.TH "SRC/zheevx_2stage.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
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.SH NAME
SRC/zheevx_2stage.f
.SH SYNOPSIS
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.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBzheevx_2stage\fP (jobz, range, uplo, n, a, lda, vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, rwork, iwork, ifail, info)"
.br
.RI "\fB ZHEEVX_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 zheevx_2stage (character jobz, character range, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision vl, double precision vu, integer il, integer iu, double precision abstol, integer m, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)"

.PP
\fB ZHEEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices\fP  
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\fBPurpose:\fP
.RS 4

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!>
!> ZHEEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
!> of a complex Hermitian matrix A using the 2stage technique for
!> the reduction to tridiagonal\&.  Eigenvalues and eigenvectors can
!> be selected by specifying either a range of values or a range of
!> indices for the desired eigenvalues\&.
!> 
.fi
.PP
 
.RE
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\fBParameters\fP
.RS 4
\fIJOBZ\fP 
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.nf
!>          JOBZ is CHARACTER*1
!>          = 'N':  Compute eigenvalues only;
!>          = 'V':  Compute eigenvalues and eigenvectors\&.
!>                  Not available in this release\&.
!> 
.fi
.PP
.br
\fIRANGE\fP 
.PP
.nf
!>          RANGE is CHARACTER*1
!>          = 'A': all eigenvalues will be found\&.
!>          = 'V': all eigenvalues in the half-open interval (VL,VU]
!>                 will be found\&.
!>          = 'I': the IL-th through IU-th eigenvalues will be found\&.
!> 
.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
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.br
\fIN\fP 
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!>          N is INTEGER
!>          The order of the matrix A\&.  N >= 0\&.
!> 
.fi
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.br
\fIA\fP 
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!>          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, 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 
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.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIVL\fP 
.PP
.nf
!>          VL is DOUBLE PRECISION
!>          If RANGE='V', the lower bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIVU\fP 
.PP
.nf
!>          VU is DOUBLE PRECISION
!>          If RANGE='V', the upper bound of the interval to
!>          be searched for eigenvalues\&. VL < VU\&.
!>          Not referenced if RANGE = 'A' or 'I'\&.
!> 
.fi
.PP
.br
\fIIL\fP 
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.nf
!>          IL is INTEGER
!>          If RANGE='I', the index of the
!>          smallest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIIU\fP 
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!>          IU is INTEGER
!>          If RANGE='I', the index of the
!>          largest eigenvalue to be returned\&.
!>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0\&.
!>          Not referenced if RANGE = 'A' or 'V'\&.
!> 
.fi
.PP
.br
\fIABSTOL\fP 
.PP
.nf
!>          ABSTOL is DOUBLE PRECISION
!>          The absolute error tolerance for the eigenvalues\&.
!>          An approximate eigenvalue is accepted as converged
!>          when it is determined to lie in an interval [a,b]
!>          of width less than or equal to
!>
!>                  ABSTOL + EPS *   max( |a|,|b| ) ,
!>
!>          where EPS is the machine precision\&.  If ABSTOL is less than
!>          or equal to zero, then  EPS*|T|  will be used in its place,
!>          where |T| is the 1-norm of the tridiagonal matrix obtained
!>          by reducing A to tridiagonal form\&.
!>
!>          Eigenvalues will be computed most accurately when ABSTOL is
!>          set to twice the underflow threshold 2*DLAMCH('S'), not zero\&.
!>          If this routine returns with INFO>0, indicating that some
!>          eigenvectors did not converge, try setting ABSTOL to
!>          2*DLAMCH('S')\&.
!>
!>          See  by Demmel and
!>          Kahan, LAPACK Working Note #3\&.
!> 
.fi
.PP
.br
\fIM\fP 
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!>          M is INTEGER
!>          The total number of eigenvalues found\&.  0 <= M <= N\&.
!>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1\&.
!> 
.fi
.PP
.br
\fIW\fP 
.PP
.nf
!>          W is DOUBLE PRECISION array, dimension (N)
!>          On normal exit, the first M elements contain the selected
!>          eigenvalues in ascending order\&.
!> 
.fi
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.br
\fIZ\fP 
.PP
.nf
!>          Z is COMPLEX*16 array, dimension (LDZ, max(1,M))
!>          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
!>          contain the orthonormal eigenvectors of the matrix A
!>          corresponding to the selected eigenvalues, with the i-th
!>          column of Z holding the eigenvector associated with W(i)\&.
!>          If an eigenvector fails to converge, then that column of Z
!>          contains the latest approximation to the eigenvector, and the
!>          index of the eigenvector is returned in IFAIL\&.
!>          If JOBZ = 'N', then Z is not referenced\&.
!>          Note: the user must ensure that at least max(1,M) columns are
!>          supplied in the array Z; if RANGE = 'V', the exact value of M
!>          is not known in advance and an upper bound must be used\&.
!> 
.fi
.PP
.br
\fILDZ\fP 
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.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 
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.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
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.br
\fILWORK\fP 
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.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, 8*N, 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\&.
!> 
.fi
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.br
\fIRWORK\fP 
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!>          RWORK is DOUBLE PRECISION array, dimension (7*N)
!> 
.fi
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.br
\fIIWORK\fP 
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!>          IWORK is INTEGER array, dimension (5*N)
!> 
.fi
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.br
\fIIFAIL\fP 
.PP
.nf
!>          IFAIL is INTEGER array, dimension (N)
!>          If JOBZ = 'V', then if INFO = 0, the first M elements of
!>          IFAIL are zero\&.  If INFO > 0, then IFAIL contains the
!>          indices of the eigenvectors that failed to converge\&.
!>          If JOBZ = 'N', then IFAIL is not referenced\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
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!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  if INFO = i, then i eigenvectors failed to converge\&.
!>                Their indices are stored in array IFAIL\&.
!> 
.fi
.PP
 
.RE
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\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

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Univ\&. of California Berkeley 

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Univ\&. of Colorado Denver 

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NAG Ltd\&. 
.RE
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\fBFurther Details:\fP
.RS 4

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.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 \fB303\fP of file \fBzheevx_2stage\&.f\fP\&.
.SH "Author"
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Generated automatically by Doxygen for LAPACK from the source code\&.