hbev_2stage(3)

NAME
hbev_2stage - {hb,sb}ev_2stage: eig, QR iteration

SYNOPSIS

  Functions

subroutine chbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)
CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine dsbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, info)
DSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine ssbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, info)
SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices
subroutine zhbev_2stage (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)
ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Detailed Description

Function Documentation

  subroutine chbev_2stage (character jobz, character uplo, integer n, integer kd, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, complex, dimension( ldz, * ) z, integer ldz, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
    !> a complex Hermitian band 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is COMPLEX array, dimension (LDAB, N)
    !>          On entry, the upper or lower triangle of the Hermitian band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, AB is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the first
    !>          superdiagonal and the diagonal of the tridiagonal matrix T
    !>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
    !>          the diagonal and first subdiagonal of T are returned in the
    !>          first two rows of AB.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD + 1.
    !>

    W

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

    Z

    !>          Z is COMPLEX array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX 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 = (2KD+1)*N + KD*NTHREADS
    !>                                   where KD is the size of the band.
    !>                                   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 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 (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 dsbev_2stage (character jobz, character uplo, integer n, integer kd, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer info)

DSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> DSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
    !> a real symmetric band 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is DOUBLE PRECISION array, dimension (LDAB, N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, AB is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the first
    !>          superdiagonal and the diagonal of the tridiagonal matrix T
    !>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
    !>          the diagonal and first subdiagonal of T are returned in the
    !>          first two rows of AB.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD + 1.
    !>

    W

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

    Z

    !>          Z is DOUBLE PRECISION array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    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 = (2KD+1)*N + KD*NTHREADS + N
    !>                                   where KD is the size of the band.
    !>                                   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 ssbev_2stage (character jobz, character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer lwork, integer info)

SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> SSBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
    !> a real symmetric band 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is REAL array, dimension (LDAB, N)
    !>          On entry, the upper or lower triangle of the symmetric band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, AB is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the first
    !>          superdiagonal and the diagonal of the tridiagonal matrix T
    !>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
    !>          the diagonal and first subdiagonal of T are returned in the
    !>          first two rows of AB.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD + 1.
    !>

    W

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

    Z

    !>          Z is REAL array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    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 = (2KD+1)*N + KD*NTHREADS + N
    !>                                   where KD is the size of the band.
    !>                                   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 zhbev_2stage (character jobz, character uplo, integer n, integer kd, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)

ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

Purpose:

    !>
    !> ZHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
    !> a complex Hermitian band 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.
    !>

    KD

    !>          KD is INTEGER
    !>          The number of superdiagonals of the matrix A if UPLO = 'U',
    !>          or the number of subdiagonals if UPLO = 'L'.  KD >= 0.
    !>

    AB

    !>          AB is COMPLEX*16 array, dimension (LDAB, N)
    !>          On entry, the upper or lower triangle of the Hermitian band
    !>          matrix A, stored in the first KD+1 rows of the array.  The
    !>          j-th column of A is stored in the j-th column of the array AB
    !>          as follows:
    !>          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
    !>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
    !>
    !>          On exit, AB is overwritten by values generated during the
    !>          reduction to tridiagonal form.  If UPLO = 'U', the first
    !>          superdiagonal and the diagonal of the tridiagonal matrix T
    !>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
    !>          the diagonal and first subdiagonal of T are returned in the
    !>          first two rows of AB.
    !>

    LDAB

    !>          LDAB is INTEGER
    !>          The leading dimension of the array AB.  LDAB >= KD + 1.
    !>

    W

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

    Z

    !>          Z is COMPLEX*16 array, dimension (LDZ, N)
    !>          If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
    !>          eigenvectors of the matrix A, with the i-th column of Z
    !>          holding the eigenvector associated with W(i).
    !>          If JOBZ = 'N', then Z is not referenced.
    !>

    LDZ

    !>          LDZ is INTEGER
    !>          The leading dimension of the array Z.  LDZ >= 1, and if
    !>          JOBZ = 'V', LDZ >= max(1,N).
    !>

    WORK

    !>          WORK is COMPLEX*16 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 = (2KD+1)*N + KD*NTHREADS
    !>                                   where KD is the size of the band.
    !>                                   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 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 (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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