org.netlib.lapack
Class Dtgsy2
java.lang.Object
org.netlib.lapack.Dtgsy2
public class Dtgsy2
 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
* =======
*
* DTGSY2 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 DLACON.
*
* DTGSY2 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
* DTGSYL. 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. (DGECON 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION
* 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) DOUBLE PRECISION
* On entry, the sum of squares of computed contributions to
* the Difestimate under computation by DTGSYL, 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 DTGSY2 is called by STGSYL.
*
* RDSCAL (input/output) DOUBLE PRECISION
* 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 DTGSY2 is called by
* DTGSYL.
*
* 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 
dtgsy2(java.lang.String trans,
int ijob,
int m,
int n,
double[] a,
int _a_offset,
int lda,
double[] b,
int _b_offset,
int ldb,
double[] c,
int _c_offset,
int Ldc,
double[] d,
int _d_offset,
int ldd,
double[] e,
int _e_offset,
int lde,
double[] f,
int _f_offset,
int ldf,
doubleW scale,
doubleW rdsum,
doubleW rdscal,
int[] iwork,
int _iwork_offset,
intW pq,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Dtgsy2
public Dtgsy2()
dtgsy2
public static void dtgsy2(java.lang.String trans,
int ijob,
int m,
int n,
double[] a,
int _a_offset,
int lda,
double[] b,
int _b_offset,
int ldb,
double[] c,
int _c_offset,
int Ldc,
double[] d,
int _d_offset,
int ldd,
double[] e,
int _e_offset,
int lde,
double[] f,
int _f_offset,
int ldf,
doubleW scale,
doubleW rdsum,
doubleW rdscal,
int[] iwork,
int _iwork_offset,
intW pq,
intW info)