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9aed94de6d78beddb218baaebce809193b8160fc
lapack/SRC/ssbgvx.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

527 lines
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*> \brief \b SSBGVX
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> Download SSBGVX + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssbgvx.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssbgvx.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssbgvx.f">
*> [TXT]</a>
*
* Definition:
* ===========
*
* SUBROUTINE SSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
* LDBB, 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, KA, KB, LDAB, LDBB, LDQ, LDZ, M,
* $ N
* REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
* INTEGER IFAIL( * ), IWORK( * )
* REAL AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
* $ W( * ), WORK( * ), Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SSBGVX computes selected eigenvalues, and optionally, eigenvectors
*> of a real generalized symmetric-definite banded eigenproblem, of
*> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
*> and banded, and B is also positive definite. Eigenvalues and
*> eigenvectors can be selected by specifying either all eigenvalues,
*> 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 triangles of A and B are stored;
*> = 'L': Lower triangles of A and B are stored.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in] KA
*> \verbatim
*> KA is INTEGER
*> The number of superdiagonals of the matrix A if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
*> \endverbatim
*>
*> \param[in] KB
*> \verbatim
*> KB is INTEGER
*> The number of superdiagonals of the matrix B if UPLO = 'U',
*> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
*> \endverbatim
*>
*> \param[in,out] AB
*> \verbatim
*> AB is REAL array, dimension (LDAB, N)
*> On entry, the upper or lower triangle of the symmetric band
*> matrix A, stored in the first ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
*>
*> On exit, the contents of AB are destroyed.
*> \endverbatim
*>
*> \param[in] LDAB
*> \verbatim
*> LDAB is INTEGER
*> The leading dimension of the array AB. LDAB >= KA+1.
*> \endverbatim
*>
*> \param[in,out] BB
*> \verbatim
*> BB is REAL array, dimension (LDBB, N)
*> On entry, the upper or lower triangle of the symmetric band
*> matrix B, stored in the first kb+1 rows of the array. The
*> j-th column of B is stored in the j-th column of the array BB
*> as follows:
*> if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
*>
*> On exit, the factor S from the split Cholesky factorization
*> B = S**T*S, as returned by SPBSTF.
*> \endverbatim
*>
*> \param[in] LDBB
*> \verbatim
*> LDBB is INTEGER
*> The leading dimension of the array BB. LDBB >= KB+1.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is REAL array, dimension (LDQ, N)
*> If JOBZ = 'V', the n-by-n matrix used in the reduction of
*> A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
*> and consequently C 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 = 'N',
*> LDQ >= 1. If JOBZ = 'V', LDQ >= 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.
*>
*> 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').
*> \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)
*> If INFO = 0, the eigenvalues in ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*> Z is REAL array, dimension (LDZ, N)
*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
*> eigenvectors, with the i-th column of Z holding the
*> eigenvector associated with W(i). The eigenvectors are
*> normalized so Z**T*B*Z = I.
*> If JOBZ = 'N', then Z is not referenced.
*> \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 (7*N)
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*> IWORK is INTEGER array, dimension (5*N)
*> \endverbatim
*>
*> \param[out] IFAIL
*> \verbatim
*> IFAIL is INTEGER array, dimension (M)
*> 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 eigenvalues 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
*> <= N: if INFO = i, then i eigenvectors failed to converge
*> in SSTEIN; their indices are stored in IFAIL.
*> N+1..2N: if INFO = N + i, for 1 <= i <= N, then SPBSTF
*> returned an error code; the leading principal minor
*> of order i of B is not positive. No eigenvalues or
*> eigenvectors were computed.
