chbgv-f(3)

chbgv.f –

Synopsis

Functions/Subroutines

subroutine chbgv (JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, RWORK, INFO)
CHBGST

Function/Subroutine Documentation

subroutine chbgv (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, real, dimension( * )RWORK, integerINFO)

CHBGST

Purpose:

 CHBGV 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.

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

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

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

 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 (N)

RWORK

 RWORK is REAL array, dimension (3*N)

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

Definition at line 183 of file chbgv.f.

Author

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