SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, WORK, LWORK, 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, LWORK, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ WORK( * ), Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* DTGEXC reorders the generalized real Schur decomposition of a real
* matrix pair (A,B) using an orthogonal 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 real Schur canonical form (as returned
* by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2
* diagonal blocks. 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)'
* 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) DOUBLE PRECISION array, dimension (LDA,N)
* On entry, the matrix A in generalized real Schur canonical
* form.
* On exit, the updated matrix A, again in generalized
* real Schur canonical form.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB,N)
* On entry, the matrix B in generalized real Schur canonical
* form (A,B).
* On exit, the updated matrix B, again in generalized
* real Schur canonical form (A,B).
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* Q (input/output) DOUBLE PRECISION array, dimension (LDZ,N)
* On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N)
* On entry, if WANTZ = .TRUE., the orthogonal 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/output) 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.
* On exit, if IFST pointed on entry to the second row of
* a 2-by-2 block, it is changed to point to the first row;
* ILST always points to the first row of the block in its
* final position (which may differ from its input value by
* +1 or -1). 1 <= IFST, ILST <= N.
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
* LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* 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.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL LQUERY
INTEGER HERE, LWMIN, NBF, NBL, NBNEXT
* ..
* .. External Subroutines ..
EXTERNAL DTGEX2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Decode and test input arguments.
*
INFO = 0
LQUERY = ( LWORK.EQ.-1 )
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.EQ.0 ) THEN
IF( N.LE.1 ) THEN
LWMIN = 1
ELSE
LWMIN = 4*N + 16
END IF
WORK(1) = LWMIN
*
IF (LWORK.LT.LWMIN .AND. .NOT.LQUERY) THEN
INFO = -15
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DTGEXC', -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 )
$ RETURN
*
* Determine the first row of the specified block and find out
* if it is 1-by-1 or 2-by-2.
*
IF( IFST.GT.1 ) THEN
IF( A( IFST, IFST-1 ).NE.ZERO )
$ IFST = IFST - 1
END IF
NBF = 1
IF( IFST.LT.N ) THEN
IF( A( IFST+1, IFST ).NE.ZERO )
$ NBF = 2
END IF
*
* Determine the first row of the final block
* and find out if it is 1-by-1 or 2-by-2.
*
IF( ILST.GT.1 ) THEN
IF( A( ILST, ILST-1 ).NE.ZERO )
$ ILST = ILST - 1
END IF
NBL = 1
IF( ILST.LT.N ) THEN
IF( A( ILST+1, ILST ).NE.ZERO )
$ NBL = 2
END IF
IF( IFST.EQ.ILST )
$ RETURN
*
IF( IFST.LT.ILST ) THEN
*
* Update ILST.
*
IF( NBF.EQ.2 .AND. NBL.EQ.1 )
$ ILST = ILST - 1
IF( NBF.EQ.1 .AND. NBL.EQ.2 )
$ ILST = ILST + 1
*
HERE = IFST
*
10 CONTINUE
*
* Swap with next one below.
*
IF( NBF.EQ.1 .OR. NBF.EQ.2 ) THEN
*
* Current block either 1-by-1 or 2-by-2.
*
NBNEXT = 1
IF( HERE+NBF+1.LE.N ) THEN
IF( A( HERE+NBF+1, HERE+NBF ).NE.ZERO )
$ NBNEXT = 2
END IF
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, HERE, NBF, NBNEXT, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + NBNEXT
*
* Test if 2-by-2 block breaks into two 1-by-1 blocks.
*
IF( NBF.EQ.2 ) THEN
IF( A( HERE+1, HERE ).EQ.ZERO )
$ NBF = 3
END IF
*
ELSE
*
* Current block consists of two 1-by-1 blocks, each of which
* must be swapped individually.
*
NBNEXT = 1
IF( HERE+3.LE.N ) THEN
IF( A( HERE+3, HERE+2 ).NE.ZERO )
$ NBNEXT = 2
END IF
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, HERE+1, 1, NBNEXT, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
IF( NBNEXT.EQ.1 ) THEN
*
* Swap two 1-by-1 blocks.
*
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, HERE, 1, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 1
*
ELSE
*
* Recompute NBNEXT in case of 2-by-2 split.
*
IF( A( HERE+2, HERE+1 ).EQ.ZERO )
$ NBNEXT = 1
IF( NBNEXT.EQ.2 ) THEN
*
* 2-by-2 block did not split.
*
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, HERE, 1, NBNEXT, WORK, LWORK,
$ INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 2
ELSE
*
* 2-by-2 block did split.
*
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 1
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 1
END IF
*
END IF
END IF
IF( HERE.LT.ILST )
$ GO TO 10
ELSE
HERE = IFST
*
20 CONTINUE
*
* Swap with next one below.
*
IF( NBF.EQ.1 .OR. NBF.EQ.2 ) THEN
*
* Current block either 1-by-1 or 2-by-2.
*
NBNEXT = 1
IF( HERE.GE.3 ) THEN
IF( A( HERE-1, HERE-2 ).NE.ZERO )
$ NBNEXT = 2
END IF
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, HERE-NBNEXT, NBNEXT, NBF, WORK, LWORK,
$ INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - NBNEXT
*
* Test if 2-by-2 block breaks into two 1-by-1 blocks.
*
IF( NBF.EQ.2 ) THEN
IF( A( HERE+1, HERE ).EQ.ZERO )
$ NBF = 3
END IF
*
ELSE
*
* Current block consists of two 1-by-1 blocks, each of which
* must be swapped individually.
*
NBNEXT = 1
IF( HERE.GE.3 ) THEN
IF( A( HERE-1, HERE-2 ).NE.ZERO )
$ NBNEXT = 2
END IF
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, HERE-NBNEXT, NBNEXT, 1, WORK, LWORK,
$ INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
IF( NBNEXT.EQ.1 ) THEN
*
* Swap two 1-by-1 blocks.
*
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, HERE, NBNEXT, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 1
ELSE
*
* Recompute NBNEXT in case of 2-by-2 split.
*
IF( A( HERE, HERE-1 ).EQ.ZERO )
$ NBNEXT = 1
IF( NBNEXT.EQ.2 ) THEN
*
* 2-by-2 block did not split.
*
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, HERE-1, 2, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 2
ELSE
*
* 2-by-2 block did split.
*
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 1
CALL DTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ,
$ Z, LDZ, HERE, 1, 1, WORK, LWORK, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 1
END IF
END IF
END IF
IF( HERE.GT.ILST )
$ GO TO 20
END IF
ILST = HERE
WORK( 1 ) = LWMIN
RETURN
*
* End of DTGEXC
*
END