*> \brief <b> CHEEVR_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
*
* @generated from zheevr_2stage.f, fortran z -> c, Sat Nov 5 23:18:11 2016
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download CHEEVR_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevr_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevr_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevr_2stage.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
* IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ,
* WORK, LWORK, RWORK, LRWORK, IWORK,
* LIWORK, INFO )
*
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, RANGE, UPLO
* INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK,
* $ M, N
* REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
* INTEGER ISUPPZ( * ), IWORK( * )
* REAL RWORK( * ), W( * )
* COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CHEEVR_2STAGE computes selected eigenvalues and, optionally, eigenvectors
*> of a complex Hermitian matrix A using the 2stage technique for
*> the reduction to tridiagonal. Eigenvalues and eigenvectors can
*> be selected by specifying either a range of values or a range of
*> indices for the desired eigenvalues.
*>
*> CHEEVR_2STAGE first reduces the matrix A to tridiagonal form T with a call
*> to CHETRD. Then, whenever possible, CHEEVR_2STAGE calls CSTEMR to compute
*> eigenspectrum using Relatively Robust Representations. CSTEMR
*> computes eigenvalues by the dqds algorithm, while orthogonal
*> eigenvectors are computed from various "good" L D L^T representations
*> (also known as Relatively Robust Representations). Gram-Schmidt
*> orthogonalization is avoided as far as possible. More specifically,
*> the various steps of the algorithm are as follows.
*>
*> For each unreduced block (submatrix) of T,
*> (a) Compute T - sigma I = L D L^T, so that L and D
*> define all the wanted eigenvalues to high relative accuracy.
*> This means that small relative changes in the entries of D and L
*> cause only small relative changes in the eigenvalues and
*> eigenvectors. The standard (unfactored) representation of the
*> tridiagonal matrix T does not have this property in general.
*> (b) Compute the eigenvalues to suitable accuracy.
*> If the eigenvectors are desired, the algorithm attains full
*> accuracy of the computed eigenvalues only right before
*> the corresponding vectors have to be computed, see steps c) and d).
*> (c) For each cluster of close eigenvalues, select a new
*> shift close to the cluster, find a new factorization, and refine
*> the shifted eigenvalues to suitable accuracy.
*> (d) For each eigenvalue with a large enough relative separation compute
*> the corresponding eigenvector by forming a rank revealing twisted
*> factorization. Go back to (c) for any clusters that remain.
*>
*> The desired accuracy of the output can be specified by the input
*> parameter ABSTOL.
*>
*> For more details, see CSTEMR's documentation and:
*> - Inderjit S. Dhillon and Beresford N. Parlett: "Multiple representations
*> to compute orthogonal eigenvectors of symmetric tridiagonal matrices,"
*> Linear Algebra and its Applications, 387(1), pp. 1-28, August 2004.
*> - Inderjit Dhillon and Beresford Parlett: "Orthogonal Eigenvectors and
*> Relative Gaps," SIAM Journal on Matrix Analysis and Applications, Vol. 25,
*> 2004. Also LAPACK Working Note 154.
*> - Inderjit Dhillon: "A new O(n^2) algorithm for the symmetric
*> tridiagonal eigenvalue/eigenvector problem",
*> Computer Science Division Technical Report No. UCB/CSD-97-971,
*> UC Berkeley, May 1997.
*>
*>
*> Note 1 : CHEEVR_2STAGE calls CSTEMR when the full spectrum is requested
*> on machines which conform to the ieee-754 floating point standard.
*> CHEEVR_2STAGE calls SSTEBZ and CSTEIN on non-ieee machines and
*> when partial spectrum requests are made.
*>
*> Normal execution of CSTEMR may create NaNs and infinities and
*> hence may abort due to a floating point exception in environments
*> which do not handle NaNs and infinities in the ieee standard default
*> manner.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] JOBZ
*> \verbatim
*> JOBZ is CHARACTER*1
*> = 'N': Compute eigenvalues only;
*> = 'V': Compute eigenvalues and eigenvectors.
*> Not available in this release.
