Contents
dsygv - compute all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite eigen-
problem, of the form A*x=(lambda)*B*x, A*Bx=(lambda)*x, or
B*A*x=(lambda)*x
SUBROUTINE DSYGV(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LDWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER ITYPE, N, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), WORK(*)
SUBROUTINE DSYGV_64(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
LDWORK, INFO)
CHARACTER * 1 JOBZ, UPLO
INTEGER*8 ITYPE, N, LDA, LDB, LDWORK, INFO
DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), WORK(*)
F95 INTERFACE
SUBROUTINE SYGV(ITYPE, JOBZ, UPLO, N, A, [LDA], B, [LDB], W, [WORK],
[LDWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER :: ITYPE, N, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, B
SUBROUTINE SYGV_64(ITYPE, JOBZ, UPLO, N, A, [LDA], B, [LDB], W, [WORK],
[LDWORK], [INFO])
CHARACTER(LEN=1) :: JOBZ, UPLO
INTEGER(8) :: ITYPE, N, LDA, LDB, LDWORK, INFO
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, B
C INTERFACE
#include <sunperf.h>
void dsygv(int itype, char jobz, char uplo, int n, double
*a, int lda, double *b, int ldb, double *w, int
*info);
void dsygv_64(long itype, char jobz, char uplo, long n, dou-
ble *a, long lda, double *b, long ldb, double *w,
long *info);
dsygv computes all the eigenvalues, and optionally, the
eigenvectors of a real generalized symmetric-definite eigen-
problem, 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.
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 symmetric 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**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.
LDA (input)
The leading dimension of the array A. LDA >=
max(1,N).
B (input/output)
On entry, the symmetric 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**T*U
or B = L*L**T.
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(1,3*N-1). For optimal efficiency, LDWORK >=
(NB+2)*N, where NB is the blocksize for SSYTRD
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.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: SPOTRF or SSYEV returned an error code:
<= N: if INFO = i, SSYEV 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.