chbgvx-f(3)

chbgvx.f –

Synopsis

Functions/Subroutines

subroutine chbgvx (JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
CHBGST

Function/Subroutine Documentation

subroutine chbgvx (characterJOBZ, characterRANGE, characterUPLO, integerN, integerKA, integerKB, complex, dimension( ldab, * )AB, integerLDAB, complex, dimension( ldbb, * )BB, integerLDBB, complex, dimension( ldq, * )Q, integerLDQ, realVL, realVU, integerIL, integerIU, realABSTOL, integerM, real, dimension( * )W, complex, dimension( ldz, * )Z, integerLDZ, complex, dimension( * )WORK, real, dimension( * )RWORK, integer, dimension( * )IWORK, integer, dimension( * )IFAIL, integerINFO)

CHBGST

Purpose:

 CHBGVX 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. Eigenvalues and
 eigenvectors can be selected by specifying either all eigenvalues,
 a range of values or a range of indices for the desired eigenvalues.

Parameters:

JOBZ

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

RANGE

 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.

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.

 Q is COMPLEX array, dimension (LDQ, N)
 If JOBZ = 'V', the n-by-n matrix used in the reduction of
 A*x = (lambda)*B*x to standard form, i.e. C*x = (lambda)*x,
 and consequently C to tridiagonal form.
 If JOBZ = 'N', the array Q is not referenced.

LDQ

 LDQ is INTEGER
 The leading dimension of the array Q. If JOBZ = 'N',
 LDQ >= 1. If JOBZ = 'V', LDQ >= max(1,N).

 VL is REAL

 VU is REAL
 If RANGE='V', the lower and upper bounds of the interval to
 be searched for eigenvalues. VL < VU.
 Not referenced if RANGE = 'A' or 'I'.

 IL is INTEGER

 IU is INTEGER
 If RANGE='I', the indices (in ascending order) of the
 smallest and largest eigenvalues 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'.

ABSTOL

 ABSTOL is REAL
 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 AP to tridiagonal form.
 Eigenvalues will be computed most accurately when ABSTOL is
 set to twice the underflow threshold 2*SLAMCH('S'), not zero.
 If this routine returns with INFO>0, indicating that some
 eigenvectors did not converge, try setting ABSTOL to
 2*SLAMCH('S').

 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.

 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 (7*N)

IWORK

 IWORK is INTEGER array, dimension (5*N)

IFAIL

 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.

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: then i eigenvectors failed to converge. Their
 indices are stored in array IFAIL.
 > 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 290 of file chbgvx.f.

Author

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