org.netlib.lapack
Class DTGSY2

java.lang.Object
  extended by org.netlib.lapack.DTGSY2

public class DTGSY2
extends java.lang.Object

DTGSY2 is a simplified interface to the JLAPACK routine dtgsy2.
This interface converts Java-style 2D row-major arrays into
the 1D column-major 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 * ======= * * 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 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 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 sub-pencils 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 * 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. (DGECON 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) 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 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) 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 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) 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 Dif-estimate 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 sub-system. * 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 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 ..


Constructor Summary
DTGSY2()
           
 
Method Summary
static void DTGSY2(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 rdsum, doubleW 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
 

Constructor Detail

DTGSY2

public DTGSY2()
Method Detail

DTGSY2

public static void DTGSY2(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 rdsum,
                          doubleW rdscal,
                          int[] iwork,
                          intW pq,
                          intW info)