Purpose
To swap adjacent diagonal blocks A11*B11 and A22*B22 of size
1-by-1 or 2-by-2 in an upper (quasi) triangular matrix product
A*B by an orthogonal equivalence transformation.
(A, B) must be in periodic real Schur canonical form (as returned
by SLICOT Library routine MB03XP), i.e., A is block upper
triangular with 1-by-1 and 2-by-2 diagonal blocks, and B is upper
triangular.
Optionally, the matrices Q and Z of generalized Schur vectors are
updated.
Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)',
Z(in) * B(in) * Q(in)' = Z(out) * B(out) * Q(out)'.
This routine is largely based on the LAPACK routine DTGEX2
developed by Bo Kagstrom and Peter Poromaa.
Specification
SUBROUTINE MB03WA( WANTQ, WANTZ, N1, N2, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, INFO )
C .. Scalar Arguments ..
LOGICAL WANTQ, WANTZ
INTEGER INFO, LDA, LDB, LDQ, LDZ, N1, N2
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), B(LDB,*), Q(LDQ,*), Z(LDZ,*)
Arguments
Mode Parameters
WANTQ LOGICAL
Indicates whether or not the user wishes to accumulate
the matrix Q as follows:
= .TRUE. : The matrix Q is updated;
= .FALSE.: the matrix Q is not required.
WANTZ LOGICAL
Indicates whether or not the user wishes to accumulate
the matrix Z as follows:
= .TRUE. : The matrix Z is updated;
= .FALSE.: the matrix Z is not required.
Input/Output Parameters
N1 (input) INTEGER
The order of the first block A11*B11. N1 = 0, 1 or 2.
N2 (input) INTEGER
The order of the second block A22*B22. N2 = 0, 1 or 2.
A (input/output) DOUBLE PRECISION array, dimension
(LDA,N1+N2)
On entry, the leading (N1+N2)-by-(N1+N2) part of this
array must contain the matrix A.
On exit, the leading (N1+N2)-by-(N1+N2) part of this array
contains the matrix A of the reordered pair.
LDA INTEGER
The leading dimension of the array A. LDA >= MAX(1,N1+N2).
B (input/output) DOUBLE PRECISION array, dimension
(LDB,N1+N2)
On entry, the leading (N1+N2)-by-(N1+N2) part of this
array must contain the matrix B.
On exit, the leading (N1+N2)-by-(N1+N2) part of this array
contains the matrix B of the reordered pair.
LDB INTEGER
The leading dimension of the array B. LDB >= MAX(1,N1+N2).
Q (input/output) DOUBLE PRECISION array, dimension
(LDQ,N1+N2)
On entry, if WANTQ = .TRUE., the leading
(N1+N2)-by-(N1+N2) part of this array must contain the
orthogonal matrix Q.
On exit, the leading (N1+N2)-by-(N1+N2) part of this array
contains the updated matrix Q. Q will be a rotation
matrix for N1=N2=1.
This array is not referenced if WANTQ = .FALSE..
LDQ INTEGER
The leading dimension of the array Q. LDQ >= 1.
If WANTQ = .TRUE., LDQ >= N1+N2.
Z (input/output) DOUBLE PRECISION array, dimension
(LDZ,N1+N2)
On entry, if WANTZ = .TRUE., the leading
(N1+N2)-by-(N1+N2) part of this array must contain the
orthogonal matrix Z.
On exit, the leading (N1+N2)-by-(N1+N2) part of this array
contains the updated matrix Z. Z will be a rotation
matrix for N1=N2=1.
This array is not referenced if WANTZ = .FALSE..
LDZ INTEGER
The leading dimension of the array Z. LDZ >= 1.
If WANTZ = .TRUE., LDZ >= N1+N2.
Error Indicator
INFO INTEGER
= 0: successful exit;
= 1: the transformed matrix (A, B) would be
too far from periodic Schur form; the blocks are
not swapped and (A,B) and (Q,Z) are unchanged.
Method
In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.References
[1] Kagstrom, B.
A direct method for reordering eigenvalues in the generalized
real Schur form of a regular matrix pair (A,B), in M.S. Moonen
et al (eds.), Linear Algebra for Large Scale and Real-Time
Applications, Kluwer Academic Publ., 1993, pp. 195-218.
[2] Kagstrom, B., and Poromaa, P.
Computing eigenspaces with specified eigenvalues of a regular
matrix pair (A, B) and condition estimation: Theory,
algorithms and software, Numer. Algorithms, 1996, vol. 12,
pp. 369-407.
Further Comments
NoneExample
Program Text
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