Annotation of rpl/lapack/lapack/ztgexc.f, revision 1.9
1.9 ! bertrand 1: *> \brief \b ZTGEXC
! 2: *
! 3: * =========== DOCUMENTATION ===========
! 4: *
! 5: * Online html documentation available at
! 6: * http://www.netlib.org/lapack/explore-html/
! 7: *
! 8: *> \htmlonly
! 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">
! 15: *> [TXT]</a>
! 16: *> \endhtmlonly
! 17: *
! 18: * Definition:
! 19: * ===========
! 20: *
! 21: * SUBROUTINE ZTGEXC( 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*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
! 30: * $ Z( LDZ, * )
! 31: * ..
! 32: *
! 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
! 105: *> Q is COMPLEX*16 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*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: *
! 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 complex16GEcomputational
! 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: * =====================================================================
1.1 bertrand 200: SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
201: $ LDZ, IFST, ILST, INFO )
202: *
1.9 ! bertrand 203: * -- LAPACK computational routine (version 3.4.0) --
1.1 bertrand 204: * -- LAPACK is a software package provided by Univ. of Tennessee, --
205: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.9 ! bertrand 206: * November 2011
1.1 bertrand 207: *
208: * .. Scalar Arguments ..
209: LOGICAL WANTQ, WANTZ
210: INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
211: * ..
212: * .. Array Arguments ..
213: COMPLEX*16 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 XERBLA, ZTGEX2
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( 'ZTGEXC', -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 ZTGEX2( 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 ZTGEX2( 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 ZTGEXC
299: *
300: END
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