*> \endverbatim
*>
*> \param[in] RANGE
*> \verbatim
*> RANGE is CHARACTER*1
*> = 'A': all eigenvalues will be found.
*> = 'V': all eigenvalues in the half-open interval (VL,VU]
*> will be found.
*> = 'I': the IL-th through IU-th eigenvalues will be found.
*> For RANGE = 'V' or 'I' and IU - IL < N - 1, SSTEBZ and
*> CSTEIN are called
*> \endverbatim
*>
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> = 'U': Upper triangle of A is stored;
*> = 'L': Lower triangle of A is stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix A. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA, N)
*> On entry, the Hermitian matrix A. If UPLO = 'U', the
*> leading N-by-N upper triangular part of A contains the
*> upper triangular part of the matrix A. If UPLO = 'L',
*> the leading N-by-N lower triangular part of A contains
*> the lower triangular part of the matrix A.
*> On exit, the lower triangle (if UPLO='L') or the upper
*> triangle (if UPLO='U') of A, including the diagonal, is
*> destroyed.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in] VL
*> \verbatim
*> VL is REAL
*> If RANGE='V', the lower bound of the interval to
*> be searched for eigenvalues. VL < VU.
*> Not referenced if RANGE = 'A' or 'I'.
*> \endverbatim
*>
*> \param[in] VU
*> \verbatim
*> VU is REAL
*> If RANGE='V', the upper bound of the interval to
*> be searched for eigenvalues. VL < VU.
*> Not referenced if RANGE = 'A' or 'I'.
*> \endverbatim
*>
*> \param[in] IL
*> \verbatim
*> IL is INTEGER
*> If RANGE='I', the index of the
*> smallest eigenvalue to be returned.
*> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
*> Not referenced if RANGE = 'A' or 'V'.
*> \endverbatim
*>
*> \param[in] IU
*> \verbatim
*> IU is INTEGER
*> If RANGE='I', the index of the
*> largest eigenvalue to be returned.
*> 1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
*> Not referenced if RANGE = 'A' or 'V'.
*> \endverbatim
*>
*> \param[in] ABSTOL
*> \verbatim
*> ABSTOL is REAL
*> The absolute error tolerance for the eigenvalues.
*> An approximate eigenvalue is accepted as converged
*> when it is determined to lie in an interval [a,b]
*> of width less than or equal to
*>
*> ABSTOL + EPS * max( |a|,|b| ) ,
*>
*> where EPS is the machine precision. If ABSTOL is less than
*> or equal to zero, then EPS*|T| will be used in its place,
*> where |T| is the 1-norm of the tridiagonal matrix obtained
*> by reducing A to tridiagonal form.
*>
*> See "Computing Small Singular Values of Bidiagonal Matrices
*> with Guaranteed High Relative Accuracy," by Demmel and
*> Kahan, LAPACK Working Note #3.
*>
*> If high relative accuracy is important, set ABSTOL to
*> SLAMCH( 'Safe minimum' ). Doing so will guarantee that
*> eigenvalues are computed to high relative accuracy when
*> possible in future releases. The current code does not
*> make any guarantees about high relative accuracy, but
*> future releases will. See J. Barlow and J. Demmel,
*> "Computing Accurate Eigensystems of Scaled Diagonally
*> Dominant Matrices", LAPACK Working Note #7, for a discussion
*> of which matrices define their eigenvalues to high relative
*> accuracy.
*> \endverbatim
*>
*> \param[out] M
*> \verbatim
*> M is INTEGER
*> The total number of eigenvalues found. 0 <= M <= N.
*> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*> W is REAL array, dimension (N)
*> The first M elements contain the selected eigenvalues in
*> ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is COMPLEX array, dimension (LDZ, max(1,M))
*> If JOBZ = 'V', then if INFO = 0, the first M columns of Z
*> contain the orthonormal eigenvectors of the matrix A
*> corresponding to the selected eigenvalues, with the i-th
*> column of Z holding the eigenvector associated with W(i).
*> If JOBZ = 'N', then Z is not referenced.
