ztrexc.f

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      SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
*  -- LAPACK routine (version 3.2) --
*  -- 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
      INTEGER            IFST, ILST, INFO, LDQ, LDT, N
*     ..
*     .. Array Arguments ..
      COMPLEX*16         Q( LDQ, * ), T( LDT, * )
*     ..
*
*  Purpose
*  =======
*
*  ZTREXC reorders the Schur factorization of a complex matrix
*  A = Q*T*Q**H, so that the diagonal element of T with row index IFST
*  is moved to row ILST.
*
*  The Schur form T is reordered by a unitary similarity transformation
*  Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
*  postmultplying it with Z.
*
*  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) COMPLEX*16 array, dimension (LDT,N)
*          On entry, the upper triangular matrix T.
*          On exit, the reordered upper triangular matrix.
*
*  LDT     (input) INTEGER
*          The leading dimension of the array T. LDT >= max(1,N).
*
*  Q       (input/output) COMPLEX*16 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
*          unitary 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) INTEGER
*  ILST    (input) INTEGER
*          Specify the reordering of the diagonal elements of T:
*          The element with row index IFST is moved to row ILST by a
*          sequence of transpositions between adjacent elements.
*          1 <= IFST <= N; 1 <= ILST <= N.
*
*  INFO    (output) INTEGER
*          = 0:  successful exit
*          < 0:  if INFO = -i, the i-th argument had an illegal value
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL            WANTQ
      INTEGER            K, M1, M2, M3
      DOUBLE PRECISION   CS
      COMPLEX*16         SN, T11, T22, TEMP
*     ..
*     .. External Functions ..
      LOGICAL            LSAME
      EXTERNAL           LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL           XERBLA, ZLARTG, ZROT
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          DCONJG, MAX
*     ..
*     .. Executable Statements ..
*
*     Decode and test the input parameters.
*
      INFO = 0
      WANTQ = LSAME( COMPQ, 'V' )
      IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) 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( 'ZTREXC', -INFO )
         RETURN
      END IF
*
*     Quick return if possible
*
      IF( N.EQ.1 .OR. IFST.EQ.ILST )
     $   RETURN
*
      IF( IFST.LT.ILST ) THEN
*
*        Move the IFST-th diagonal element forward down the diagonal.
*
         M1 = 0
         M2 = -1
         M3 = 1
      ELSE
*
*        Move the IFST-th diagonal element backward up the diagonal.
*
         M1 = -1
         M2 = 0
         M3 = -1
      END IF
*
      DO 10 K = IFST + M1, ILST + M2, M3
*
*        Interchange the k-th and (k+1)-th diagonal elements.
*
         T11 = T( K, K )
         T22 = T( K+1, K+1 )
*
*        Determine the transformation to perform the interchange.
*
         CALL ZLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
*
*        Apply transformation to the matrix T.
*
         IF( K+2.LE.N )
     $      CALL ZROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
     $                 SN )
         CALL ZROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS,
     $              DCONJG( SN ) )
*
         T( K, K ) = T22
         T( K+1, K+1 ) = T11
*
         IF( WANTQ ) THEN
*
*           Accumulate transformation in the matrix Q.
*
            CALL ZROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
     $                 DCONJG( SN ) )
         END IF
*
   10 CONTINUE
*
      RETURN
*
*     End of ZTREXC
*
      END