ctgsy2.f (3) Linux Manual Page

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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