SUBROUTINE DSYEVD( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK, \$ LIWORK, 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, UPLO INTEGER INFO, LDA, LIWORK, LWORK, N * .. * .. Array Arguments .. INTEGER IWORK( * ) DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ) * .. * * Purpose * ======= * * DSYEVD computes all eigenvalues and, optionally, eigenvectors of a * real symmetric 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. * * Because of large use of BLAS of level 3, DSYEVD needs N**2 more * workspace than DSYEVX. * * 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) DOUBLE PRECISION array, dimension (LDA, N) * On entry, the symmetric 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) DOUBLE PRECISION array, dimension (N) * If INFO = 0, the eigenvalues in ascending order. * * WORK (workspace/output) DOUBLE PRECISION array, * dimension (LWORK) * On exit, if INFO = 0, WORK(1) returns the optimal LWORK. * * LWORK (input) INTEGER * The dimension of the array WORK. * If N <= 1, LWORK must be at least 1. * If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1. * If JOBZ = 'V' and N > 1, LWORK must be at least * 1 + 6*N + 2*N**2. * * If LWORK = -1, then a workspace query is assumed; the routine * only calculates the optimal sizes of the WORK and IWORK * arrays, returns these values as the first entries of the WORK * and IWORK arrays, and no error message related to LWORK or * LIWORK is issued by XERBLA. * * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) * On exit, if INFO = 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 3 + 5*N. * * If LIWORK = -1, then a workspace query is assumed; the * routine only calculates the optimal sizes of the WORK and * IWORK arrays, returns these values as the first entries of * the WORK and IWORK arrays, and no error message related to * LWORK or LIWORK is issued by XERBLA. * * INFO (output) INTEGER * = 0: successful exit * < 0: if INFO = -i, the i-th argument had an illegal value * > 0: if INFO = i and JOBZ = 'N', then the algorithm failed * to converge; i off-diagonal elements of an intermediate * tridiagonal form did not converge to zero; * if INFO = i and JOBZ = 'V', then the algorithm failed * to compute an eigenvalue while working on the submatrix * lying in rows and columns INFO/(N+1) through * mod(INFO,N+1). * * Further Details * =============== * * Based on contributions by * Jeff Rutter, Computer Science Division, University of California * at Berkeley, USA * Modified by Francoise Tisseur, University of Tennessee. * * Modified description of INFO. Sven, 16 Feb 05. * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) * .. * .. Local Scalars .. * LOGICAL LOWER, LQUERY, WANTZ INTEGER IINFO, INDE, INDTAU, INDWK2, INDWRK, ISCALE, \$ LIOPT, LIWMIN, LLWORK, LLWRK2, LOPT, LWMIN DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, \$ SMLNUM * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV DOUBLE PRECISION DLAMCH, DLANSY EXTERNAL LSAME, DLAMCH, DLANSY, ILAENV * .. * .. External Subroutines .. EXTERNAL DLACPY, DLASCL, DORMTR, DSCAL, DSTEDC, DSTERF, \$ DSYTRD, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, SQRT * .. * .. Executable Statements .. * * Test the input parameters. * WANTZ = LSAME( JOBZ, 'V' ) LOWER = LSAME( UPLO, 'L' ) LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) * 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( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF * IF( INFO.EQ.0 ) THEN IF( N.LE.1 ) THEN LIWMIN = 1 LWMIN = 1 LOPT = LWMIN LIOPT = LIWMIN ELSE IF( WANTZ ) THEN LIWMIN = 3 + 5*N LWMIN = 1 + 6*N + 2*N**2 ELSE LIWMIN = 1 LWMIN = 2*N + 1 END IF LOPT = MAX( LWMIN, 2*N + \$ ILAENV( 1, 'DSYTRD', UPLO, N, -1, -1, -1 ) ) LIOPT = LIWMIN END IF WORK( 1 ) = LOPT IWORK( 1 ) = LIOPT * IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN INFO = -8 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN INFO = -10 END IF END IF * IF( INFO.NE.0 ) THEN CALL XERBLA( 'DSYEVD', -INFO ) RETURN ELSE IF( LQUERY ) THEN RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * IF( N.EQ.1 ) THEN W( 1 ) = A( 1, 1 ) IF( WANTZ ) \$ A( 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 = DLANSY( 'M', UPLO, N, A, LDA, WORK ) 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 DLASCL( UPLO, 0, 0, ONE, SIGMA, N, N, A, LDA, INFO ) * * Call DSYTRD to reduce symmetric matrix to tridiagonal form. * INDE = 1 INDTAU = INDE + N INDWRK = INDTAU + N LLWORK = LWORK - INDWRK + 1 INDWK2 = INDWRK + N*N LLWRK2 = LWORK - INDWK2 + 1 * CALL DSYTRD( UPLO, N, A, LDA, W, WORK( INDE ), WORK( INDTAU ), \$ WORK( INDWRK ), LLWORK, IINFO ) LOPT = 2*N + WORK( INDWRK ) * * For eigenvalues only, call DSTERF. For eigenvectors, first call * DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the * tridiagonal matrix, then call DORMTR to multiply it by the * Householder transformations stored in A. * IF( .NOT.WANTZ ) THEN CALL DSTERF( N, W, WORK( INDE ), INFO ) ELSE CALL DSTEDC( 'I', N, W, WORK( INDE ), WORK( INDWRK ), N, \$ WORK( INDWK2 ), LLWRK2, IWORK, LIWORK, INFO ) CALL DORMTR( 'L', UPLO, 'N', N, N, A, LDA, WORK( INDTAU ), \$ WORK( INDWRK ), N, WORK( INDWK2 ), LLWRK2, IINFO ) CALL DLACPY( 'A', N, N, WORK( INDWRK ), N, A, LDA ) LOPT = MAX( LOPT, 1+6*N+2*N**2 ) END IF * * If matrix was scaled, then rescale eigenvalues appropriately. * IF( ISCALE.EQ.1 ) \$ CALL DSCAL( N, ONE / SIGMA, W, 1 ) * WORK( 1 ) = LOPT IWORK( 1 ) = LIOPT * RETURN * * End of DSYEVD * END