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9aed94de6d78beddb218baaebce809193b8160fc
lapack/SRC/sstevx.f
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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

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*> \brief <b> SSTEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> Download SSTEVX + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sstevx.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstevx.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstevx.f">
*> [TXT]</a>
*
* Definition:
* ===========
*
* SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL,
* M, W, Z, LDZ, WORK, IWORK, IFAIL, INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, RANGE
* INTEGER IL, INFO, IU, LDZ, M, N
* REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
* INTEGER IFAIL( * ), IWORK( * )
* REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SSTEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix A. 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.
*> \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] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix. N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*> D is REAL array, dimension (N)
*> On entry, the n diagonal elements of the tridiagonal matrix
*> A.
*> On exit, D may be multiplied by a constant factor chosen
*> to avoid over/underflow in computing the eigenvalues.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*> E is REAL array, dimension (max(1,N-1))
*> On entry, the (n-1) subdiagonal elements of the tridiagonal
*> matrix A in elements 1 to N-1 of E.
*> On exit, E may be multiplied by a constant factor chosen
*> to avoid over/underflow in computing the eigenvalues.
*> \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.
*>
*> Eigenvalues will be computed most accurately when ABSTOL is
*> set to twice the underflow threshold 2*SLAMCH('S'), not zero.
*> If this routine returns with INFO>0, indicating that some
*> eigenvectors did not converge, try setting ABSTOL to
*> 2*SLAMCH('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 REAL array, dimension (N)
*> The first M elements contain the selected eigenvalues in
*> ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is REAL 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 (INFO > 0), 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 REAL array, dimension (5*N)
*> \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
*> SSTEIN; their indices are stored in IFAIL.
*> > N: SSTEBZ returned INFO = INFO - N;
*> see SSTEBZ for details.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup stevx
*
* =====================================================================
SUBROUTINE SSTEVX( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
$ ABSTOL,
$ M, W, Z, LDZ, WORK, 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
INTEGER IL, INFO, IU, LDZ, M, N
REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
INTEGER IFAIL( * ), IWORK( * )
REAL D( * ), E( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
LOGICAL ALLEIG, INDEIG, TEST, VALEIG, WANTZ
CHARACTER ORDER
INTEGER I, IINFO, IMAX, INDISP, INDIWO, INDWRK,
$ ISCALE, ITMP1, J, JJ, NSPLIT
REAL BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, SMLNUM,
$ TMP1, TNRM, VLL, VUU
* ..
* .. External Functions ..
LOGICAL LSAME
REAL SLAMCH, SLANST
EXTERNAL LSAME, SLAMCH, SLANST
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SSCAL, SSTEBZ, SSTEIN, SSTEQR,
$ SSTERF,
$ SSWAP, XERBLA
* ..
* .. 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' )
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE
IF( VALEIG ) THEN
IF( N.GT.0 .AND. VU.LE.VL )
$ INFO = -7
ELSE IF( INDEIG ) THEN
IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
INFO = -8
ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
INFO = -9
END IF
END IF
END IF
IF( INFO.EQ.0 ) THEN
IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) )
$ INFO = -14
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSTEVX', -INFO )
RETURN
END IF
*
* Quick return if possible
*
M = 0
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
IF( ALLEIG .OR. INDEIG ) THEN
M = 1
W( 1 ) = D( 1 )
ELSE
IF( VL.LT.D( 1 ) .AND. VU.GE.D( 1 ) ) THEN
M = 1
W( 1 ) = D( 1 )
END IF
END IF
IF( WANTZ )
$ Z( 1, 1 ) = ONE
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
IF ( VALEIG ) THEN
VLL = VL
VUU = VU
ELSE
VLL = ZERO
VUU = ZERO
ENDIF
TNRM = SLANST( 'M', N, D, E )
IF( TNRM.GT.ZERO .AND. TNRM.LT.RMIN ) THEN
ISCALE = 1
SIGMA = RMIN / TNRM
ELSE IF( TNRM.GT.RMAX ) THEN
ISCALE = 1
SIGMA = RMAX / TNRM
END IF
IF( ISCALE.EQ.1 ) THEN
CALL SSCAL( N, SIGMA, D, 1 )
CALL SSCAL( N-1, SIGMA, E( 1 ), 1 )
IF( VALEIG ) THEN
VLL = VL*SIGMA
VUU = VU*SIGMA
END IF
END IF
*
* If all eigenvalues are desired and ABSTOL is less than zero, then
* call SSTERF or SSTEQR. If this fails for some eigenvalue, then
* try SSTEBZ.
*
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 SCOPY( N, D, 1, W, 1 )
CALL SCOPY( N-1, E( 1 ), 1, WORK( 1 ), 1 )
INDWRK = N + 1
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, WORK, INFO )
ELSE
CALL SSTEQR( 'I', N, W, WORK, 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 20
END IF
INFO = 0
END IF
*
* Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN.
*
IF( WANTZ ) THEN
ORDER = 'B'
ELSE
ORDER = 'E'
END IF
INDWRK = 1
INDISP = 1 + N
INDIWO = INDISP + N
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTOL, D, E,
$ M,
$ NSPLIT, W, IWORK( 1 ), IWORK( INDISP ),
$ WORK( INDWRK ), IWORK( INDIWO ), IINFO )
IF( IINFO.NE.0 ) THEN
INFO = N + IINFO
IF( IINFO.NE.1 )
$ GO TO 20
END IF
*
IF( WANTZ ) THEN
CALL SSTEIN( N, D, E, M, W, IWORK( 1 ), IWORK( INDISP ),
$ Z, LDZ, WORK( INDWRK ), IWORK( INDIWO ), IFAIL,
$ IINFO )
IF( IINFO.NE.0 .AND. INFO.EQ.0 )
$ INFO = IINFO
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
20 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 40 J = 1, M - 1
I = 0
TMP1 = W( J )
DO 30 JJ = J + 1, M
IF( W( JJ ).LT.TMP1 ) THEN
I = JJ
TMP1 = W( JJ )
END IF
30 CONTINUE
*
IF( I.NE.0 ) THEN
ITMP1 = IWORK( 1 + I-1 )
W( I ) = W( J )
IWORK( 1 + I-1 ) = IWORK( 1 + J-1 )
W( J ) = TMP1
IWORK( 1 + J-1 ) = ITMP1
CALL SSWAP( 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
40 CONTINUE
END IF
*
RETURN
*
* End of SSTEVX
*
END
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