DSYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a


 real symmetric matrix A using the 2stage technique for


 the reduction to tridiagonal.

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 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

          LDA is INTEGER


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

W

          W is DOUBLE PRECISION array, dimension (N)


          If INFO = 0, the eigenvalues in ascending order.

WORK

          WORK is DOUBLE PRECISION array, dimension LWORK


          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

LWORK

          LWORK is INTEGER


          The length of the array WORK. LWORK >= 1, when N <= 1;


          otherwise  


          If JOBZ = 'N' and N > 1, LWORK must be queried.


                                   LWORK = MAX(1, dimension) where


                                   dimension = max(stage1,stage2) + (KD+1)*N + 2*N


                                             = N*KD + N*max(KD+1,FACTOPTNB) 


                                               + max(2*KD*KD, KD*NTHREADS) 


                                               + (KD+1)*N + 2*N


                                   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 queried. Not yet available


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal size of the WORK array, returns


          this value as the first entry of the WORK array, and no error


          message related to LWORK 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, the algorithm failed to converge; i


                off-diagonal elements of an intermediate tridiagonal


                form did not converge to zero.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

November 2017

  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