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SUBROUTINE <a name="DSYEVD.1"></a><a href="dsyevd.f.html#DSYEVD.1">DSYEVD</a>( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, IWORK,
$ LIWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK driver routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> CHARACTER JOBZ, UPLO
INTEGER INFO, LDA, LIWORK, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="DSYEVD.20"></a><a href="dsyevd.f.html#DSYEVD.1">DSYEVD</a> computes all eigenvalues and, optionally, eigenvectors of a
</span><span class="comment">*</span><span class="comment"> real symmetric matrix A. If eigenvectors are desired, it uses a
</span><span class="comment">*</span><span class="comment"> divide and conquer algorithm.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The divide and conquer algorithm makes very mild assumptions about
</span><span class="comment">*</span><span class="comment"> floating point arithmetic. It will work on machines with a guard
</span><span class="comment">*</span><span class="comment"> digit in add/subtract, or on those binary machines without guard
</span><span class="comment">*</span><span class="comment"> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
</span><span class="comment">*</span><span class="comment"> Cray-2. It could conceivably fail on hexadecimal or decimal machines
</span><span class="comment">*</span><span class="comment"> without guard digits, but we know of none.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Because of large use of BLAS of level 3, <a name="DSYEVD.31"></a><a href="dsyevd.f.html#DSYEVD.1">DSYEVD</a> needs N**2 more
</span><span class="comment">*</span><span class="comment"> workspace than <a name="DSYEVX.32"></a><a href="dsyevx.f.html#DSYEVX.1">DSYEVX</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> JOBZ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'N': Compute eigenvalues only;
</span><span class="comment">*</span><span class="comment"> = 'V': Compute eigenvalues and eigenvectors.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> UPLO (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'U': Upper triangle of A is stored;
</span><span class="comment">*</span><span class="comment"> = 'L': Lower triangle of A is stored.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrix A. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment"> On entry, the symmetric matrix A. If UPLO = 'U', the
</span><span class="comment">*</span><span class="comment"> leading N-by-N upper triangular part of A contains the
</span><span class="comment">*</span><span class="comment"> upper triangular part of the matrix A. If UPLO = 'L',
</span><span class="comment">*</span><span class="comment"> the leading N-by-N lower triangular part of A contains
</span><span class="comment">*</span><span class="comment"> the lower triangular part of the matrix A.
</span><span class="comment">*</span><span class="comment"> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
</span><span class="comment">*</span><span class="comment"> orthonormal eigenvectors of the matrix A.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
</span><span class="comment">*</span><span class="comment"> or the upper triangle (if UPLO='U') of A, including the
</span><span class="comment">*</span><span class="comment"> diagonal, is destroyed.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> W (output) DOUBLE PRECISION array, dimension (N)
</span><span class="comment">*</span><span class="comment"> If INFO = 0, the eigenvalues in ascending order.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) DOUBLE PRECISION array,
</span><span class="comment">*</span><span class="comment"> dimension (LWORK)
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LWORK must be at least 2*N+1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LWORK must be at least
</span><span class="comment">*</span><span class="comment"> 1 + 6*N + 2*N**2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal sizes of the WORK and IWORK
</span><span class="comment">*</span><span class="comment"> arrays, returns these values as the first entries of the WORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, and no error message related to LWORK or
</span><span class="comment">*</span><span class="comment"> LIWORK is issued by <a name="XERBLA.81"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LIWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array IWORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LIWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LIWORK = -1, then a workspace query is assumed; the
</span><span class="comment">*</span><span class="comment"> routine only calculates the optimal sizes of the WORK and
</span><span class="comment">*</span><span class="comment"> IWORK arrays, returns these values as the first entries of
</span><span class="comment">*</span><span class="comment"> the WORK and IWORK arrays, and no error message related to
</span><span class="comment">*</span><span class="comment"> LWORK or LIWORK is issued by <a name="XERBLA.96"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> = 0: successful exit
</span><span class="comment">*</span><span class="comment"> < 0: if INFO = -i, the i-th argument had an illegal value
</span><span class="comment">*</span><span class="comment"> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed
</span><span class="comment">*</span><span class="comment"> to converge; i off-diagonal elements of an intermediate
</span><span class="comment">*</span><span class="comment"> tridiagonal form did not converge to zero;
</span><span class="comment">*</span><span class="comment"> if INFO = i and JOBZ = 'V', then the algorithm failed
</span><span class="comment">*</span><span class="comment"> to compute an eigenvalue while working on the submatrix
</span><span class="comment">*</span><span class="comment"> lying in rows and columns INFO/(N+1) through
</span><span class="comment">*</span><span class="comment"> mod(INFO,N+1).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Based on contributions by
</span><span class="comment">*</span><span class="comment"> Jeff Rutter, Computer Science Division, University of California
</span><span class="comment">*</span><span class="comment"> at Berkeley, USA
</span><span class="comment">*</span><span class="comment"> Modified by Francoise Tisseur, University of Tennessee.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Modified description of INFO. Sven, 16 Feb 05.
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment"> ..
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