dstegr2b()

subroutine dstegr2b	(	character	jobz,
		integer	n,
		double precision, dimension( * )	d,
		double precision, dimension( * )	e,
		integer	m,
		double precision, dimension( * )	w,
		double precision, dimension( ldz, * )	z,
		integer	ldz,
		integer	nzc,
		integer, dimension( * )	isuppz,
		double precision, dimension( * )	work,
		integer	lwork,
		integer, dimension( * )	iwork,
		integer	liwork,
		integer	dol,
		integer	dou,
		integer	needil,
		integer	neediu,
		integer	indwlc,
		double precision	pivmin,
		double precision	scale,
		double precision	wl,
		double precision	wu,
		logical	vstart,
		logical	finish,
		integer	maxcls,
		integer	ndepth,
		integer	parity,
		integer	zoffset,
		integer	info
	)

Definition at line 1 of file dstegr2b.f.

*
*  -- ScaLAPACK auxiliary routine (version 2.0) --
*     Univ. of Tennessee, Univ. of California Berkeley, Univ. of Colorado Denver
*     July 4, 2010
*
      IMPLICIT NONE
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ
      INTEGER            DOL, DOU, INDWLC, INFO, LDZ, LIWORK, LWORK, M,
     $                   MAXCLS, N, NDEPTH, NEEDIL, NEEDIU, NZC, PARITY,
     $                   ZOFFSET
 
