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hetrd_2stage(3) Library Functions Manual hetrd_2stage(3)

NAME

hetrd_2stage - {he,sy}trd_2stage: reduction to tridiagonal, 2-stage

SYNOPSIS

Functions


subroutine CHETRD_2STAGE (vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
CHETRD_2STAGE subroutine DSYTRD_2STAGE (vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
DSYTRD_2STAGE subroutine SSYTRD_2STAGE (vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
SSYTRD_2STAGE subroutine ZHETRD_2STAGE (vect, uplo, n, a, lda, d, e, tau, hous2, lhous2, work, lwork, info)
ZHETRD_2STAGE

Detailed Description

Function Documentation

subroutine CHETRD_2STAGE (character vect, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( * ) tau, complex, dimension( * ) hous2, integer lhous2, complex, dimension( * ) work, integer lwork, integer info)

CHETRD_2STAGE

Purpose:

!>
!> CHETRD_2STAGE reduces a complex Hermitian matrix A to real symmetric
!> tridiagonal form T by a unitary similarity transformation:
!> Q1**H Q2**H* A * Q2 * Q1 = T.
!>

Parameters

VECT 

!>          VECT is CHARACTER*1
!>          = 'N':  No need for the Housholder representation,
!>                  in particular for the second stage (Band to
!>                  tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
!>          = 'V':  the Householder representation is needed to
!>                  either generate Q1 Q2 or to apply Q1 Q2,
!>                  then LHOUS2 is to be queried and computed.
!>                  (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, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>          On exit, if UPLO = 'U', the band superdiagonal
!>          of A are overwritten by the corresponding elements of the
!>          internal band-diagonal matrix AB, and the elements above
!>          the KD superdiagonal, with the array TAU, represent the unitary
!>          matrix Q1 as a product of elementary reflectors; if UPLO
!>          = 'L', the diagonal and band subdiagonal of A are over-
!>          written by the corresponding elements of the internal band-diagonal
!>          matrix AB, and the elements below the KD subdiagonal, with
!>          the array TAU, represent the unitary matrix Q1 as a product
!>          of elementary reflectors. See Further Details.
!>

LDA

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

D

!>          D is REAL array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T.
!>

E

!>          E is REAL array, dimension (N-1)
!>          The off-diagonal elements of the tridiagonal matrix T.
!>

TAU

!>          TAU is COMPLEX array, dimension (N-KD)
!>          The scalar factors of the elementary reflectors of
!>          the first stage (see Further Details).
!>

HOUS2

!>          HOUS2 is COMPLEX array, dimension (LHOUS2)
!>          Stores the Householder representation of the stage2
!>          band to tridiagonal.
!>

LHOUS2

!>          LHOUS2 is INTEGER
!>          The dimension of the array HOUS2.
!>          If LWORK = -1, or LHOUS2=-1,
!>          then a query is assumed; the routine
!>          only calculates the optimal size of the HOUS2 array, returns
!>          this value as the first entry of the HOUS2 array, and no error
!>          message related to LHOUS2 is issued by XERBLA.
!>          If VECT='N', LHOUS2 = max(1, 4*n);
!>          if VECT='V', option not yet available.
!>

WORK

!>          WORK is COMPLEX array, dimension (LWORK)
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK = MAX(1, dimension)
!>          If LWORK = -1, or LHOUS2 = -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.
!>          LWORK = MAX(1, dimension) where
!>          dimension   = max(stage1,stage2) + (KD+1)*N
!>                      = N*KD + N*max(KD+1,FACTOPTNB)
!>                        + max(2*KD*KD, KD*NTHREADS)
!>                        + (KD+1)*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.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Implemented by Azzam Haidar.
!>
!>  All details are available on technical report, SC11, SC13 papers.
!>
!>  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 222 of file chetrd_2stage.f.

subroutine DSYTRD_2STAGE (character vect, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( * ) tau, double precision, dimension( * ) hous2, integer lhous2, double precision, dimension( * ) work, integer lwork, integer info)

DSYTRD_2STAGE

Purpose:

!>
!> DSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric
!> tridiagonal form T by a orthogonal similarity transformation:
!> Q1**T Q2**T* A * Q2 * Q1 = T.
!>

