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9aed94de6d78beddb218baaebce809193b8160fc
lapack/SRC/dsbevx_2stage.f
T
NAKATA Maho 94f05be6c3 Fix incorrect INFO return codes from xSTEBZ in driver routines 
In 26 driver routines across all four precisions (S, D, C, Z),
xSTEBZ was called writing directly to INFO, which was then
silently overwritten by xSTEIN.  Two bugs are fixed:

1. xSTEBZ errors were not propagated to the caller at all.

2. When xSTEBZ returned INFO > 0, eigenvectors were computed
   with an incomplete or empty eigenvalue set (INFO=2,3,4) or
   with reduced accuracy (INFO=1), producing silently wrong
   results.

Fix: route xSTEBZ return value through IINFO.  For INFO != 1,
skip xSTEIN entirely via GO TO.  For INFO == 1 (bisection
convergence warning), xSTEIN is still called since M eigenvalues
are available; the warning is preserved in INFO.

The xSTEBZ error is encoded as INFO = N + IINFO to distinguish
it from xSTEIN failures (1..N), matching the convention already
used for xPBSTF errors in the xBGVX routines.  For the four
xBGVX routines, which already use INFO = N+i for xPBSTF, the
xSTEBZ error is encoded as INFO = 2*N + IINFO.

Update INFO documentation in all 26 files accordingly.
Also add IINFO to the INTEGER declaration in dstevx.f and
sstevx.f where it was missing.

Files modified (26):
  SRC/chbevx.f, SRC/chbevx_2stage.f, SRC/chbgvx.f,
  SRC/cheevx.f, SRC/cheevx_2stage.f, SRC/chpevx.f,
  SRC/dsbevx.f, SRC/dsbevx_2stage.f, SRC/dsbgvx.f,
  SRC/dspevx.f, SRC/dstevx.f, SRC/dsyevx.f, SRC/dsyevx_2stage.f,
  SRC/ssbevx.f, SRC/ssbevx_2stage.f, SRC/ssbgvx.f,
  SRC/sspevx.f, SRC/sstevx.f, SRC/ssyevx.f, SRC/ssyevx_2stage.f,
  SRC/zhbevx.f, SRC/zhbevx_2stage.f, SRC/zhbgvx.f,
  SRC/zheevx.f, SRC/zheevx_2stage.f, SRC/zhpevx.f
2026-03-23 13:58:37 +09:00

