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lapack/SRC/chbevx.f
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julie be91086043 Big commit before 3.2.1 release. 
Those are just cosmetic changes to update version number and various other minor change.
2009-04-16 18:10:16 +00:00

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SUBROUTINE CHBEVX( JOBZ, RANGE, UPLO, N, KD, AB, LDAB, Q, LDQ, VL,
$ VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK,
$ IWORK, IFAIL, INFO )
*
* -- LAPACK driver routine (version 3.2) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2006
*
* .. Scalar Arguments ..
CHARACTER JOBZ, RANGE, UPLO
INTEGER IL, INFO, IU, KD, LDAB, LDQ, LDZ, M, N
REAL ABSTOL, VL, VU
* ..
* .. Array Arguments ..
INTEGER IFAIL( * ), IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX AB( LDAB, * ), Q( LDQ, * ), WORK( * ),
$ Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* CHBEVX computes selected eigenvalues and, optionally, eigenvectors
* of a complex Hermitian 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.
*
* Arguments
* =========
*
* JOBZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only;
* = 'V': Compute eigenvalues and eigenvectors.
*
* RANGE (input) 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.
*
* UPLO (input) CHARACTER*1
* = 'U': Upper triangle of A is stored;
* = 'L': Lower triangle of A is stored.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* KD (input) INTEGER
* The number of superdiagonals of the matrix A if UPLO = 'U',
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.
*
* AB (input/output) COMPLEX array, dimension (LDAB, N)
* On entry, the upper or lower triangle of the Hermitian 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.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD + 1.
*
* Q (output) COMPLEX array, dimension (LDQ, N)
* If JOBZ = 'V', the N-by-N unitary matrix used in the
* reduction to tridiagonal form.
* If JOBZ = 'N', the array Q is not referenced.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. If JOBZ = 'V', then
* LDQ >= max(1,N).
*
* VL (input) REAL
* VU (input) REAL
* If RANGE='V', the lower and upper bounds of the interval to
* be searched for eigenvalues. VL < VU.
* Not referenced if RANGE = 'A' or 'I'.
*
* IL (input) INTEGER
* IU (input) INTEGER
* If RANGE='I', the indices (in ascending order) of the
* smallest and largest eigenvalues 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'.
*
* ABSTOL (input) 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 AB 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').
*
* See "Computing Small Singular Values of Bidiagonal Matrices
* with Guaranteed High Relative Accuracy," by Demmel and
* Kahan, LAPACK Working Note #3.
*
* M (output) INTEGER
* The total number of eigenvalues found. 0 <= M <= N.
* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
*
* W (output) REAL array, dimension (N)
* The first M elements contain the selected eigenvalues in
* ascending order.
*
* Z (output) 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 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.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1, and if
* JOBZ = 'V', LDZ >= max(1,N).
*
* WORK (workspace) COMPLEX array, dimension (N)
*
* RWORK (workspace) REAL array, dimension (7*N)
*
* IWORK (workspace) INTEGER array, dimension (5*N)
*
* IFAIL (output) 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.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = i, then i eigenvectors failed to converge.
* Their indices are stored in array IFAIL.
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
COMPLEX CZERO, CONE
PARAMETER ( CZERO = ( 0.0E0, 0.0E0 ),
$ CONE = ( 1.0E0, 0.0E0 ) )
* ..
* .. Local Scalars ..
LOGICAL ALLEIG, INDEIG, LOWER, TEST, VALEIG, WANTZ
CHARACTER ORDER
INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
$ INDISP, INDIWK, INDRWK, INDWRK, ISCALE, ITMP1,
$ J, JJ, NSPLIT
REAL ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
$ SIGMA, SMLNUM, TMP1, VLL, VUU
COMPLEX CTMP1
* ..
* .. External Functions ..
LOGICAL LSAME
REAL CLANHB, SLAMCH
EXTERNAL LSAME, CLANHB, SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL CCOPY, CGEMV, CHBTRD, CLACPY, CLASCL, CSTEIN,
$ CSTEQR, CSWAP, SCOPY, SSCAL, SSTEBZ, SSTERF,
$ XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, REAL, 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( 'CHBEVX', -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
CTMP1 = AB( 1, 1 )
ELSE
CTMP1 = AB( KD+1, 1 )
END IF
TMP1 = REAL( CTMP1 )
IF( VALEIG ) THEN
IF( .NOT.( VL.LT.TMP1 .AND. VU.GE.TMP1 ) )
$ M = 0
END IF
IF( M.EQ.1 ) THEN
W( 1 ) = CTMP1
IF( WANTZ )
$ Z( 1, 1 ) = CONE
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
ELSE
VLL = ZERO
VUU = ZERO
ENDIF
ANRM = CLANHB( 'M', UPLO, N, KD, AB, LDAB, 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
CALL CLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
ELSE
CALL CLASCL( '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 CHBTRD to reduce Hermitian band matrix to tridiagonal form.
*
INDD = 1
INDE = INDD + N
INDRWK = INDE + N
INDWRK = 1
CALL CHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, RWORK( INDD ),
$ RWORK( INDE ), Q, LDQ, WORK( INDWRK ), IINFO )
*
* If all eigenvalues are desired and ABSTOL is less than or equal
* to zero, then call SSTERF or CSTEQR. 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, RWORK( INDD ), 1, W, 1 )
INDEE = INDRWK + 2*N
IF( .NOT.WANTZ ) THEN
CALL SCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
CALL SSTERF( N, W, RWORK( INDEE ), INFO )
ELSE
CALL CLACPY( 'A', N, N, Q, LDQ, Z, LDZ )
CALL SCOPY( N-1, RWORK( INDE ), 1, RWORK( INDEE ), 1 )
CALL CSTEQR( JOBZ, N, W, RWORK( INDEE ), Z, LDZ,
$ RWORK( INDRWK ), 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, CSTEIN.
*
IF( WANTZ ) THEN
ORDER = 'B'
ELSE
ORDER = 'E'
END IF
INDIBL = 1
INDISP = INDIBL + N
INDIWK = INDISP + N
CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
$ RWORK( INDD ), RWORK( INDE ), M, NSPLIT, W,
$ IWORK( INDIBL ), IWORK( INDISP ), RWORK( INDRWK ),
$ IWORK( INDIWK ), INFO )
*
IF( WANTZ ) THEN
CALL CSTEIN( N, RWORK( INDD ), RWORK( INDE ), M, W,
$ IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
$ RWORK( INDRWK ), IWORK( INDIWK ), IFAIL, INFO )
*
* Apply unitary matrix used in reduction to tridiagonal
* form to eigenvectors returned by CSTEIN.
*
DO 20 J = 1, M
CALL CCOPY( N, Z( 1, J ), 1, WORK( 1 ), 1 )
CALL CGEMV( 'N', N, N, CONE, Q, LDQ, WORK, 1, CZERO,
$ 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 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 )
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 CHBEVX
*
END
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