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SUBROUTINE <a name="CHEEVD.1"></a><a href="cheevd.f.html#CHEEVD.1">CHEEVD</a>( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
$ LRWORK, 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, LRWORK, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> INTEGER IWORK( * )
REAL RWORK( * ), W( * )
COMPLEX A( LDA, * ), 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="CHEEVD.21"></a><a href="cheevd.f.html#CHEEVD.1">CHEEVD</a> computes all eigenvalues and, optionally, eigenvectors of a
</span><span class="comment">*</span><span class="comment"> complex Hermitian 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"> 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) COMPLEX array, dimension (LDA, N)
</span><span class="comment">*</span><span class="comment"> On entry, the Hermitian 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) REAL 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) COMPLEX array, dimension (MAX(1,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 length 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 N + 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + 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, RWORK 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, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.77"></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"> RWORK (workspace/output) REAL array,
</span><span class="comment">*</span><span class="comment"> dimension (LRWORK)
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LRWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array RWORK.
</span><span class="comment">*</span><span class="comment"> If N <= 1, LRWORK must be at least 1.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
</span><span class="comment">*</span><span class="comment"> If JOBZ = 'V' and N > 1, LRWORK must be at least
</span><span class="comment">*</span><span class="comment"> 1 + 5*N + 2*N**2.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LRWORK = -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, RWORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment"> of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.94"></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, RWORK
</span><span class="comment">*</span><span class="comment"> and IWORK arrays, returns these values as the first entries
</span><span class="comment">*</span><span class="comment"> of the WORK, RWORK and IWORK arrays, and no error message
</span><span class="comment">*</span><span class="comment"> related to LWORK or LRWORK or LIWORK is issued by <a name="XERBLA.109"></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">
</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> REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E0, 0.0E0 ) )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL LOWER, LQUERY, WANTZ
INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2,
$ INDWRK, ISCALE, LIOPT, LIWMIN, LLRWK, LLWORK,
$ LLWRK2, LOPT, LROPT, LRWMIN, LWMIN
REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
$ SMLNUM
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
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