org.netlib.lapack
Class DGGESX
java.lang.Object
org.netlib.lapack.DGGESX
public class DGGESX
 extends java.lang.Object
DGGESX is a simplified interface to the JLAPACK routine dggesx.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor 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
* =======
*
* DGGESX computes for a pair of NbyN real nonsymmetric matrices
* (A,B), the generalized eigenvalues, the real Schur form (S,T), and,
* optionally, the left and/or right matrices of Schur vectors (VSL and
* VSR). This gives the generalized Schur factorization
*
* (A,B) = ( (VSL) S (VSR)**T, (VSL) T (VSR)**T )
*
* Optionally, it also orders the eigenvalues so that a selected cluster
* of eigenvalues appears in the leading diagonal blocks of the upper
* quasitriangular matrix S and the upper triangular matrix T; computes
* a reciprocal condition number for the average of the selected
* eigenvalues (RCONDE); and computes a reciprocal condition number for
* the right and left deflating subspaces corresponding to the selected
* eigenvalues (RCONDV). The leading columns of VSL and VSR then form
* an orthonormal basis for the corresponding left and right eigenspaces
* (deflating subspaces).
*
* A generalized eigenvalue for a pair of matrices (A,B) is a scalar w
* or a ratio alpha/beta = w, such that A  w*B is singular. It is
* usually represented as the pair (alpha,beta), as there is a
* reasonable interpretation for beta=0 or for both being zero.
*
* A pair of matrices (S,T) is in generalized real Schur form if T is
* upper triangular with nonnegative diagonal and S is block upper
* triangular with 1by1 and 2by2 blocks. 1by1 blocks correspond
* to real generalized eigenvalues, while 2by2 blocks of S will be
* "standardized" by making the corresponding elements of T have the
* form:
* [ a 0 ]
* [ 0 b ]
*
* and the pair of corresponding 2by2 blocks in S and T will have a
* complex conjugate pair of generalized eigenvalues.
*
*
* Arguments
* =========
*
* JOBVSL (input) CHARACTER*1
* = 'N': do not compute the left Schur vectors;
* = 'V': compute the left Schur vectors.
*
* JOBVSR (input) CHARACTER*1
* = 'N': do not compute the right Schur vectors;
* = 'V': compute the right Schur vectors.
*
* SORT (input) CHARACTER*1
* Specifies whether or not to order the eigenvalues on the
* diagonal of the generalized Schur form.
* = 'N': Eigenvalues are not ordered;
* = 'S': Eigenvalues are ordered (see DELZTG).
*
* DELZTG (input) LOGICAL FUNCTION of three DOUBLE PRECISION arguments
* DELZTG must be declared EXTERNAL in the calling subroutine.
* If SORT = 'N', DELZTG is not referenced.
* If SORT = 'S', DELZTG is used to select eigenvalues to sort
* to the top left of the Schur form.
* An eigenvalue (ALPHAR(j)+ALPHAI(j))/BETA(j) is selected if
* DELZTG(ALPHAR(j),ALPHAI(j),BETA(j)) is true; i.e. if either
* one of a complex conjugate pair of eigenvalues is selected,
* then both complex eigenvalues are selected.
* Note that a selected complex eigenvalue may no longer satisfy
* DELZTG(ALPHAR(j),ALPHAI(j),BETA(j)) = .TRUE. after ordering,
* since ordering may change the value of complex eigenvalues
* (especially if the eigenvalue is illconditioned), in this
* case INFO is set to N+3.
*
* SENSE (input) CHARACTER
* Determines which reciprocal condition numbers are computed.
* = 'N' : None are computed;
* = 'E' : Computed for average of selected eigenvalues only;
* = 'V' : Computed for selected deflating subspaces only;
* = 'B' : Computed for both.
* If SENSE = 'E', 'V', or 'B', SORT must equal 'S'.
*
* N (input) INTEGER
* The order of the matrices A, B, VSL, and VSR. N >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
* On entry, the first of the pair of matrices.
* On exit, A has been overwritten by its generalized Schur
* form S.
*
* LDA (input) INTEGER
* The leading dimension of A. LDA >= max(1,N).
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
* On entry, the second of the pair of matrices.
* On exit, B has been overwritten by its generalized Schur
* form T.
*
* LDB (input) INTEGER
* The leading dimension of B. LDB >= max(1,N).
*
* SDIM (output) INTEGER
* If SORT = 'N', SDIM = 0.
* If SORT = 'S', SDIM = number of eigenvalues (after sorting)
* for which DELZTG is true. (Complex conjugate pairs for which
* DELZTG is true for either eigenvalue count as 2.)
