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