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SUBROUTINE <a name="STREXC.1"></a><a href="strexc.f.html#STREXC.1">STREXC</a>( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
$ 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> CHARACTER COMPQ
INTEGER IFST, ILST, INFO, LDQ, LDT, N
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. Array Arguments ..
</span> REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
<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="STREXC.19"></a><a href="strexc.f.html#STREXC.1">STREXC</a> reorders the real Schur factorization of a real matrix
</span><span class="comment">*</span><span class="comment"> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is
</span><span class="comment">*</span><span class="comment"> moved to row ILST.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> The real Schur form T is reordered by an orthogonal similarity
</span><span class="comment">*</span><span class="comment"> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors
</span><span class="comment">*</span><span class="comment"> is updated by postmultiplying it with Z.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T must be in Schur canonical form (as returned by <a name="SHSEQR.27"></a><a href="shseqr.f.html#SHSEQR.1">SHSEQR</a>), that is,
</span><span class="comment">*</span><span class="comment"> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
</span><span class="comment">*</span><span class="comment"> 2-by-2 diagonal block has its diagonal elements equal and its
</span><span class="comment">*</span><span class="comment"> off-diagonal elements of opposite sign.
</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"> COMPQ (input) CHARACTER*1
</span><span class="comment">*</span><span class="comment"> = 'V': update the matrix Q of Schur vectors;
</span><span class="comment">*</span><span class="comment"> = 'N': do not update Q.
</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 matrix T. N >= 0.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> T (input/output) REAL array, dimension (LDT,N)
</span><span class="comment">*</span><span class="comment"> On entry, the upper quasi-triangular matrix T, in Schur
</span><span class="comment">*</span><span class="comment"> Schur canonical form.
</span><span class="comment">*</span><span class="comment"> On exit, the reordered upper quasi-triangular matrix, again
</span><span class="comment">*</span><span class="comment"> in Schur canonical form.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> LDT (input) INTEGER
</span><span class="comment">*</span><span class="comment"> The leading dimension of the array T. LDT >= 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 (LDQ,N)
</span><span class="comment">*</span><span class="comment"> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
</span><span class="comment">*</span><span class="comment"> On exit, if COMPQ = 'V', Q has been postmultiplied by the
</span><span class="comment">*</span><span class="comment"> orthogonal transformation matrix Z which reorders T.
</span><span class="comment">*</span><span class="comment"> If COMPQ = 'N', 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 >= max(1,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 T.
</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 transpositions between adjacent blocks.
</span><span class="comment">*</span><span class="comment"> On exit, if IFST pointed on entry to the second row of a
</span><span class="comment">*</span><span class="comment"> 2-by-2 block, it is changed to point to the first row; ILST
</span><span class="comment">*</span><span class="comment"> always points to the first row of the block in its final
</span><span class="comment">*</span><span class="comment"> position (which may differ from its input value by +1 or -1).
</span><span class="comment">*</span><span class="comment"> 1 <= IFST <= N; 1 <= ILST <= N.
</span><span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> WORK (workspace) REAL array, dimension (N)
</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: two adjacent blocks were too close to swap (the problem
</span><span class="comment">*</span><span class="comment"> is very ill-conditioned); T may have been partially
</span><span class="comment">*</span><span class="comment"> reordered, and ILST points to the first row of the
</span><span class="comment">*</span><span class="comment"> current position of the block being moved.
</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 WANTQ
INTEGER HERE, NBF, NBL, NBNEXT
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Functions ..
</span> LOGICAL <a name="LSAME.92"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
EXTERNAL <a name="LSAME.93"></a><a href="lsame.f.html#LSAME.1">LSAME</a>
<span class="comment">*</span><span class="comment"> ..
</span><span class="comment">*</span><span class="comment"> .. External Subroutines ..
</span> EXTERNAL <a name="SLAEXC.96"></a><a href="slaexc.f.html#SLAEXC.1">SLAEXC</a>, <a name="XERBLA.96"></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 the input arguments.
</span><span class="comment">*</span><span class="comment">
</span> INFO = 0
WANTQ = <a name="LSAME.106"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPQ, <span class="string">'V'</span> )
IF( .NOT.WANTQ .AND. .NOT.<a name="LSAME.107"></a><a href="lsame.f.html#LSAME.1">LSAME</a>( COMPQ, <span class="string">'N'</span> ) ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
INFO = -6
ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
INFO = -7
ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL <a name="XERBLA.121"></a><a href="xerbla.f.html#XERBLA.1">XERBLA</a>( <span class="string">'<a name="STREXC.121"></a><a href="strexc.f.html#STREXC.1">STREXC</a>'</span>, -INFO )
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 specified block
</span><span class="comment">*</span><span class="comment"> and find out it is 1 by 1 or 2 by 2.
</span><span class="comment">*</span><span class="comment">
</span> IF( IFST.GT.1 ) THEN
IF( T( IFST, IFST-1 ).NE.ZERO )
$ IFST = IFST - 1
END IF
NBF = 1
IF( IFST.LT.N ) THEN
IF( T( 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 it is 1 by 1 or 2 by 2.
</span><span class="comment">*</span><span class="comment">
</span> IF( ILST.GT.1 ) THEN
IF( T( ILST, ILST-1 ).NE.ZERO )
$ ILST = ILST - 1
END IF
NBL = 1
IF( ILST.LT.N ) THEN
IF( T( ILST+1, ILST ).NE.ZERO )
$ NBL = 2
END IF
<span class="comment">*</span><span class="comment">
</span> IF( IFST.EQ.ILST )
$ RETURN
<span class="comment">*</span><span class="comment">
</span> IF( IFST.LT.ILST ) THEN
<span class="comment">*</span><span class="comment">
</span><span class="comment">*</span><span class="comment"> Update ILST
</span><span class="comment">*</span><span class="comment">
</span> IF( NBF.EQ.2 .AND. NBL.EQ.1 )
$ ILST = ILST - 1
IF( NBF.EQ.1 .AND. NBL.EQ.2 )
$ ILST = ILST + 1
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