org.netlib.lapack
Class STGSY2
java.lang.Object
org.netlib.lapack.STGSY2
public class STGSY2
 extends java.lang.Object
STGSY2 is a simplified interface to the JLAPACK routine stgsy2.
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
* =======
*
* STGSY2 solves the generalized Sylvester equation:
*
* A * R  L * B = scale * C (1)
* D * R  L * E = scale * F,
*
* using Level 1 and 2 BLAS. 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 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 solving equation (1) corresponds to solve
* Z*x = scale*b, where Z is defined as
*
* Z = [ kron(In, A) kron(B', Im) ] (2)
* [ kron(In, D) kron(E', Im) ],
*
* 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.
* In the process of solving (1), we solve a number of such systems
* where Dim(In), Dim(In) = 1 or 2.
*
* If TRANS = 'T', solve the transposed system Z'*y = scale*b for y,
* 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 is used to compute an estimate of Dif[(A, D), (B, E)] =
* sigma_min(Z) using reverse communicaton with SLACON.
*
* STGSY2 also (IJOB >= 1) contributes to the computation in STGSYL
* of an upper bound on the separation between to matrix pairs. Then
* the input (A, D), (B, E) are subpencils of the matrix pair in
* STGSYL. See STGSYL for details.
*
* Arguments
* =========
*
* TRANS (input) CHARACTER
* = '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: A contribution from this subsystem to a Frobenius
* normbased estimate of the separation between two matrix
* pairs is computed. (look ahead strategy is used).
* = 2: A contribution from this subsystem to a Frobenius
* normbased estimate of the separation between two matrix
* pairs is computed. (SGECON on subsystems is used.)
* Not referenced if TRANS = 'T'.
*
* M (input) INTEGER
* On entry, M specifies the order of A and D, and the row
* dimension of C, F, R and L.
*
* N (input) INTEGER
* On entry, N specifies the order of B and E, and the column
* dimension of C, F, R and L.
*
* A (input) REAL array, dimension (LDA, M)
* On entry, A contains an upper quasi triangular matrix.
*
* LDA (input) INTEGER
* The leading dimension of the matrix A. LDA >= max(1, M).
*
* B (input) REAL array, dimension (LDB, N)
* On entry, B contains an upper quasi triangular matrix.
*
* LDB (input) INTEGER
* The leading dimension of the matrix 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).
* On exit, if IJOB = 0, C has been overwritten by the
* solution R.
*
* LDC (input) INTEGER
* The leading dimension of the matrix C. LDC >= max(1, M).
*
* D (input) REAL array, dimension (LDD, M)
* On entry, D contains an upper triangular matrix.
*
* LDD (input) INTEGER
* The leading dimension of the matrix D. LDD >= max(1, M).
*
* E (input) REAL array, dimension (LDE, N)
* On entry, E contains an upper triangular matrix.
*
* LDE (input) INTEGER
* The leading dimension of the matrix 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).
* On exit, if IJOB = 0, F has been overwritten by the
* solution L.
*
* LDF (input) INTEGER
* The leading dimension of the matrix F. LDF >= max(1, M).
*
* SCALE (output) REAL
* On exit, 0 <= SCALE <= 1. If 0 < SCALE < 1, the solutions
* R and L (C and F on entry) will hold the solutions to a
* slightly perturbed system but the input matrices A, B, D and
* E have not been changed. If SCALE = 0, R and L will hold the
* solutions to the homogeneous system with C = F = 0. Normally,
* SCALE = 1.
*
* RDSUM (input/output) REAL
* On entry, the sum of squares of computed contributions to
* the Difestimate under computation by STGSYL, where the
* scaling factor RDSCAL (see below) has been factored out.
* On exit, the corresponding sum of squares updated with the
* contributions from the current subsystem.
* If TRANS = 'T' RDSUM is not touched.
* NOTE: RDSUM only makes sense when STGSY2 is called by STGSYL.
*
* RDSCAL (input/output) REAL
* On entry, scaling factor used to prevent overflow in RDSUM.
* On exit, RDSCAL is updated w.r.t. the current contributions
* in RDSUM.
* If TRANS = 'T', RDSCAL is not touched.
* NOTE: RDSCAL only makes sense when STGSY2 is called by
* STGSYL.
*
* IWORK (workspace) INTEGER array, dimension (M+N+2)
*
* PQ (output) INTEGER
* On exit, the number of subsystems (of size 2by2, 4by4 and
* 8by8) solved by this routine.
*
* INFO (output) INTEGER
* On exit, if INFO is set to
* =0: Successful exit
* <0: If INFO = i, the ith argument had an illegal value.
* >0: The matrix pairs (A, D) and (B, E) have common or very
* close eigenvalues.
*
* Further Details
* ===============
*
* Based on contributions by
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
* Umea University, S901 87 Umea, Sweden.
*
* =====================================================================
*
* .. Parameters ..
Method Summary 
static void 
STGSY2(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 rdsum,
floatW rdscal,
int[] iwork,
intW pq,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
STGSY2
public STGSY2()
STGSY2
public static void STGSY2(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 rdsum,
floatW rdscal,
int[] iwork,
intW pq,
intW info)