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RedHat 9 (Linux i386) - man page for dlaed8 (redhat section l)

DLAED8(l)					)					DLAED8(l)

NAME
       DLAED8 - merge the two sets of eigenvalues together into a single sorted set

SYNOPSIS
       SUBROUTINE DLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, Z, DLAMDA, Q2, LDQ2,
			  W, PERM, GIVPTR, GIVCOL, GIVNUM, INDXP, INDX, INFO )

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

	   DOUBLE	  PRECISION RHO

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

	   DOUBLE	  PRECISION D( * ), DLAMDA( * ), GIVNUM( 2, * ), Q( LDQ, * ), Q2( LDQ2, *
			  ), W( * ), Z( * )

PURPOSE
       DLAED8 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
       ICOMPQ  (input) INTEGER
	       = 0:  Compute eigenvalues only.
	       =  1:   Compute eigenvectors of original dense symmetric matrix also.  On entry, Q
	       contains the orthogonal matrix used to reduce the original matrix  to  tridiagonal
	       form.

       K      (output) INTEGER
	      The  number of non-deflated eigenvalues, and the order of the related secular equa-
	      tion.

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

       QSIZ   (input) INTEGER
	      The dimension of the orthogonal matrix used to reduce the full matrix to	tridiago-
	      nal form.  QSIZ >= N if ICOMPQ = 1.

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

       Q      (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
	      If  ICOMPQ = 0, Q is not referenced.  Otherwise, on entry, Q contains the eigenvec-
	      tors 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).

       INDXQ  (input) INTEGER array, dimension (N)
	      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.

       RHO    (input/output) DOUBLE PRECISION
	      On  entry, the off-diagonal element associated with the rank-1 cut which originally
	      split the two submatrices which are now being recombined.  On exit,  RHO	has  been
	      modified to the value required by DLAED3.

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

       Z      (input) DOUBLE PRECISION array, dimension (N)
	      On entry, Z contains the updating vector (the last row of the first sub-eigenvector
	      matrix  and the first row of the second sub-eigenvector matrix).	On exit, the con-
	      tents of Z are destroyed by the updating process.

	      DLAMDA (output) DOUBLE PRECISION array, dimension (N) A copy of the first K  eigen-
	      values which will be used by DLAED3 to form the secular equation.

       Q2     (output) DOUBLE PRECISION array, dimension (LDQ2,N)
	      If ICOMPQ = 0, Q2 is not referenced.  Otherwise, a copy of the first K eigenvectors
	      which will be used by DLAED7 in a matrix multiply (DGEMM) to update the new  eigen-
	      vectors.

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

       W      (output) DOUBLE PRECISION array, dimension (N)
	      The  first  k  values of the final deflation-altered z-vector and will be passed to
	      DLAED3.

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

	      GIVPTR (output) INTEGER 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) DOUBLE PRECISION array, dimension (2, N) Each number indicates  the
	      S value to be used in the corresponding Givens rotation.

       INDXP  (workspace) INTEGER array, dimension (N)
	      The  permutation	used  to  place  deflated  values  of  D at the end of the array.
	      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)
	      The permutation used to sort the contents of D into ascending order.

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

FURTHER DETAILS
       Based on contributions by
	  Jeff Rutter, Computer Science Division, University of California
	  at Berkeley, USA

LAPACK version 3.0			   15 June 2000 				DLAED8(l)


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