*> Note: the user must ensure that at least max(1,M) columns are
*> supplied in the array Z; if RANGE = 'V', the exact value of M
*> is not known in advance and an upper bound must be used.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. LDZ >= 1, and if
*> JOBZ = 'V', LDZ >= max(1,N).
*> \endverbatim
*>
*> \param[out] ISUPPZ
*> \verbatim
*> ISUPPZ is 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 eigenvector
*> is nonzero only in elements ISUPPZ( 2*i-1 ) through
*> ISUPPZ( 2*i ). This is an output of CSTEMR (tridiagonal
*> matrix). The support of the eigenvectors of A is typically
*> 1:N because of the unitary transformations applied by CUNMTR.
*> Implemented only for RANGE = 'A' or 'I' and IU - IL = N - 1
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> If N <= 1, LWORK must be at least 1.
*> If JOBZ = 'N' and N > 1, LWORK must be queried.
*> LWORK = MAX(1, 26*N, dimension) where
*> dimension = max(stage1,stage2) + (KD+1)*N + N
*> = N*KD + N*max(KD+1,FACTOPTNB)
*> + max(2*KD*KD, KD*NTHREADS)
*> + (KD+1)*N + N
*> where KD is the blocking size of the reduction,
*> FACTOPTNB is the blocking used by the QR or LQ
*> algorithm, usually FACTOPTNB=128 is a good choice
*> NTHREADS is the number of threads used when
*> openMP compilation is enabled, otherwise =1.
*> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
*>
*> If LWORK = -1, then a workspace query is assumed; the routine
*> only calculates the optimal sizes of the WORK, RWORK and
*> IWORK arrays, returns these values as the first entries of
*> the WORK, RWORK and IWORK arrays, and no error message
*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is REAL array, dimension (MAX(1,LRWORK))
*> On exit, if INFO = 0, RWORK(1) returns the optimal
*> (and minimal) LRWORK.
*> \endverbatim
*>
*> \param[in] LRWORK
*> \verbatim
*> LRWORK is INTEGER
*> The length of the array RWORK.
*> If N <= 1, LRWORK >= 1, else LRWORK >= 24*N.
*>
*> If LRWORK = -1, then a workspace query is assumed; the
*> routine only calculates the optimal sizes of the WORK, RWORK
*> and IWORK arrays, returns these values as the first entries
*> of the WORK, RWORK and IWORK arrays, and no error message
*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
*> On exit, if INFO = 0, IWORK(1) returns the optimal
*> (and minimal) LIWORK.
*> \endverbatim
*>
*> \param[in] LIWORK
*> \verbatim
*> LIWORK is INTEGER
*> The dimension of the array IWORK.
*> If N <= 1, LIWORK >= 1, else LIWORK >= 10*N.
*>
*> If LIWORK = -1, then a workspace query is assumed; the
*> routine only calculates the optimal sizes of the WORK, RWORK
*> and IWORK arrays, returns these values as the first entries
*> of the WORK, RWORK and IWORK arrays, and no error message
*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> > 0: Internal error
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup heevr_2stage
*
*> \par Contributors:
* ==================
*>
*> Inderjit Dhillon, IBM Almaden, USA \n
*> Osni Marques, LBNL/NERSC, USA \n
*> Ken Stanley, Computer Science Division, University of
*> California at Berkeley, USA \n
*> Jason Riedy, Computer Science Division, University of
*> California at Berkeley, USA \n
*>
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> All details about the 2stage techniques are available in:
*>
*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
*> Parallel reduction to condensed forms for symmetric eigenvalue problems
*> using aggregated fine-grained and memory-aware kernels. In Proceedings
*> of 2011 International Conference for High Performance Computing,
*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
*> Article 8 , 11 pages.
*> http://doi.acm.org/10.1145/2063384.2063394
*>
*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
*> An improved parallel singular value algorithm and its implementation
*> for multicore hardware, In Proceedings of 2013 International Conference
*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
*> Denver, Colorado, USA, 2013.
*> Article 90, 12 pages.
*> http://doi.acm.org/10.1145/2503210.2503292
*>
*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
*> calculations based on fine-grained memory aware tasks.
*> International Journal of High Performance Computing Applications.
