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RedHat 9 (Linux i386) - man page for claed8 (redhat section l)

CLAED8(l)					)					CLAED8(l)

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 ).

       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	eigenval-
	      ues 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 eigen-
	      values.

       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.

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

	      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.

LAPACK version 3.0			   15 June 2000 				CLAED8(l)


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