org.netlib.lapack
Class Dggesx

java.lang.Object
  extended by org.netlib.lapack.Dggesx

public class Dggesx
extends java.lang.Object

Following is the description from the original
Fortran source.  For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.

* .. * * Purpose * ======= * * DGGESX computes for a pair of N-by-N 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 * quasi-triangular 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 non-negative diagonal and S is block upper * triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond * to real generalized eigenvalues, while 2-by-2 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 2-by-2 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 ill-conditioned), 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 2-by-2 diagonal blocks of * the real Schur form of (A,B) were further reduced to * triangular form using 2-by-2 complex unitary transformations. * If ALPHAI(j) is zero, then the j-th eigenvalue is real; if * positive, then the j-th 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*(N-SDIM) ). * * 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 i-th 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 ..


Constructor Summary
Dggesx()
           
 
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, int _a_offset, int lda, double[] b, int _b_offset, int ldb, intW sdim, double[] alphar, int _alphar_offset, double[] alphai, int _alphai_offset, double[] beta, int _beta_offset, double[] vsl, int _vsl_offset, int ldvsl, double[] vsr, int _vsr_offset, int ldvsr, double[] rconde, int _rconde_offset, double[] rcondv, int _rcondv_offset, double[] work, int _work_offset, int lwork, int[] iwork, int _iwork_offset, int liwork, boolean[] bwork, int _bwork_offset, intW info)
           
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

Dggesx

public Dggesx()
Method Detail

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,
                          int _a_offset,
                          int lda,
                          double[] b,
                          int _b_offset,
                          int ldb,
                          intW sdim,
                          double[] alphar,
                          int _alphar_offset,
                          double[] alphai,
                          int _alphai_offset,
                          double[] beta,
                          int _beta_offset,
                          double[] vsl,
                          int _vsl_offset,
                          int ldvsl,
                          double[] vsr,
                          int _vsr_offset,
                          int ldvsr,
                          double[] rconde,
                          int _rconde_offset,
                          double[] rcondv,
                          int _rcondv_offset,
                          double[] work,
                          int _work_offset,
                          int lwork,
                          int[] iwork,
                          int _iwork_offset,
                          int liwork,
                          boolean[] bwork,
                          int _bwork_offset,
                          intW info)