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SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO )
*
* -- LAPACK routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
LOGICAL WANTQ, WANTZ
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* ZTGEXC reorders the generalized Schur decomposition of a complex
* matrix pair (A,B), using an unitary equivalence transformation
* (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with
* row index IFST is moved to row ILST.
*
* (A, B) must be in generalized Schur canonical form, that is, A and
* B are both 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)'
* Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
*
* Arguments
* =========
*
* WANTQ (input) LOGICAL
* .TRUE. : update the left transformation matrix Q;
* .FALSE.: do not update Q.
*
* WANTZ (input) LOGICAL
* .TRUE. : update the right transformation matrix Z;
* .FALSE.: do not update Z.
*
* N (input) INTEGER
* The order of the matrices A and B. N >= 0.
*
* A (input/output) COMPLEX*16 array, dimension (LDA,N)
* On entry, the upper triangular matrix A in the pair (A, B).
* On exit, the updated matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* B (input/output) COMPLEX*16 array, dimension (LDB,N)
* On entry, the upper triangular matrix B in the pair (A, B).
* On exit, the updated matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* Q (input/output) COMPLEX*16 array, dimension (LDZ,N)
* On entry, if WANTQ = .TRUE., the unitary matrix Q.
* On exit, the updated matrix Q.
* If WANTQ = .FALSE., Q is not referenced.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= 1;
* If WANTQ = .TRUE., LDQ >= N.
*
* Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
* On entry, if WANTZ = .TRUE., the unitary matrix Z.
* On exit, the updated matrix Z.
* If WANTZ = .FALSE., Z is not referenced.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1;
* If WANTZ = .TRUE., LDZ >= N.
*
* IFST (input) INTEGER
* ILST (input/output) INTEGER
* Specify the reordering of the diagonal blocks of (A, B).
* The block with row index IFST is moved to row ILST, by a
* sequence of swapping between adjacent blocks.
*
* INFO (output) INTEGER
* =0: Successful exit.
* <0: if INFO = -i, the i-th argument had an illegal value.
* =1: The transformed matrix pair (A, B) would be too far
* from generalized Schur form; the problem is ill-
* conditioned. (A, B) may have been partially reordered,
* and ILST points to the first row of the current
* position of the block being moved.
*
*
* Further Details
* ===============
*
* Based on contributions by
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
* Umea University, S-901 87 Umea, Sweden.
*
* [1] B. Kagstrom; 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] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
* Eigenvalues of a Regular Matrix Pair (A, B) and Condition
* Estimation: Theory, Algorithms and Software, Report
* UMINF - 94.04, Department of Computing Science, Umea University,
* S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
* To appear in Numerical Algorithms, 1996.
*
* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
* for Solving the Generalized Sylvester Equation and Estimating the
* Separation between Regular Matrix Pairs, Report UMINF - 93.23,
* Department of Computing Science, Umea University, S-901 87 Umea,
* Sweden, December 1993, Revised April 1994, Also as LAPACK working
* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
* 1996.
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER HERE
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZTGEX2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Decode and test input arguments.
INFO = 0
IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
INFO = -9
ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
INFO = -11
ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
INFO = -12
ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
INFO = -13
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZTGEXC', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 )
$ RETURN
IF( IFST.EQ.ILST )
$ RETURN
*
IF( IFST.LT.ILST ) THEN
*
HERE = IFST
*
10 CONTINUE
*
* Swap with next one below
*
CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
$ HERE, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 1
IF( HERE.LT.ILST )
$ GO TO 10
HERE = HERE - 1
ELSE
HERE = IFST - 1
*
20 CONTINUE
*
* Swap with next one above
*
CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
$ HERE, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 1
IF( HERE.GE.ILST )
$ GO TO 20
HERE = HERE + 1
END IF
ILST = HERE
RETURN
*
* End of ZTGEXC
*
END
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