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SUBROUTINE <a name="STGEXC.1"></a><a href="stgexc.f.html#STGEXC.1">STGEXC</a>( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, WORK, LWORK, INFO )
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> -- LAPACK routine (version 3.1) --
</span><span class="comment">*</span><span class="comment"> Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
</span><span class="comment">*</span><span class="comment"> November 2006
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Scalar Arguments ..
</span> LOGICAL WANTQ, WANTZ
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, LWORK, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ WORK( * ), Z( LDZ, * )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Purpose
</span><span class="comment">*</span><span class="comment"> =======
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> <a name="STGEXC.20"></a><a href="stgexc.f.html#STGEXC.1">STGEXC</a> reorders the generalized real Schur decomposition of a real
</span><span class="comment">*</span><span class="comment"> matrix pair (A,B) using an orthogonal equivalence transformation
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> (A, B) = Q * (A, B) * Z',
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> so that the diagonal block of (A, B) with row index IFST is moved
</span><span class="comment">*</span><span class="comment"> to row ILST.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> (A, B) must be in generalized real Schur canonical form (as returned
</span><span class="comment">*</span><span class="comment"> by <a name="SGGES.29"></a><a href="sgges.f.html#SGGES.1">SGGES</a>), i.e. A is block upper triangular with 1-by-1 and 2-by-2
</span><span class="comment">*</span><span class="comment"> diagonal blocks. B is upper triangular.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Optionally, the matrices Q and Z of generalized Schur vectors are
</span><span class="comment">*</span><span class="comment"> updated.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
</span><span class="comment">*</span><span class="comment"> Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Arguments
</span><span class="comment">*</span><span class="comment"> =========
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTQ (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> .TRUE. : update the left transformation matrix Q;
</span><span class="comment">*</span><span class="comment"> .FALSE.: do not update Q.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WANTZ (input) LOGICAL
</span><span class="comment">*</span><span class="comment"> .TRUE. : update the right transformation matrix Z;
</span><span class="comment">*</span><span class="comment"> .FALSE.: do not update Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> N (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The order of the matrices A and B. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> A (input/output) REAL array, dimension (LDA,N)
</span><span class="comment">*</span><span class="comment"> On entry, the matrix A in generalized real Schur canonical
</span><span class="comment">*</span><span class="comment"> form.
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix A, again in generalized
</span><span class="comment">*</span><span class="comment"> real Schur canonical form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDA (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array A. LDA >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> B (input/output) REAL array, dimension (LDB,N)
</span><span class="comment">*</span><span class="comment"> On entry, the matrix B in generalized real Schur canonical
</span><span class="comment">*</span><span class="comment"> form (A,B).
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix B, again in generalized
</span><span class="comment">*</span><span class="comment"> real Schur canonical form (A,B).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDB (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array B. LDB >= max(1,N).
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Q (input/output) REAL array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if WANTQ = .TRUE., the orthogonal matrix Q.
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix Q.
</span><span class="comment">*</span><span class="comment"> If WANTQ = .FALSE., Q is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDQ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Q. LDQ >= 1.
</span><span class="comment">*</span><span class="comment"> If WANTQ = .TRUE., LDQ >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Z (input/output) REAL array, dimension (LDZ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if WANTZ = .TRUE., the orthogonal matrix Z.
</span><span class="comment">*</span><span class="comment"> On exit, the updated matrix Z.
</span><span class="comment">*</span><span class="comment"> If WANTZ = .FALSE., Z is not referenced.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDZ (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array Z. LDZ >= 1.
</span><span class="comment">*</span><span class="comment"> If WANTZ = .TRUE., LDZ >= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> IFST (input/output) INTEGER
</span><span class="comment">*</span><span class="comment"> ILST (input/output) INTEGER
</span><span class="comment">*</span><span class="comment"> Specify the reordering of the diagonal blocks of (A, B).
</span><span class="comment">*</span><span class="comment"> The block with row index IFST is moved to row ILST, by a
</span><span class="comment">*</span><span class="comment"> sequence of swapping between adjacent blocks.
