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ctgsy2-f(3)

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 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. 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 sub-pencils 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).

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
 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

 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 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 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 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

 LDC is INTEGER
 The leading dimension of the matrix C. LDC >= max(1, M).

D

 D is COMPLEX 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 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 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

 LDF is INTEGER
 The leading dimension of the matrix F. LDF >= max(1, M).

SCALE

 SCALE 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.

RDSUM

 RDSUM is REAL
 On entry, the sum of squares of computed contributions to
 the Dif-estimate 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 sub-system.
 If TRANS = 'T' RDSUM is not touched.
 NOTE: RDSUM only makes sense when CTGSY2 is called by
 CTGSYL.

RDSCAL

 RDSCAL 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.

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.

 

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, S-901 87 Umea, Sweden.

Definition at line 258 of file ctgsy2.f.

Author

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