chbgvd(3P) Sun Performance Library chbgvd(3P)NAMEchbgvd - compute all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of the
form A*x=(lambda)*B*x
SYNOPSIS
SUBROUTINE CHBGVD(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
INTEGER N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL W(*), RWORK(*)
SUBROUTINE CHBGVD_64(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX AB(LDAB,*), BB(LDBB,*), Z(LDZ,*), WORK(*)
INTEGER*8 N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HBGVD(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB], W,
Z, [LDZ], [WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK],
[INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, Z
INTEGER :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
SUBROUTINE HBGVD_64(JOBZ, UPLO, [N], KA, KB, AB, [LDAB], BB, [LDBB],
W, Z, [LDZ], [WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK],
[INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: AB, BB, Z
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDZ, LWORK, LRWORK, LIWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void chbgvd(char jobz, char uplo, int n, int ka, int kb, complex *ab,
int ldab, complex *bb, int ldbb, float *w, complex *z, int
ldz, int *info);
void chbgvd_64(char jobz, char uplo, long n, long ka, long kb, complex
*ab, long ldab, complex *bb, long ldbb, float *w, complex *z,
long ldz, long *info);
PURPOSEchbgvd 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 dig‐
its, but we know of none.
ARGUMENTS
JOBZ (input)
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
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.
KA (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input)
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
AB (input/output)
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 (input)
The leading dimension of the array AB. LDAB >= KA+1.
BB (input/output)
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 (input)
The leading dimension of the array BB. LDBB >= KB+1.
W (output)
If INFO = 0, the eigenvalues in ascending order.
Z (output)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the eigenvec‐
tor associated with W(i). The eigenvectors are normalized so
that Z**H*B*Z = I. If JOBZ = 'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= N.
WORK (workspace)
On exit, if INFO=0, WORK(1) returns the optimal LWORK.
LWORK (input)
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 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)
On exit, if INFO=0, RWORK(1) returns the optimal LRWORK.
LRWORK (input)
The dimension of array RWORK. If N <= 1,
LRWORK >= 1. If JOBZ = 'N' and N > 1, LRWORK >= 2*N. If
JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
If LRWORK = -1, then a workspace query is assumed; the rou‐
tine only calculates the optimal size of the RWORK array,
returns this value as the first entry of the RWORK array, and
no error message related to LRWORK is issued by XERBLA.
IWORK (workspace/output)
On exit, if INFO=0, IWORK(1) returns the optimal LIWORK.
LIWORK (input)
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 rou‐
tine only calculates the optimal size of the IWORK array,
returns this value as the first entry of the IWORK array, and
no error message related to LIWORK is issued by XERBLA.
INFO (output)
= 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 ele‐
ments 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 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
23 Apr 2009 chbgvd(3P)
