--- rpl/lapack/lapack/dtrexc.f 2010/08/07 13:22:28 1.5 +++ rpl/lapack/lapack/dtrexc.f 2023/08/07 08:39:13 1.17 @@ -1,10 +1,154 @@ +*> \brief \b DTREXC +* +* =========== DOCUMENTATION =========== +* +* Online html documentation available at +* http://www.netlib.org/lapack/explore-html/ +* +*> \htmlonly +*> Download DTREXC + dependencies +*> +*> [TGZ] +*> +*> [ZIP] +*> +*> [TXT] +*> \endhtmlonly +* +* Definition: +* =========== +* +* SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, +* INFO ) +* +* .. Scalar Arguments .. +* CHARACTER COMPQ +* INTEGER IFST, ILST, INFO, LDQ, LDT, N +* .. +* .. Array Arguments .. +* DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) +* .. +* +* +*> \par Purpose: +* ============= +*> +*> \verbatim +*> +*> DTREXC 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 DHSEQR), 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 doubleOTHERcomputational +* +* ===================================================================== SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, $ INFO ) * -* -- LAPACK routine (version 3.2) -- +* -- LAPACK computational routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- -* November 2006 * * .. Scalar Arguments .. CHARACTER COMPQ @@ -14,71 +158,6 @@ DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) * .. * -* Purpose -* ======= -* -* DTREXC 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 DHSEQR), 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. -* -* Arguments -* ========= -* -* COMPQ (input) CHARACTER*1 -* = 'V': update the matrix Q of Schur vectors; -* = 'N': do not update Q. -* -* N (input) INTEGER -* The order of the matrix T. N >= 0. -* -* T (input/output) DOUBLE PRECISION 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. -* -* LDT (input) INTEGER -* The leading dimension of the array T. LDT >= max(1,N). -* -* Q (input/output) DOUBLE PRECISION 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. -* -* LDQ (input) INTEGER -* The leading dimension of the array Q. LDQ >= max(1,N). -* -* IFST (input/output) INTEGER -* ILST (input/output) 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. -* -* WORK (workspace) DOUBLE PRECISION array, dimension (N) -* -* INFO (output) 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. -* * ===================================================================== * * .. Parameters .. @@ -113,9 +192,9 @@ 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 + 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 ) THEN + ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN INFO = -8 END IF IF( INFO.NE.0 ) THEN