      DOUBLE PRECISION PIVMIN, SCALE, WL, WU
      LOGICAL VSTART, FINISH
 
*     ..
*     .. Array Arguments ..
      INTEGER            ISUPPZ( * ), IWORK( * )
      DOUBLE PRECISION   D( * ), E( * ), W( * ), WORK( * )
      DOUBLE PRECISION   Z( LDZ, * )
*     ..
*
*  Purpose
*  =======
*
*  DSTEGR2B should only be called after a call to DSTEGR2A.
*  From eigenvalues and initial representations computed by DSTEGR2A,
*  DSTEGR2B computes the selected eigenvalues and eigenvectors
*  of the real symmetric tridiagonal matrix in parallel 
*  on multiple processors. It is potentially invoked multiple times
*  on a given processor because the locally relevant representation tree 
*  might depend on spectral information that is "owned" by other processors
*  and might need to be communicated. 
* 
*  Please note:
*  1. The calling sequence has two additional INTEGER parameters, 
*     DOL and DOU, that should satisfy M>=DOU>=DOL>=1. 
*     These parameters are only relevant for the case JOBZ = 'V'.
*     DSTEGR2B  ONLY computes the eigenVECTORS 
*     corresponding to eigenvalues DOL through DOU in W. (That is,
*     instead of computing the eigenvectors belonging to W(1) 
*     through W(M), only the eigenvectors belonging to eigenvalues
*     W(DOL) through W(DOU) are computed. In this case, only the
*     eigenvalues DOL:DOU are guaranteed to be accurately refined
*     to all figures by Rayleigh-Quotient iteration.
*
*  2. The additional arguments VSTART, FINISH, NDEPTH, PARITY, ZOFFSET 
*     are included as a thread-safe implementation equivalent to SAVE variables.
*     These variables store details about the local representation tree which is
*     computed layerwise. For scalability reasons, eigenvalues belonging to the 
*     locally relevant representation tree might be computed on other processors.
*     These need to be communicated before the inspection of the RRRs can proceed
*     on any given layer.           
*     Note that only when the variable FINISH is true, the computation has ended
*     All eigenpairs between DOL and DOU have been computed. M is set = DOU - DOL + 1.
*
*  3. DSTEGR2B needs more workspace in Z than the sequential DSTEGR. 
*     It is used to store the conformal embedding of the local representation tree.  
*  
*  Arguments
*  =========
*
*  JOBZ    (input) CHARACTER*1
*          = 'N':  Compute eigenvalues only;
*          = 'V':  Compute eigenvalues and eigenvectors.
*
*  N       (input) INTEGER
*          The order of the matrix.  N >= 0.
*
*  D       (input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the N diagonal elements of the tridiagonal matrix
*          T. On exit, D is overwritten.
*
*  E       (input/output) DOUBLE PRECISION array, dimension (N)
*          On entry, the (N-1) subdiagonal elements of the tridiagonal
*          matrix T in elements 1 to N-1 of E. E(N) need not be set on
*          input, but is used internally as workspace.
*          On exit, E is overwritten.
*
*  M       (input) INTEGER
*          The total number of eigenvalues found
*          in DSTEGR2A.  0 <= M <= N.
*
*  W       (input) DOUBLE PRECISION array, dimension (N)
*          The first M elements contain approximations to the selected 
*          eigenvalues in ascending order. Note that only the eigenvalues from
*          the locally relevant part of the representation tree, that is
*          all the clusters that include eigenvalues from DOL:DOU, are reliable 
*          on this processor. (It does not need to know about any others anyway.)
*
*  Z       (output) DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
*          If JOBZ = 'V', and if INFO = 0, then 
*          a subset of the first M columns of Z
*          contain the orthonormal eigenvectors of the matrix T
*          corresponding to the selected eigenvalues, with the i-th
*          column of Z holding the eigenvector associated with W(i).
*          See DOL, DOU for more information.
*
*  LDZ     (input) INTEGER
*          The leading dimension of the array Z.  LDZ >= 1, and if
*          JOBZ = 'V', then LDZ >= max(1,N).
*
*  NZC     (input) INTEGER
*          The number of eigenvectors to be held in the array Z.  
*
*  ISUPPZ  (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
*          The support of the eigenvectors in Z, i.e., the indices
*          indicating the nonzero elements in Z. The i-th computed eigenvector
*          is nonzero only in elements ISUPPZ( 2*i-1 ) through
*          ISUPPZ( 2*i ). This is relevant in the case when the matrix 
*          is split. ISUPPZ is only set if N>2.
*
*  WORK    (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
*          On exit, if INFO = 0, WORK(1) returns the optimal
*          (and minimal) LWORK.
*
*  LWORK   (input) INTEGER
*          The dimension of the array WORK. LWORK >= max(1,18*N)
*          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
*          If LWORK = -1, then a workspace query is assumed; the routine
*          only calculates the optimal size of the WORK array, returns
*          this value as the first entry of the WORK array, and no error
*          message related to LWORK is issued.
*
*  IWORK   (workspace/output) INTEGER array, dimension (LIWORK)
*          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
*  LIWORK  (input) INTEGER
*          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
*          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
*          if only the eigenvalues are to be computed.
*          If LIWORK = -1, then a workspace query is assumed; the
*          routine only calculates the optimal size of the IWORK array,
*          returns this value as the first entry of the IWORK array, and
*          no error message related to LIWORK is issued.
*
*  DOL     (input) INTEGER
*  DOU     (input) INTEGER
*          From the eigenvalues W(1:M), only eigenvectors 
*          Z(:,DOL) to Z(:,DOU) are computed.
*          If DOL > 1, then Z(:,DOL-1-ZOFFSET) is used and overwritten.
*          If DOU < M, then Z(:,DOU+1-ZOFFSET) is used and overwritten.
*
*  NEEDIL  (input/output) INTEGER 
*  NEEDIU  (input/output) INTEGER
*          Describes which are the left and right outermost eigenvalues 
*          still to be computed. Initially computed by DLARRE2A,
*          modified in the course of the algorithm.
*
*  INDWLC  (output) DOUBLE PRECISION
*          Pointer into the workspace, location where the local
*          eigenvalue representations are stored. ("Local eigenvalues"
*          are those relative to the individual shifts of the RRRs.)
*
*  PIVMIN  (input) DOUBLE PRECISION
*          The minimum pivot in the sturm sequence for T.
*
*  SCALE   (input) DOUBLE PRECISION 
*          The scaling factor for T. Used for unscaling the eigenvalues
*          at the very end of the algorithm.
*
*  WL      (input) DOUBLE PRECISION
*  WU      (input) DOUBLE PRECISION
*          The interval (WL, WU] contains all the wanted eigenvalues.         
*
*  VSTART  (input/output) LOGICAL 
*          .TRUE. on initialization, set to .FALSE. afterwards.
*
*  FINISH  (input/output) LOGICAL
*          indicates whether all eigenpairs have been computed
*
*  MAXCLS  (input/output) INTEGER
*          The largest cluster worked on by this processor in the
*          representation tree.
*
*  NDEPTH  (input/output) INTEGER
*          The current depth of the representation tree. Set to
*          zero on initial pass, changed when the deeper levels of
*          the representation tree are generated. 
*
*  PARITY  (input/output) INTEGER
*          An internal parameter needed for the storage of the
*          clusters on the current level of the representation tree.
*
*  ZOFFSET (input) INTEGER
*          Offset for storing the eigenpairs when Z is distributed
*          in 1D-cyclic fashion
*
*  INFO    (output) INTEGER
*          On exit, INFO
*          = 0:  successful exit
*          other:if INFO = -i, the i-th argument had an illegal value
*                if INFO = 20X, internal error in DLARRV2.
*                Here, the digit X = ABS( IINFO ) < 10, where IINFO is 
*                the nonzero error code returned by DLARRV2.
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, FOUR, MINRGP
      parameter( one = 1.0d0,
     $                     four = 4.0d0,
     $                     minrgp = 1.0d-3 )
*     ..
*     .. Local Scalars ..
      LOGICAL            LQUERY, WANTZ, ZQUERY
      INTEGER            IINDBL, IINDW, IINDWK, IINFO, IINSPL, INDERR,
     $                   INDGP, INDGRS, INDSDM, INDWRK, ITMP, J, LIWMIN,
     $                   LWMIN
      DOUBLE PRECISION   EPS, RTOL1, RTOL2
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLAMCH, DLANST
      EXTERNAL           lsame, dlamch, dlanst
*     ..
*     .. External Subroutines ..
      EXTERNAL           dlarrv2, dscal
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, max, min, sqrt
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
      wantz = lsame( jobz, 'V' )
*
      lquery = ( ( lwork.EQ.-1 ).OR.( liwork.EQ.-1 ) )
      zquery = ( nzc.EQ.-1 )
 
