Annotation of rpl/lapack/lapack/ztrexc.f, revision 1.14
1.8 bertrand 1: *> \brief \b ZTREXC
2: *
3: * =========== DOCUMENTATION ===========
4: *
1.14 ! bertrand 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.14 ! bertrand 9: *> Download ZTREXC + dependencies
! 10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrexc.f">
! 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">
1.8 bertrand 15: *> [TXT]</a>
1.14 ! bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
1.14 ! bertrand 22: *
1.8 bertrand 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: * ..
1.14 ! bertrand 30: *
1.8 bertrand 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.
1.14 ! bertrand 60: *> If N == 0 arguments ILST and IFST may be any value.
1.8 bertrand 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
1.14 ! bertrand 88: *> The leading dimension of the array Q. LDQ >= 1, and if
! 89: *> COMPQ = 'V', LDQ >= max(1,N).
1.8 bertrand 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: *
1.14 ! bertrand 117: *> \author Univ. of Tennessee
! 118: *> \author Univ. of California Berkeley
! 119: *> \author Univ. of Colorado Denver
! 120: *> \author NAG Ltd.
1.8 bertrand 121: *
1.14 ! bertrand 122: *> \date December 2016
1.8 bertrand 123: *
124: *> \ingroup complex16OTHERcomputational
125: *
126: * =====================================================================
1.1 bertrand 127: SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
128: *
1.14 ! bertrand 129: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 130: * -- LAPACK is a software package provided by Univ. of Tennessee, --
131: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 132: * December 2016
1.1 bertrand 133: *
134: * .. Scalar Arguments ..
135: CHARACTER COMPQ
136: INTEGER IFST, ILST, INFO, LDQ, LDT, N
137: * ..
138: * .. Array Arguments ..
139: COMPLEX*16 Q( LDQ, * ), T( LDT, * )
140: * ..
141: *
142: * =====================================================================
143: *
144: * .. Local Scalars ..
145: LOGICAL WANTQ
146: INTEGER K, M1, M2, M3
147: DOUBLE PRECISION CS
148: COMPLEX*16 SN, T11, T22, TEMP
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: EXTERNAL LSAME
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL XERBLA, ZLARTG, ZROT
156: * ..
157: * .. Intrinsic Functions ..
158: INTRINSIC DCONJG, MAX
159: * ..
160: * .. Executable Statements ..
161: *
162: * Decode and test the input parameters.
163: *
164: INFO = 0
165: WANTQ = LSAME( COMPQ, 'V' )
166: IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
167: INFO = -1
168: ELSE IF( N.LT.0 ) THEN
169: INFO = -2
170: ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
171: INFO = -4
172: ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
173: INFO = -6
1.14 ! bertrand 174: ELSE IF(( IFST.LT.1 .OR. IFST.GT.N ).AND.( N.GT.0 )) THEN
1.1 bertrand 175: INFO = -7
1.14 ! bertrand 176: ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN
1.1 bertrand 177: INFO = -8
178: END IF
179: IF( INFO.NE.0 ) THEN
180: CALL XERBLA( 'ZTREXC', -INFO )
181: RETURN
182: END IF
183: *
184: * Quick return if possible
185: *
1.14 ! bertrand 186: IF( N.LE.1 .OR. IFST.EQ.ILST )
1.1 bertrand 187: $ RETURN
188: *
189: IF( IFST.LT.ILST ) THEN
190: *
191: * Move the IFST-th diagonal element forward down the diagonal.
192: *
193: M1 = 0
194: M2 = -1
195: M3 = 1
196: ELSE
197: *
198: * Move the IFST-th diagonal element backward up the diagonal.
199: *
200: M1 = -1
201: M2 = 0
202: M3 = -1
203: END IF
204: *
205: DO 10 K = IFST + M1, ILST + M2, M3
206: *
207: * Interchange the k-th and (k+1)-th diagonal elements.
208: *
209: T11 = T( K, K )
210: T22 = T( K+1, K+1 )
211: *
212: * Determine the transformation to perform the interchange.
213: *
214: CALL ZLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
215: *
216: * Apply transformation to the matrix T.
217: *
218: IF( K+2.LE.N )
219: $ CALL ZROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
220: $ SN )
221: CALL ZROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS,
222: $ DCONJG( SN ) )
223: *
224: T( K, K ) = T22
225: T( K+1, K+1 ) = T11
226: *
227: IF( WANTQ ) THEN
228: *
229: * Accumulate transformation in the matrix Q.
230: *
231: CALL ZROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
232: $ DCONJG( SN ) )
233: END IF
234: *
235: 10 CONTINUE
236: *
237: RETURN
238: *
239: * End of ZTREXC
240: *
241: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to ztrexc.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack