org.netlib.lapack
Class DTGSYL
java.lang.Object
org.netlib.lapack.DTGSYL
public class DTGSYL
 extends java.lang.Object
DTGSYL is a simplified interface to the JLAPACK routine dtgsyl.
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
* =======
*
* DTGSYL solves the generalized Sylvester equation:
*
* A * R  L * B = scale * C (1)
* D * R  L * E = scale * F
*
* where R and L are unknown mbyn matrices, (A, D), (B, E) and
* (C, F) are given matrix pairs of size mbym, nbyn and mbyn,
* respectively, with real entries. (A, D) and (B, E) must be in
* generalized (real) Schur canonical form, i.e. A, B are upper quasi
* triangular and D, E are upper triangular.
*
* The solution (R, L) overwrites (C, F). 0 <= SCALE <= 1 is an output
* scaling factor chosen to avoid overflow.
*
* In matrix notation (1) is equivalent to solve Zx = scale b, where
* Z is defined as
*
* Z = [ kron(In, A) kron(B', Im) ] (2)
* [ kron(In, D) kron(E', Im) ].
*
* Here Ik is the identity matrix of size k and X' is the transpose of
* X. kron(X, Y) is the Kronecker product between the matrices X and Y.
*
* If TRANS = 'T', DTGSYL solves the transposed system Z'*y = scale*b,
* which is equivalent to solve for R and L in
*
* A' * R + D' * L = scale * C (3)
* R * B' + L * E' = scale * (F)
*
* This case (TRANS = 'T') is used to compute an onenormbased estimate
* of Dif[(A,D), (B,E)], the separation between the matrix pairs (A,D)
* and (B,E), using DLACON.
*
* If IJOB >= 1, DTGSYL computes a Frobenius normbased estimate
* of Dif[(A,D),(B,E)]. That is, the reciprocal of a lower bound on the
* reciprocal of the smallest singular value of Z. See [12] for more
* information.
*
* This is a level 3 BLAS algorithm.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER*1
* = 'N', solve the generalized Sylvester equation (1).
* = 'T', solve the 'transposed' system (3).
*
* IJOB (input) INTEGER
* Specifies what kind of functionality to be performed.
* =0: solve (1) only.
* =1: The functionality of 0 and 3.
* =2: The functionality of 0 and 4.
* =3: Only an estimate of Dif[(A,D), (B,E)] is computed.
* (look ahead strategy IJOB = 1 is used).
* =4: Only an estimate of Dif[(A,D), (B,E)] is computed.
* ( DGECON on subsystems is used ).
* Not referenced if TRANS = 'T'.
*
* M (input) INTEGER
* The order of the matrices A and D, and the row dimension of
* the matrices C, F, R and L.
*
* N (input) INTEGER
* The order of the matrices B and E, and the column dimension
* of the matrices C, F, R and L.
*
* A (input) DOUBLE PRECISION array, dimension (LDA, M)
* The upper quasi triangular matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1, M).
*
* B (input) DOUBLE PRECISION array, dimension (LDB, N)
* The upper quasi triangular matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1, N).
*
* C (input/output) DOUBLE PRECISION array, dimension (LDC, N)
* On entry, C contains the righthandside of the first matrix
* equation in (1) or (3).
* On exit, if IJOB = 0, 1 or 2, C has been overwritten by
* the solution R. If IJOB = 3 or 4 and TRANS = 'N', C holds R,
* the solution achieved during the computation of the
* Difestimate.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1, M).
*
* D (input) DOUBLE PRECISION array, dimension (LDD, M)
* The upper triangular matrix D.
*
* LDD (input) INTEGER
* The leading dimension of the array D. LDD >= max(1, M).
*
* E (input) DOUBLE PRECISION array, dimension (LDE, N)
* The upper triangular matrix E.
*
* LDE (input) INTEGER
* The leading dimension of the array E. LDE >= max(1, N).
*
* F (input/output) DOUBLE PRECISION array, dimension (LDF, N)
* On entry, F contains the righthandside of the second matrix
* equation in (1) or (3).
* On exit, if IJOB = 0, 1 or 2, F has been overwritten by
* the solution L. If IJOB = 3 or 4 and TRANS = 'N', F holds L,
* the solution achieved during the computation of the
* Difestimate.
*
* LDF (input) INTEGER
* The leading dimension of the array F. LDF >= max(1, M).
*
* DIF (output) DOUBLE PRECISION
* On exit DIF is the reciprocal of a lower bound of the
* reciprocal of the Diffunction, i.e. DIF is an upper bound of
* Dif[(A,D), (B,E)] = sigma_min(Z), where Z as in (2).
* IF IJOB = 0 or TRANS = 'T', DIF is not touched.
*
* SCALE (output) DOUBLE PRECISION
* On exit SCALE is the scaling factor in (1) or (3).
* If 0 < SCALE < 1, C and F hold the solutions R and L, resp.,
* to a slightly perturbed system but the input matrices A, B, D
* and E have not been changed. If SCALE = 0, C and F hold the
* solutions R and L, respectively, to the homogeneous system
* with C = F = 0. Normally, SCALE = 1.
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
* If IJOB = 0, WORK is not referenced. Otherwise,
* on exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK > = 1.
* If IJOB = 1 or 2 and TRANS = 'N', LWORK >= 2*M*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) INTEGER array, dimension (M+N+6)
*
* INFO (output) INTEGER
* =0: successful exit
* <0: If INFO = i, the ith argument had an illegal value.
* >0: (A, D) and (B, E) have common or close eigenvalues.
*
* Further Details
* ===============
*
* Based on contributions by
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
* Umea University, S901 87 Umea, Sweden.
*
* [1] B. Kagstrom and P. Poromaa, LAPACKStyle Algorithms and Software
* for Solving the Generalized Sylvester Equation and Estimating the
* Separation between Regular Matrix Pairs, Report UMINF  93.23,
* Department of Computing Science, Umea University, S901 87 Umea,
* Sweden, December 1993, Revised April 1994, Also as LAPACK Working
* Note 75. To appear in ACM Trans. on Math. Software, Vol 22,
* No 1, 1996.
*
* [2] B. Kagstrom, A Perturbation Analysis of the Generalized Sylvester
* Equation (AR  LB, DR  LE ) = (C, F), SIAM J. Matrix Anal.
* Appl., 15(4):10451060, 1994
*
* [3] B. Kagstrom and L. Westin, Generalized Schur Methods with
* Condition Estimators for Solving the Generalized Sylvester
* Equation, IEEE Transactions on Automatic Control, Vol. 34, No. 7,
* July 1989, pp 745751.
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
DTGSYL(java.lang.String trans,
int ijob,
int m,
int n,
double[][] a,
double[][] b,
double[][] c,
double[][] d,
double[][] e,
double[][] f,
doubleW scale,
doubleW dif,
double[] work,
int lwork,
int[] iwork,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
DTGSYL
public DTGSYL()
DTGSYL
public static void DTGSYL(java.lang.String trans,
int ijob,
int m,
int n,
double[][] a,
double[][] b,
double[][] c,
double[][] d,
double[][] e,
double[][] f,
doubleW scale,
doubleW dif,
double[] work,
int lwork,
int[] iwork,
intW info)