647 lines
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*> \brief <b> DSBEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
*
* @precisions fortran d -> s
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> Download DSBEVX_2STAGE + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbevx_2stage.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbevx_2stage.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbevx_2stage.f">
*> [TXT]</a>
*
* Definition:
* ===========
*
* SUBROUTINE DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q,
* LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
* LDZ, WORK, LWORK, IWORK, IFAIL, INFO )
*
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, RANGE, UPLO
* INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N, LWORK
* DOUBLE PRECISION ABSTOL, VL, VU
* ..
* .. Array Arguments ..
* INTEGER IFAIL( * ), IWORK( * )
* DOUBLE PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ),
* $ Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSBEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric band 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.
*> \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.
*> \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] KD
*> \verbatim
*> KD is INTEGER
*> The number of superdiagonals of the matrix A if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is DOUBLE PRECISION array, dimension (LDAB, N)
*> On entry, the upper or lower triangle of the symmetric band
*> matrix A, stored in the first KD+1 rows of the array. The
*> j-th column of A is stored in the j-th column of the array AB
*> as follows:
*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
*>
*> On exit, AB is overwritten by values generated during the
*> reduction to tridiagonal form. If UPLO = 'U', the first
*> superdiagonal and the diagonal of the tridiagonal matrix T
*> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
*> the diagonal and first subdiagonal of T are returned in the
*> first two rows of AB.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KD + 1.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is DOUBLE PRECISION array, dimension (LDQ, N)
*> If JOBZ = 'V', the N-by-N orthogonal matrix used in the
*> reduction to tridiagonal form.
*> If JOBZ = 'N', the array Q is not referenced.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. If JOBZ = 'V', then
*> LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[in] VL
*> \verbatim
*> VL is DOUBLE PRECISION
*> 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 DOUBLE PRECISION
*> 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 DOUBLE PRECISION
*> 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 AB to tridiagonal form.
*>
*> Eigenvalues will be computed most accurately when ABSTOL is
*> set to twice the underflow threshold 2*DLAMCH('S'), not zero.
*> If this routine returns with INFO>0, indicating that some
*> eigenvectors did not converge, try setting ABSTOL to
*> 2*DLAMCH('S').
*>
*> See "Computing Small Singular Values of Bidiagonal Matrices
*> with Guaranteed High Relative Accuracy," by Demmel and
*> Kahan, LAPACK Working Note #3.
*> \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 DOUBLE PRECISION array, dimension (N)
*> The first M elements contain the selected eigenvalues in
*> ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is DOUBLE PRECISION 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 an eigenvector fails to converge, then that column of Z
*> contains the latest approximation to the eigenvector, and the
*> index of the eigenvector is returned in IFAIL.
*> 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] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The length of the array WORK. LWORK >= 1, when N <= 1;
*> otherwise
*> If JOBZ = 'N' and N > 1, LWORK must be queried.
*> LWORK = MAX(1, 7*N, dimension) where
*> dimension = (2KD+1)*N + KD*NTHREADS + 2*N
*> where KD is the size of the band.
*> 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 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 by XERBLA.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (5*N)
*> \endverbatim
*>
*> \param[out] IFAIL
*> \verbatim
*> IFAIL is INTEGER array, dimension (N)
*> If JOBZ = 'V', then if INFO = 0, the first M elements of
*> IFAIL are zero. If INFO > 0, then IFAIL contains the
*> indices of the eigenvectors that failed to converge.
*> If JOBZ = 'N', then IFAIL is not referenced.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit.
*> < 0: if INFO = -i, the i-th argument had an illegal value.
*> > 0: if INFO = i, and i is:
*> <= N: then i eigenvectors failed to converge in
*> DSTEIN; their indices are stored in IFAIL.
*> > N: DSTEBZ returned INFO = INFO - N;
*> see DSTEBZ for details.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hbevx_2stage
*
*> \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 DSBEVX_2STAGE( JOBZ, RANGE, UPLO, N, KD, AB, LDAB,
$ Q,
$ LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z,
$ LDZ, WORK, LWORK, IWORK, IFAIL, 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, KD, LDAB, LDQ, LDZ, M, N, LWORK
DOUBLE PRECISION ABSTOL, VL, VU
* ..
* .. Array Arguments ..
INTEGER IFAIL( * ), IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ),
$ Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
LOGICAL ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ,
$ LQUERY
CHARACTER ORDER
INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
$ INDISP, INDIWO, INDWRK, ISCALE, ITMP1, J, JJ,
$ LLWORK, LWMIN, LHTRD, LWTRD, IB, INDHOUS,
$ NSPLIT
DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
$ SIGMA, SMLNUM, TMP1, VLL, VUU
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILAENV2STAGE
DOUBLE PRECISION DLAMCH, DLANSB
EXTERNAL LSAME, DLAMCH, DLANSB, ILAENV2STAGE
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMV, DLACPY, DLASCL,
$ DSCAL,
$ DSTEBZ, DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA,
$ DSYTRD_SB2ST
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
ALLEIG = LSAME( RANGE, 'A' )
VALEIG = LSAME( RANGE, 'V' )
INDEIG = LSAME( RANGE, 'I' )
LOWER = LSAME( UPLO, 'L' )
LQUERY = ( LWORK.EQ.-1 )
*
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( KD.LT.0 ) THEN
INFO = -5
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -7
ELSE IF( WANTZ .AND. LDQ.LT.MAX( 1, N ) ) THEN
INFO = -9
ELSE
IF( VALEIG ) THEN
IF( N.GT.0 .AND. VU.LE.VL )
$ INFO = -11
ELSE IF( INDEIG ) THEN
IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
INFO = -12
ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
INFO = -13
END IF
END IF
END IF
IF( INFO.EQ.0 ) THEN
IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
$ INFO = -18
END IF
*
IF( INFO.EQ.0 ) THEN
IF( N.LE.1 ) THEN
LWMIN = 1
WORK( 1 ) = LWMIN
ELSE
IB = ILAENV2STAGE( 2, 'DSYTRD_SB2ST', JOBZ,
$ N, KD, -1, -1 )
LHTRD = ILAENV2STAGE( 3, 'DSYTRD_SB2ST', JOBZ,
$ N, KD, IB, -1 )
LWTRD = ILAENV2STAGE( 4, 'DSYTRD_SB2ST', JOBZ,
$ N, KD, IB, -1 )
LWMIN = 2*N + LHTRD + LWTRD
WORK( 1 ) = LWMIN
ENDIF
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
$ INFO = -20
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSBEVX_2STAGE ', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
M = 0
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
M = 1
IF( LOWER ) THEN
TMP1 = AB( 1, 1 )
ELSE
TMP1 = AB( KD+1, 1 )
END IF
IF( VALEIG ) THEN
IF( .NOT.( VL.LT.TMP1 .AND. VU.GE.TMP1 ) )
$ M = 0
END IF
IF( M.EQ.1 ) THEN
W( 1 ) = TMP1
IF( WANTZ )
$ Z( 1, 1 ) = ONE
END IF
RETURN
END IF
*
* Get machine constants.
*
SAFMIN = DLAMCH( 'Safe minimum' )
EPS = DLAMCH( '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
ELSE
VLL = ZERO
VUU = ZERO
END IF
ANRM = DLANSB( 'M', UPLO, N, KD, AB, LDAB, WORK )
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
CALL DLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB,
$ INFO )
ELSE
CALL DLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB,
$ INFO )
END IF
IF( ABSTOL.GT.0 )
$ ABSTLL = ABSTOL*SIGMA
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
END IF
END IF
*
* Call DSYTRD_SB2ST to reduce symmetric band matrix to tridiagonal form.
*
INDD = 1
INDE = INDD + N
INDHOUS = INDE + N
INDWRK = INDHOUS + LHTRD
LLWORK = LWORK - INDWRK + 1
*
CALL DSYTRD_SB2ST( "N", JOBZ, UPLO, N, KD, AB, LDAB,
$ WORK( INDD ),
$ WORK( INDE ), WORK( INDHOUS ), LHTRD,
$ WORK( INDWRK ), LLWORK, IINFO )
*
* If all eigenvalues are desired and ABSTOL is less than or equal
* to zero, then call DSTERF or SSTEQR. If this fails for some
* eigenvalue, then try DSTEBZ.
*
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. (ABSTOL.LE.ZERO)) THEN
CALL DCOPY( N, WORK( INDD ), 1, W, 1 )
INDEE = INDWRK + 2*N
IF( .NOT.WANTZ ) THEN
CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
CALL DSTERF( N, W, WORK( INDEE ), INFO )
ELSE
CALL DLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
CALL DCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
CALL DSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
$ WORK( INDWRK ), INFO )
IF( INFO.EQ.0 ) THEN
DO 10 I = 1, N
IFAIL( I ) = 0
10 CONTINUE
END IF
END IF
IF( INFO.EQ.0 ) THEN
M = N
GO TO 30
END IF
INFO = 0
END IF
*
* Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
*
IF( WANTZ ) THEN
ORDER = 'B'
ELSE
ORDER = 'E'
END IF
INDIBL = 1
INDISP = INDIBL + N
INDIWO = INDISP + N
CALL DSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
$ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
$ IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
$ IWORK( INDIWO ), IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + IINFO
IF( IINFO.NE.1 )
$ GO TO 30
END IF
*
IF( WANTZ ) THEN
CALL DSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
$ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
$ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, IINFO )
IF( IINFO.NE.0 .AND. INFO.EQ.0 )
$ INFO = IINFO
*
* Apply orthogonal matrix used in reduction to tridiagonal
* form to eigenvectors returned by DSTEIN.
*
DO 20 J = 1, M
CALL DCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
CALL DGEMV( 'N', N, N, ONE, Q, LDQ, WORK, 1, ZERO,
$ Z( 1, J ), 1 )
20 CONTINUE
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 DSCAL( 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 DSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
IF( INFO.NE.0 ) THEN
ITMP1 = IFAIL( I )
IFAIL( I ) = IFAIL( J )
IFAIL( J ) = ITMP1
END IF
END IF
50 CONTINUE
END IF
*
* Set WORK(1) to optimal workspace size.
*
WORK( 1 ) = LWMIN
*
RETURN
*
* End of DSBEVX_2STAGE
*
END
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