.TH "SRC/zheevd_2stage.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/zheevd_2stage.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzheevd_2stage\fP (jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork, iwork, liwork, info)"
.br
.RI "\fB ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zheevd_2stage (character jobz, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) w, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)"

.PP
\fB ZHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP  
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\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
!> complex Hermitian matrix A using the 2stage technique for
!> the reduction to tridiagonal\&.  If eigenvectors are desired, it uses a
!> divide and conquer algorithm\&.
!>
!> 
.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 
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.nf
!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          A is COMPLEX*16 array, dimension (LDA, N)
!>          On entry, the Hermitian matrix A\&.  If UPLO = 'U', the
!>          leading N-by-N upper triangular part of A contains the
!>          upper triangular part of the matrix A\&.  If UPLO = 'L',
!>          the leading N-by-N lower triangular part of A contains
!>          the lower triangular part of the matrix A\&.
!>          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
!>          orthonormal eigenvectors of the matrix A\&.
!>          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
!>          or the upper triangle (if UPLO='U') of A, including the
!>          diagonal, is destroyed\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.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
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>          The dimension of the array WORK\&.
!>          If N <= 1,               LWORK must be at least 1\&.
!>          If JOBZ = 'N' and N > 1, LWORK must be queried\&.
!>                                   LWORK = MAX(1, dimension) where
!>                                   dimension = max(stage1,stage2) + (KD+1)*N + N+1
!>                                             = N*KD + N*max(KD+1,FACTOPTNB)
!>                                               + max(2*KD*KD, KD*NTHREADS)
!>                                               + (KD+1)*N + N+1
!>                                   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 at least 2*N + N**2
!>
!>          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 (LRWORK)
!>          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK\&.
!> 
.fi
.PP
.br
\fILRWORK\fP 
.PP
.nf
!>          LRWORK is INTEGER
!>          The dimension of the array RWORK\&.
!>          If N <= 1,                LRWORK must be at least 1\&.
!>          If JOBZ  = 'N' and N > 1, LRWORK must be at least N\&.
!>          If JOBZ  = 'V' and N > 1, LRWORK must be at least
!>                         1 + 5*N + 2*N**2\&.
!>
!>          If LRWORK = -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
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK\&.
!> 
.fi
.PP
.br
\fILIWORK\fP 
.PP
.nf
!>          LIWORK is INTEGER
!>          The dimension of the array IWORK\&.
!>          If N <= 1,                LIWORK must be at least 1\&.
!>          If JOBZ  = 'N' and N > 1, LIWORK must be at least 1\&.
!>          If JOBZ  = 'V' and N > 1, LIWORK must be at least 3 + 5*N\&.
!>
!>          If LIWORK = -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
\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 and JOBZ = 'N', then the algorithm failed
!>                to converge; i off-diagonal elements of an intermediate
!>                tridiagonal form did not converge to zero;
!>                if INFO = i and JOBZ = 'V', then the algorithm failed
!>                to compute an eigenvalue while working on the submatrix
!>                lying in rows and columns INFO/(N+1) through
!>                mod(INFO,N+1)\&.
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4
Modified description of INFO\&. Sven, 16 Feb 05\&. 
.RE
.PP
\fBContributors:\fP
.RS 4
Jeff Rutter, Computer Science Division, University of California at Berkeley, USA
.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
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Definition at line \fB245\fP of file \fBzheevd_2stage\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.