
NAMEztgsy2.f SYNOPSISFunctions/Subroutinessubroutine ztgsy2 (TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, INFO) Function/Subroutine Documentationsubroutine ztgsy2 (characterTRANS, integerIJOB, integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldc, * )C, integerLDC, complex*16, dimension( ldd, * )D, integerLDD, complex*16, dimension( lde, * )E, integerLDE, complex*16, dimension( ldf, * )F, integerLDF, double precisionSCALE, double precisionRDSUM, double precisionRDSCAL, integerINFO)ZTGSY2 solves the generalized Sylvester equation (unblocked algorithm). Purpose:ZTGSY2 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. A, B, D and E are upper triangular (i.e., (A,D) and (B,E) in generalized Schur form). 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 Zx = scale * b, where Z is defined as Z = [ kron(In, A) kron(B**H, Im) ] (2) [ kron(In, D) kron(E**H, Im) ], Ik is the identity matrix of size k and X**H is the conjuguate transpose of X. kron(X, Y) is the Kronecker product between the matrices X and Y. If TRANS = 'C', y in the conjugate transposed system Z**H*y = scale*b is solved for, which is equivalent to solve for R and L in A**H * R + D**H * L = scale * C (3) R * B**H + L * E**H = scale * F This case is used to compute an estimate of Dif[(A, D), (B, E)] = = sigma_min(Z) using reverse communicaton with ZLACON. ZTGSY2 also (IJOB >= 1) contributes to the computation in ZTGSYL of an upper bound on the separation between to matrix pairs. Then the input (A, D), (B, E) are subpencils of two matrix pairs in ZTGSYL. TRANS
Author:
TRANS is CHARACTER*1 = 'N', solve the generalized Sylvester equation (1). = 'T': solve the 'transposed' system (3).IJOB IJOB is 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 M is INTEGER On entry, M specifies the order of A and D, and the row dimension of C, F, R and L.N N is INTEGER On entry, N specifies the order of B and E, and the column dimension of C, F, R and L.A A is COMPLEX*16 array, dimension (LDA, M) On entry, A contains an upper triangular matrix.LDA LDA is INTEGER The leading dimension of the matrix A. LDA >= max(1, M).B B is COMPLEX*16 array, dimension (LDB, N) On entry, B contains an upper triangular matrix.LDB LDB is INTEGER The leading dimension of the matrix B. LDB >= max(1, N).C C is COMPLEX*16 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 LDC is INTEGER The leading dimension of the matrix C. LDC >= max(1, M).D D is COMPLEX*16 array, dimension (LDD, M) On entry, D contains an upper triangular matrix.LDD LDD is INTEGER The leading dimension of the matrix D. LDD >= max(1, M).E E is COMPLEX*16 array, dimension (LDE, N) On entry, E contains an upper triangular matrix.LDE LDE is INTEGER The leading dimension of the matrix E. LDE >= max(1, N).F F is COMPLEX*16 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 LDF is INTEGER The leading dimension of the matrix F. LDF >= max(1, M).SCALE SCALE is 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 RDSUM is DOUBLE PRECISION On entry, the sum of squares of computed contributions to the Difestimate under computation by ZTGSYL, 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 ZTGSY2 is called by ZTGSYL.RDSCAL RDSCAL is 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 ZTGSY2 is called by ZTGSYL.INFO INFO is INTEGER On exit, if INFO is set to =0: Successful exit <0: If INFO = i, input argument number i is illegal. >0: The matrix pairs (A, D) and (B, E) have common or very close eigenvalues. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
September 2012
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing
Science, Umea University, S901 87 Umea, Sweden.
Definition at line 258 of file ztgsy2.f.
AuthorGenerated automatically by Doxygen for LAPACK from the source code.
Visit the GSP FreeBSD Man Page Interface. 