*> > 2N: if INFO = 2*N + i, then SSTEBZ returned
*> INFO = i; see SSTEBZ for details.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup hbgvx
*
*> \par Contributors:
* ==================
*>
*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
*
* =====================================================================
SUBROUTINE SSBGVX( JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
$ LDBB, 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, KA, KB, LDAB, LDBB, LDQ, LDZ, M,
$ N
REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
INTEGER IFAIL( * ), IWORK( * )
REAL AB( LDAB, * ), BB( LDBB, * ), Q( LDQ, * ),
$ W( * ), WORK( * ), Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL ALLEIG, INDEIG, TEST, UPPER, VALEIG, WANTZ
CHARACTER ORDER, VECT
INTEGER I, IINFO, INDD, INDE, INDEE, INDISP,
$ INDIWO, INDWRK, ITMP1, J, JJ, NSPLIT
REAL TMP1
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SGEMV, SLACPY, SPBSTF, SSBGST,
$ SSBTRD,
$ SSTEBZ, SSTEIN, SSTEQR, SSTERF, SSWAP, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
UPPER = LSAME( UPLO, 'U' )
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( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( KA.LT.0 ) THEN
INFO = -5
ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN
INFO = -6
ELSE IF( LDAB.LT.KA+1 ) THEN
INFO = -8
ELSE IF( LDBB.LT.KB+1 ) THEN
INFO = -10
ELSE IF( LDQ.LT.1 .OR. ( WANTZ .AND. LDQ.LT.N ) ) THEN
INFO = -12
ELSE
IF( VALEIG ) THEN
IF( N.GT.0 .AND. VU.LE.VL )
$ INFO = -14
ELSE IF( INDEIG ) THEN
IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
INFO = -15
ELSE IF ( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
INFO = -16
END IF
END IF
END IF
IF( INFO.EQ.0) THEN
IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -21
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'SSBGVX', -INFO )
RETURN
END IF
*
* Quick return if possible
*
M = 0
IF( N.EQ.0 )
$ RETURN
*
* Form a split Cholesky factorization of B.
*
CALL SPBSTF( UPLO, N, KB, BB, LDBB, INFO )
IF( INFO.NE.0 ) THEN
INFO = N + INFO
RETURN
END IF
*
* Transform problem to standard eigenvalue problem.
*
CALL SSBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ,
$ WORK, IINFO )
*
* Reduce symmetric band matrix to tridiagonal form.
*
INDD = 1
INDE = INDD + N
INDWRK = INDE + N
IF( WANTZ ) THEN
VECT = 'U'
ELSE
VECT = 'N'
END IF
CALL SSBTRD( VECT, UPLO, N, KA, 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 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, WORK( INDD ), 1, W, 1 )
INDEE = INDWRK + 2*N
CALL SCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
IF( .NOT.WANTZ ) THEN
CALL SSTERF( N, W, WORK( INDEE ), INFO )
ELSE
CALL SLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
CALL SSTEQR( 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 SSTEBZ and, if eigenvectors are desired,
* call SSTEIN.
*
IF( WANTZ ) THEN
ORDER = 'B'
ELSE
ORDER = 'E'
END IF
INDISP = 1 + N
INDIWO = INDISP + N
CALL SSTEBZ( RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL,
$ WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
$ IWORK( 1 ), IWORK( INDISP ), WORK( INDWRK ),
$ IWORK( INDIWO ), IINFO )
IF( IINFO.NE.0 ) THEN
INFO = 2*N + IINFO
IF( IINFO.NE.1 )
$ GO TO 30
END IF
*
IF( WANTZ ) THEN
CALL SSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
$ IWORK( 1 ), IWORK( INDISP ), Z, LDZ,
$ WORK( INDWRK ), IWORK( INDIWO ), IFAIL, IINFO )
IF( IINFO.NE.0 .AND. INFO.EQ.0 )
$ INFO = IINFO
*
* Apply transformation matrix used in reduction to tridiagonal
* form to eigenvectors returned by SSTEIN.
*
DO 20 J = 1, M
CALL SCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
CALL SGEMV( 'N', N, N, ONE, Q, LDQ, WORK, 1, ZERO,
$ Z( 1, J ), 1 )
20 CONTINUE
END IF
*
30 CONTINUE
*
* 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( 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
50 CONTINUE
END IF
*
RETURN
*
* End of SSBGVX
*
END
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