ssbgvx(3P) Sun Performance Library ssbgvx(3P)NAMEssbgvx - compute selected eigenvalues, and optionally, eigenvectors of
a real generalized symmetric-definite banded eigenproblem, of the form
A*x=(lambda)*B*x
SYNOPSIS
SUBROUTINE SSBGVX(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB, LDBB,
Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK, IFAIL,
INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SSBGVX_64(JOBZ, RANGE, UPLO, N, KA, KB, AB, LDAB, BB,
LDBB, Q, LDQ, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, IWORK,
IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER*8 IWORK(*), IFAIL(*)
REAL VL, VU, ABSTOL
REAL AB(LDAB,*), BB(LDBB,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)
F95 INTERFACE
SUBROUTINE SBGVX(JOBZ, RANGE, UPLO, [N], KA, KB, AB, [LDAB], BB,
[LDBB], Q, [LDQ], VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK],
[IWORK], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, BB, Q, Z
SUBROUTINE SBGVX_64(JOBZ, RANGE, UPLO, [N], KA, KB, AB, [LDAB], BB,
[LDBB], Q, [LDQ], VL, VU, IL, IU, ABSTOL, M, W, Z, [LDZ], [WORK],
[IWORK], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: N, KA, KB, LDAB, LDBB, LDQ, IL, IU, M, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK, IFAIL
REAL :: VL, VU, ABSTOL
REAL, DIMENSION(:) :: W, WORK
REAL, DIMENSION(:,:) :: AB, BB, Q, Z
C INTERFACE
#include <sunperf.h>
void ssbgvx(char jobz, char range, char uplo, int n, int ka, int kb,
float *ab, int ldab, float *bb, int ldbb, float *q, int ldq,
float vl, float vu, int il, int iu, float abstol, int *m,
float *w, float *z, int ldz, int *ifail, int *info);
void ssbgvx_64(char jobz, char range, char uplo, long n, long ka, long
kb, float *ab, long ldab, float *bb, long ldbb, float *q,
long ldq, float vl, float vu, long il, long iu, float abstol,
long *m, float *w, float *z, long ldz, long *ifail, long
*info);
PURPOSEssbgvx computes selected eigenvalues, and optionally, eigenvectors of a
real generalized symmetric-definite banded eigenproblem, of the form
A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded,
and B is also positive definite. Eigenvalues and eigenvectors can be
selected by specifying either all eigenvalues, a range of values or a
range of indices for the desired eigenvalues.
ARGUMENTS
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 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.
KA (input)
The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KA >= 0.
KB (input)
The number of superdiagonals of the matrix B if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. KB >= 0.
AB (input/output)
On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first ka+1 rows of the array. The j-
th column of A is stored in the j-th column of the array AB
as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for
max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for
j<=i<=min(n,j+ka).
On exit, the contents of AB are destroyed.
LDAB (input)
The leading dimension of the array AB. LDAB >= KA+1.
BB (input/output)
On entry, the upper or lower triangle of the symmetric band
matrix B, stored in the first kb+1 rows of the array. The j-
th column of B is stored in the j-th column of the array BB
as follows: if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for
max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for
j<=i<=min(n,j+kb).
On exit, the factor S from the split Cholesky factorization B
= S**T*S, as returned by SPBSTF.
LDBB (input)
The leading dimension of the array BB. LDBB >= KB+1.
Q (output)
If JOBZ = 'V', the n-by-n matrix used in the reduction of A*x
= (lambda)*B*x to standard form, i.e. C*x = (lambda)*x, and
consequently C to tridiagonal form. If JOBZ = 'N', the array
Q is not referenced.
LDQ (input)
The leading dimension of the array Q. If JOBZ = 'N', LDQ >=
1. If JOBZ = 'V', LDQ >= 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*SLAMCH('S'), not zero.
If this routine returns with INFO>0, indicating that some
eigenvectors did not converge, try setting ABSTOL to
2*SLAMCH('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)
If INFO = 0, the eigenvalues in ascending order.
Z (output)
If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
eigenvectors, with the i-th column of Z holding the eigenvec‐
tor associated with W(i). The eigenvectors are normalized so
Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.
LDZ (input)
The leading dimension of the array Z. LDZ >= 1, and if JOBZ
= 'V', LDZ >= max(1,N).
WORK (workspace)
dimension(7*N)
IWORK (workspace/output)
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 eigenvalues 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
<= N: if INFO = i, then i eigenvectors failed to converge.
Their indices are stored in IFAIL. > N : SPBSTF returned an
error code; i.e., 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.
FURTHER DETAILS
Based on contributions by
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
6 Mar 2009 ssbgvx(3P)