Annotation of rpl/lapack/lapack/ztrexc.f, revision 1.8
1.8 ! bertrand 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
! 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">
! 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: *> \endverbatim
! 61: *>
! 62: *> \param[in,out] T
! 63: *> \verbatim
! 64: *> T is COMPLEX*16 array, dimension (LDT,N)
! 65: *> On entry, the upper triangular matrix T.
! 66: *> On exit, the reordered upper triangular matrix.
! 67: *> \endverbatim
! 68: *>
! 69: *> \param[in] LDT
! 70: *> \verbatim
! 71: *> LDT is INTEGER
! 72: *> The leading dimension of the array T. LDT >= max(1,N).
! 73: *> \endverbatim
! 74: *>
! 75: *> \param[in,out] Q
! 76: *> \verbatim
! 77: *> Q is COMPLEX*16 array, dimension (LDQ,N)
! 78: *> On entry, if COMPQ = 'V', the matrix Q of Schur vectors.
! 79: *> On exit, if COMPQ = 'V', Q has been postmultiplied by the
! 80: *> unitary transformation matrix Z which reorders T.
! 81: *> If COMPQ = 'N', Q is not referenced.
! 82: *> \endverbatim
! 83: *>
! 84: *> \param[in] LDQ
! 85: *> \verbatim
! 86: *> LDQ is INTEGER
! 87: *> The leading dimension of the array Q. LDQ >= max(1,N).
! 88: *> \endverbatim
! 89: *>
! 90: *> \param[in] IFST
! 91: *> \verbatim
! 92: *> IFST is INTEGER
! 93: *> \endverbatim
! 94: *>
! 95: *> \param[in] ILST
! 96: *> \verbatim
! 97: *> ILST is INTEGER
! 98: *>
! 99: *> Specify the reordering of the diagonal elements of T:
! 100: *> The element with row index IFST is moved to row ILST by a
! 101: *> sequence of transpositions between adjacent elements.
! 102: *> 1 <= IFST <= N; 1 <= ILST <= N.
! 103: *> \endverbatim
! 104: *>
! 105: *> \param[out] INFO
! 106: *> \verbatim
! 107: *> INFO is INTEGER
! 108: *> = 0: successful exit
! 109: *> < 0: if INFO = -i, the i-th argument had an illegal value
! 110: *> \endverbatim
! 111: *
! 112: * Authors:
! 113: * ========
! 114: *
! 115: *> \author Univ. of Tennessee
! 116: *> \author Univ. of California Berkeley
! 117: *> \author Univ. of Colorado Denver
! 118: *> \author NAG Ltd.
! 119: *
! 120: *> \date November 2011
! 121: *
! 122: *> \ingroup complex16OTHERcomputational
! 123: *
! 124: * =====================================================================
1.1 bertrand 125: SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
126: *
1.8 ! bertrand 127: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 128: * -- LAPACK is a software package provided by Univ. of Tennessee, --
129: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 130: * November 2011
1.1 bertrand 131: *
132: * .. Scalar Arguments ..
133: CHARACTER COMPQ
134: INTEGER IFST, ILST, INFO, LDQ, LDT, N
135: * ..
136: * .. Array Arguments ..
137: COMPLEX*16 Q( LDQ, * ), T( LDT, * )
138: * ..
139: *
140: * =====================================================================
141: *
142: * .. Local Scalars ..
143: LOGICAL WANTQ
144: INTEGER K, M1, M2, M3
145: DOUBLE PRECISION CS
146: COMPLEX*16 SN, T11, T22, TEMP
147: * ..
148: * .. External Functions ..
149: LOGICAL LSAME
150: EXTERNAL LSAME
151: * ..
152: * .. External Subroutines ..
153: EXTERNAL XERBLA, ZLARTG, ZROT
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC DCONJG, MAX
157: * ..
158: * .. Executable Statements ..
159: *
160: * Decode and test the input parameters.
161: *
162: INFO = 0
163: WANTQ = LSAME( COMPQ, 'V' )
164: IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
165: INFO = -1
166: ELSE IF( N.LT.0 ) THEN
167: INFO = -2
168: ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
169: INFO = -4
170: ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
171: INFO = -6
172: ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
173: INFO = -7
174: ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
175: INFO = -8
176: END IF
177: IF( INFO.NE.0 ) THEN
178: CALL XERBLA( 'ZTREXC', -INFO )
179: RETURN
180: END IF
181: *
182: * Quick return if possible
183: *
184: IF( N.EQ.1 .OR. IFST.EQ.ILST )
185: $ RETURN
186: *
187: IF( IFST.LT.ILST ) THEN
188: *
189: * Move the IFST-th diagonal element forward down the diagonal.
190: *
191: M1 = 0
192: M2 = -1
193: M3 = 1
194: ELSE
195: *
196: * Move the IFST-th diagonal element backward up the diagonal.
197: *
198: M1 = -1
199: M2 = 0
200: M3 = -1
201: END IF
202: *
203: DO 10 K = IFST + M1, ILST + M2, M3
204: *
205: * Interchange the k-th and (k+1)-th diagonal elements.
206: *
207: T11 = T( K, K )
208: T22 = T( K+1, K+1 )
209: *
210: * Determine the transformation to perform the interchange.
211: *
212: CALL ZLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
213: *
214: * Apply transformation to the matrix T.
215: *
216: IF( K+2.LE.N )
217: $ CALL ZROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
218: $ SN )
219: CALL ZROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS,
220: $ DCONJG( SN ) )
221: *
222: T( K, K ) = T22
223: T( K+1, K+1 ) = T11
224: *
225: IF( WANTQ ) THEN
226: *
227: * Accumulate transformation in the matrix Q.
228: *
229: CALL ZROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
230: $ DCONJG( SN ) )
231: END IF
232: *
233: 10 CONTINUE
234: *
235: RETURN
236: *
237: * End of ZTREXC
238: *
239: END
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