zhegvd - 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 ZHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, UPLO DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE ZHEGVD_64( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, * LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, UPLO DOUBLE COMPLEX A(LDA,*), B(LDB,*), WORK(*) INTEGER*8 ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION W(*), RWORK(*)
SUBROUTINE HEGVD( ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, * [WORK], [LWORK], [RWORK], [LRWORK], [IWORK], [LIWORK], [INFO]) CHARACTER(LEN=1) :: JOBZ, UPLO COMPLEX(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER :: ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), 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(8), DIMENSION(:) :: WORK COMPLEX(8), DIMENSION(:,:) :: A, B INTEGER(8) :: ITYPE, N, LDA, LDB, LWORK, LRWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, RWORK
#include <sunperf.h>
void zhegvd(int itype, char jobz, char uplo, int n, doublecomplex *a, int lda, doublecomplex *b, int ldb, double *w, int *info);
void zhegvd_64(long itype, char jobz, char uplo, long n, doublecomplex *a, long lda, doublecomplex *b, long ldb, double *w, long *info);
zhegvd 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 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.
= 1: A*x = (lambda)*B*x
= 2: A*B*x = (lambda)*x
= 3: B*A*x = (lambda)*x
= 'N': Compute eigenvalues only;
= 'V': Compute eigenvalues and eigenvectors.
= 'U': Upper triangles of A and B are stored;
= 'L': Lower triangles of A and B are stored.
On exit, if JOBZ = 'V', then if INFO = 0, A contains the matrix Z of eigenvectors. The eigenvectors 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.
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.
WORK(1)
returns the optimal LWORK.
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(1)
returns the optimal LRWORK.
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(1)
returns the optimal LIWORK.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: CPOTRF or CHEEVD returned an error code:
< = N: if INFO = i, CHEEVD 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 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