.TH "hbev_2stage" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
hbev_2stage \- {hb,sb}ev_2stage: eig, QR iteration
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBchbev_2stage\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)"
.br
.RI "\fB CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBdsbev_2stage\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, info)"
.br
.RI "\fB DSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBssbev_2stage\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, info)"
.br
.RI "\fB SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.ti -1c
.RI "subroutine \fBzhbev_2stage\fP (jobz, uplo, n, kd, ab, ldab, w, z, ldz, work, lwork, rwork, info)"
.br
.RI "\fB ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "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)"

.PP
\fB CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors\&.
                  Not available in this release\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
          LDZ is INTEGER
          The leading dimension of the array Z\&.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension LWORK
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is REAL array, dimension (max(1,3*N-2))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SS "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)"

.PP
\fB DSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors\&.
                  Not available in this release\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
          LDZ is INTEGER
          The leading dimension of the array Z\&.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension LWORK
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SS "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)"

.PP
\fB SSBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors\&.
                  Not available in this release\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is REAL array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
          LDZ is INTEGER
          The leading dimension of the array Z\&.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension LWORK
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SS "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)"

.PP
\fB ZHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIJOBZ\fP 
.PP
.nf
          JOBZ is CHARACTER*1
          = 'N':  Compute eigenvalues only;
          = 'V':  Compute eigenvalues and eigenvectors\&.
                  Not available in this release\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIKD\fP 
.PP
.nf
          KD is INTEGER
          The number of superdiagonals of the matrix A if UPLO = 'U',
          or the number of subdiagonals if UPLO = 'L'\&.  KD >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= KD + 1\&.
.fi
.PP
.br
\fIW\fP 
.PP
.nf
          W is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order\&.
.fi
.PP
.br
\fIZ\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fILDZ\fP 
.PP
.nf
          LDZ is INTEGER
          The leading dimension of the array Z\&.  LDZ >= 1, and if
          JOBZ = 'V', LDZ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension LWORK
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          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\&.
.fi
.PP
.br
\fIRWORK\fP 
.PP
.nf
          RWORK is DOUBLE PRECISION array, dimension (max(1,3*N-2))
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          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\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
  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
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.