1: *> \brief \b ZTREXC
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZTREXC + dependencies
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11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrexc.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrexc.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER COMPQ
25: * INTEGER IFST, ILST, INFO, LDQ, LDT, N
26: * ..
27: * .. Array Arguments ..
28: * COMPLEX*16 Q( LDQ, * ), T( LDT, * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> ZTREXC reorders the Schur factorization of a complex matrix
38: *> A = Q*T*Q**H, so that the diagonal element of T with row index IFST
39: *> is moved to row ILST.
40: *>
41: *> The Schur form T is reordered by a unitary similarity transformation
42: *> Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
43: *> postmultplying it with Z.
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] COMPQ
50: *> \verbatim
51: *> COMPQ is CHARACTER*1
52: *> = 'V': update the matrix Q of Schur vectors;
53: *> = 'N': do not update Q.
54: *> \endverbatim
55: *>
56: *> \param[in] N
57: *> \verbatim
58: *> N is INTEGER
59: *> The order of the matrix T. N >= 0.
60: *> If N == 0 arguments ILST and IFST may be any value.
61: *> \endverbatim
62: *>
63: *> \param[in,out] T
64: *> \verbatim
65: *> T is COMPLEX*16 array, dimension (LDT,N)
66: *> On entry, the upper triangular matrix T.
67: *> On exit, the reordered upper triangular matrix.
68: *> \endverbatim
69: *>
70: *> \param[in] LDT
71: *> \verbatim
72: *> LDT is INTEGER
73: *> The leading dimension of the array T. LDT >= max(1,N).
74: *> \endverbatim
75: *>
76: *> \param[in,out] Q
77: *> \verbatim
78: *> Q is COMPLEX*16 array, dimension (LDQ,N)
79: *> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
80: *> On exit, if COMPQ = 'V', Q has been postmultiplied by the
81: *> unitary transformation matrix Z which reorders T.
82: *> If COMPQ = 'N', Q is not referenced.
83: *> \endverbatim
84: *>
85: *> \param[in] LDQ
86: *> \verbatim
87: *> LDQ is INTEGER
88: *> The leading dimension of the array Q. LDQ >= 1, and if
89: *> COMPQ = 'V', LDQ >= max(1,N).
90: *> \endverbatim
91: *>
92: *> \param[in] IFST
93: *> \verbatim
94: *> IFST is INTEGER
95: *> \endverbatim
96: *>
97: *> \param[in] ILST
98: *> \verbatim
99: *> ILST is INTEGER
100: *>
101: *> Specify the reordering of the diagonal elements of T:
102: *> The element with row index IFST is moved to row ILST by a
103: *> sequence of transpositions between adjacent elements.
104: *> 1 <= IFST <= N; 1 <= ILST <= N.
105: *> \endverbatim
106: *>
107: *> \param[out] INFO
108: *> \verbatim
109: *> INFO is INTEGER
110: *> = 0: successful exit
111: *> < 0: if INFO = -i, the i-th argument had an illegal value
112: *> \endverbatim
113: *
114: * Authors:
115: * ========
116: *
117: *> \author Univ. of Tennessee
118: *> \author Univ. of California Berkeley
119: *> \author Univ. of Colorado Denver
120: *> \author NAG Ltd.
121: *
122: *> \ingroup complex16OTHERcomputational
123: *
124: * =====================================================================
125: SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
126: *
127: * -- LAPACK computational routine --
128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130: *
131: * .. Scalar Arguments ..
132: CHARACTER COMPQ
133: INTEGER IFST, ILST, INFO, LDQ, LDT, N
134: * ..
135: * .. Array Arguments ..
136: COMPLEX*16 Q( LDQ, * ), T( LDT, * )
137: * ..
138: *
139: * =====================================================================
140: *
141: * .. Local Scalars ..
142: LOGICAL WANTQ
143: INTEGER K, M1, M2, M3
144: DOUBLE PRECISION CS
145: COMPLEX*16 SN, T11, T22, TEMP
146: * ..
147: * .. External Functions ..
148: LOGICAL LSAME
149: EXTERNAL LSAME
150: * ..
151: * .. External Subroutines ..
152: EXTERNAL XERBLA, ZLARTG, ZROT
153: * ..
154: * .. Intrinsic Functions ..
155: INTRINSIC DCONJG, MAX
156: * ..
157: * .. Executable Statements ..
158: *
159: * Decode and test the input parameters.
160: *
161: INFO = 0
162: WANTQ = LSAME( COMPQ, 'V' )
163: IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
164: INFO = -1
165: ELSE IF( N.LT.0 ) THEN
166: INFO = -2
167: ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
168: INFO = -4
169: ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
170: INFO = -6
171: ELSE IF(( IFST.LT.1 .OR. IFST.GT.N ).AND.( N.GT.0 )) THEN
172: INFO = -7
173: ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN
174: INFO = -8
175: END IF
176: IF( INFO.NE.0 ) THEN
177: CALL XERBLA( 'ZTREXC', -INFO )
178: RETURN
179: END IF
180: *
181: * Quick return if possible
182: *
183: IF( N.LE.1 .OR. IFST.EQ.ILST )
184: $ RETURN
185: *
186: IF( IFST.LT.ILST ) THEN
187: *
188: * Move the IFST-th diagonal element forward down the diagonal.
189: *
190: M1 = 0
191: M2 = -1
192: M3 = 1
193: ELSE
194: *
195: * Move the IFST-th diagonal element backward up the diagonal.
196: *
197: M1 = -1
198: M2 = 0
199: M3 = -1
200: END IF
201: *
202: DO 10 K = IFST + M1, ILST + M2, M3
203: *
204: * Interchange the k-th and (k+1)-th diagonal elements.
205: *
206: T11 = T( K, K )
207: T22 = T( K+1, K+1 )
208: *
209: * Determine the transformation to perform the interchange.
210: *
211: CALL ZLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
212: *
213: * Apply transformation to the matrix T.
214: *
215: IF( K+2.LE.N )
216: $ CALL ZROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
217: $ SN )
218: CALL ZROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS,
219: $ DCONJG( SN ) )
220: *
221: T( K, K ) = T22
222: T( K+1, K+1 ) = T11
223: *
224: IF( WANTQ ) THEN
225: *
226: * Accumulate transformation in the matrix Q.
227: *
228: CALL ZROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
229: $ DCONJG( SN ) )
230: END IF
231: *
232: 10 CONTINUE
233: *
234: RETURN
235: *
236: * End of ZTREXC
237: *
238: END
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