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

NAME

       heev_2stage - {he,sy}ev_2stage: eig, QR iteration

SYNOPSIS

   Functions
       subroutine cheev_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
            CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for HE matrices
       subroutine dsyev_2stage (jobz, uplo, n, a, lda, w, work, lwork, info)
            DSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for SY matrices
       subroutine ssyev_2stage (jobz, uplo, n, a, lda, w, work, lwork, info)
            SSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for SY matrices
       subroutine zheev_2stage (jobz, uplo, n, a, lda, w, work, lwork, rwork, info)
            ZHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right
           eigenvectors for HE matrices

Detailed Description

Function Documentation

   subroutine cheev_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 info)
        CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors
       for HE matrices

       Purpose:

            CHEEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
            complex Hermitian matrix A using the 2stage technique for
            the reduction to tridiagonal.

       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 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 + N
                                                        = N*KD + N*max(KD+1,FACTOPTNB)
                                                          + max(2*KD*KD, KD*NTHREADS)
                                                          + (KD+1)*N + 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.

           RWORK

                     RWORK is REAL array, dimension (max(1, 3*N-2))

           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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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 dsyev_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 info)
        DSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors
       for SY matrices

       Purpose:

            DSYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
            real symmetric matrix A using the 2stage technique for
            the reduction to tridiagonal.

       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 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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 ssyev_2stage (character jobz, character uplo, integer n, real, dimension( lda, * )
       a, integer lda, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer
       info)
        SSYEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors
       for SY matrices

       Purpose:

            SSYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
            real symmetric matrix A using the 2stage technique for
            the reduction to tridiagonal.

       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 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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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 zheev_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 info)
        ZHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors
       for HE matrices

       Purpose:

            ZHEEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
            complex Hermitian matrix A using the 2stage technique for
            the reduction to tridiagonal.

       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 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 + N
                                                        = N*KD + N*max(KD+1,FACTOPTNB)
                                                          + max(2*KD*KD, KD*NTHREADS)
                                                          + (KD+1)*N + 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.

           RWORK

                     RWORK is DOUBLE PRECISION array, dimension (max(1, 3*N-2))

           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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       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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