SUBROUTINE CHEEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, $ LRWORK, IWORK, LIWORK, INFO ) * * -- LAPACK driver routine (version 2.0) -- * Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., * Courant Institute, Argonne National Lab, and Rice University * September 30, 1994 * * .. Scalar Arguments .. CHARACTER JOBZ, UPLO INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) REAL RWORK( * ), W( * ) COMPLEX A( LDA, * ), WORK( * ) * .. * * Purpose * ======= * * CHEEVD computes all eigenvalues and, optionally, eigenvectors of a * complex Hermitian matrix A. If eigenvectors are desired, it uses a * divide and conquer algorithm. * * The divide and conquer algorithm makes very mild assumptions about * floating point arithmetic. It will work on machines with a guard * digit in add/subtract, or on those binary machines without guard * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or * Cray-2. It could conceivably fail on hexadecimal or decimal machines * without guard digits, but we know of none. * * 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. * * A (input/output) COMPLEX array, dimension (LDA, N) * On entry, the Hermitian matrix A. If UPLO = 'U', the * leading N-by-N upper triangular part of A contains the * upper triangular part of the matrix A. If UPLO = 'L', * the leading N-by-N lower triangular part of A contains * the lower triangular part of the matrix A. * On exit, if JOBZ = 'V', then if INFO = 0, A contains the * orthonormal eigenvectors of the matrix A. * If JOBZ = 'N', then on exit the lower triangle (if UPLO='L') * or the upper triangle (if UPLO='U') of A, including the * diagonal, is destroyed. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * W (output) REAL array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * WORK (workspace/output) COMPLEX array, dimension (LWORK) * On exit, if LWORK > 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The length of the array WORK. * If N <= 1, LWORK must be at least 1. * If JOBZ = 'N' and N > 1, LWORK must be at least N + 1. * If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2. * * RWORK (workspace/output) REAL array, * dimension (LRWORK) * On exit, if LRWORK > 0, RWORK(1) returns the optimal LRWORK. * * LRWORK (input) INTEGER * The dimension of the array RWORK. * If N <= 1, LRWORK must be at least 1. * If JOBZ = 'N' and N > 1, LRWORK must be at least N. * If JOBZ = 'V' and N > 1, LRWORK must be at least * 1 + 4*N + 2*N*lg N + 3*N**2 , * where lg( N ) = smallest integer k such * that 2**k >= N . * * IWORK (workspace/output) INTEGER array, dimension (LIWORK) * On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK. * * LIWORK (input) INTEGER * The dimension of the array IWORK. * If N <= 1, LIWORK must be at least 1. * If JOBZ = 'N' and N > 1, LIWORK must be at least 1. * If JOBZ = 'V' and N > 1, LIWORK must be at least 2 + 5*N. * * 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 .. REAL ZERO, ONE, TWO PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 ) COMPLEX CONE PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) ) * .. * .. Local Scalars .. LOGICAL LOWER, WANTZ INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2, $ INDWRK, ISCALE, LGN, LIOPT, LIWMIN, LLRWK, $ LLWORK, LLWRK2, LOPT, LROPT, LRWMIN, LWMIN REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, $ SMLNUM * .. * .. External Functions .. LOGICAL LSAME REAL CLANHE, SLAMCH EXTERNAL LSAME, CLANHE, SLAMCH * .. * .. External Subroutines .. EXTERNAL CHETRD, CLACPY, CLASCL, CSTEDC, CUNMTR, SSCAL, $ SSTERF, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC INT, LOG, MAX, REAL, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) * INFO = 0 IF( N.LE.1 ) THEN LGN = 0 LWMIN = 1 LRWMIN = 1 LIWMIN = 1 LOPT = LWMIN LROPT = LRWMIN LIOPT = LIWMIN ELSE LGN = INT( LOG( REAL( N ) ) / LOG( TWO ) ) IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( 2**LGN.LT.N ) $ LGN = LGN + 1 IF( WANTZ ) THEN LWMIN = 2*N + N*N LRWMIN = 1 + 4*N + 2*N*LGN + 3*N**2 LIWMIN = 2 + 5*N ELSE LWMIN = N + 1 LRWMIN = N LIWMIN = 1 END IF LOPT = LWMIN LROPT = LRWMIN LIOPT = LIWMIN END IF 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( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 ELSE IF( LWORK.LT.LWMIN ) THEN INFO = -8 ELSE IF( LRWORK.LT.LRWMIN ) THEN INFO = -10 ELSE IF( LIWORK.LT.LIWMIN ) THEN INFO = -12 END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'CHEEVD ', -INFO ) GO TO 10 END IF * * Quick return if possible * IF( N.EQ.0 ) $ GO TO 10 * IF( N.EQ.1 ) THEN W( 1 ) = A( 1, 1 ) IF( WANTZ ) $ A( 1, 1 ) = CONE GO TO 10 END IF * * Get machine constants. * SAFMIN = SLAMCH( 'Safe minimum' ) EPS = SLAMCH( 'Precision' ) SMLNUM = SAFMIN / EPS BIGNUM = ONE / SMLNUM RMIN = SQRT( SMLNUM ) RMAX = SQRT( BIGNUM ) * * Scale matrix to allowable range, if necessary. * ANRM = CLANHE( 'M', UPLO, N, A, LDA, 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 ) $ CALL CLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) * * Call CHETRD to reduce Hermitian matrix to tridiagonal form. * INDE = 1 INDTAU = 1 INDWRK = INDTAU + N INDRWK = INDE + N INDWK2 = INDWRK + N*N LLWORK = LWORK - INDWRK + 1 LLWRK2 = LWORK - INDWK2 + 1 LLRWK = LRWORK - INDRWK + 1 CALL CHETRD( UPLO, N, A, LDA, W, RWORK( INDE ), WORK( INDTAU ), $ WORK( INDWRK ), LLWORK, IINFO ) LOPT = MAX( REAL( LOPT ), REAL( N )+REAL( WORK( INDWRK ) ) ) * * For eigenvalues only, call SSTERF. For eigenvectors, first call * CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the * tridiagonal matrix, then call CUNMTR to multiply it to the * Householder transformations represented as Householder vectors in * A. * IF( .NOT.WANTZ ) THEN CALL SSTERF( N, W, RWORK( INDE ), INFO ) ELSE CALL CSTEDC( 'I', N, W, RWORK( INDE ), WORK( INDWRK ), N, $ WORK( INDWK2 ), LLWRK2, RWORK( INDRWK ), LLRWK, $ IWORK, LIWORK, INFO ) CALL CUNMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), $ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) CALL CLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) LOPT = MAX( LOPT, N+N**2+INT( WORK( INDWK2 ) ) ) 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 SSCAL( IMAX, ONE / SIGMA, W, 1 ) END IF * 10 CONTINUE IF( LWORK.GT.0 ) $ WORK( 1 ) = LOPT IF( LRWORK.GT.0 ) $ RWORK( 1 ) = LROPT IF( LIWORK.GT.0 ) $ IWORK( 1 ) = LIOPT RETURN * * End of CHEEVD * END