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SUBROUTINE ZHBEV( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK,
$ RWORK, INFO )
*
* -- LAPACK driver routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER JOBZ, UPLO
INTEGER INFO, KD, LDAB, LDZ, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION RWORK( * ), W( * )
COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* ZHBEV computes all the eigenvalues and, optionally, eigenvectors of
* a complex Hermitian band matrix A.
*
* Arguments
* =========
*
* JOBZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only;
* = 'V': Compute eigenvalues and eigenvectors.
*
* 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*16 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. 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.
*
* LDAB (input) INTEGER
* The leading dimension of the array AB. LDAB >= KD + 1.
*
* W (output) DOUBLE PRECISION array, dimension (N)
* If INFO = 0, the eigenvalues in ascending order.
*
* Z (output) COMPLEX*16 array, dimension (LDZ, N)
* If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
* eigenvectors of the matrix A, with the i-th column of Z
* holding the eigenvector associated with W(i).
* If JOBZ = 'N', then Z is not referenced.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1, and if
* JOBZ = 'V', LDZ >= max(1,N).
*
* WORK (workspace) COMPLEX*16 array, dimension (N)
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (max(1,3*N-2))
*
* INFO (output) INTEGER
* = 0: successful exit.
* < 0: if INFO = -i, the i-th argument had an illegal value.
* > 0: if INFO = i, the algorithm failed to converge; i
* off-diagonal elements of an intermediate tridiagonal
* form did not converge to zero.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
* ..
* .. Local Scalars ..
LOGICAL LOWER, WANTZ
INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, ZLANHB
EXTERNAL LSAME, DLAMCH, ZLANHB
* ..
* .. External Subroutines ..
EXTERNAL DSCAL, DSTERF, XERBLA, ZHBTRD, ZLASCL, ZSTEQR
* ..
* .. Intrinsic Functions ..
INTRINSIC SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LOWER = LSAME( UPLO, 'L' )
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( KD.LT.0 ) THEN
INFO = -4
ELSE IF( LDAB.LT.KD+1 ) THEN
INFO = -6
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -9
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZHBEV ', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
IF( N.EQ.1 ) THEN
IF( LOWER ) THEN
W( 1 ) = AB( 1, 1 )
ELSE
W( 1 ) = AB( KD+1, 1 )
END IF
IF( WANTZ )
$ Z( 1, 1 ) = ONE
RETURN
END IF
*
* Get machine constants.
*
SAFMIN = DLAMCH( 'Safe minimum' )
EPS = DLAMCH( 'Precision' )
SMLNUM = SAFMIN / EPS
BIGNUM = ONE / SMLNUM
RMIN = SQRT( SMLNUM )
RMAX = SQRT( BIGNUM )
*
* Scale matrix to allowable range, if necessary.
*
ANRM = ZLANHB( 'M', UPLO, N, KD, AB, LDAB, RWORK )
ISCALE = 0
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 ZLASCL( 'B', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
ELSE
CALL ZLASCL( 'Q', KD, KD, ONE, SIGMA, N, N, AB, LDAB, INFO )
END IF
END IF
*
* Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
*
INDE = 1
CALL ZHBTRD( JOBZ, UPLO, N, KD, AB, LDAB, W, RWORK( INDE ), Z,
$ LDZ, WORK, IINFO )
*
* For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, RWORK( INDE ), INFO )
ELSE
INDRWK = INDE + N
CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ,
$ RWORK( INDRWK ), INFO )
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 ) THEN
IF( INFO.EQ.0 ) THEN
IMAX = N
ELSE
IMAX = INFO - 1
END IF
CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
END IF
*
RETURN
*
* End of ZHBEV
*
END
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