*> \brief \b STREXC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download STREXC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE STREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, * INFO ) * * .. Scalar Arguments .. * CHARACTER COMPQ * INTEGER IFST, ILST, INFO, LDQ, LDT, N * .. * .. Array Arguments .. * REAL Q( LDQ, * ), T( LDT, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STREXC reorders the real Schur factorization of a real matrix *> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is *> moved to row ILST. *> *> The real Schur form T is reordered by an orthogonal similarity *> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors *> is updated by postmultiplying it with Z. *> *> T must be in Schur canonical form (as returned by SHSEQR), that is, *> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each *> 2-by-2 diagonal block has its diagonal elements equal and its *> off-diagonal elements of opposite sign. *> \endverbatim * * Arguments: * ========== * *> \param[in] COMPQ *> \verbatim *> COMPQ is CHARACTER*1 *> = 'V': update the matrix Q of Schur vectors; *> = 'N': do not update Q. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix T. N >= 0. *> If N == 0 arguments ILST and IFST may be any value. *> \endverbatim *> *> \param[in,out] T *> \verbatim *> T is REAL array, dimension (LDT,N) *> On entry, the upper quasi-triangular matrix T, in Schur *> Schur canonical form. *> On exit, the reordered upper quasi-triangular matrix, again *> in Schur canonical form. *> \endverbatim *> *> \param[in] LDT *> \verbatim *> LDT is INTEGER *> The leading dimension of the array T. LDT >= max(1,N). *> \endverbatim *> *> \param[in,out] Q *> \verbatim *> Q is REAL array, dimension (LDQ,N) *> On entry, if COMPQ = 'V', the matrix Q of Schur vectors. *> On exit, if COMPQ = 'V', Q has been postmultiplied by the *> orthogonal transformation matrix Z which reorders T. *> If COMPQ = 'N', Q is not referenced. *> \endverbatim *> *> \param[in] LDQ *> \verbatim *> LDQ is INTEGER *> The leading dimension of the array Q. LDQ >= 1, and if *> COMPQ = 'V', LDQ >= max(1,N). *> \endverbatim *> *> \param[in,out] IFST *> \verbatim *> IFST is INTEGER *> \endverbatim *> *> \param[in,out] ILST *> \verbatim *> ILST is INTEGER *> *> Specify the reordering of the diagonal blocks of T. *> The block with row index IFST is moved to row ILST, by a *> sequence of transpositions 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 <= N; 1 <= ILST <= N. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> = 1: two adjacent blocks were too close to swap (the problem *> is very ill-conditioned); T may have been partially *> reordered, and ILST points to the first row of the *> current position of the block being moved. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup realOTHERcomputational * * ===================================================================== SUBROUTINE STREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, \$ INFO ) * * -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER COMPQ INTEGER IFST, ILST, INFO, LDQ, LDT, N * .. * .. Array Arguments .. REAL Q( LDQ, * ), T( LDT, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL WANTQ INTEGER HERE, NBF, NBL, NBNEXT * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SLAEXC, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Decode and test the input arguments. * INFO = 0 WANTQ = LSAME( COMPQ, 'V' ) IF( .NOT.WANTQ .AND. .NOT.LSAME( COMPQ, 'N' ) ) 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 ).AND.( N.GT.0 )) THEN INFO = -7 ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STREXC', -INFO ) RETURN END IF * * Quick return if possible * IF( N.LE.1 ) \$ RETURN * * Determine the first row of specified block * and find out it is 1 by 1 or 2 by 2. * 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 * * Determine the first row of the final block * and find out it is 1 by 1 or 2 by 2. * 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 * 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 block 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( T( HERE+NBF+1, HERE+NBF ).NE.ZERO ) \$ NBNEXT = 2 END IF CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, NBF, NBNEXT, \$ WORK, 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( T( 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( T( HERE+3, HERE+2 ).NE.ZERO ) \$ NBNEXT = 2 END IF CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE+1, 1, NBNEXT, \$ WORK, INFO ) IF( INFO.NE.0 ) THEN ILST = HERE RETURN END IF IF( NBNEXT.EQ.1 ) THEN * * Swap two 1 by 1 blocks, no problems possible * CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, 1, NBNEXT, \$ WORK, INFO ) HERE = HERE + 1 ELSE * * Recompute NBNEXT in case 2 by 2 split * IF( T( HERE+2, HERE+1 ).EQ.ZERO ) \$ NBNEXT = 1 IF( NBNEXT.EQ.2 ) THEN * * 2 by 2 Block did not split * CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, 1, \$ NBNEXT, WORK, INFO ) IF( INFO.NE.0 ) THEN ILST = HERE RETURN END IF HERE = HERE + 2 ELSE * * 2 by 2 Block did split * CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, 1, 1, \$ WORK, INFO ) CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE+1, 1, 1, \$ WORK, INFO ) HERE = HERE + 2 END IF END IF END IF IF( HERE.LT.ILST ) \$ GO TO 10 * ELSE * HERE = IFST 20 CONTINUE * * Swap block with next one above * 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( T( HERE-1, HERE-2 ).NE.ZERO ) \$ NBNEXT = 2 END IF CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE-NBNEXT, NBNEXT, \$ NBF, WORK, 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( T( 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( T( HERE-1, HERE-2 ).NE.ZERO ) \$ NBNEXT = 2 END IF CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE-NBNEXT, NBNEXT, \$ 1, WORK, INFO ) IF( INFO.NE.0 ) THEN ILST = HERE RETURN END IF IF( NBNEXT.EQ.1 ) THEN * * Swap two 1 by 1 blocks, no problems possible * CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, NBNEXT, 1, \$ WORK, INFO ) HERE = HERE - 1 ELSE * * Recompute NBNEXT in case 2 by 2 split * IF( T( HERE, HERE-1 ).EQ.ZERO ) \$ NBNEXT = 1 IF( NBNEXT.EQ.2 ) THEN * * 2 by 2 Block did not split * CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE-1, 2, 1, \$ WORK, INFO ) IF( INFO.NE.0 ) THEN ILST = HERE RETURN END IF HERE = HERE - 2 ELSE * * 2 by 2 Block did split * CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, 1, 1, \$ WORK, INFO ) CALL SLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE-1, 1, 1, \$ WORK, INFO ) HERE = HERE - 2 END IF END IF END IF IF( HERE.GT.ILST ) \$ GO TO 20 END IF ILST = HERE * RETURN * * End of STREXC * END