SUBROUTINE DSPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
$ IWORK, LIWORK, 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, LDZ, LIWORK, LWORK, N
* ..
* .. Array Arguments ..
INTEGER IWORK( * )
DOUBLE PRECISION AP( * ), W( * ), WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* DSPEVD computes all the eigenvalues and, optionally, eigenvectors
* of a real symmetric matrix A in packed storage. 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.
*
* AP (input/output) DOUBLE PRECISION array, dimension (N*(N+1)/2)
* On entry, the upper or lower triangle of the symmetric matrix
* A, packed columnwise in a linear array. The j-th column of A
* is stored in the array AP as follows:
* if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
* if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
*
* On exit, AP is overwritten by values generated during the
* reduction to tridiagonal form. If UPLO = 'U', the diagonal
* and first superdiagonal of the tridiagonal matrix T overwrite
* the corresponding elements of A, and if UPLO = 'L', the
* diagonal and first subdiagonal of T overwrite the
* corresponding elements of A.
*
* W (output) DOUBLE PRECISION array, dimension (N)
* If INFO = 0, the eigenvalues in ascending order.
*
* Z (output) DOUBLE PRECISION 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/output) DOUBLE PRECISION array,
* dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the required 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.
* If JOBZ = 'V' and N > 1, LWORK must be at least
* 1 + 6*N + N**2.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the required 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 required LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK.
* If JOBZ = 'N' or 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 required 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, 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 = 0.0D+0, ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY, WANTZ
INTEGER IINFO, INDE, INDTAU, INDWRK, ISCALE, LIWMIN,
$ LLWORK, LWMIN
DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
* ..
* .. External Functions ..
LOGICAL LSAME
DOUBLE PRECISION DLAMCH, DLANSP
EXTERNAL LSAME, DLAMCH, DLANSP
* ..
* .. External Subroutines ..
EXTERNAL DOPMTR, DSCAL, DSPTRD, DSTEDC, DSTERF, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC SQRT
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
WANTZ = LSAME( JOBZ, 'V' )
LQUERY = ( LWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
*
INFO = 0
IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
INFO = -1
ELSE IF( .NOT.( LSAME( UPLO, 'U' ) .OR. LSAME( UPLO, 'L' ) ) )
$ THEN
INFO = -2
ELSE IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
INFO = -7
END IF
*
IF( INFO.EQ.0 ) THEN
IF( N.LE.1 ) THEN
LIWMIN = 1
LWMIN = 1
ELSE
IF( WANTZ ) THEN
LIWMIN = 3 + 5*N
LWMIN = 1 + 6*N + N**2
ELSE
LIWMIN = 1
LWMIN = 2*N
END IF
END IF
IWORK( 1 ) = LIWMIN
WORK( 1 ) = LWMIN
*
IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
INFO = -9
ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
INFO = -11
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DSPEVD', -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 ) = AP( 1 )
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 = DLANSP( 'M', UPLO, N, AP, 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 ) THEN
CALL DSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
END IF
*
* Call DSPTRD to reduce symmetric packed matrix to tridiagonal form.
*
INDE = 1
INDTAU = INDE + N
CALL DSPTRD( UPLO, N, AP, W, WORK( INDE ), WORK( INDTAU ), IINFO )
*
* For eigenvalues only, call DSTERF. For eigenvectors, first call
* DSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
* tridiagonal matrix, then call DOPMTR to multiply it by the
* Householder transformations represented in AP.
*
IF( .NOT.WANTZ ) THEN
CALL DSTERF( N, W, WORK( INDE ), INFO )
ELSE
INDWRK = INDTAU + N
LLWORK = LWORK - INDWRK + 1
CALL DSTEDC( 'I', N, W, WORK( INDE ), Z, LDZ, WORK( INDWRK ),
$ LLWORK, IWORK, LIWORK, INFO )
CALL DOPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
$ WORK( INDWRK ), IINFO )
END IF
*
* If matrix was scaled, then rescale eigenvalues appropriately.
*
IF( ISCALE.EQ.1 )
$ CALL DSCAL( N, ONE / SIGMA, W, 1 )
*
WORK( 1 ) = LWMIN
IWORK( 1 ) = LIWMIN
RETURN
*
* End of DSPEVD
*
END