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

.in +1c
.ti -1c
.RI "subroutine \fBdsygvx\fP (itype, jobz, range, uplo, n, a, lda, b, ldb, vl, vu, il, iu, abstol, m, w, z, ldz, work, lwork, iwork, ifail, info)"
.br
.RI "\fBDSYGVX\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine dsygvx (integer itype, character jobz, character range, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( ldb, * ) b, integer ldb, double precision vl, double precision vu, integer il, integer iu, double precision abstol, integer m, double precision, dimension( * ) w, double precision, dimension( ldz, * ) z, integer ldz, double precision, dimension( * ) work, integer lwork, integer, dimension( * ) iwork, integer, dimension( * ) ifail, integer info)"

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

.PP
.nf
!>
!> DSYGVX computes selected eigenvalues, and optionally, 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\&.
!> 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
.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\&.
!> 
.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 and B are stored;
!>          = 'L':  Lower triangle of A and B are stored\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix pencil (A,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, 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
\fIB\fP 
.PP
.nf
!>          B is DOUBLE PRECISION array, dimension (LDB, N)
!>          On entry, the symmetric 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
\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 
.PP
.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 
.PP
.nf
!>          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 C to tridiagonal form, where C is the symmetric
!>          matrix of the standard symmetric problem to which the
!>          generalized problem is transformed\&.
!>
!>          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')\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          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
.PP
.br
\fIZ\fP 
.PP
.nf
!>          Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M))
!>          If JOBZ = 'N', then Z is not referenced\&.
!>          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)\&.
!>          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 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\&.
!>          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 
.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 (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 >= max(1,8*N)\&.
!>          For optimal efficiency, LWORK >= (NB+3)*N,
!>          where NB is the blocksize for DSYTRD returned by ILAENV\&.
!>
!>          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
\fIIWORK\fP 
.PP
.nf
!>          IWORK is INTEGER array, dimension (5*N)
!> 
.fi
.PP
.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 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>          > 0:  DPOTRF or DSYEVX returned an error code:
!>             <= N:  if INFO = i, DSYEVX failed to converge;
!>                    i eigenvectors failed to converge\&.  Their indices
!>                    are stored in array IFAIL\&.
!>             > 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
\fBContributors:\fP
.RS 4
Mark Fahey, Department of Mathematics, Univ\&. of Kentucky, USA 
.RE
.PP

.PP
Definition at line \fB294\fP of file \fBdsygvx\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.