CLAED7 man page on IRIX

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CLAED7(3F)							    CLAED7(3F)

NAME
     CLAED7 - compute the updated eigensystem of a diagonal matrix after
     modification by a rank-one symmetric matrix

SYNOPSIS
     SUBROUTINE CLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, LDQ,
			RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, GIVPTR,
			GIVCOL, GIVNUM, WORK, RWORK, IWORK, INFO )

	 INTEGER	CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, TLVLS

	 REAL		RHO

	 INTEGER	GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), IWORK( * ),
			PERM( * ), PRMPTR( * ), QPTR( * )

	 REAL		D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * )

	 COMPLEX	Q( LDQ, * ), WORK( * )

PURPOSE
     CLAED7 computes the updated eigensystem of a diagonal matrix after
     modification by a rank-one symmetric matrix. This routine is used only
     for the eigenproblem which requires all eigenvalues and optionally
     eigenvectors of a dense or banded Hermitian matrix that has been reduced
     to tridiagonal form.

       T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)

       where Z = Q'u, u is a vector of length N with ones in the
       CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.

	The eigenvectors of the original matrix are stored in Q, and the
	eigenvalues are in D.  The algorithm consists of three stages:

	   The first stage consists of deflating the size of the problem
	   when there are multiple eigenvalues or if there is a zero in
	   the Z vector.  For each such occurence the dimension of the
	   secular equation problem is reduced by one.	This stage is
	   performed by the routine SLAED2.

	   The second stage consists of calculating the updated
	   eigenvalues. This is done by finding the roots of the secular
	   equation via the routine SLAED4 (as called by SLAED3).
	   This routine also calculates the eigenvectors of the current
	   problem.

	   The final stage consists of computing the updated eigenvectors
	   directly using the updated eigenvalues.  The eigenvectors for
	   the current problem are multiplied with the eigenvectors from
	   the overall problem.

									Page 1

CLAED7(3F)							    CLAED7(3F)

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

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

     QSIZ   (input) INTEGER
	    The dimension of the unitary matrix used to reduce the full matrix
	    to tridiagonal form.  QSIZ >= N.

     TLVLS  (input) INTEGER
	    The total number of merging levels in the overall divide and
	    conquer tree.

	    CURLVL (input) INTEGER The current level in the overall merge
	    routine, 0 <= curlvl <= tlvls.

	    CURPBM (input) INTEGER The current problem in the current level in
	    the overall merge routine (counting from upper left to lower
	    right).

     D	    (input/output) REAL array, dimension (N)
	    On entry, the eigenvalues of the rank-1-perturbed matrix.  On
	    exit, the eigenvalues of the repaired matrix.

     Q	    (input/output) COMPLEX array, dimension (LDQ,N)
	    On entry, the eigenvectors of the rank-1-perturbed matrix.	On
	    exit, the eigenvectors of the repaired tridiagonal matrix.

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

     RHO    (input) REAL
	    Contains the subdiagonal element used to create the rank-1
	    modification.

     INDXQ  (output) INTEGER array, dimension (N)
	    This contains the permutation which will reintegrate the
	    subproblem just solved back into sorted order, ie. D( INDXQ( I =
	    1, N ) ) will be in ascending order.

     IWORK  (workspace) INTEGER array, dimension (4*N)

     RWORK  (workspace) REAL array,
	    dimension (3*N+2*QSIZ*N)

     WORK   (workspace) COMPLEX array, dimension (QSIZ*N)

	    QSTORE (input/output) REAL array, dimension (N**2+1) Stores
	    eigenvectors of submatrices encountered during divide and conquer,
	    packed together. QPTR points to beginning of the submatrices.

									Page 2

CLAED7(3F)							    CLAED7(3F)

     QPTR   (input/output) INTEGER array, dimension (N+2)
	    List of indices pointing to beginning of submatrices stored in
	    QSTORE. The submatrices are numbered starting at the bottom left
	    of the divide and conquer tree, from left to right and bottom to
	    top.

	    PRMPTR (input) INTEGER array, dimension (N lg N) Contains a list
	    of pointers which indicate where in PERM a level's permutation is
	    stored.  PRMPTR(i+1) - PRMPTR(i) indicates the size of the
	    permutation and also the size of the full, non-deflated problem.

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

	    GIVPTR (input) INTEGER array, dimension (N lg N) Contains a list
	    of pointers which indicate where in GIVCOL a level's Givens
	    rotations are stored.  GIVPTR(i+1) - GIVPTR(i) indicates the
	    number of Givens rotations.

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

	    GIVNUM (input) REAL array, dimension (2, N lg 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.
	    > 0:  if INFO = 1, an eigenvalue did not converge

									Page 3

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