Contents
chbgvd - compute all the eigenvalues, and optionally, the
eigenvectors of a complex generalized Hermitian-definite
banded eigenproblem, of the form A*x=(lambda)*B*x
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);
chbgvd 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
digits, but we know of none.
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 Her-
mitian 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 Her-
mitian 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 fac-
torization 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 (input) 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 (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 >=
N. If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N +
2*N**2.
If LRWORK = -1, then a workspace query is assumed;
the routine 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 routine 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 ille-
gal 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.
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA