org.netlib.lapack
Class STGSYL
java.lang.Object
org.netlib.lapack.STGSYL
public class STGSYL
 extends java.lang.Object
STGSYL is a simplified interface to the JLAPACK routine stgsyl.
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
* =======
*
* STGSYL 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', STGSYL 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 SLACON.
*
* If IJOB >= 1, STGSYL 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.
* ( SGECON 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL 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) REAL
* 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) REAL
* 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) REAL 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 
STGSYL(java.lang.String trans,
int ijob,
int m,
int n,
float[][] a,
float[][] b,
float[][] c,
float[][] d,
float[][] e,
float[][] f,
floatW scale,
floatW dif,
float[] 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 
STGSYL
public STGSYL()
STGSYL
public static void STGSYL(java.lang.String trans,
int ijob,
int m,
int n,
float[][] a,
float[][] b,
float[][] c,
float[][] d,
float[][] e,
float[][] f,
floatW scale,
floatW dif,
float[] work,
int lwork,
int[] iwork,
intW info)