dsbevx
dsbevx - compute selected eigenvalues and, optionally, eigenvectors of a real symmetric band matrix A
SUBROUTINE DSBEVX( JOBZ, RANGE, UPLO, N, NDIAG, A, LDA, Q, LDQ, VL,
* VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL, INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER N, NDIAG, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE DSBEVX_64( JOBZ, RANGE, UPLO, N, NDIAG, A, LDA, Q, LDQ,
* VL, VU, IL, IU, ABTOL, NFOUND, W, Z, LDZ, WORK, IWORK2, IFAIL,
* INFO)
CHARACTER * 1 JOBZ, RANGE, UPLO
INTEGER*8 N, NDIAG, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER*8 IWORK2(*), IFAIL(*)
DOUBLE PRECISION VL, VU, ABTOL
DOUBLE PRECISION A(LDA,*), Q(LDQ,*), W(*), Z(LDZ,*), WORK(*)
SUBROUTINE SBEVX( JOBZ, RANGE, UPLO, [N], NDIAG, A, [LDA], Q, [LDQ],
* VL, VU, IL, IU, ABTOL, NFOUND, W, Z, [LDZ], [WORK], [IWORK2],
* IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER :: N, NDIAG, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER, DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, Q, Z
SUBROUTINE SBEVX_64( JOBZ, RANGE, UPLO, [N], NDIAG, A, [LDA], Q,
* [LDQ], VL, VU, IL, IU, ABTOL, NFOUND, W, Z, [LDZ], [WORK],
* [IWORK2], IFAIL, [INFO])
CHARACTER(LEN=1) :: JOBZ, RANGE, UPLO
INTEGER(8) :: N, NDIAG, LDA, LDQ, IL, IU, NFOUND, LDZ, INFO
INTEGER(8), DIMENSION(:) :: IWORK2, IFAIL
REAL(8) :: VL, VU, ABTOL
REAL(8), DIMENSION(:) :: W, WORK
REAL(8), DIMENSION(:,:) :: A, Q, Z
#include <sunperf.h>
void dsbevx(char jobz, char range, char uplo, int n, int ndiag, double *a, int lda, double *q, int ldq, double vl, double vu, int il, int iu, double abtol, int *nfound, double *w, double *z, int ldz, int *ifail, int *info);
void dsbevx_64(char jobz, char range, char uplo, long n, long ndiag, double *a, long lda, double *q, long ldq, double vl, double vu, long il, long iu, double abtol, long *nfound, double *w, double *z, long ldz, long *ifail, long *info);
dsbevx computes selected eigenvalues and, optionally, eigenvectors
of a real symmetric band matrix A. Eigenvalues and eigenvectors can
be selected by specifying either a range of values or a range of
indices for the desired eigenvalues.
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* JOBZ (input)
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* RANGE (input)
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* UPLO (input)
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* N (input)
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The order of the matrix A. N >= 0.
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* NDIAG (input)
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The number of superdiagonals of the matrix A if UPLO = 'U',
or the number of subdiagonals if UPLO = 'L'. NDIAG >= 0.
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* A (input/output)
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On entry, the upper or lower triangle of the symmetric band
matrix A, stored in the first NDIAG+1 rows of the array. The
j-th column of A is stored in the j-th column of the array A
as follows:
if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
On exit, A is overwritten by values generated during the
reduction to tridiagonal form. If UPLO = 'U', the first
superdiagonal and the diagonal of the tridiagonal matrix T
are returned in rows NDIAG and NDIAG+1 of A, and if UPLO = 'L',
the diagonal and first subdiagonal of T are returned in the
first two rows of A.
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* LDA (input)
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The leading dimension of the array A. LDA >= NDIAG + 1.
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* Q (output)
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If JOBZ = 'V', the N-by-N orthogonal matrix used in the
reduction to tridiagonal form.
If JOBZ = 'N', the array Q is not referenced.
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* LDQ (input)
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The leading dimension of the array Q. If JOBZ = 'V', then
LDQ >= max(1,N).
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* VL (input)
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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'.
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* VU (input)
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See the description of VL.
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* IL (input)
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If RANGE='I', the indices (in ascending order) of the
smallest 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'.
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* IU (input)
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See the description of IL.
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* ABTOL (input)
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The absolute error tolerance for the eigenvalues.
An approximate eigenvalue is accepted as converged
when it is determined to lie in an interval [a,b]
of width less than or equal to
ABTOL + EPS * max( |a|,|b| ) ,
where EPS is the machine precision. If ABTOL 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 ABTOL 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 ABTOL to
2*SLAMCH('S').
See "Computing Small Singular Values of Bidiagonal Matrices
with Guaranteed High Relative Accuracy," by Demmel and
Kahan, LAPACK Working Note #3.
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* NFOUND (output)
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The total number of eigenvalues found. 0 <= NFOUND <= N.
If RANGE = 'A', NFOUND = N, and if RANGE = 'I', NFOUND = IU-IL+1.
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* W (output)
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The first NFOUND elements contain the selected eigenvalues in
ascending order.
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* Z (input)
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If JOBZ = 'V', then if INFO = 0, the first NFOUND 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 eigenvector associated with W(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.
If JOBZ = 'N', then Z is not referenced.
Note: the user must ensure that at least max(1,NFOUND) columns are
supplied in the array Z; if RANGE = 'V', the exact value of NFOUND
is not known in advance and an upper bound must be used.
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* LDZ (input)
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The leading dimension of the array Z. LDZ >= 1, and if
JOBZ = 'V', LDZ >= max(1,N).
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* WORK (workspace)
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dimension(7*N)
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* IWORK2 (workspace)
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* IFAIL (output)
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If JOBZ = 'V', then if INFO = 0, the first NFOUND 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.
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* INFO (output)
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