ctgsy2.f (3)  Linux Manuals
NAME
ctgsy2.f 
SYNOPSIS
Functions/Subroutines
subroutine ctgsy2 (TRANS, IJOB, M, N, A, LDA, B, LDB, C, LDC, D, LDD, E, LDE, F, LDF, SCALE, RDSUM, RDSCAL, INFO)
CTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
Function/Subroutine Documentation
subroutine ctgsy2 (characterTRANS, integerIJOB, integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( ldb, * )B, integerLDB, complex, dimension( ldc, * )C, integerLDC, complex, dimension( ldd, * )D, integerLDD, complex, dimension( lde, * )E, integerLDE, complex, dimension( ldf, * )F, integerLDF, realSCALE, realRDSUM, realRDSCAL, integerINFO)
CTGSY2 solves the generalized Sylvester equation (unblocked algorithm).
Purpose:

CTGSY2 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 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 CLACON. CTGSY2 also (IJOB >= 1) contributes to the computation in CTGSYL 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 CTGSYL.
Parameters:

TRANS
TRANS is CHARACTER*1 = 'N', solve the generalized Sylvester equation (1). = 'T': solve the 'transposed' system (3).
IJOBIJOB 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. (SGECON on subsystems is used.) Not referenced if TRANS = 'T'.
MM is INTEGER On entry, M specifies the order of A and D, and the row dimension of C, F, R and L.
NN is INTEGER On entry, N specifies the order of B and E, and the column dimension of C, F, R and L.
AA is COMPLEX array, dimension (LDA, M) On entry, A contains an upper triangular matrix.
LDALDA is INTEGER The leading dimension of the matrix A. LDA >= max(1, M).
BB is COMPLEX array, dimension (LDB, N) On entry, B contains an upper triangular matrix.
LDBLDB is INTEGER The leading dimension of the matrix B. LDB >= max(1, N).
CC is COMPLEX 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.
LDCLDC is INTEGER The leading dimension of the matrix C. LDC >= max(1, M).
DD is COMPLEX array, dimension (LDD, M) On entry, D contains an upper triangular matrix.
LDDLDD is INTEGER The leading dimension of the matrix D. LDD >= max(1, M).
EE is COMPLEX array, dimension (LDE, N) On entry, E contains an upper triangular matrix.
LDELDE is INTEGER The leading dimension of the matrix E. LDE >= max(1, N).
FF is COMPLEX 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.
LDFLDF is INTEGER The leading dimension of the matrix F. LDF >= max(1, M).
SCALESCALE is 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.
RDSUMRDSUM is REAL On entry, the sum of squares of computed contributions to the Difestimate under computation by CTGSYL, 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 CTGSY2 is called by CTGSYL.
RDSCALRDSCAL is 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 CTGSY2 is called by CTGSYL.
INFOINFO 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.
Author:

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 ctgsy2.f.
Author
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