*> Volume 28 Issue 2, Pages 196-209, May 2014.
*> http://hpc.sagepub.com/content/28/2/196
*>
*> \endverbatim
*
* =====================================================================
SUBROUTINE CHEEVR_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
$ IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ,
$ WORK, LWORK, RWORK, LRWORK, IWORK,
$ LIWORK, INFO )
*
IMPLICIT NONE
*
* -- LAPACK driver routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
CHARACTER JOBZ, RANGE, UPLO
INTEGER IL, INFO, IU, LDA, LDZ, LIWORK, LRWORK, LWORK,
$ M, N
REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
INTEGER ISUPPZ( * ), IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), WORK( * ), Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0, TWO = 2.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
$ WANTZ, TRYRAC
CHARACTER ORDER
INTEGER I, IEEEOK, IINFO, IMAX, INDIBL, INDIFL, INDISP,
$ INDIWO, INDRD, INDRDD, INDRE, INDREE, INDRWK,
$ INDTAU, INDWK, INDWKN, ISCALE, ITMP1, J, JJ,
$ LIWMIN, LLWORK, LLRWORK, LLWRKN, LRWMIN,
$ LWMIN, NSPLIT, LHTRD, LWTRD, KD, IB, INDHOUS
REAL ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
$ SIGMA, SMLNUM, TMP1, VLL, VUU
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV, ILAENV2STAGE
REAL SLAMCH, CLANSY, SROUNDUP_LWORK
EXTERNAL LSAME, SLAMCH, CLANSY, ILAENV, ILAENV2STAGE,
$ SROUNDUP_LWORK
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SSCAL, SSTEBZ, SSTERF, XERBLA,
$ CSSCAL,
$ CHETRD_2STAGE, CSTEMR, CSTEIN, CSWAP, CUNMTR
* ..
* .. Intrinsic Functions ..
INTRINSIC REAL, MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
IEEEOK = ILAENV( 10, 'CHEEVR', 'N', 1, 2, 3, 4 )
*
LOWER = LSAME( UPLO, 'L' )
WANTZ = LSAME( JOBZ, 'V' )
ALLEIG = LSAME( RANGE, 'A' )
VALEIG = LSAME( RANGE, 'V' )
INDEIG = LSAME( RANGE, 'I' )
*
LQUERY = ( ( LWORK.EQ.-1 ) .OR. ( LRWORK.EQ.-1 ) .OR.
$ ( LIWORK.EQ.-1 ) )
*
KD = ILAENV2STAGE( 1, 'CHETRD_2STAGE', JOBZ, N, -1, -1,
$ -1 )
IB = ILAENV2STAGE( 2, 'CHETRD_2STAGE', JOBZ, N, KD, -1,
$ -1 )
LHTRD = ILAENV2STAGE( 3, 'CHETRD_2STAGE', JOBZ, N, KD, IB,
$ -1 )
LWTRD = ILAENV2STAGE( 4, 'CHETRD_2STAGE', JOBZ, N, KD, IB,
$ -1 )
*
IF( N.LE.1 ) THEN
LWMIN = 1
LRWMIN = 1
LIWMIN = 1
ELSE
LWMIN = N + LHTRD + LWTRD
LRWMIN = 24*N
LIWMIN = 10*N
END IF
*
INFO = 0
IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
INFO = -2
ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -6
ELSE
IF( VALEIG ) THEN
IF( N.GT.0 .AND. VU.LE.VL )
$ INFO = -8
ELSE IF( INDEIG ) THEN
IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
INFO = -9
ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
INFO = -10
END IF
END IF
END IF
IF( INFO.EQ.0 ) THEN
IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -15
END IF
END IF
*
IF( INFO.EQ.0 ) THEN
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
IWORK( 1 ) = LIWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -18
ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
INFO = -20
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -22
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CHEEVR_2STAGE', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
M = 0
IF( N.EQ.0 ) THEN
WORK( 1 ) = 1
RETURN
END IF
*
IF( N.EQ.1 ) THEN
WORK( 1 ) = 1
IF( ALLEIG .OR. INDEIG ) THEN
M = 1
W( 1 ) = REAL( A( 1, 1 ) )
ELSE
IF( VL.LT.REAL( A( 1, 1 ) ) .AND. VU.GE.REAL( A( 1, 1 ) ) )
$ THEN
M = 1
W( 1 ) = REAL( A( 1, 1 ) )
END IF
END IF
IF( WANTZ ) THEN
Z( 1, 1 ) = ONE
ISUPPZ( 1 ) = 1
ISUPPZ( 2 ) = 1
END IF
RETURN
END IF
*
* Get machine constants.
