dsygvx(3P) Sun Performance Library dsygvx(3P)NAMEdsygvx - compute selected eigenvalues, and optionally, 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 DSYGVX(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL,
VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER IWORK(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABSTOL
DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSYGVX_64(ITYPE, JOBZ, RANGE, UPLO, N, A, LDA, B, LDB, VL,
VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER*8 IWORK(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABSTOL
DOUBLE PRECISION A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SYGVX(ITYPE, JOBZ, RANGE, UPLO, [N], A, [LDA], B, [LDB],
VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK], [LWORK], [IWORK],
IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER, DIMENSION(:) :: IWORK, IFAIL
REAL(8) :: VL, VU, ABSTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, B, Z
SUBROUTINE SYGVX_64(ITYPE, JOBZ, RANGE, UPLO, [N], A, [LDA], B, [LDB],
VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK], [LWORK], [IWORK],
IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: ITYPE, N, LDA, LDB, IL, IU, M, LDZ, LWORK, INFO
INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
REAL(8) :: VL, VU, ABSTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, B, Z
C INTERFACE
#include <sunperf.h>
void dsygvx(int itype, char jobz, char range, char uplo, int n, double
*a, int lda, double *b, int ldb, double vl, double vu, int
il, int iu, double abstol, int *m, double *w, double *z, int
ldz, int *ifail, int *info);
void dsygvx_64(long itype, char jobz, char range, char uplo, long n,
double *a, long lda, double *b, long ldb, double vl, double
vu, long il, long iu, double abstol, long *m, double *w, dou‐
ble *z, long ldz, long *ifail, long *info);
PURPOSEdsygvx computes selected eigenvalues, and optionally, 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. Eigenval‐
ues and eigenvectors can be selected by specifying either a range of
values or a range of indices for the desired eigenvalues.
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.
RANGE (input)
= 'A': all eigenvalues will be found.
= 'V': all eigenvalues in the half-open interval (VL,VU] will
be found. = 'I': the IL-th through IU-th eigenvalues will be
found.
UPLO (input)
= 'U': Upper triangle of A and B are stored;
= 'L': Lower triangle of A and B are stored.
N (input) The order of the matrix pencil (A,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, the lower triangle (if UPLO='L') or the upper trian‐
gle (if UPLO='U') 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 matrix B. If UPLO = 'U', the leading
N-by-N upper triangular part of B contains the upper triangu‐
lar 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).
VL (input)
If RANGE='V', the lower and upper bounds of the interval to
be searched for eigenvalues. VL < VU. Not referenced if
RANGE = 'A' or 'I'.
VU (input)
See the description of VL.
IL (input)
If RANGE='I', the indices (in ascending order) of the small‐
est and largest eigenvalues to be returned. 1 <= IL <= IU <=
N, if N > 0; IL = 1 and IU = 0 if N = 0. Not referenced if
RANGE = 'A' or 'V'.
IU (input)
See the description of IL.
ABSTOL (input)
The absolute error tolerance for the eigenvalues. An approx‐
imate eigenvalue is accepted as converged when it is deter‐
mined to lie in an interval [a,b] of width less than or equal
to
ABSTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABSTOL is less than
or equal to zero, then EPS*|T| will be used in its place,
where |T| is the 1-norm of the tridiagonal matrix obtained by
reducing A to tridiagonal form.
Eigenvalues will be computed most accurately when ABSTOL is
set to twice the underflow threshold 2*DLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*DLAMCH('S').
M (output)
The total number of eigenvalues found. 0 <= M <= N. If
RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
W (output)
On normal exit, the first M elements contain the selected ei‐
genvalues in ascending order.
Z (output)
If JOBZ = 'N', then Z is not referenced. If JOBZ = 'V', then
if INFO = 0, the first M columns of Z contain the orthonormal
eigenvectors of the matrix A corresponding to the selected
eigenvalues, with the i-th column of Z holding the eigenvec‐
tor associated with W(i). 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 an eigenvector fails to converge, then that column of Z
contains the latest approximation to the eigenvector, and the
index of the eigenvector is returned in IFAIL. Note: the
user must ensure that at least max(1,M) columns are supplied
in the array Z; if RANGE = 'V', the exact value of M is not
known in advance and an upper bound must be used.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input)
The length of the array WORK. LWORK >= max(1,8*N). For
optimal efficiency, LWORK >= (NB+3)*N, where NB is the block‐
size for DSYTRD returned by ILAENV.
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 (workspace)
dimension(5*N)
IFAIL (output)
If JOBZ = 'V', then if INFO = 0, the first M elements of
IFAIL are zero. If INFO > 0, then IFAIL contains the indices
of the eigenvectors that failed to converge. If JOBZ = 'N',
then IFAIL is not referenced.
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: DPOTRF or DSYEVX returned an error code:
<= N: if INFO = i, DSYEVX failed to converge; i eigenvectors
failed to converge. Their indices are stored in array IFAIL.
> N: if INFO = N + i, for 1 <= i <= N, then the leading
minor of order i of B is not positive definite. The factor‐
ization of B could not be completed and no eigenvalues or
eigenvectors were computed.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
6 Mar 2009 dsygvx(3P)
