org.netlib.lapack
Class SSTEGR
java.lang.Object
org.netlib.lapack.SSTEGR
public class SSTEGR
- extends java.lang.Object
SSTEGR is a simplified interface to the JLAPACK routine sstegr.
This interface converts Java-style 2D row-major arrays into
the 1D column-major linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* SSTEGR computes selected eigenvalues and, optionally, eigenvectors
* of a real symmetric tridiagonal matrix T. Eigenvalues and
* eigenvectors can be selected by specifying either a range of values
* or a range of indices for the desired eigenvalues. The eigenvalues
* are computed by the dqds algorithm, while orthogonal eigenvectors are
* computed from various ``good'' L D L^T representations (also known as
* Relatively Robust Representations). Gram-Schmidt orthogonalization is
* avoided as far as possible. More specifically, the various steps of
* the algorithm are as follows. For the i-th unreduced block of T,
* (a) Compute T - sigma_i = L_i D_i L_i^T, such that L_i D_i L_i^T
* is a relatively robust representation,
* (b) Compute the eigenvalues, lambda_j, of L_i D_i L_i^T to high
* relative accuracy by the dqds algorithm,
* (c) If there is a cluster of close eigenvalues, "choose" sigma_i
* close to the cluster, and go to step (a),
* (d) Given the approximate eigenvalue lambda_j of L_i D_i L_i^T,
* compute the corresponding eigenvector by forming a
* rank-revealing twisted factorization.
* The desired accuracy of the output can be specified by the input
* parameter ABSTOL.
*
* For more details, see "A new O(n^2) algorithm for the symmetric
* tridiagonal eigenvalue/eigenvector problem", by Inderjit Dhillon,
* Computer Science Division Technical Report No. UCB/CSD-97-971,
* UC Berkeley, May 1997.
*
* Note 1 : Currently SSTEGR is only set up to find ALL the n
* eigenvalues and eigenvectors of T in O(n^2) time
* Note 2 : Currently the routine SSTEIN is called when an appropriate
* sigma_i cannot be chosen in step (c) above. SSTEIN invokes modified
* Gram-Schmidt when eigenvalues are close.
* Note 3 : SSTEGR works only on machines which follow ieee-754
* floating-point standard in their handling of infinities and NaNs.
* Normal execution of SSTEGR may create NaNs and infinities and hence
* may abort due to a floating point exception in environments which
* do not conform to the ieee standard.
*
* Arguments
* =========
*
* JOBZ (input) CHARACTER*1
* = 'N': Compute eigenvalues only;
* = 'V': Compute eigenvalues and eigenvectors.
*
* RANGE (input) CHARACTER*1
* = '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.
********** Only RANGE = 'A' is currently supported *********************
*
* N (input) INTEGER
* The order of the matrix. N >= 0.
*
* D (input/output) REAL array, dimension (N)
* On entry, the n diagonal elements of the tridiagonal matrix
* T. On exit, D is overwritten.
*
* E (input/output) REAL array, dimension (N)
* On entry, the (n-1) subdiagonal elements of the tridiagonal
* matrix T in elements 1 to N-1 of E; E(N) need not be set.
* On exit, E is overwritten.
*
* VL (input) REAL
* VU (input) REAL
* 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'.
*
* IL (input) INTEGER
* IU (input) INTEGER
* 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'.
*
* ABSTOL (input) REAL
* The absolute error tolerance for the
* eigenvalues/eigenvectors. IF JOBZ = 'V', the eigenvalues and
* eigenvectors output have residual norms bounded by ABSTOL,
* and the dot products between different eigenvectors are
* bounded by ABSTOL. If ABSTOL is less than N*EPS*|T|, then
* N*EPS*|T| will be used in its place, where EPS is the
* machine precision and |T| is the 1-norm of the tridiagonal
* matrix. The eigenvalues are computed to an accuracy of
* EPS*|T| irrespective of ABSTOL. If high relative accuracy
* is important, set ABSTOL to DLAMCH( 'Safe minimum' ).
* See Barlow and Demmel "Computing Accurate Eigensystems of
* Scaled Diagonally Dominant Matrices", LAPACK Working Note #7
* for a discussion of which matrices define their eigenvalues
* to high relative accuracy.
*
* M (output) INTEGER
* The total number of eigenvalues found. 0 <= M <= N.
* If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
*
* W (output) REAL array, dimension (N)
* The first M elements contain the selected eigenvalues in
* ascending order.
*
* Z (output) REAL array, dimension (LDZ, max(1,M) )
* If JOBZ = 'V', then if INFO = 0, the first M columns of Z
* contain the orthonormal eigenvectors of the matrix T
* corresponding to the selected eigenvalues, with the i-th
* column of Z holding the eigenvector associated with W(i).
* If JOBZ = 'N', then Z is not referenced.
* 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) INTEGER
* The leading dimension of the array Z. LDZ >= 1, and if
* JOBZ = 'V', LDZ >= max(1,N).
*
* ISUPPZ (output) INTEGER ARRAY, dimension ( 2*max(1,M) )
* The support of the eigenvectors in Z, i.e., the indices
* indicating the nonzero elements in Z. The i-th eigenvector
* is nonzero only in elements ISUPPZ( 2*i-1 ) through
* ISUPPZ( 2*i ).
*
* WORK (workspace/output) REAL array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal
* (and minimal) LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK >= max(1,18*N)
*
* 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/output) INTEGER array, dimension (LIWORK)
* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK. LIWORK >= max(1,10*N)
*
* If LIWORK = -1, then a workspace query is assumed; the
* routine only calculates the optimal size of the IWORK array,
* returns this value as the first entry of the IWORK array, and
* no error message related to LIWORK is issued by XERBLA.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
* > 0: if INFO = 1, internal error in SLARRE,
* if INFO = 2, internal error in SLARRV.
*
* Further Details
* ===============
*
* Based on contributions by
* Inderjit Dhillon, IBM Almaden, USA
* Osni Marques, LBNL/NERSC, USA
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
SSTEGR(java.lang.String jobz,
java.lang.String range,
int n,
float[] d,
float[] e,
float vl,
float vu,
int il,
int iu,
float abstol,
intW m,
float[] w,
float[][] z,
int[] isuppz,
float[] work,
int lwork,
int[] iwork,
int liwork,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SSTEGR
public SSTEGR()
SSTEGR
public static void SSTEGR(java.lang.String jobz,
java.lang.String range,
int n,
float[] d,
float[] e,
float vl,
float vu,
int il,
int iu,
float abstol,
intW m,
float[] w,
float[][] z,
int[] isuppz,
float[] work,
int lwork,
int[] iwork,
int liwork,
intW info)