hegv_2stage(3)

NAME
hegv_2stage - {he,sy}gv_2stage: eig, QR iteration, 2-stage

SYNOPSIS

  Functions
subroutine chegv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info)
CHEGV_2STAGE
subroutine dsygv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, info)
DSYGV_2STAGE
subroutine ssygv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, info)
SSYGV_2STAGE
subroutine zhegv_2stage (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, rwork, info)
ZHEGV_2STAGE

Detailed Description

Function Documentation

  subroutine chegv_2stage (integer itype, character jobz, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info)

CHEGV_2STAGE

Purpose:

     CHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
     of a complex generalized Hermitian-definite eigenproblem, of the form
     A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
     Here A and B are assumed to be Hermitian and B is also
     positive definite.
     This routine use the 2stage technique for the reduction to tridiagonal
     which showed higher performance on recent architecture and for large
     sizes N>2000.

Parameters
    ITYPE

              ITYPE is INTEGER
              Specifies the problem type to be solved:
              = 1:  A*x = (lambda)*B*x
              = 2:  A*B*x = (lambda)*x
              = 3:  B*A*x = (lambda)*x

    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 triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  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
              matrix Z of eigenvectors.  The eigenvectors are normalized
              as follows:
              if ITYPE = 1 or 2, Z**H*B*Z = I;
              if ITYPE = 3, Z**H*inv(B)*Z = I.
              If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
              or the lower triangle (if UPLO='L') of A, including the
              diagonal, is destroyed.

    LDA

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

    B

              B is COMPLEX array, dimension (LDB, N)
              On entry, the Hermitian positive definite matrix B.
              If UPLO = 'U', the leading N-by-N upper triangular part of B
              contains the upper triangular part of the matrix B.
              If UPLO = 'L', the leading N-by-N lower triangular part of B
              contains the lower triangular part of the matrix B.
              On exit, if INFO <= N, the part of B containing the matrix is
              overwritten by the triangular factor U or L from the Cholesky
              factorization B = U**H*U or B = L*L**H.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= 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:  CPOTRF or CHEEV returned an error code:
                 <= N:  if INFO = i, CHEEV failed to converge;
                        i off-diagonal elements of an intermediate
                        tridiagonal form did not converge to zero;
                 > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                        principal minor of order i of B is not positive.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

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

Definition at line 230 of file chegv_2stage.f.

  subroutine dsygv_2stage (integer itype, character jobz, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w, double precision, dimension( * ) work, integer lwork, integer info)

DSYGV_2STAGE

Purpose:

     DSYGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
     of a real generalized symmetric-definite eigenproblem, of the form
     A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
     Here A and B are assumed to be symmetric and B is also
     positive definite.
     This routine use the 2stage technique for the reduction to tridiagonal
     which showed higher performance on recent architecture and for large
     sizes N>2000.

Parameters
    ITYPE

              ITYPE is INTEGER
              Specifies the problem type to be solved:
              = 1:  A*x = (lambda)*B*x
              = 2:  A*B*x = (lambda)*x
              = 3:  B*A*x = (lambda)*x

    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 triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  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
              matrix Z of eigenvectors.  The eigenvectors are normalized
              as follows:
              if ITYPE = 1 or 2, Z**T*B*Z = I;
              if ITYPE = 3, Z**T*inv(B)*Z = I.
              If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
              or the lower triangle (if UPLO='L') of A, including the
              diagonal, is destroyed.

    LDA

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

    B

              B is DOUBLE PRECISION array, dimension (LDB, N)
              On entry, the symmetric positive definite matrix B.
              If UPLO = 'U', the leading N-by-N upper triangular part of B
              contains the upper triangular part of the matrix B.
              If UPLO = 'L', the leading N-by-N lower triangular part of B
              contains the lower triangular part of the matrix B.
              On exit, if INFO <= N, the part of B containing the matrix is
              overwritten by the triangular factor U or L from the Cholesky
              factorization B = U**T*U or B = L*L**T.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= 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 (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 + 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:  DPOTRF or DSYEV returned an error code:
                 <= N:  if INFO = i, DSYEV failed to converge;
                        i off-diagonal elements of an intermediate
                        tridiagonal form did not converge to zero;
                 > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                        principal minor of order i of B is not positive.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

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

Definition at line 224 of file dsygv_2stage.f.

  subroutine ssygv_2stage (integer itype, character jobz, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( ldb, * ) b, integer ldb, real, dimension( * ) w, real, dimension( * ) work, integer lwork, integer info)

SSYGV_2STAGE

Purpose:

     SSYGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
     of a real generalized symmetric-definite eigenproblem, of the form
     A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
     Here A and B are assumed to be symmetric and B is also
     positive definite.
     This routine use the 2stage technique for the reduction to tridiagonal
     which showed higher performance on recent architecture and for large
     sizes N>2000.

