dsygvd - compute all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite eigenproblem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x
SUBROUTINE DSYGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, * LWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, UPLO INTEGER ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER IWORK(*) DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), WORK(*)
SUBROUTINE DSYGVD_64( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, * LWORK, IWORK, LIWORK, INFO) CHARACTER * 1 JOBZ, UPLO INTEGER*8 ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER*8 IWORK(*) DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), WORK(*)
SUBROUTINE SYGVD( ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, * [WORK], [LWORK], [IWORK], [LIWORK], [INFO]) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER :: ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER, DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, WORK REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE SYGVD_64( ITYPE, JOBZ, UPLO, [N], A, [LDA], B, [LDB], W, * [WORK], [LWORK], [IWORK], [LIWORK], [INFO]) CHARACTER(LEN=1) :: JOBZ, UPLO INTEGER(8) :: ITYPE, N, LDA, LDB, LWORK, LIWORK, INFO INTEGER(8), DIMENSION(:) :: IWORK REAL(8), DIMENSION(:) :: W, WORK REAL(8), DIMENSION(:,:) :: A, B
#include <sunperf.h>
void dsygvd(int itype, char jobz, char uplo, int n, double *a, int lda, double *b, int ldb, double *w, int *info);
void dsygvd_64(long itype, char jobz, char uplo, long n, double *a, long lda, double *b, long ldb, double *w, long *info);
dsygvd computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-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 symmetric 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**T*B*Z = I; if ITYPE = 3, Z**T*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**T*U or B = L*L**T.
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.
IWORK(1)
returns the optimal LIWORK.
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.
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPOTRF or SSYEVD returned an error code:
< = N: if INFO = i, SSYEVD 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