1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
|
SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*
* .. Scalar Arguments ..
LOGICAL WANTQ, WANTZ
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
* ..
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ Z( LDZ, * )
* ..
*
* Purpose
* =======
*
* ZTGEXC reorders the generalized Schur decomposition of a complex
* matrix pair (A,B), using an unitary equivalence transformation
* (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
* row index IFST is moved to row ILST.
*
* (A, B) must be in generalized Schur canonical form, that is, A and
* B are both upper triangular.
*
* Optionally, the matrices Q and Z of generalized Schur vectors are
* updated.
*
* Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
* Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
*
* Arguments
* =========
*
* WANTQ (input) LOGICAL
* .TRUE. : update the left transformation matrix Q;
* .FALSE.: do not update Q.
*
* WANTZ (input) LOGICAL
* .TRUE. : update the right transformation matrix Z;
* .FALSE.: do not update Z.
*
* N (input) INTEGER
* The order of the matrices A and B. N >= 0.
*
* A (input/output) COMPLEX*16 array, dimension (LDA,N)
* On entry, the upper triangular matrix A in the pair (A, B).
* On exit, the updated matrix A.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,N).
*
* B (input/output) COMPLEX*16 array, dimension (LDB,N)
* On entry, the upper triangular matrix B in the pair (A, B).
* On exit, the updated matrix B.
*
* LDB (input) INTEGER
* The leading dimension of the array B. LDB >= max(1,N).
*
* Q (input/output) COMPLEX*16 array, dimension (LDZ,N)
* On entry, if WANTQ = .TRUE., the unitary matrix Q.
* On exit, the updated matrix Q.
* If WANTQ = .FALSE., Q is not referenced.
*
* LDQ (input) INTEGER
* The leading dimension of the array Q. LDQ >= 1;
* If WANTQ = .TRUE., LDQ >= N.
*
* Z (input/output) COMPLEX*16 array, dimension (LDZ,N)
* On entry, if WANTZ = .TRUE., the unitary matrix Z.
* On exit, the updated matrix Z.
* If WANTZ = .FALSE., Z is not referenced.
*
* LDZ (input) INTEGER
* The leading dimension of the array Z. LDZ >= 1;
* If WANTZ = .TRUE., LDZ >= N.
*
* IFST (input) INTEGER
*
* ILST (input/output) INTEGER
* Specify the reordering of the diagonal blocks of (A, B).
* The block with row index IFST is moved to row ILST, by a
* sequence of swapping between adjacent blocks.
*
* INFO (output) INTEGER
* =0: Successful exit.
* <0: if INFO = -i, the i-th argument had an illegal value.
* =1: The transformed matrix pair (A, B) would be too far
* from generalized Schur form; the problem is ill-
* conditioned. (A, B) may have been partially reordered,
* and ILST points to the first row of the current
* position of the block being moved.
*
*
* Further Details
* ===============
*
* Based on contributions by
* Bo Kagstrom and Peter Poromaa, Department of Computing Science,
* Umea University, S-901 87 Umea, Sweden.
*
* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
* M.S. Moonen et al (eds), Linear Algebra for Large Scale and
* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
*
* [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
* Eigenvalues of a Regular Matrix Pair (A, B) and Condition
* Estimation: Theory, Algorithms and Software, Report
* UMINF - 94.04, Department of Computing Science, Umea University,
* S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
* To appear in Numerical Algorithms, 1996.
*
* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
* for Solving the Generalized Sylvester Equation and Estimating the
* Separation between Regular Matrix Pairs, Report UMINF - 93.23,
* Department of Computing Science, Umea University, S-901 87 Umea,
* Sweden, December 1993, Revised April 1994, Also as LAPACK working
* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
* 1996.
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER HERE
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZTGEX2
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Decode and test input arguments.
INFO = 0
IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
INFO = -9
ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
INFO = -11
ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
INFO = -12
ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
INFO = -13
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZTGEXC', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 )
$ RETURN
IF( IFST.EQ.ILST )
$ RETURN
*
IF( IFST.LT.ILST ) THEN
*
HERE = IFST
*
10 CONTINUE
*
* Swap with next one below
*
CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
$ HERE, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 1
IF( HERE.LT.ILST )
$ GO TO 10
HERE = HERE - 1
ELSE
HERE = IFST - 1
*
20 CONTINUE
*
* Swap with next one above
*
CALL ZTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
$ HERE, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 1
IF( HERE.GE.ILST )
$ GO TO 20
HERE = HERE + 1
END IF
ILST = HERE
RETURN
*
* End of ZTGEXC
*
END
|