Parameters
    ITYPE

              ITYPE is INTEGER
              Specifies the problem type to be solved:
              = 1:  A*x = (lambda)*B*x
              = 2:  A*B*x = (lambda)*x
              = 3:  B*A*x = (lambda)*x

    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 triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  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
              matrix Z of eigenvectors.  The eigenvectors are normalized
              as follows:
              if ITYPE = 1 or 2, Z**T*B*Z = I;
              if ITYPE = 3, Z**T*inv(B)*Z = I.
              If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
              or the lower triangle (if UPLO='L') of A, including the
              diagonal, is destroyed.

    LDA

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

    B

              B is REAL array, dimension (LDB, N)
              On entry, the symmetric positive definite matrix B.
              If UPLO = 'U', the leading N-by-N upper triangular part of B
              contains the upper triangular part of the matrix B.
              If UPLO = 'L', the leading N-by-N lower triangular part of B
              contains the lower triangular part of the matrix B.
              On exit, if INFO <= N, the part of B containing the matrix is
              overwritten by the triangular factor U or L from the Cholesky
              factorization B = U**T*U or B = L*L**T.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= max(1,N).

    W

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

    WORK

              WORK is REAL 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 + 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:  SPOTRF or SSYEV returned an error code:
                 <= N:  if INFO = i, SSYEV failed to converge;
                        i off-diagonal elements of an intermediate
                        tridiagonal form did not converge to zero;
                 > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                        principal minor of order i of B is not positive.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

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

Definition at line 224 of file ssygv_2stage.f.

  subroutine zhegv_2stage (integer itype, character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldb, * ) b, integer ldb, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)

ZHEGV_2STAGE

Purpose:

     ZHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
     of a complex generalized Hermitian-definite eigenproblem, of the form
     A*x=(lambda)*B*x,  A*Bx=(lambda)*x,  or B*A*x=(lambda)*x.
     Here A and B are assumed to be Hermitian and B is also
     positive definite.
     This routine use the 2stage technique for the reduction to tridiagonal
     which showed higher performance on recent architecture and for large
     sizes N>2000.

Parameters
    ITYPE

              ITYPE is INTEGER
              Specifies the problem type to be solved:
              = 1:  A*x = (lambda)*B*x
              = 2:  A*B*x = (lambda)*x
              = 3:  B*A*x = (lambda)*x

    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 triangles of A and B are stored;
              = 'L':  Lower triangles of A and B are stored.

    N

              N is INTEGER
              The order of the matrices A and B.  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
              matrix Z of eigenvectors.  The eigenvectors are normalized
              as follows:
              if ITYPE = 1 or 2, Z**H*B*Z = I;
              if ITYPE = 3, Z**H*inv(B)*Z = I.
              If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
              or the lower triangle (if UPLO='L') of A, including the
              diagonal, is destroyed.

    LDA

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

    B

              B is COMPLEX*16 array, dimension (LDB, N)
              On entry, the Hermitian positive definite matrix B.
              If UPLO = 'U', the leading N-by-N upper triangular part of B
              contains the upper triangular part of the matrix B.
              If UPLO = 'L', the leading N-by-N lower triangular part of B
              contains the lower triangular part of the matrix B.
              On exit, if INFO <= N, the part of B containing the matrix is
              overwritten by the triangular factor U or L from the Cholesky
              factorization B = U**H*U or B = L*L**H.

    LDB

              LDB is INTEGER
              The leading dimension of the array B.  LDB >= 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:  ZPOTRF or ZHEEV returned an error code:
                 <= N:  if INFO = i, ZHEEV failed to converge;
                        i off-diagonal elements of an intermediate
                        tridiagonal form did not converge to zero;
                 > N:   if INFO = N + i, for 1 <= i <= N, then the leading
                        principal minor of order i of B is not positive.
                        The factorization of B could not be completed and
                        no eigenvalues or eigenvectors were computed.

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

Definition at line 230 of file zhegv_2stage.f.

Author

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