
chpgvx.f(3) LAPACK chpgvx.f(3)
NAME
chpgvx.f 
SYNOPSIS
Functions/Subroutines
subroutine chpgvx (ITYPE, JOBZ, RANGE, UPLO, N, AP, BP, VL, VU, IL, IU, ABSTOL, M, W, Z,
LDZ, WORK, RWORK, IWORK, IFAIL, INFO)
CHPGST
Function/Subroutine Documentation
subroutine chpgvx (integerITYPE, characterJOBZ, characterRANGE, characterUPLO, integerN,
complex, dimension( * )AP, complex, dimension( * )BP, 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)
CHPGST
Purpose:
CHPGVX computes selected eigenvalues and, optionally, eigenvectors
of a complex generalized Hermitiandefinite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
B are assumed to be Hermitian, stored in packed format, and B is also
positive definite. Eigenvalues and eigenvectors can be selected by
specifying either a range of values or a range of indices for the
desired eigenvalues.
Parameters:
ITYPE
ITYPE is INTEGER
Specifies the problem type to be solved:
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
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 halfopen interval (VL,VU]
will be found;
= 'I': the ILth through IUth 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
N is INTEGER
The order of the matrices A and B. N >= 0.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
A, packed columnwise in a linear array. The jth column of A
is stored in the array AP as follows:
if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j1)*(2*nj)/2) = A(i,j) for j<=i<=n.
On exit, the contents of AP are destroyed.
BP
BP is COMPLEX array, dimension (N*(N+1)/2)
On entry, the upper or lower triangle of the Hermitian matrix
B, packed columnwise in a linear array. The jth column of B
is stored in the array BP as follows:
if UPLO = 'U', BP(i + (j1)*j/2) = B(i,j) for 1<=i<=j;
if UPLO = 'L', BP(i + (j1)*(2*nj)/2) = B(i,j) for j<=i<=n.
On exit, the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H, in the same storage
format as B.
VL
VL is REAL
VU
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
IL is INTEGER
IU
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 1norm 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
M is INTEGER
The total number of eigenvalues found. 0 <= M <= N.
If RANGE = 'A', M = N, and if RANGE = 'I', M = IUIL+1.
W
W is REAL array, dimension (N)
On normal exit, the first M elements contain the selected
eigenvalues in ascending order.
Z
Z is COMPLEX array, dimension (LDZ, N)
If JOBZ = 'N', then Z is not referenced.
If JOBZ = 'V', then if INFO = 0, the first M columns of Z
contain the orthonormal eigenvectors of the matrix A
corresponding to the selected eigenvalues, with the ith
column of Z holding the eigenvector associated with W(i).
The eigenvectors are normalized as follows:
if ITYPE = 1 or 2, Z**H*B*Z = I;
if ITYPE = 3, Z**H*inv(B)*Z = I.
If an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL.
Note: the user must ensure that at least max(1,M) columns are
supplied in the array Z; if RANGE = 'V', the exact value of M
is not known in advance and an upper bound must be used.
LDZ
LDZ is INTEGER
The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
WORK
WORK is COMPLEX array, dimension (2*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 ith argument had an illegal value
> 0: CPPTRF or CHPEVX returned an error code:
<= N: if INFO = i, CHPEVX failed to converge;
i eigenvectors failed to converge. Their indices
are stored in array IFAIL.
> N: if INFO = N + i, for 1 <= i <= n, then the leading
minor of order i of 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 267 of file chpgvx.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 chpgvx.f(3) 
