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chbgvd.f(3)				      LAPACK				      chbgvd.f(3)

NAME
       chbgvd.f -

SYNOPSIS
   Functions/Subroutines
       subroutine chbgvd (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, LWORK,
	   RWORK, LRWORK, IWORK, LIWORK, INFO)
	   CHBGST

Function/Subroutine Documentation
   subroutine chbgvd (characterJOBZ, characterUPLO, integerN, integerKA, integerKB, complex,
       dimension( ldab, * )AB, integerLDAB, complex, dimension( ldbb, * )BB, integerLDBB, real,
       dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK,
       integerLWORK, real, dimension( * )RWORK, integerLRWORK, integer, dimension( * )IWORK,
       integerLIWORK, integerINFO)
       CHBGST

       Purpose:

	    CHBGVD 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.

	    The divide and conquer algorithm makes very mild assumptions about
	    floating point arithmetic. It will work on machines with a guard
	    digit in add/subtract, or on those binary machines without guard
	    digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
	    Cray-2. It could conceivably fail on hexadecimal or decimal machines
	    without guard digits, but we know of none.

       Parameters:
	   JOBZ

		     JOBZ is CHARACTER*1
		     = 'N':  Compute eigenvalues only;
		     = 'V':  Compute eigenvalues and eigenvectors.

	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangles of A and B are stored;
		     = 'L':  Lower triangles of A and B are stored.

	   N

		     N is INTEGER
		     The order of the matrices A and B.  N >= 0.

	   KA

		     KA is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'. KA >= 0.

	   KB

		     KB is INTEGER
		     The number of superdiagonals of the matrix B if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'. KB >= 0.

	   AB

		     AB is COMPLEX 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.

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KA+1.

	   BB

		     BB is COMPLEX 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 CPBSTF.

	   LDBB

		     LDBB is INTEGER
		     The leading dimension of the array BB.  LDBB >= KB+1.

	   W

		     W is REAL array, dimension (N)
		     If INFO = 0, the eigenvalues in ascending order.

	   Z

		     Z is COMPLEX 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.

	   LDZ

		     LDZ is INTEGER
		     The leading dimension of the array Z.  LDZ >= 1, and if
		     JOBZ = 'V', LDZ >= N.

	   WORK

		     WORK is COMPLEX array, dimension (MAX(1,LWORK))
		     On exit, if INFO=0, WORK(1) returns the optimal LWORK.

	   LWORK

		     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.

	   RWORK

		     RWORK is REAL array, dimension (MAX(1,LRWORK))
		     On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.

	   LRWORK

		     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.

	   IWORK

		     IWORK is INTEGER array, dimension (MAX(1,LIWORK))
		     On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.

	   LIWORK

		     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.

	   INFO

		     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 CPBSTF
			       returned INFO = i: B is not positive definite.
			       The factorization of B could not be completed and
			       no eigenvalues or eigenvectors were computed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Contributors:
	   Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

       Definition at line 251 of file chbgvd.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			      chbgvd.f(3)
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