!>
!> SSYEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
!> real symmetric matrix A using the 2stage technique for
!> the reduction to tridiagonal. If eigenvectors are desired, it uses a
!> divide and conquer algorithm.
!>
!> 

JOBZ

!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors.
!>                  Not available in this release.
!> 

UPLO

!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!> 

N

!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!> 

A

!>          A is REAL 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

!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!> 

W

!>          W is REAL array, dimension (N)
!>          If INFO = 0, the eigenvalues in ascending order.
!> 

WORK

!>          WORK is REAL array,
!>                                         dimension (LWORK)
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!> 

LWORK

!>          LWORK is 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 queried.
!>                                   LWORK = MAX(1, dimension) where
!>                                   dimension = max(stage1,stage2) + (KD+1)*N + 2*N+1
!>                                             = N*KD + N*max(KD+1,FACTOPTNB)
!>                                               + max(2*KD*KD, KD*NTHREADS)
!>                                               + (KD+1)*N + 2*N+1
!>                                   where KD is the blocking size of the reduction,
!>                                   FACTOPTNB is the blocking used by the QR or LQ
!>                                   algorithm, usually FACTOPTNB=128 is a good choice
!>                                   NTHREADS is the number of threads used when
!>                                   openMP compilation is enabled, otherwise =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

!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
!> 

LIWORK

!>          LIWORK is 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

!>          INFO is 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).
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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.

!>
!>  All details about the 2stage techniques are available in:
!>
!>  Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
!>  Parallel reduction to condensed forms for symmetric eigenvalue problems
!>  using aggregated fine-grained and memory-aware kernels. In Proceedings
!>  of 2011 International Conference for High Performance Computing,
!>  Networking, Storage and Analysis (SC '11), New York, NY, USA,
!>  Article 8 , 11 pages.
!>  http://doi.acm.org/10.1145/2063384.2063394
!>
!>  A. Haidar, J. Kurzak, P. Luszczek, 2013.
!>  An improved parallel singular value algorithm and its implementation
!>  for multicore hardware, In Proceedings of 2013 International Conference
!>  for High Performance Computing, Networking, Storage and Analysis (SC '13).
!>  Denver, Colorado, USA, 2013.
!>  Article 90, 12 pages.
!>  http://doi.acm.org/10.1145/2503210.2503292
!>
!>  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
!>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure
!>  calculations based on fine-grained memory aware tasks.
!>  International Journal of High Performance Computing Applications.
!>  Volume 28 Issue 2, Pages 196-209, May 2014.
!>  http://hpc.sagepub.com/content/28/2/196
!>
!>