Annotation of rpl/lapack/lapack/ztgexc.f, revision 1.19
1.9 bertrand 1: *> \brief \b ZTGEXC
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.9 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download ZTGEXC + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgexc.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgexc.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgexc.f">
1.9 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.9 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
22: * LDZ, IFST, ILST, INFO )
1.15 bertrand 23: *
1.9 bertrand 24: * .. Scalar Arguments ..
25: * LOGICAL WANTQ, WANTZ
26: * INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
30: * $ Z( LDZ, * )
31: * ..
1.15 bertrand 32: *
1.9 bertrand 33: *
34: *> \par Purpose:
35: * =============
36: *>
37: *> \verbatim
38: *>
39: *> ZTGEXC 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*16 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*16 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
1.17 bertrand 105: *> Q is COMPLEX*16 array, dimension (LDQ,N)
1.9 bertrand 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*16 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: *
1.15 bertrand 161: *> \author Univ. of Tennessee
162: *> \author Univ. of California Berkeley
163: *> \author Univ. of Colorado Denver
164: *> \author NAG Ltd.
1.9 bertrand 165: *
166: *> \ingroup complex16GEcomputational
167: *
168: *> \par Contributors:
169: * ==================
170: *>
171: *> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
172: *> Umea University, S-901 87 Umea, Sweden.
173: *
174: *> \par References:
175: * ================
176: *>
177: *> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
178: *> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
179: *> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
180: *> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
181: *> \n
182: *> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
183: *> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
184: *> Estimation: Theory, Algorithms and Software, Report
185: *> UMINF - 94.04, Department of Computing Science, Umea University,
186: *> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
187: *> To appear in Numerical Algorithms, 1996.
188: *> \n
189: *> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
190: *> for Solving the Generalized Sylvester Equation and Estimating the
191: *> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
192: *> Department of Computing Science, Umea University, S-901 87 Umea,
193: *> Sweden, December 1993, Revised April 1994, Also as LAPACK working
194: *> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
195: *> 1996.
196: *>
197: * =====================================================================
1.1 bertrand 198: SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
199: $ LDZ, IFST, ILST, INFO )
200: *
1.19 ! bertrand 201: * -- LAPACK computational routine --
1.1 bertrand 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: *
297: END
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