Parameters

VECT 

!>          VECT is CHARACTER*1
!>          = 'N':  No need for the Housholder representation,
!>                  in particular for the second stage (Band to
!>                  tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
!>          = 'V':  the Householder representation is needed to
!>                  either generate Q1 Q2 or to apply Q1 Q2,
!>                  then LHOUS2 is to be queried and computed.
!>                  (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, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>          On exit, if UPLO = 'U', the band superdiagonal
!>          of A are overwritten by the corresponding elements of the
!>          internal band-diagonal matrix AB, and the elements above
!>          the KD superdiagonal, with the array TAU, represent the orthogonal
!>          matrix Q1 as a product of elementary reflectors; if UPLO
!>          = 'L', the diagonal and band subdiagonal of A are over-
!>          written by the corresponding elements of the internal band-diagonal
!>          matrix AB, and the elements below the KD subdiagonal, with
!>          the array TAU, represent the orthogonal matrix Q1 as a product
!>          of elementary reflectors. See Further Details.
!>

LDA

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

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T.
!>

E

!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The off-diagonal elements of the tridiagonal matrix T.
!>

TAU

!>          TAU is DOUBLE PRECISION array, dimension (N-KD)
!>          The scalar factors of the elementary reflectors of
!>          the first stage (see Further Details).
!>

HOUS2

!>          HOUS2 is DOUBLE PRECISION array, dimension (LHOUS2)
!>          Stores the Householder representation of the stage2
!>          band to tridiagonal.
!>

LHOUS2

!>          LHOUS2 is INTEGER
!>          The dimension of the array HOUS2.
!>          If LWORK = -1, or LHOUS2 = -1,
!>          then a query is assumed; the routine
!>          only calculates the optimal size of the HOUS2 array, returns
!>          this value as the first entry of the HOUS2 array, and no error
!>          message related to LHOUS2 is issued by XERBLA.
!>          If VECT='N', LHOUS2 = max(1, 4*n);
!>          if VECT='V', option not yet available.
!>

WORK

!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK = MAX(1, dimension)
!>          If LWORK = -1, or LHOUS2=-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.
!>          LWORK = MAX(1, dimension) where
!>          dimension   = max(stage1,stage2) + (KD+1)*N
!>                      = N*KD + N*max(KD+1,FACTOPTNB)
!>                        + max(2*KD*KD, KD*NTHREADS)
!>                        + (KD+1)*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.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Implemented by Azzam Haidar.
!>
!>  All details are available on technical report, SC11, SC13 papers.
!>
!>  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 222 of file dsytrd_2stage.f.

subroutine SSYTRD_2STAGE (character vect, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) d, real, dimension( * ) e, real, dimension( * ) tau, real, dimension( * ) hous2, integer lhous2, real, dimension( * ) work, integer lwork, integer info)

SSYTRD_2STAGE

Purpose:

!>
!> SSYTRD_2STAGE reduces a real symmetric matrix A to real symmetric
!> tridiagonal form T by a orthogonal similarity transformation:
!> Q1**T Q2**T* A * Q2 * Q1 = T.
!>

Parameters

VECT 

!>          VECT is CHARACTER*1
!>          = 'N':  No need for the Housholder representation,
!>                  in particular for the second stage (Band to
!>                  tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
!>          = 'V':  the Householder representation is needed to
!>                  either generate Q1 Q2 or to apply Q1 Q2,
!>                  then LHOUS2 is to be queried and computed.
!>                  (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, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>          On exit, if UPLO = 'U', the band superdiagonal
!>          of A are overwritten by the corresponding elements of the
!>          internal band-diagonal matrix AB, and the elements above
!>          the KD superdiagonal, with the array TAU, represent the orthogonal
!>          matrix Q1 as a product of elementary reflectors; if UPLO
!>          = 'L', the diagonal and band subdiagonal of A are over-
!>          written by the corresponding elements of the internal band-diagonal
!>          matrix AB, and the elements below the KD subdiagonal, with
!>          the array TAU, represent the orthogonal matrix Q1 as a product
!>          of elementary reflectors. See Further Details.
!>

LDA

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

D

!>          D is REAL array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T.
!>

E

!>          E is REAL array, dimension (N-1)
!>          The off-diagonal elements of the tridiagonal matrix T.
!>

TAU

!>          TAU is REAL array, dimension (N-KD)
!>          The scalar factors of the elementary reflectors of
!>          the first stage (see Further Details).
!>

HOUS2

!>          HOUS2 is REAL array, dimension (LHOUS2)
!>          Stores the Householder representation of the stage2
!>          band to tridiagonal.
!>

LHOUS2

!>          LHOUS2 is INTEGER
!>          The dimension of the array HOUS2.
!>          If LWORK = -1, or LHOUS2 = -1,
!>          then a query is assumed; the routine
!>          only calculates the optimal size of the HOUS2 array, returns
!>          this value as the first entry of the HOUS2 array, and no error
!>          message related to LHOUS2 is issued by XERBLA.
!>          If VECT='N', LHOUS2 = max(1, 4*n);
!>          if VECT='V', option not yet available.
!>