*
SAFMIN = SLAMCH( 'Safe minimum' )
EPS = SLAMCH( 'Precision' )
SMLNUM = SAFMIN / EPS
BIGNUM = ONE / SMLNUM
RMIN = SQRT( SMLNUM )
RMAX = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
*
* Scale matrix to allowable range, if necessary.
*
ISCALE = 0
ABSTLL = ABSTOL
IF (VALEIG) THEN
VLL = VL
VUU = VU
END IF
ANRM = CLANSY( 'M', UPLO, N, A, LDA, RWORK )
IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / ANRM
ELSE IF( ANRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / ANRM
END IF
IF( ISCALE.EQ.1 ) THEN
IF( LOWER ) THEN
DO 10 J = 1, N
CALL CSSCAL( N-J+1, SIGMA, A( J, J ), 1 )
10 CONTINUE
ELSE
DO 20 J = 1, N
CALL CSSCAL( J, SIGMA, A( 1, J ), 1 )
20 CONTINUE
END IF
IF( ABSTOL.GT.0 )
$ ABSTLL = ABSTOL*SIGMA
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
END IF
END IF
* Initialize indices into workspaces. Note: The IWORK indices are
* used only if SSTERF or CSTEMR fail.
* WORK(INDTAU:INDTAU+N-1) stores the complex scalar factors of the
* elementary reflectors used in CHETRD.
INDTAU = 1
* INDWK is the starting offset of the remaining complex workspace,
* and LLWORK is the remaining complex workspace size.
INDHOUS = INDTAU + N
INDWK = INDHOUS + LHTRD
LLWORK = LWORK - INDWK + 1
* RWORK(INDRD:INDRD+N-1) stores the real tridiagonal's diagonal
* entries.
INDRD = 1
* RWORK(INDRE:INDRE+N-1) stores the off-diagonal entries of the
* tridiagonal matrix from CHETRD.
INDRE = INDRD + N
* RWORK(INDRDD:INDRDD+N-1) is a copy of the diagonal entries over
* -written by CSTEMR (the SSTERF path copies the diagonal to W).
INDRDD = INDRE + N
* RWORK(INDREE:INDREE+N-1) is a copy of the off-diagonal entries over
* -written while computing the eigenvalues in SSTERF and CSTEMR.
INDREE = INDRDD + N
* INDRWK is the starting offset of the left-over real workspace, and
* LLRWORK is the remaining workspace size.
INDRWK = INDREE + N
LLRWORK = LRWORK - INDRWK + 1
* IWORK(INDIBL:INDIBL+M-1) corresponds to IBLOCK in SSTEBZ and
* stores the block indices of each of the M<=N eigenvalues.
INDIBL = 1
* IWORK(INDISP:INDISP+NSPLIT-1) corresponds to ISPLIT in SSTEBZ and
* stores the starting and finishing indices of each block.
INDISP = INDIBL + N
* IWORK(INDIFL:INDIFL+N-1) stores the indices of eigenvectors
* that corresponding to eigenvectors that fail to converge in
* CSTEIN. This information is discarded; if any fail, the driver
* returns INFO > 0.
INDIFL = INDISP + N
* INDIWO is the offset of the remaining integer workspace.
INDIWO = INDIFL + N
*
* Call CHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
*
CALL CHETRD_2STAGE( JOBZ, UPLO, N, A, LDA, RWORK( INDRD ),
$ RWORK( INDRE ), WORK( INDTAU ),
$ WORK( INDHOUS ), LHTRD,
$ WORK( INDWK ), LLWORK, IINFO )
*
* If all eigenvalues are desired
* then call SSTERF or CSTEMR and CUNMTR.
