219 lines
6.6 KiB
FortranFixed
219 lines
6.6 KiB
FortranFixed
SUBROUTINE CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
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$ 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, LDA, LWORK, N
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* ..
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* .. Array Arguments ..
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REAL RWORK( * ), W( * )
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COMPLEX A( LDA, * ), WORK( * )
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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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* CHEEV computes all eigenvalues and, optionally, eigenvectors of a
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* complex Hermitian 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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* A (input/output) COMPLEX array, dimension (LDA, N)
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* On entry, the Hermitian matrix A. If UPLO = 'U', the
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* leading N-by-N upper triangular part of A contains the
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* upper triangular part of the matrix A. If UPLO = 'L',
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* the leading N-by-N lower triangular part of A contains
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* the lower triangular part of the matrix A.
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* On exit, if JOBZ = 'V', then if INFO = 0, A contains the
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* orthonormal eigenvectors of the matrix A.
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* If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
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* or the upper triangle (if UPLO='U') of A, including the
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* diagonal, is destroyed.
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*
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* LDA (input) INTEGER
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* The leading dimension of the array A. LDA >= max(1,N).
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*
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* W (output) REAL array, dimension (N)
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* If INFO = 0, the eigenvalues in ascending order.
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*
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* WORK (workspace/output) COMPLEX array, dimension (MAX(1,LWORK))
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
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*
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* LWORK (input) INTEGER
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* The length of the array WORK. LWORK >= max(1,2*N-1).
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* For optimal efficiency, LWORK >= (NB+1)*N,
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* where NB is the blocksize for CHETRD returned by ILAENV.
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*
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* If LWORK = -1, then a workspace query is assumed; the routine
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* only calculates the optimal size of the WORK array, returns
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* this value as the first entry of the WORK array, and no error
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* message related to LWORK is issued by XERBLA.
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*
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* RWORK (workspace) REAL 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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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
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COMPLEX CONE
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PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) )
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* ..
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* .. Local Scalars ..
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LOGICAL LOWER, LQUERY, WANTZ
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INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
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$ LLWORK, LWKOPT, NB
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REAL 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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INTEGER ILAENV
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REAL CLANHE, SLAMCH
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EXTERNAL ILAENV, LSAME, CLANHE, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CHETRD, CLASCL, CSTEQR, CUNGTR, SSCAL, SSTERF,
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$ XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, 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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LQUERY = ( LWORK.EQ.-1 )
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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( LDA.LT.MAX( 1, N ) ) THEN
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INFO = -5
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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NB = ILAENV( 1, 'CHETRD', UPLO, N, -1, -1, -1 )
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LWKOPT = MAX( 1, ( NB+1 )*N )
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WORK( 1 ) = LWKOPT
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*
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IF( LWORK.LT.MAX( 1, 2*N-1 ) .AND. .NOT.LQUERY )
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$ INFO = -8
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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( 'CHEEV ', -INFO )
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RETURN
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ELSE IF( LQUERY ) THEN
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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 ) THEN
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RETURN
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END IF
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*
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IF( N.EQ.1 ) THEN
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W( 1 ) = A( 1, 1 )
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WORK( 1 ) = 1
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IF( WANTZ )
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$ A( 1, 1 ) = CONE
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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 = SLAMCH( 'Safe minimum' )
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EPS = SLAMCH( '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 = CLANHE( 'M', UPLO, N, A, LDA, 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 )
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$ CALL CLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO )
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*
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* Call CHETRD to reduce Hermitian matrix to tridiagonal form.
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*
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INDE = 1
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INDTAU = 1
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INDWRK = INDTAU + N
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LLWORK = LWORK - INDWRK + 1
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CALL CHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ),
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$ WORK( INDWRK ), LLWORK, IINFO )
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*
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* For eigenvalues only, call SSTERF. For eigenvectors, first call
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* CUNGTR to generate the unitary matrix, then call CSTEQR.
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*
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IF( .NOT.WANTZ ) THEN
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CALL SSTERF( N, W, RWORK( INDE ), INFO )
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ELSE
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CALL CUNGTR( UPLO, N, A, LDA, WORK( INDTAU ), WORK( INDWRK ),
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$ LLWORK, IINFO )
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INDWRK = INDE + N
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CALL CSTEQR( JOBZ, N, W, RWORK( INDE ), A, LDA,
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$ RWORK( INDWRK ), 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 SSCAL( IMAX, ONE / SIGMA, W, 1 )
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END IF
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*
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* Set WORK(1) to optimal complex workspace size.
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*
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WORK( 1 ) = LWKOPT
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*
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RETURN
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*
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* End of CHEEV
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*
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END
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