Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       heevd_2stage - {he,sy}evd_2stage: eig, divide and conquer

SYNOPSIS

   Functions
       subroutine cheevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork,
           liwork, info)
            CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for HE matrices
       subroutine dsyevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
            DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for SY matrices
       subroutine ssyevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, iwork, liwork, info)
            SSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for SY matrices
       subroutine zheevd_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork,
           liwork, info)
            ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for HE matrices

Detailed Description

Function Documentation

   subroutine cheevd_2stage (character jobz, character uplo, integer n, complex, dimension( lda,
       * ) a, integer lda, real, dimension( * ) w, complex, dimension( * ) work, integer lwork,
       real, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork,
       integer info)
        CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for HE matrices

       Purpose:

            CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
            complex Hermitian matrix A using the 2stage technique for
            the reduction to tridiagonal.  If eigenvectors are desired, it uses a
            divide and conquer algorithm.

       Parameters
           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 COMPLEX array, dimension (LDA, N)
                     On entry, the Hermitian 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 COMPLEX array, dimension (MAX(1,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 + N+1
                                                        = N*KD + N*max(KD+1,FACTOPTNB)
                                                          + max(2*KD*KD, KD*NTHREADS)
                                                          + (KD+1)*N + 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 2*N + N**2

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal sizes of the WORK, RWORK and
                     IWORK arrays, returns these values as the first entries of
                     the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

           RWORK

                     RWORK is REAL array,
                                                    dimension (LRWORK)
                     On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

           LRWORK

                     LRWORK is INTEGER
                     The dimension of the array RWORK.
                     If N <= 1,                LRWORK must be at least 1.
                     If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
                     If JOBZ  = 'V' and N > 1, LRWORK must be at least
                                    1 + 5*N + 2*N**2.

                     If LRWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal sizes of the WORK, RWORK
                     and IWORK arrays, returns these values as the first entries
                     of the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK 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, RWORK
                     and IWORK arrays, returns these values as the first entries
                     of the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK 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).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:
           Modified description of INFO. Sven, 16 Feb 05.

       Contributors:
           Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

       Further Details:

             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

   subroutine dsyevd_2stage (character jobz, character uplo, integer n, double precision,
       dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, double precision,
       dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer liwork, integer
       info)
        DSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for SY matrices

       Purpose:

            DSYEVD_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.

       Parameters
           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 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).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           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.

       Further Details:

             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

   subroutine ssyevd_2stage (character jobz, character uplo, integer n, real, dimension( lda, * )
       a, integer lda, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer,
       dimension( * ) iwork, integer liwork, integer info)
        SSYEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for SY matrices

       Purpose:

            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.

       Parameters
           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).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           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.

       Further Details:

             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

   subroutine zheevd_2stage (character jobz, character uplo, integer n, complex*16, dimension(
       lda, * ) a, integer lda, double precision, dimension( * ) w, complex*16, dimension( * )
       work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer,
       dimension( * ) iwork, integer liwork, integer info)
        ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right
       eigenvectors for HE matrices

       Purpose:

            ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
            complex Hermitian matrix A using the 2stage technique for
            the reduction to tridiagonal.  If eigenvectors are desired, it uses a
            divide and conquer algorithm.

       Parameters
           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 COMPLEX*16 array, dimension (LDA, N)
                     On entry, the Hermitian 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 COMPLEX*16 array, dimension (MAX(1,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 + N+1
                                                        = N*KD + N*max(KD+1,FACTOPTNB)
                                                          + max(2*KD*KD, KD*NTHREADS)
                                                          + (KD+1)*N + 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 2*N + N**2

                     If LWORK = -1, then a workspace query is assumed; the routine
                     only calculates the optimal sizes of the WORK, RWORK and
                     IWORK arrays, returns these values as the first entries of
                     the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK or LIWORK is issued by XERBLA.

           RWORK

                     RWORK is DOUBLE PRECISION array,
                                                    dimension (LRWORK)
                     On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

           LRWORK

                     LRWORK is INTEGER
                     The dimension of the array RWORK.
                     If N <= 1,                LRWORK must be at least 1.
                     If JOBZ  = 'N' and N > 1, LRWORK must be at least N.
                     If JOBZ  = 'V' and N > 1, LRWORK must be at least
                                    1 + 5*N + 2*N**2.

                     If LRWORK = -1, then a workspace query is assumed; the
                     routine only calculates the optimal sizes of the WORK, RWORK
                     and IWORK arrays, returns these values as the first entries
                     of the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK 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, RWORK
                     and IWORK arrays, returns these values as the first entries
                     of the WORK, RWORK and IWORK arrays, and no error message
                     related to LWORK or LRWORK 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).

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Further Details:
           Modified description of INFO. Sven, 16 Feb 05.

       Contributors:
           Jeff Rutter, Computer Science Division, University of California at Berkeley, USA

       Further Details:

             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

Author

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