Annotation of rpl/lapack/lapack/ztgexc.f, revision 1.7
1.1 bertrand 1: SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
2: $ LDZ, IFST, ILST, INFO )
3: *
4: * -- LAPACK routine (version 3.2) --
5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
7: * November 2006
8: *
9: * .. Scalar Arguments ..
10: LOGICAL WANTQ, WANTZ
11: INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
12: * ..
13: * .. Array Arguments ..
14: COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
15: $ Z( LDZ, * )
16: * ..
17: *
18: * Purpose
19: * =======
20: *
21: * ZTGEXC reorders the generalized Schur decomposition of a complex
22: * matrix pair (A,B), using an unitary equivalence transformation
23: * (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with
24: * row index IFST is moved to row ILST.
25: *
26: * (A, B) must be in generalized Schur canonical form, that is, A and
27: * B are both upper triangular.
28: *
29: * Optionally, the matrices Q and Z of generalized Schur vectors are
30: * updated.
31: *
32: * Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)'
33: * Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)'
34: *
35: * Arguments
36: * =========
37: *
38: * WANTQ (input) LOGICAL
39: * .TRUE. : update the left transformation matrix Q;
40: * .FALSE.: do not update Q.
41: *
42: * WANTZ (input) LOGICAL
43: * .TRUE. : update the right transformation matrix Z;
44: * .FALSE.: do not update Z.
45: *
46: * N (input) INTEGER
47: * The order of the matrices A and B. N >= 0.
48: *
49: * A (input/output) COMPLEX*16 array, dimension (LDA,N)
50: * On entry, the upper triangular matrix A in the pair (A, B).
51: * On exit, the updated matrix A.
52: *
53: * LDA (input) INTEGER
54: * The leading dimension of the array A. LDA >= max(1,N).
55: *
56: * B (input/output) COMPLEX*16 array, dimension (LDB,N)
57: * On entry, the upper triangular matrix B in the pair (A, B).
58: * On exit, the updated matrix B.
59: *
60: * LDB (input) INTEGER
61: * The leading dimension of the array B. LDB >= max(1,N).
62: *
63: * Q (input/output) COMPLEX*16 array, dimension (LDZ,N)
64: * On entry, if WANTQ = .TRUE., the unitary matrix Q.
65: * On exit, the updated matrix Q.
66: * If WANTQ = .FALSE., Q is not referenced.
67: *
68: * LDQ (input) INTEGER
69: * The leading dimension of the array Q. LDQ >= 1;
70: * If WANTQ = .TRUE., LDQ >= N.
71: *
72: * Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
73: * On entry, if WANTZ = .TRUE., the unitary matrix Z.
74: * On exit, the updated matrix Z.
75: * If WANTZ = .FALSE., Z is not referenced.
76: *
77: * LDZ (input) INTEGER
78: * The leading dimension of the array Z. LDZ >= 1;
79: * If WANTZ = .TRUE., LDZ >= N.
80: *
81: * IFST (input) INTEGER
82: * ILST (input/output) INTEGER
83: * Specify the reordering of the diagonal blocks of (A, B).
84: * The block with row index IFST is moved to row ILST, by a
85: * sequence of swapping between adjacent blocks.
86: *
87: * INFO (output) INTEGER
88: * =0: Successful exit.
89: * <0: if INFO = -i, the i-th argument had an illegal value.
90: * =1: The transformed matrix pair (A, B) would be too far
91: * from generalized Schur form; the problem is ill-
92: * conditioned. (A, B) may have been partially reordered,
93: * and ILST points to the first row of the current
94: * position of the block being moved.
95: *
96: *
97: * Further Details
98: * ===============
99: *
100: * Based on contributions by
101: * Bo Kagstrom and Peter Poromaa, Department of Computing Science,
102: * Umea University, S-901 87 Umea, Sweden.
103: *
104: * [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
105: * Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
106: * M.S. Moonen et al (eds), Linear Algebra for Large Scale and
107: * Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
108: *
109: * [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
110: * Eigenvalues of a Regular Matrix Pair (A, B) and Condition
111: * Estimation: Theory, Algorithms and Software, Report
112: * UMINF - 94.04, Department of Computing Science, Umea University,
113: * S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
114: * To appear in Numerical Algorithms, 1996.
115: *
116: * [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
117: * for Solving the Generalized Sylvester Equation and Estimating the
118: * Separation between Regular Matrix Pairs, Report UMINF - 93.23,
119: * Department of Computing Science, Umea University, S-901 87 Umea,
120: * Sweden, December 1993, Revised April 1994, Also as LAPACK working
121: * Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
122: * 1996.
123: *
124: * =====================================================================
125: *
126: * .. Local Scalars ..
127: INTEGER HERE
128: * ..
129: * .. External Subroutines ..
130: EXTERNAL XERBLA, ZTGEX2
131: * ..
132: * .. Intrinsic Functions ..
133: INTRINSIC MAX
134: * ..
135: * .. Executable Statements ..
136: *
137: * Decode and test input arguments.
138: INFO = 0
139: IF( N.LT.0 ) THEN
140: INFO = -3
141: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
142: INFO = -5
143: ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
144: INFO = -7
145: ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
146: INFO = -9
147: ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
148: INFO = -11
149: ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
150: INFO = -12
151: ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
152: INFO = -13
153: END IF
154: IF( INFO.NE.0 ) THEN
155: CALL XERBLA( 'ZTGEXC', -INFO )
156: RETURN
157: END IF
158: *
159: * Quick return if possible
160: *
161: IF( N.LE.1 )
162: $ RETURN
163: IF( IFST.EQ.ILST )
164: $ RETURN
165: *
166: IF( IFST.LT.ILST ) THEN
167: *
168: HERE = IFST
169: *
170: 10 CONTINUE
171: *
172: * Swap with next one below
173: *
174: CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
175: $ HERE, INFO )
176: IF( INFO.NE.0 ) THEN
177: ILST = HERE
178: RETURN
179: END IF
180: HERE = HERE + 1
181: IF( HERE.LT.ILST )
182: $ GO TO 10
183: HERE = HERE - 1
184: ELSE
185: HERE = IFST - 1
186: *
187: 20 CONTINUE
188: *
189: * Swap with next one above
190: *
191: CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
192: $ HERE, INFO )
193: IF( INFO.NE.0 ) THEN
194: ILST = HERE
195: RETURN
196: END IF
197: HERE = HERE - 1
198: IF( HERE.GE.ILST )
199: $ GO TO 20
200: HERE = HERE + 1
201: END IF
202: ILST = HERE
203: RETURN
204: *
205: * End of ZTGEXC
206: *
207: END
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