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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
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