LAPACK  3.6.0
LAPACK: Linear Algebra PACKage
ctgexc.f
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1 *> \brief \b CTGEXC
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download CTGEXC + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ctgexc.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ctgexc.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ctgexc.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
22 * LDZ, IFST, ILST, INFO )
23 *
24 * .. Scalar Arguments ..
25 * LOGICAL WANTQ, WANTZ
26 * INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
27 * ..
28 * .. Array Arguments ..
29 * COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
30 * $ Z( LDZ, * )
31 * ..
32 *
33 *
34 *> \par Purpose:
35 * =============
36 *>
37 *> \verbatim
38 *>
39 *> CTGEXC reorders the generalized Schur decomposition of a complex
40 *> matrix pair (A,B), using an unitary equivalence transformation
41 *> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
42 *> row index IFST is moved to row ILST.
43 *>
44 *> (A, B) must be in generalized Schur canonical form, that is, A and
45 *> B are both upper triangular.
46 *>
47 *> Optionally, the matrices Q and Z of generalized Schur vectors are
48 *> updated.
49 *>
50 *> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
51 *> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
52 *> \endverbatim
53 *
54 * Arguments:
55 * ==========
56 *
57 *> \param[in] WANTQ
58 *> \verbatim
59 *> WANTQ is LOGICAL
60 *> .TRUE. : update the left transformation matrix Q;
61 *> .FALSE.: do not update Q.
62 *> \endverbatim
63 *>
64 *> \param[in] WANTZ
65 *> \verbatim
66 *> WANTZ is LOGICAL
67 *> .TRUE. : update the right transformation matrix Z;
68 *> .FALSE.: do not update Z.
69 *> \endverbatim
70 *>
71 *> \param[in] N
72 *> \verbatim
73 *> N is INTEGER
74 *> The order of the matrices A and B. N >= 0.
75 *> \endverbatim
76 *>
77 *> \param[in,out] A
78 *> \verbatim
79 *> A is COMPLEX array, dimension (LDA,N)
80 *> On entry, the upper triangular matrix A in the pair (A, B).
81 *> On exit, the updated matrix A.
82 *> \endverbatim
83 *>
84 *> \param[in] LDA
85 *> \verbatim
86 *> LDA is INTEGER
87 *> The leading dimension of the array A. LDA >= max(1,N).
88 *> \endverbatim
89 *>
90 *> \param[in,out] B
91 *> \verbatim
92 *> B is COMPLEX array, dimension (LDB,N)
93 *> On entry, the upper triangular matrix B in the pair (A, B).
94 *> On exit, the updated matrix B.
95 *> \endverbatim
96 *>
97 *> \param[in] LDB
98 *> \verbatim
99 *> LDB is INTEGER
100 *> The leading dimension of the array B. LDB >= max(1,N).
101 *> \endverbatim
102 *>
103 *> \param[in,out] Q
104 *> \verbatim
105 *> Q is COMPLEX array, dimension (LDZ,N)
106 *> On entry, if WANTQ = .TRUE., the unitary matrix Q.
107 *> On exit, the updated matrix Q.
108 *> If WANTQ = .FALSE., Q is not referenced.
109 *> \endverbatim
110 *>
111 *> \param[in] LDQ
112 *> \verbatim
113 *> LDQ is INTEGER
114 *> The leading dimension of the array Q. LDQ >= 1;
115 *> If WANTQ = .TRUE., LDQ >= N.
116 *> \endverbatim
117 *>
118 *> \param[in,out] Z
119 *> \verbatim
120 *> Z is COMPLEX array, dimension (LDZ,N)
121 *> On entry, if WANTZ = .TRUE., the unitary matrix Z.
122 *> On exit, the updated matrix Z.
123 *> If WANTZ = .FALSE., Z is not referenced.
124 *> \endverbatim
125 *>
126 *> \param[in] LDZ
127 *> \verbatim
128 *> LDZ is INTEGER
129 *> The leading dimension of the array Z. LDZ >= 1;
130 *> If WANTZ = .TRUE., LDZ >= N.
131 *> \endverbatim
132 *>
133 *> \param[in] IFST
134 *> \verbatim
135 *> IFST is INTEGER
136 *> \endverbatim
137 *>
138 *> \param[in,out] ILST
139 *> \verbatim
140 *> ILST is INTEGER
141 *> Specify the reordering of the diagonal blocks of (A, B).
142 *> The block with row index IFST is moved to row ILST, by a
143 *> sequence of swapping between adjacent blocks.
144 *> \endverbatim
145 *>
146 *> \param[out] INFO
147 *> \verbatim
148 *> INFO is INTEGER
149 *> =0: Successful exit.
150 *> <0: if INFO = -i, the i-th argument had an illegal value.
151 *> =1: The transformed matrix pair (A, B) would be too far
152 *> from generalized Schur form; the problem is ill-
153 *> conditioned. (A, B) may have been partially reordered,
154 *> and ILST points to the first row of the current
155 *> position of the block being moved.
156 *> \endverbatim
157 *
158 * Authors:
159 * ========
160 *
161 *> \author Univ. of Tennessee
162 *> \author Univ. of California Berkeley
163 *> \author Univ. of Colorado Denver
164 *> \author NAG Ltd.
165 *
166 *> \date November 2011
167 *
168 *> \ingroup complexGEcomputational
169 *
170 *> \par Contributors:
171 * ==================
172 *>
173 *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
174 *> Umea University, S-901 87 Umea, Sweden.
175 *
176 *> \par References:
177 * ================
178 *>
179 *> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
180 *> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
181 *> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
182 *> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
183 *> \n
184 *> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
185 *> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
186 *> Estimation: Theory, Algorithms and Software, Report
187 *> UMINF - 94.04, Department of Computing Science, Umea University,
188 *> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
189 *> To appear in Numerical Algorithms, 1996.
190 *> \n
191 *> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
192 *> for Solving the Generalized Sylvester Equation and Estimating the
193 *> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
194 *> Department of Computing Science, Umea University, S-901 87 Umea,
195 *> Sweden, December 1993, Revised April 1994, Also as LAPACK working
196 *> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
197 *> 1996.
198 *>
199 * =====================================================================
200  SUBROUTINE ctgexc( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
201  $ ldz, ifst, ilst, info )
202 *
203 * -- LAPACK computational routine (version 3.4.0) --
204 * -- LAPACK is a software package provided by Univ. of Tennessee, --
205 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
206 * November 2011
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 *
300  END
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
subroutine ctgexc(WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, IFST, ILST, INFO)
CTGEXC
Definition: ctgexc.f:202