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9aed94de6d78beddb218baaebce809193b8160fc
lapack/SRC/dsbevx.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

554 lines
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*> \brief <b> DSBEVX 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 DSBEVX + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsbevx.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbevx.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbevx.f">
*> [TXT]</a>
*
* Definition:
* ===========
*
* SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
* VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
* IFAIL, INFO )
*
* .. Scalar Arguments ..
* CHARACTER JOBZ, RANGE, UPLO
* INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
* DOUBLE PRECISION ABSTOL, VL, VU
* ..
* .. Array Arguments ..
* INTEGER IFAIL( * ), IWORK( * )
* DOUBLE PRECISION AB( LDAB, * ), Q( LDQ, * ), W( * ), WORK( * ),
* $ Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSBEVX computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric band 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] 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 (7*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
*> 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
*
* =====================================================================
SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ,
$ 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, UPLO
INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
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
CHARACTER ORDER
INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
$ INDISP, INDIWO, INDWRK, ISCALE, ITMP1, J, JJ,
$ NSPLIT
DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
$ SIGMA, SMLNUM, TMP1, VLL, VUU
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DLANSB
EXTERNAL LSAME, DLAMCH, DLANSB
* ..
* .. External Subroutines ..
EXTERNAL DCOPY, DGEMV, DLACPY, DLASCL, DSBTRD,
$ DSCAL,
$ DSTEBZ, DSTEIN, DSTEQR, DSTERF, DSWAP, 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' )
LOWER = LSAME( UPLO, 'L' )
*
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( .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.NE.0 ) THEN
CALL XERBLA( 'DSBEVX', -INFO )
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 DSBTRD to reduce symmetric band matrix to tridiagonal form.
*
INDD = 1
INDE = INDD + N
INDWRK = INDE + N
CALL DSBTRD( JOBZ, UPLO, N, KD, AB, LDAB, WORK( INDD ),
$ WORK( INDE ), Q, LDQ, WORK( INDWRK ), 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
*
RETURN
*
* End of DSBEVX
*
END
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