*     DSTEGR2B needs WORK of size 6*N, IWORK of size 3*N.
*     In addition, DLARRE2A needed WORK of size 6*N, IWORK of size 5*N.
*     Workspace is kept consistent even though DLARRE2A is not called here.
*     Furthermore, DLARRV2 needs WORK of size 12*N, IWORK of size 7*N.
      IF( wantz ) THEN
         lwmin = 18*n
         liwmin = 10*n
      ELSE
*        need less workspace if only the eigenvalues are wanted         
         lwmin = 12*n
         liwmin = 8*n
      ENDIF
*
      info = 0
*
*     Get machine constants.
*
      eps = dlamch( 'Precision' )
*
      IF( (n.EQ.0).OR.(n.EQ.1) ) THEN 
         finish = .true.       
         RETURN
      ENDIF
 
      IF(zquery.OR.lquery)
     $   RETURN
*
      indgrs = 1
      inderr = 2*n + 1
      indgp = 3*n + 1
      indsdm = 4*n + 1
      indwrk = 6*n + 1
      indwlc = indwrk
*
      iinspl = 1
      iindbl = n + 1
      iindw = 2*n + 1
      iindwk = 3*n + 1
 
*     Set the tolerance parameters for bisection
      rtol1 = four*sqrt(eps)
      rtol2 = max( sqrt(eps)*5.0d-3, four * eps )
 
 
      IF( wantz ) THEN
*
*        Compute the desired eigenvectors corresponding to the computed
*        eigenvalues
*
         CALL dlarrv2( n, wl, wu, d, e,
     $                pivmin, iwork( iinspl ), m, 
     $                dol, dou, needil, neediu, minrgp, rtol1, rtol2, 
     $                w, work( inderr ), work( indgp ), iwork( iindbl ),
     $                iwork( iindw ), work( indgrs ), 
     $                work( indsdm ), z, ldz,
     $                isuppz, work( indwrk ), iwork( iindwk ), 
     $                vstart, finish, 
     $                maxcls, ndepth, parity, zoffset, iinfo )
         IF( iinfo.NE.0 ) THEN
            info = 200 + abs( iinfo )
            RETURN
         END IF
*
      ELSE
*        DLARRE2A computed eigenvalues of the (shifted) root representation
*        DLARRV2 returns the eigenvalues of the unshifted matrix.
*        However, if the eigenvectors are not desired by the user, we need
*        to apply the corresponding shifts from DLARRE2A to obtain the 
*        eigenvalues of the original matrix. 
         DO 30 j = 1, m
            itmp = iwork( iindbl+j-1 )
            w( j ) = w( j ) + e( iwork( iinspl+itmp-1 ) )
 30      CONTINUE
*
         finish = .true.
*
      END IF
*
 
      IF(finish) THEN        
*        All eigenpairs have been computed       
 
*
*        If matrix was scaled, then rescale eigenvalues appropriately.
*
         IF( scale.NE.one ) THEN
            CALL dscal( m, one / scale, w, 1 )
         END IF
*
*        Correct M if needed 
*
         IF ( wantz ) THEN
            IF( dol.NE.1 .OR. dou.NE.m ) THEN
               m = dou - dol +1
            ENDIF
         ENDIF
*
*        No sorting of eigenpairs is done here, done later in the
*        calling subroutine
*
         work( 1 ) = lwmin
         iwork( 1 ) = liwmin
      ENDIF
 
      RETURN
*
*     End of DSTEGR2B
*

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