</span><span class="comment">*</span><span class="comment"> On exit, if IFST pointed on entry to the second row of
</span><span class="comment">*</span><span class="comment"> a 2-by-2 block, it is changed to point to the first row;
</span><span class="comment">*</span><span class="comment"> ILST always points to the first row of the block in its
</span><span class="comment">*</span><span class="comment"> final position (which may differ from its input value by
</span><span class="comment">*</span><span class="comment"> +1 or -1). 1 <= IFST, ILST <= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace/output) REAL array, dimension (MAX(1,LWORK))
</span><span class="comment">*</span><span class="comment"> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LWORK (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The dimension of the array WORK.
</span><span class="comment">*</span><span class="comment"> LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> If LWORK = -1, then a workspace query is assumed; the routine
</span><span class="comment">*</span><span class="comment"> only calculates the optimal size of the WORK array, returns
</span><span class="comment">*</span><span class="comment"> this value as the first entry of the WORK array, and no error
</span><span class="comment">*</span><span class="comment"> message related to LWORK is issued by <a name="XERBLA.110"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> INFO (output) INTEGER
</span><span class="comment">*</span><span class="comment"> =0: successful exit.
</span><span class="comment">*</span><span class="comment"> <0: if INFO = -i, the i-th argument had an illegal value.
</span><span class="comment">*</span><span class="comment"> =1: The transformed matrix pair (A, B) would be too far
</span><span class="comment">*</span><span class="comment"> from generalized Schur form; the problem is ill-
</span><span class="comment">*</span><span class="comment"> conditioned. (A, B) may have been partially reordered,
</span><span class="comment">*</span><span class="comment"> and ILST points to the first row of the current
</span><span class="comment">*</span><span class="comment"> position of the block being moved.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Further Details
</span><span class="comment">*</span><span class="comment"> ===============
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Based on contributions by
</span><span class="comment">*</span><span class="comment"> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
</span><span class="comment">*</span><span class="comment"> Umea University, S-901 87 Umea, Sweden.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
</span><span class="comment">*</span><span class="comment"> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
</span><span class="comment">*</span><span class="comment"> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
</span><span class="comment">*</span><span class="comment"> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> =====================================================================
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> .. Parameters ..
</span> REAL ZERO
PARAMETER ( ZERO = 0.0E+0 )
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Local Scalars ..
</span> LOGICAL LQUERY
INTEGER HERE, LWMIN, NBF, NBL, NBNEXT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="STGEX2.144"></a><a href="stgex2.f.html#STGEX2.1">STGEX2</a>, <a name="XERBLA.144"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Intrinsic Functions ..
</span> INTRINSIC MAX
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Executable Statements ..
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Decode and test input arguments.
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span> IF( INFO.EQ.0 ) THEN
IF( N.LE.1 ) THEN
LWMIN = 1
ELSE
LWMIN = 4*N + 16
END IF
WORK(1) = LWMIN
<span class="comment">*</span><span class="comment">
</span> IF (LWORK.LT.LWMIN .AND. .NOT.LQUERY) THEN
INFO = -15
END IF
END IF
<span class="comment">*</span><span class="comment">
</span> IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.185"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="STGEXC.185"></a><a href="stgexc.f.html#STGEXC.1">STGEXC</a>'</span>, -INFO )
RETURN
ELSE IF( LQUERY ) THEN
RETURN
END IF
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Quick return if possible
</span><span class="comment">*</span><span class="comment">
</span> IF( N.LE.1 )
$ RETURN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine the first row of the specified block and find out
</span><span class="comment">*</span><span class="comment"> if it is 1-by-1 or 2-by-2.
</span><span class="comment">*</span><span class="comment">
</span> 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
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Determine the first row of the final block
</span><span class="comment">*</span><span class="comment"> and find out if it is 1-by-1 or 2-by-2.
</span><span class="comment">*</span><span class="comment">
</span> IF( ILST.GT.1 ) THEN
IF( A( ILST, ILST-1 ).NE.ZERO )
$ ILST = ILST - 1
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