*
TEST = .FALSE.
IF( INDEIG ) THEN
IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
TEST = .TRUE.
END IF
END IF
IF( ( ALLEIG.OR.TEST ) .AND. ( IEEEOK.EQ.1 ) ) THEN
IF( .NOT.WANTZ ) THEN
CALL SCOPY( N, RWORK( INDRD ), 1, W, 1 )
CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 )
CALL SSTERF( N, W, RWORK( INDREE ), INFO )
ELSE
CALL SCOPY( N-1, RWORK( INDRE ), 1, RWORK( INDREE ), 1 )
CALL SCOPY( N, RWORK( INDRD ), 1, RWORK( INDRDD ), 1 )
*
IF ( ABSTOL .LE. TWO*REAL( N )*EPS ) THEN
TRYRAC = .TRUE.
ELSE
TRYRAC = .FALSE.
END IF
CALL CSTEMR( JOBZ, 'A', N, RWORK( INDRDD ),
$ RWORK( INDREE ), VL, VU, IL, IU, M, W,
$ Z, LDZ, N, ISUPPZ, TRYRAC,
$ RWORK( INDRWK ), LLRWORK,
$ IWORK, LIWORK, INFO )
*
* Apply unitary matrix used in reduction to tridiagonal
* form to eigenvectors returned by CSTEMR.
*
IF( WANTZ .AND. INFO.EQ.0 ) THEN
INDWKN = INDWK
LLWRKN = LWORK - INDWKN + 1
CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA,
$ WORK( INDTAU ), Z, LDZ, WORK( INDWKN ),
$ LLWRKN, IINFO )
END IF
END IF
*
*
IF( INFO.EQ.0 ) THEN
M = N
GO TO 30
END IF
INFO = 0
END IF
*
* Otherwise, call SSTEBZ and, if eigenvectors are desired, CSTEIN.
* Also call SSTEBZ and CSTEIN if CSTEMR fails.
*
IF( WANTZ ) THEN
ORDER = 'B'
ELSE
ORDER = 'E'
END IF
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
$ RWORK( INDRD ), RWORK( INDRE ), M, NSPLIT, W,
$ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
$ IWORK( INDIWO ), INFO )
*
IF( WANTZ ) THEN
CALL CSTEIN( N, RWORK( INDRD ), RWORK( INDRE ), M, W,
$ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
$ RWORK( INDRWK ), IWORK( INDIWO ), IWORK( INDIFL ),
$ INFO )
*
* Apply unitary matrix used in reduction to tridiagonal
* form to eigenvectors returned by CSTEIN.
*
INDWKN = INDWK
LLWRKN = LWORK - INDWKN + 1
CALL CUNMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ),
$ Z,
$ LDZ, WORK( INDWKN ), LLWRKN, IINFO )
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
30 CONTINUE
IF( ISCALE.EQ.1 ) THEN
IF( INFO.EQ.0 ) THEN
IMAX = M
ELSE
IMAX = INFO - 1
END IF
CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
* If eigenvalues are not in order, then sort them, along with
* eigenvectors.
*
IF( WANTZ ) THEN
DO 50 J = 1, M - 1
I = 0
TMP1 = W( J )
DO 40 JJ = J + 1, M
IF( W( JJ ).LT.TMP1 ) THEN
I = JJ
TMP1 = W( JJ )
END IF
40 CONTINUE
*
IF( I.NE.0 ) THEN
ITMP1 = IWORK( INDIBL+I-1 )
W( I ) = W( J )
IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
W( J ) = TMP1
IWORK( INDIBL+J-1 ) = ITMP1
CALL CSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
END IF
50 CONTINUE
END IF
*
* Set WORK(1) to optimal workspace size.
*
WORK( 1 ) = SROUNDUP_LWORK( LWMIN )
RWORK( 1 ) = SROUNDUP_LWORK( LRWMIN )
IWORK( 1 ) = LIWMIN
*
RETURN
*
* End of CHEEVR_2STAGE
*
END