*
* ALPHAR (output) DOUBLE PRECISION array, dimension (N)
* ALPHAI (output) DOUBLE PRECISION array, dimension (N)
* BETA (output) DOUBLE PRECISION array, dimension (N)
* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
* be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i
* and BETA(j),j=1,...,N are the diagonals of the complex Schur
* form (S,T) that would result if the 2by2 diagonal blocks of
* the real Schur form of (A,B) were further reduced to
* triangular form using 2by2 complex unitary transformations.
* If ALPHAI(j) is zero, then the jth eigenvalue is real; if
* positive, then the jth and (j+1)st eigenvalues are a
* complex conjugate pair, with ALPHAI(j+1) negative.
*
* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
* may easily over or underflow, and BETA(j) may even be zero.
* Thus, the user should avoid naively computing the ratio.
* However, ALPHAR and ALPHAI will be always less than and
* usually comparable with norm(A) in magnitude, and BETA always
* less than and usually comparable with norm(B).
*
* VSL (output) DOUBLE PRECISION array, dimension (LDVSL,N)
* If JOBVSL = 'V', VSL will contain the left Schur vectors.
* Not referenced if JOBVSL = 'N'.
*
* LDVSL (input) INTEGER
* The leading dimension of the matrix VSL. LDVSL >=1, and
* if JOBVSL = 'V', LDVSL >= N.
*
* VSR (output) DOUBLE PRECISION array, dimension (LDVSR,N)
* If JOBVSR = 'V', VSR will contain the right Schur vectors.
* Not referenced if JOBVSR = 'N'.
*
* LDVSR (input) INTEGER
* The leading dimension of the matrix VSR. LDVSR >= 1, and
* if JOBVSR = 'V', LDVSR >= N.
*
* RCONDE (output) DOUBLE PRECISION array, dimension ( 2 )
* If SENSE = 'E' or 'B', RCONDE(1) and RCONDE(2) contain the
* reciprocal condition numbers for the average of the selected
* eigenvalues.
* Not referenced if SENSE = 'N' or 'V'.
*
* RCONDV (output) DOUBLE PRECISION array, dimension ( 2 )
* If SENSE = 'V' or 'B', RCONDV(1) and RCONDV(2) contain the
* reciprocal condition numbers for the selected deflating
* subspaces.
* Not referenced if SENSE = 'N' or 'E'.
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK >= 8*(N+1)+16.
* If SENSE = 'E', 'V', or 'B',
* LWORK >= MAX( 8*(N+1)+16, 2*SDIM*(NSDIM) ).
*
* IWORK (workspace) INTEGER array, dimension (LIWORK)
* Not referenced if SENSE = 'N'.
*
* LIWORK (input) INTEGER
* The dimension of the array WORK. LIWORK >= N+6.
*
* BWORK (workspace) LOGICAL array, dimension (N)
* Not referenced if SORT = 'N'.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = i, the ith argument had an illegal value.
* = 1,...,N:
* The QZ iteration failed. (A,B) are not in Schur
* form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
* be correct for j=INFO+1,...,N.
* > N: =N+1: other than QZ iteration failed in DHGEQZ
* =N+2: after reordering, roundoff changed values of
* some complex eigenvalues so that leading
* eigenvalues in the Generalized Schur form no
* longer satisfy DELZTG=.TRUE. This could also
* be caused due to scaling.
* =N+3: reordering failed in DTGSEN.
*
* Further details
* ===============
*
* An approximate (asymptotic) bound on the average absolute error of
* the selected eigenvalues is
*
* EPS * norm((A, B)) / RCONDE( 1 ).
*
* An approximate (asymptotic) bound on the maximum angular error in
* the computed deflating subspaces is
*
* EPS * norm((A, B)) / RCONDV( 2 ).
*
* See LAPACK User's Guide, section 4.11 for more information.
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
DGGESX(java.lang.String jobvsl,
java.lang.String jobvsr,
java.lang.String sort,
java.lang.Object delctg,
java.lang.String sense,
int n,
double[][] a,
double[][] b,
intW sdim,
double[] alphar,
double[] alphai,
double[] beta,
double[][] vsl,
double[][] vsr,
double[] rconde,
double[] rcondv,
double[] 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 
DGGESX
public DGGESX()
DGGESX
public static void DGGESX(java.lang.String jobvsl,
java.lang.String jobvsr,
java.lang.String sort,
java.lang.Object delctg,
java.lang.String sense,
int n,
double[][] a,
double[][] b,
intW sdim,
double[] alphar,
double[] alphai,
double[] beta,
double[][] vsl,
double[][] vsr,
double[] rconde,
double[] rcondv,
double[] work,
int lwork,
int[] iwork,
int liwork,
boolean[] bwork,
intW info)