 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ ztgexc()

 subroutine ztgexc ( logical WANTQ, logical WANTZ, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( ldb, * ) B, integer LDB, complex*16, dimension( ldq, * ) Q, integer LDQ, complex*16, dimension( ldz, * ) Z, integer LDZ, integer IFST, integer ILST, integer INFO )

ZTGEXC

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

Purpose:
``` ZTGEXC 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*16 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*16 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*16 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*16 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.```
Contributors:
Bo Kagstrom and Peter Poromaa, Department of Computing Science, Umea University, S-901 87 Umea, Sweden.
References:
 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.
 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.
 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 198 of file ztgexc.f.

200 *
201 * -- LAPACK computational routine --
202 * -- LAPACK is a software package provided by Univ. of Tennessee, --
203 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
204 *
205 * .. Scalar Arguments ..
206  LOGICAL WANTQ, WANTZ
207  INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
208 * ..
209 * .. Array Arguments ..
210  COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
211  \$ Z( LDZ, * )
212 * ..
213 *
214 * =====================================================================
215 *
216 * .. Local Scalars ..
217  INTEGER HERE
218 * ..
219 * .. External Subroutines ..
220  EXTERNAL xerbla, ztgex2
221 * ..
222 * .. Intrinsic Functions ..
223  INTRINSIC max
224 * ..
225 * .. Executable Statements ..
226 *
227 * Decode and test input arguments.
228  info = 0
229  IF( n.LT.0 ) THEN
230  info = -3
231  ELSE IF( lda.LT.max( 1, n ) ) THEN
232  info = -5
233  ELSE IF( ldb.LT.max( 1, n ) ) THEN
234  info = -7
235  ELSE IF( ldq.LT.1 .OR. wantq .AND. ( ldq.LT.max( 1, n ) ) ) THEN
236  info = -9
237  ELSE IF( ldz.LT.1 .OR. wantz .AND. ( ldz.LT.max( 1, n ) ) ) THEN
238  info = -11
239  ELSE IF( ifst.LT.1 .OR. ifst.GT.n ) THEN
240  info = -12
241  ELSE IF( ilst.LT.1 .OR. ilst.GT.n ) THEN
242  info = -13
243  END IF
244  IF( info.NE.0 ) THEN
245  CALL xerbla( 'ZTGEXC', -info )
246  RETURN
247  END IF
248 *
249 * Quick return if possible
250 *
251  IF( n.LE.1 )
252  \$ RETURN
253  IF( ifst.EQ.ilst )
254  \$ RETURN
255 *
256  IF( ifst.LT.ilst ) THEN
257 *
258  here = ifst
259 *
260  10 CONTINUE
261 *
262 * Swap with next one below
263 *
264  CALL ztgex2( wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz,
265  \$ here, info )
266  IF( info.NE.0 ) THEN
267  ilst = here
268  RETURN
269  END IF
270  here = here + 1
271  IF( here.LT.ilst )
272  \$ GO TO 10
273  here = here - 1
274  ELSE
275  here = ifst - 1
276 *
277  20 CONTINUE
278 *
279 * Swap with next one above
280 *
281  CALL ztgex2( wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz,
282  \$ here, info )
283  IF( info.NE.0 ) THEN
284  ilst = here
285  RETURN
286  END IF
287  here = here - 1
288  IF( here.GE.ilst )
289  \$ GO TO 20
290  here = here + 1
291  END IF
292  ilst = here
293  RETURN
294 *
295 * End of ZTGEXC
296 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ztgex2(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, INFO)
ZTGEX2 swaps adjacent diagonal blocks in an upper (quasi) triangular matrix pair by an unitary equiva...
Definition: ztgex2.f:190
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