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chbgvd-f(3)

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

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