Contents
chegv - 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 CHEGV(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LDWORK, WORK2, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER ITYPE, N, LDA, LDB, LDWORK, INFO
REAL W(*), WORK2(*)
SUBROUTINE CHEGV_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LDWORK, WORK2, INFO)
CHARACTER * 1 JOBZ, UPLO
COMPLEX A(LDA,*), B(LDB,*), WORK(*)
INTEGER*8 ITYPE, N, LDA, LDB, LDWORK, INFO
REAL W(*), WORK2(*)
F95 INTERFACE
SUBROUTINE HEGV(ITYPE, JOBZ, UPLO, N, A, [LDA], B, [LDB], W, [WORK],
[LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: ITYPE, N, LDA, LDB, LDWORK, INFO
REAL, DIMENSION(:) :: W, WORK2
SUBROUTINE HEGV_64(ITYPE, JOBZ, UPLO, N, A, [LDA], B, [LDB], W, [WORK],
[LDWORK], [WORK2], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
COMPLEX, DIMENSION(:) :: WORK
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: ITYPE, N, LDA, LDB, LDWORK, INFO
REAL, DIMENSION(:) :: W, WORK2
C INTERFACE
#include <sunperf.h>
void chegv(int itype, char jobz, char uplo, int n, complex
*a, int lda, complex *b, int ldb, float *w, int
*info);
void chegv_64(long itype, char jobz, char uplo, long n, com-
plex *a, long lda, complex *b, long ldb, float *w,
long *info);
chegv 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.
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 positive definite matrix
B. If UPLO = 'U', the leading N-by-N upper tri-
angular part of B contains 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
LDWORK.
LDWORK (input)
The length of the array WORK. LDWORK >=
max(1,2*N-1). For optimal efficiency, LDWORK >=
(NB+1)*N, where NB is the blocksize for CHETRD
returned by ILAENV.
If LDWORK = -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 LDWORK is issued by XERBLA.
WORK2 (workspace)
dimension(max(1,3*N-2))
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: CPOTRF or CHEEV returned an error code:
<= N: if INFO = i, CHEEV 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.