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authorSiddhesh Wani2015-05-25 14:46:31 +0530
committerSiddhesh Wani2015-05-25 14:46:31 +0530
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+ SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
+ $ INFO )
+*
+* -- LAPACK routine (version 3.1) --
+* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
+* November 2006
+*
+* .. Scalar Arguments ..
+ CHARACTER COMPQ
+ INTEGER IFST, ILST, INFO, LDQ, LDT, N
+* ..
+* .. Array Arguments ..
+ 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 ..
+ DOUBLE PRECISION ZERO
+ PARAMETER ( ZERO = 0.0D+0 )
+* ..
+* .. Local Scalars ..
+ LOGICAL WANTQ
+ INTEGER HERE, NBF, NBL, NBNEXT
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL DLAEXC, 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 ) THEN
+ INFO = -7
+ ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
+ INFO = -8
+ END IF
+ IF( INFO.NE.0 ) THEN
+ CALL XERBLA( 'DTREXC', -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 DLAEXC( 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 DLAEXC( 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 DLAEXC( 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 DLAEXC( 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 DLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, 1, 1,
+ $ WORK, INFO )
+ CALL DLAEXC( 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 DLAEXC( 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 DLAEXC( 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 DLAEXC( 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 DLAEXC( 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 DLAEXC( WANTQ, N, T, LDT, Q, LDQ, HERE, 1, 1,
+ $ WORK, INFO )
+ CALL DLAEXC( 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 DTREXC
+*
+ END