LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ ctgexc()

subroutine ctgexc ( logical  WANTQ,
logical  WANTZ,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( ldq, * )  Q,
integer  LDQ,
complex, dimension( ldz, * )  Z,
integer  LDZ,
integer  IFST,
integer  ILST,
integer  INFO 
)

CTGEXC

Download CTGEXC + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CTGEXC reorders the generalized Schur decomposition of a complex
 matrix pair (A,B), using an unitary equivalence transformation
 (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
 row index IFST is moved to row ILST.

 (A, B) must be in generalized Schur canonical form, that is, A and
 B are both upper triangular.

 Optionally, the matrices Q and Z of generalized Schur vectors are
 updated.

        Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
        Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
Parameters
[in]WANTQ
          WANTQ is LOGICAL
          .TRUE. : update the left transformation matrix Q;
          .FALSE.: do not update Q.
[in]WANTZ
          WANTZ is LOGICAL
          .TRUE. : update the right transformation matrix Z;
          .FALSE.: do not update Z.
[in]N
          N is INTEGER
          The order of the matrices A and B. N >= 0.
[in,out]A
          A is COMPLEX array, dimension (LDA,N)
          On entry, the upper triangular matrix A in the pair (A, B).
          On exit, the updated matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A. LDA >= max(1,N).
[in,out]B
          B is COMPLEX array, dimension (LDB,N)
          On entry, the upper triangular matrix B in the pair (A, B).
          On exit, the updated matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of the array B. LDB >= max(1,N).
[in,out]Q
          Q is COMPLEX array, dimension (LDQ,N)
          On entry, if WANTQ = .TRUE., the unitary matrix Q.
          On exit, the updated matrix Q.
          If WANTQ = .FALSE., Q is not referenced.
[in]LDQ
          LDQ is INTEGER
          The leading dimension of the array Q. LDQ >= 1;
          If WANTQ = .TRUE., LDQ >= N.
[in,out]Z
          Z is COMPLEX array, dimension (LDZ,N)
          On entry, if WANTZ = .TRUE., the unitary matrix Z.
          On exit, the updated matrix Z.
          If WANTZ = .FALSE., Z is not referenced.
[in]LDZ
          LDZ is INTEGER
          The leading dimension of the array Z. LDZ >= 1;
          If WANTZ = .TRUE., LDZ >= N.
[in]IFST
          IFST is INTEGER
[in,out]ILST
          ILST is INTEGER
          Specify the reordering of the diagonal blocks of (A, B).
          The block with row index IFST is moved to row ILST, by a
          sequence of swapping between adjacent blocks.
[out]INFO
          INFO is INTEGER
           =0:  Successful exit.
           <0:  if INFO = -i, the i-th argument had an illegal value.
           =1:  The transformed matrix pair (A, B) would be too far
                from generalized Schur form; the problem is ill-
                conditioned. (A, B) may have been partially reordered,
                and ILST points to the first row of the current
                position of the block being moved.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date
June 2017
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.
References:
[1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the Generalized Real Schur Form of a Regular Matrix Pair (A, B), in M.S. Moonen et al (eds), Linear Algebra for Large Scale and Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
[2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified Eigenvalues of a Regular Matrix Pair (A, B) and Condition Estimation: Theory, Algorithms and Software, Report UMINF - 94.04, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. To appear in Numerical Algorithms, 1996.
[3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software for Solving the Generalized Sylvester Equation and Estimating the Separation between Regular Matrix Pairs, Report UMINF - 93.23, Department of Computing Science, Umea University, S-901 87 Umea, Sweden, December 1993, Revised April 1994, Also as LAPACK working Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, 1996.

Definition at line 202 of file ctgexc.f.

202 *
203 * -- LAPACK computational routine (version 3.7.1) --
204 * -- LAPACK is a software package provided by Univ. of Tennessee, --
205 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
206 * June 2017
207 *
208 * .. Scalar Arguments ..
209  LOGICAL wantq, wantz
210  INTEGER ifst, ilst, info, lda, ldb, ldq, ldz, n
211 * ..
212 * .. Array Arguments ..
213  COMPLEX a( lda, * ), b( ldb, * ), q( ldq, * ),
214  $ z( ldz, * )
215 * ..
216 *
217 * =====================================================================
218 *
219 * .. Local Scalars ..
220  INTEGER here
221 * ..
222 * .. External Subroutines ..
223  EXTERNAL ctgex2, xerbla
224 * ..
225 * .. Intrinsic Functions ..
226  INTRINSIC max
227 * ..
228 * .. Executable Statements ..
229 *
230 * Decode and test input arguments.
231  info = 0
232  IF( n.LT.0 ) THEN
233  info = -3
234  ELSE IF( lda.LT.max( 1, n ) ) THEN
235  info = -5
236  ELSE IF( ldb.LT.max( 1, n ) ) THEN
237  info = -7
238  ELSE IF( ldq.LT.1 .OR. wantq .AND. ( ldq.LT.max( 1, n ) ) ) THEN
239  info = -9
240  ELSE IF( ldz.LT.1 .OR. wantz .AND. ( ldz.LT.max( 1, n ) ) ) THEN
241  info = -11
242  ELSE IF( ifst.LT.1 .OR. ifst.GT.n ) THEN
243  info = -12
244  ELSE IF( ilst.LT.1 .OR. ilst.GT.n ) THEN
245  info = -13
246  END IF
247  IF( info.NE.0 ) THEN
248  CALL xerbla( 'CTGEXC', -info )
249  RETURN
250  END IF
251 *
252 * Quick return if possible
253 *
254  IF( n.LE.1 )
255  $ RETURN
256  IF( ifst.EQ.ilst )
257  $ RETURN
258 *
259  IF( ifst.LT.ilst ) THEN
260 *
261  here = ifst
262 *
263  10 CONTINUE
264 *
265 * Swap with next one below
266 *
267  CALL ctgex2( wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz,
268  $ here, info )
269  IF( info.NE.0 ) THEN
270  ilst = here
271  RETURN
272  END IF
273  here = here + 1
274  IF( here.LT.ilst )
275  $ GO TO 10
276  here = here - 1
277  ELSE
278  here = ifst - 1
279 *
280  20 CONTINUE
281 *
282 * Swap with next one above
283 *
284  CALL ctgex2( wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz,
285  $ here, info )
286  IF( info.NE.0 ) THEN
287  ilst = here
288  RETURN
289  END IF
290  here = here - 1
291  IF( here.GE.ilst )
292  $ GO TO 20
293  here = here + 1
294  END IF
295  ilst = here
296  RETURN
297 *
298 * End of CTGEXC
299 *
subroutine ctgex2(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
CTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equiva...
Definition: ctgex2.f:192
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
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