.TH "SRC/dsygv_2stage.f" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
SRC/dsygv_2stage.f
.SH SYNOPSIS
.br
.PP
.SS "Functions/Subroutines"

.in +1c
.ti -1c
.RI "subroutine \fBdsygv_2stage\fP (itype, jobz, uplo, n, a, lda, b, ldb, w, work, lwork, info)"
.br
.RI "\fBDSYGV_2STAGE\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "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)"

.PP
\fBDSYGV_2STAGE\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIITYPE\fP 
.PP
.nf
!>          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
!> 
.fi
.PP
.br
\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 triangles of A and B are stored;
!>          = 'L':  Lower triangles of A and B are stored\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrices A and B\&.  N >= 0\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIB\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDB\fP 
.PP
.nf
!>          LDB is INTEGER
!>          The leading dimension of the array B\&.  LDB >= 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 DOUBLE PRECISION 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 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\&.
!> 
.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:  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\&.
!> 
.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

.PP
Definition at line \fB224\fP of file \fBdsygv_2stage\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.