org.netlib.lapack
Class SGEESX
java.lang.Object
org.netlib.lapack.SGEESX
public class SGEESX
- extends java.lang.Object
SGEESX is a simplified interface to the JLAPACK routine sgeesx.
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
* =======
*
* SGEESX computes for an N-by-N real nonsymmetric matrix A, the
* eigenvalues, the real Schur form T, and, optionally, the matrix of
* Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
*
* Optionally, it also orders the eigenvalues on the diagonal of the
* real Schur form so that selected eigenvalues are at the top left;
* computes a reciprocal condition number for the average of the
* selected eigenvalues (RCONDE); and computes a reciprocal condition
* number for the right invariant subspace corresponding to the
* selected eigenvalues (RCONDV). The leading columns of Z form an
* orthonormal basis for this invariant subspace.
*
* For further explanation of the reciprocal condition numbers RCONDE
* and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
* these quantities are called s and sep respectively).
*
* A real matrix is in real Schur form if it is upper quasi-triangular
* with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in
* the form
* [ a b ]
* [ c a ]
*
* where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
*
* Arguments
* =========
*
* JOBVS (input) CHARACTER*1
* = 'N': Schur vectors are not computed;
* = 'V': Schur vectors are computed.
*
* SORT (input) CHARACTER*1
* Specifies whether or not to order the eigenvalues on the
* diagonal of the Schur form.
* = 'N': Eigenvalues are not ordered;
* = 'S': Eigenvalues are ordered (see SELECT).
*
* SELECT (input) LOGICAL FUNCTION of two REAL arguments
* SELECT must be declared EXTERNAL in the calling subroutine.
* If SORT = 'S', SELECT is used to select eigenvalues to sort
* to the top left of the Schur form.
* If SORT = 'N', SELECT is not referenced.
* An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
* SELECT(WR(j),WI(j)) is true; i.e., if either one of a
* complex conjugate pair of eigenvalues is selected, then both
* are. Note that a selected complex eigenvalue may no longer
* satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
* ordering may change the value of complex eigenvalues
* (especially if the eigenvalue is ill-conditioned); in this
* case INFO may be set to N+3 (see INFO below).
*
* SENSE (input) CHARACTER*1
* Determines which reciprocal condition numbers are computed.
* = 'N': None are computed;
* = 'E': Computed for average of selected eigenvalues only;
* = 'V': Computed for selected right invariant subspace only;
* = 'B': Computed for both.
* If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.
*
* N (input) INTEGER
* The order of the matrix A. N >= 0.
*
* A (input/output) REAL array, dimension (LDA, N)
* On entry, the N-by-N matrix A.
* On exit, A is overwritten by its real Schur form T.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* SDIM (output) INTEGER
* If SORT = 'N', SDIM = 0.
* If SORT = 'S', SDIM = number of eigenvalues (after sorting)
* for which SELECT is true. (Complex conjugate
* pairs for which SELECT is true for either
* eigenvalue count as 2.)
*
* WR (output) REAL array, dimension (N)
* WI (output) REAL array, dimension (N)
* WR and WI contain the real and imaginary parts, respectively,
* of the computed eigenvalues, in the same order that they
* appear on the diagonal of the output Schur form T. Complex
* conjugate pairs of eigenvalues appear consecutively with the
* eigenvalue having the positive imaginary part first.
*
* VS (output) REAL array, dimension (LDVS,N)
* If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur
* vectors.
* If JOBVS = 'N', VS is not referenced.
*
* LDVS (input) INTEGER
* The leading dimension of the array VS. LDVS >= 1, and if
* JOBVS = 'V', LDVS >= N.
*
* RCONDE (output) REAL
* If SENSE = 'E' or 'B', RCONDE contains the reciprocal
* condition number for the average of the selected eigenvalues.
* Not referenced if SENSE = 'N' or 'V'.
*
* RCONDV (output) REAL
* If SENSE = 'V' or 'B', RCONDV contains the reciprocal
* condition number for the selected right invariant subspace.
* Not referenced if SENSE = 'N' or 'E'.
*
* WORK (workspace/output) REAL array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK >= max(1,3*N).
* Also, if SENSE = 'E' or 'V' or 'B',
* LWORK >= N+2*SDIM*(N-SDIM), where SDIM is the number of
* selected eigenvalues computed by this routine. Note that
* N+2*SDIM*(N-SDIM) <= N+N*N/2.
* For good performance, LWORK must generally be larger.
*
* IWORK (workspace/output) INTEGER array, dimension (LIWORK)
* Not referenced if SENSE = 'N' or 'E'.
* On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*
* LIWORK (input) INTEGER
* The dimension of the array IWORK.
* LIWORK >= 1; if SENSE = 'V' or 'B', LIWORK >= SDIM*(N-SDIM).
*
* BWORK (workspace) LOGICAL array, dimension (N)
* Not referenced if SORT = 'N'.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value.
* > 0: if INFO = i, and i is
* <= N: the QR algorithm failed to compute all the
* eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI
* contain those eigenvalues which have converged; if
* JOBVS = 'V', VS contains the transformation which
* reduces A to its partially converged Schur form.
* = N+1: the eigenvalues could not be reordered because some
* eigenvalues were too close to separate (the problem
* is very ill-conditioned);
* = N+2: after reordering, roundoff changed values of some
* complex eigenvalues so that leading eigenvalues in
* the Schur form no longer satisfy SELECT=.TRUE. This
* could also be caused by underflow due to scaling.
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
SGEESX(java.lang.String jobvs,
java.lang.String sort,
java.lang.Object select,
java.lang.String sense,
int n,
float[][] a,
intW sdim,
float[] wr,
float[] wi,
float[][] vs,
floatW rconde,
floatW rcondv,
float[] work,
int lwork,
int[] iwork,
int liwork,
boolean[] bwork,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
SGEESX
public SGEESX()
SGEESX
public static void SGEESX(java.lang.String jobvs,
java.lang.String sort,
java.lang.Object select,
java.lang.String sense,
int n,
float[][] a,
intW sdim,
float[] wr,
float[] wi,
float[][] vs,
floatW rconde,
floatW rcondv,
float[] work,
int lwork,
int[] iwork,
int liwork,
boolean[] bwork,
intW info)