Contents
chegvd - compute all the eigenvalues, and optionally, the
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 CHEGVD(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER IWORK(*)
REAL W(*), RWORK(*)
SUBROUTINE CHEGVD_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER*8 IWORK(*)
REAL W(*), RWORK(*)
F95 INTERFACE
SUBROUTINE HEGVD(ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, [WORK],
[LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO
INTEGER, DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
SUBROUTINE HEGVD_64(ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W,
[WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK,
INFO
INTEGER(8), DIMENSION(:) :: IWORK
REAL, DIMENSION(:) :: W, RWORK
C INTERFACE
#include <sunperf.h>
void chegvd(int itype, char jobz, char uplo, int n, complex
*a, int lda, complex *b, int ldb, float *w, int
*info);
void chegvd_64(long itype, char jobz, char uplo, long n,
complex *a, long lda, complex *b, long ldb, float
*w, long *info);
chegvd computes all the eigenvalues, and optionally, the
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. If
eigenvectors are desired, it uses a divide and conquer algo-
rithm.
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.
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.
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 con-
tains the upper triangular 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, if JOBZ = 'V', then if INFO = 0, A con-
tains the matrix Z of eigenvectors. The eigenvec-
tors are normalized as follows: if ITYPE = 1 or
2, Z**H*B*Z = I; if ITYPE = 3, Z**H*inv(B)*Z = I.
If JOBZ = 'N', then on exit the upper triangle (if
UPLO='U') or the lower triangle (if UPLO='L') 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 con-
tains the upper triangular 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).
W (output)
If INFO = 0, the eigenvalues in ascending order.
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input)
The length of the array WORK. If N <= 1,
LWORK >= 1. If JOBZ = 'N' and N > 1, LWORK >= N
+ 1. If JOBZ = 'V' and N > 1, LWORK >= 2*N +
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 the 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 the array IWORK. If N <= 1,
LIWORK >= 1. If JOBZ = 'N' and N > 1, LIWORK >=
1. If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: CPOTRF or CHEEVD returned an error code:
<= N: if INFO = i, CHEEVD failed to converge; i
off-diagonal elements of an intermediate tridiago-
nal form did not converge to zero; > 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.
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky,
USA