sub-eigenvector matrix and the first row of the second
	    sub-eigenvector matrix).  The contents of Z are destroyed during
	    the updating process.

	    DLAMDA (output) REAL array, dimension (N) Contains a copy of the
	    first K eigenvalues which will be used by SLAED3 to form the
	    secular equation.

     Q2	    (output) COMPLEX array, dimension (LDQ2,N)
	    If ICOMPQ = 0, Q2 is not referenced.  Otherwise, Contains a copy
	    of the first K eigenvectors which will be used by SLAED7 in a
	    matrix multiply (SGEMM) to update the new eigenvectors.

     LDQ2   (input) INTEGER
	    The leading dimension of the array Q2.  LDQ2 >= max( 1, N ).

     W	    (output) REAL array, dimension (N)
	    This will hold the first k values of the final deflation-altered
	    z-vector and will be passed to SLAED3.

     INDXP  (workspace) INTEGER array, dimension (N)
	    This will contain the permutation used to place deflated values of
	    D at the end of the array. On output INDXP(1:K)
	    points to the nondeflated D-values and INDXP(K+1:N) points to the
	    deflated eigenvalues.

     INDX   (workspace) INTEGER array, dimension (N)
	    This will contain the permutation used to sort the contents of D
	    into ascending order.

     INDXQ  (input) INTEGER array, dimension (N)
	    This contains the permutation which separately sorts the two sub-
	    problems in D into ascending order.	 Note that elements in the
	    second half of this permutation must first have CUTPNT added to
	    their values in order to be accurate.

									Page 2

CLAED8(3F)							    CLAED8(3F)

     PERM   (output) INTEGER array, dimension (N)
	    Contains the permutations (from deflation and sorting) to be
	    applied to each eigenblock.

	    GIVPTR (output) INTEGER Contains the number of Givens rotations
	    which took place in this subproblem.

	    GIVCOL (output) INTEGER array, dimension (2, N) Each pair of
	    numbers indicates a pair of columns to take place in a Givens
	    rotation.

	    GIVNUM (output) REAL array, dimension (2, N) Each number indicates
	    the S value to be used in the corresponding Givens rotation.

     INFO   (output) INTEGER
	    = 0:  successful exit.
	    < 0:  if INFO = -i, the i-th argument had an illegal value.

									Page 3

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