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

.in +1c
.ti -1c
.RI "subroutine \fBzhbgvd\fP (jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, lwork, rwork, lrwork, iwork, liwork, info)"
.br
.RI "\fBZHBGVD\fP "
.in -1c
.SH "Function/Subroutine Documentation"
.PP 
.SS "subroutine zhbgvd (character jobz, character uplo, integer n, integer ka, integer kb, complex*16, dimension( ldab, * ) ab, integer ldab, complex*16, dimension( ldbb, * ) bb, integer ldbb, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer lrwork, integer, dimension( * ) iwork, integer liwork, integer info)"

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

.PP
.nf
!>
!> ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors
!> of a complex generalized Hermitian-definite banded eigenproblem, of
!> the form A*x=(lambda)*B*x\&. Here A and B are assumed to be Hermitian
!> and banded, and B is also positive definite\&.  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\&.
!> 
.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
\fIKA\fP 
.PP
.nf
!>          KA is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&. KA >= 0\&.
!> 
.fi
.PP
.br
\fIKB\fP 
.PP
.nf
!>          KB is INTEGER
!>          The number of superdiagonals of the matrix B if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'\&. KB >= 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 ka+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(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+ka)\&.
!>
!>          On exit, the contents of AB are destroyed\&.
!> 
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
!>          LDAB is INTEGER
!>          The leading dimension of the array AB\&.  LDAB >= KA+1\&.
!> 
.fi
.PP
.br
\fIBB\fP 
.PP
.nf
!>          BB is COMPLEX*16 array, dimension (LDBB, N)
!>          On entry, the upper or lower triangle of the Hermitian band
!>          matrix B, stored in the first kb+1 rows of the array\&.  The
!>          j-th column of B is stored in the j-th column of the array BB
!>          as follows:
!>          if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
!>          if UPLO = 'L', BB(1+i-j,j)    = B(i,j) for j<=i<=min(n,j+kb)\&.
!>
!>          On exit, the factor S from the split Cholesky factorization
!>          B = S**H*S, as returned by ZPBSTF\&.
!> 
.fi
.PP
.br
\fILDBB\fP 
.PP
.nf
!>          LDBB is INTEGER
!>          The leading dimension of the array BB\&.  LDBB >= KB+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 matrix Z of
!>          eigenvectors, with the i-th column of Z holding the
!>          eigenvector associated with W(i)\&. The eigenvectors are
!>          normalized so that Z**H*B*Z = 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 >= N\&.
!> 
.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 >= 1\&.
!>          If JOBZ = 'N' and N > 1, LWORK >= N\&.
!>          If JOBZ = 'V' and N > 1, LWORK >= 2*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 (MAX(1,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 array RWORK\&.
!>          If N <= 1,               LRWORK >= 1\&.
!>          If JOBZ = 'N' and N > 1, LRWORK >= N\&.
!>          If JOBZ = 'V' and N > 1, LRWORK >= 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 array IWORK\&.
!>          If JOBZ = 'N' or N <= 1, LIWORK >= 1\&.
!>          If JOBZ = 'V' and N > 1, LIWORK >= 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 i is:
!>             <= N:  the algorithm 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 ZPBSTF
!>                    returned INFO = i: B is not positive definite\&.
!>                    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 \fB243\fP of file \fBzhbgvd\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.