dsygv(3P) Sun Performance Library dsygv(3P)NAMEdsygv - 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
SYNOPSIS
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, double *a, long
lda, double *b, long ldb, double *w, long *info);
PURPOSEdsygv 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.
ARGUMENTS
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 contains the upper triangu‐
lar 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 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.
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 triangular 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 DSYTRD returned by ILAENV.
If LDWORK = -1, then a workspace query is assumed; the rou‐
tine 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 illegal value
> 0: DPOTRF or DSYEV returned an error code:
<= N: if INFO = i, DSYEV 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.
6 Mar 2009 dsygv(3P)