WORK

!>          WORK is REAL array, dimension (LWORK)
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK = MAX(1, dimension)
!>          If LWORK = -1, or LHOUS2=-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.
!>          LWORK = MAX(1, dimension) where
!>          dimension   = max(stage1,stage2) + (KD+1)*N
!>                      = N*KD + N*max(KD+1,FACTOPTNB)
!>                        + max(2*KD*KD, KD*NTHREADS)
!>                        + (KD+1)*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.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Implemented by Azzam Haidar.
!>
!>  All details are available on technical report, SC11, SC13 papers.
!>
!>  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 222 of file ssytrd_2stage.f.

subroutine ZHETRD_2STAGE (character vect, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( * ) tau, complex*16, dimension( * ) hous2, integer lhous2, complex*16, dimension( * ) work, integer lwork, integer info)

ZHETRD_2STAGE

Purpose:

!>
!> ZHETRD_2STAGE reduces a complex Hermitian matrix A to real symmetric
!> tridiagonal form T by a unitary similarity transformation:
!> Q1**H Q2**H* A * Q2 * Q1 = T.
!>

Parameters

VECT 

!>          VECT is CHARACTER*1
!>          = 'N':  No need for the Housholder representation,
!>                  in particular for the second stage (Band to
!>                  tridiagonal) and thus LHOUS2 is of size max(1, 4*N);
!>          = 'V':  the Householder representation is needed to
!>                  either generate Q1 Q2 or to apply Q1 Q2,
!>                  then LHOUS2 is to be queried and computed.
!>                  (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, and the strictly lower
!>          triangular part of A is not referenced.  If UPLO = 'L', the
!>          leading N-by-N lower triangular part of A contains the lower
!>          triangular part of the matrix A, and the strictly upper
!>          triangular part of A is not referenced.
!>          On exit, if UPLO = 'U', the band superdiagonal
!>          of A are overwritten by the corresponding elements of the
!>          internal band-diagonal matrix AB, and the elements above
!>          the KD superdiagonal, with the array TAU, represent the unitary
!>          matrix Q1 as a product of elementary reflectors; if UPLO
!>          = 'L', the diagonal and band subdiagonal of A are over-
!>          written by the corresponding elements of the internal band-diagonal
!>          matrix AB, and the elements below the KD subdiagonal, with
!>          the array TAU, represent the unitary matrix Q1 as a product
!>          of elementary reflectors. See Further Details.
!>

LDA

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

D

!>          D is DOUBLE PRECISION array, dimension (N)
!>          The diagonal elements of the tridiagonal matrix T.
!>

E

!>          E is DOUBLE PRECISION array, dimension (N-1)
!>          The off-diagonal elements of the tridiagonal matrix T.
!>

TAU

!>          TAU is COMPLEX*16 array, dimension (N-KD)
!>          The scalar factors of the elementary reflectors of
!>          the first stage (see Further Details).
!>

HOUS2

!>          HOUS2 is COMPLEX*16 array, dimension (LHOUS2)
!>          Stores the Householder representation of the stage2
!>          band to tridiagonal.
!>

LHOUS2

!>          LHOUS2 is INTEGER
!>          The dimension of the array HOUS2.
!>          If LWORK = -1, or LHOUS2 = -1,
!>          then a query is assumed; the routine
!>          only calculates the optimal size of the HOUS2 array, returns
!>          this value as the first entry of the HOUS2 array, and no error
!>          message related to LHOUS2 is issued by XERBLA.
!>          If VECT='N', LHOUS2 = max(1, 4*n);
!>          if VECT='V', option not yet available.
!>

WORK

!>          WORK is COMPLEX*16 array, dimension (LWORK)
!>

LWORK

!>          LWORK is INTEGER
!>          The dimension of the array WORK. LWORK = MAX(1, dimension)
!>          If LWORK = -1, or LHOUS2=-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.
!>          LWORK = MAX(1, dimension) where
!>          dimension   = max(stage1,stage2) + (KD+1)*N
!>                      = N*KD + N*max(KD+1,FACTOPTNB)
!>                        + max(2*KD*KD, KD*NTHREADS)
!>                        + (KD+1)*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.
!>

INFO

!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details:

!>
!>  Implemented by Azzam Haidar.
!>
!>  All details are available on technical report, SC11, SC13 papers.
!>
!>  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,
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Definition at line 222 of file zhetrd_2stage.f.

Author

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