org.netlib.lapack
Class Stgsy2
java.lang.Object
org.netlib.lapack.Stgsy2
public class Stgsy2
- 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
* =======
*
* 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 M-by-N matrices,
* (A, D), (B, E) and (C, F) are given matrix pairs of size M-by-M,
* N-by-N and M-by-N, 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 sub-pencils 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
* norm-based estimate of the separation between two matrix
* pairs is computed. (look ahead strategy is used).
* = 2: A contribution from this subsystem to a Frobenius
* norm-based estimate of the separation between two matrix
* pairs is computed. (SGECON on sub-systems 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 right-hand-side 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 right-hand-side 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 Dif-estimate 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 sub-system.
* 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 2-by-2, 4-by-4 and
* 8-by-8) solved by this routine.
*
* INFO (output) INTEGER
* On exit, if INFO is set to
* =0: Successful exit
* <0: If INFO = -i, the i-th 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, S-901 87 Umea, Sweden.
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
stgsy2(java.lang.String trans,
int ijob,
int m,
int n,
float[] a,
int _a_offset,
int lda,
float[] b,
int _b_offset,
int ldb,
float[] c,
int _c_offset,
int Ldc,
float[] d,
int _d_offset,
int ldd,
float[] e,
int _e_offset,
int lde,
float[] f,
int _f_offset,
int ldf,
floatW scale,
floatW rdsum,
floatW 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 |
Stgsy2
public Stgsy2()
stgsy2
public static void stgsy2(java.lang.String trans,
int ijob,
int m,
int n,
float[] a,
int _a_offset,
int lda,
float[] b,
int _b_offset,
int ldb,
float[] c,
int _c_offset,
int Ldc,
float[] d,
int _d_offset,
int ldd,
float[] e,
int _e_offset,
int lde,
float[] f,
int _f_offset,
int ldf,
floatW scale,
floatW rdsum,
floatW rdscal,
int[] iwork,
int _iwork_offset,
intW pq,
intW info)