ssygvx - 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
SUBROUTINE SSYGVX( 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(*) REAL VL, VU, ABSTOL REAL A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSYGVX_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(*) REAL VL, VU, ABSTOL REAL A(LDA,*), B(LDB,*), W(*), Z(LDZ,*), WORK(*)
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 :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, WORK REAL, 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 :: VL, VU, ABSTOL REAL, DIMENSION(:) :: W, WORK REAL, DIMENSION(:,:) :: A, B, Z
#include <sunperf.h>
void ssygvx(int itype, char jobz, char range, char uplo, int n, float *a, int lda, float *b, int ldb, float vl, float vu, int il, int iu, float abstol, int *m, float *w, float *z, int ldz, int *ifail, int *info);
void ssygvx_64(long itype, char jobz, char range, char uplo, long n, float *a, long lda, float *b, long ldb, float vl, float vu, long il, long iu, float abstol, long *m, float *w, float *z, long ldz, long *ifail, long *info);
ssygvx 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. Eigenvalues and eigenvectors can be selected by specifying either a range of values or a range of indices for the desired eigenvalues.
= 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.
= '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.
= 'U': Upper triangle of A and B are stored;
= 'L': Lower triangle of A and B are stored.
On exit, the lower triangle (if UPLO ='L') or the upper triangle (if UPLO ='U') 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.
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*SLAMCH('S').
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.
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.
dimension(5*N)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
> 0: SPOTRF or SSYEVX returned an error code:
< = N: if INFO = i, SSYEVX 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 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