chegvx - compute selected eigenvalues, and optionally, eigenvectors of a complex generalized Hermitian-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SUBROUTINE CHEGVX(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO COMPLEX A(LDA,*), B(LDB,*), Z(LDZ,*), WORK(*) INTEGER ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO INTEGER IWORK(*), IFAIL(*) REAL VL, VU, ABSTOL REAL W(*), RWORK(*) SUBROUTINE CHEGVX_64(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO) CHARACTER*1 JOBZ, RANGE, UPLO COMPLEX A(LDA,*), B(LDB,*), Z(LDZ,*), WORK(*) INTEGER*8 ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO INTEGER*8 IWORK(*), IFAIL(*) REAL VL, VU, ABSTOL REAL W(*), RWORK(*) F95 INTERFACE SUBROUTINE HEGVX(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B, Z INTEGER :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO INTEGER, DIMENSION(:) :: IWORK, IFAIL REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, RWORK SUBROUTINE HEGVX_64(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK, IFAIL, INFO) CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO COMPLEX, DIMENSION(:) :: WORK COMPLEX, DIMENSION(:,:) :: A, B, Z INTEGER(8) :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK, IFAIL REAL :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, RWORK C INTERFACE #include <sunperf.h> void chegvx(int itype, char jobz, char range, char uplo, int n, complex *a, int lda, complex *b, int ldb, float vl, float vu, int il, int iu, float abstol, int *m, float *w, complex *z, int ldz, int *ifail, int *info); void chegvx_64(long itype, char jobz, char range, char uplo, long n, complex *a, long lda, complex *b, long ldb, float vl, float vu, long il, long iu, float abstol, long *m, float *w, com- plex *z, long ldz, long *ifail, long *info);
Oracle Solaris Studio Performance Library chegvx(3P)
NAME
chegvx - compute selected eigenvalues, and optionally, eigenvectors of
a complex generalized Hermitian-definite eigenproblem, of the form
A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SYNOPSIS
SUBROUTINE CHEGVX(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL,
VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK,
IFAIL, INFO)
CHARACTER*1 JOBZ, RANGE, UPLO
COMPLEX A(LDA,*), B(LDB,*), Z(LDZ,*), WORK(*)
INTEGER ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL W(*), RWORK(*)
SUBROUTINE CHEGVX_64(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL,
VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK, IWORK,
IFAIL, INFO)
CHARACTER*1 JOBZ, RANGE, UPLO
COMPLEX A(LDA,*), B(LDB,*), Z(LDZ,*), WORK(*)
INTEGER*8 ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER*8 IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HEGVX(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
IWORK, IFAIL, INFO)
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B, Z
INTEGER :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER, DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, RWORK
SUBROUTINE HEGVX_64(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB,
VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, RWORK,
IWORK, IFAIL, INFO)
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B, Z
INTEGER(8) :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void chegvx(int itype, char jobz, char range, char uplo, int n, complex
*a, int lda, complex *b, int ldb, float vl, float vu, int il,
int iu, float abstol, int *m, float *w, complex *z, int ldz,
int *ifail, int *info);
void chegvx_64(long itype, char jobz, char range, char uplo, long n,
complex *a, long lda, complex *b, long ldb, float vl, float
vu, long il, long iu, float abstol, long *m, float *w, com-
plex *z, long ldz, long *ifail, long *info);
PURPOSE
chegvx computes selected eigenvalues, and optionally, eigenvectors of a
complex generalized Hermitian-definite 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 and B is also positive definite. Eigenval-
ues and eigenvectors can be selected by specifying either a range of
values or a range of indices for the desired eigenvalues.
ARGUMENTS
ITYPE (input)
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 (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
RANGE (input)
= '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 (input)
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
N (input) The order of the matrices A and B. N >= 0.
A (input/output)
On entry, the Hermitian matrix A. If UPLO = 'U', the leading
N-by-N upper triangular part of A contains the upper triangu-
lar part of the matrix A. If UPLO = 'L', the leading N-by-N
lower triangular part of A contains the lower triangular part
of the matrix A.
On exit, the lower triangle (if UPLO='L') or the upper tri-
angle (if UPLO='U') of A, including the diagonal, is
destroyed.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
B (input/output)
On entry, the Hermitian matrix B. If UPLO = 'U', the leading
N-by-N upper triangular part of B contains the upper triangu-
lar part of the matrix B. If UPLO = 'L', the leading N-by-N
lower triangular part of B contains the lower triangular part
of the matrix B.
On exit, if INFO <= N, the part of B containing the matrix is
overwritten by the triangular factor U or L from the Cholesky
factorization B = U**H*U or B = L*L**H.
LDB (input)
The leading dimension of the array B. LDB >= max(1,N).
VL (input)
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'.
VU (input)
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 (input)
If RANGE='I', the indices (in ascending order) of the small-
est 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'.
IU (input)
If RANGE='I', the indices (in ascending order) of the small-
est 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 (input)
The absolute error tolerance for the eigenvalues. An approx-
imate eigenvalue is accepted as converged when it is deter-
mined 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 A 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 (output)
The total number of eigenvalues found. 0 <= M <= N. If
RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output)
The first M elements contain the selected eigenvalues in
ascending order.
Z (output)
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 i-th column of Z holding the eigenvec-
tor associated with W(i). The eigenvectors are normalized as
follows: if ITYPE = 1 or 2, Z**T*B*Z = I; if ITYPE = 3,
Z**T*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 (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace/output)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The length of the array WORK. LWORK >= max(1,2*N). For
optimal efficiency, LWORK >= (NB+1)*N, where NB is the block-
size for CHETRD returned by ILAENV.
If LWORK = -1, then a workspace query is assumed; the routine
only calculates the optimal size of the WORK array, returns
this value as the first entry of the WORK array, and no error
message related to LWORK is issued by XERBLA.
RWORK (workspace)
dimension(7*N)
IWORK (workspace)
dimension(5*N)
IFAIL (output)
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 (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPOTRF or CHEEVX returned an error code:
<= N: if INFO = i, CHEEVX 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 factor-
ization of B could not be completed and no eigenvalues or
eigenvectors were computed.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
7 Nov 2015 chegvx(3P)