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
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
|
SUBROUTINE MB01RW( UPLO, TRANS, M, N, A, LDA, Z, LDZ, DWORK,
$ INFO )
C
C SLICOT RELEASE 5.0.
C
C Copyright (c) 2002-2009 NICONET e.V.
C
C This program is free software: you can redistribute it and/or
C modify it under the terms of the GNU General Public License as
C published by the Free Software Foundation, either version 2 of
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public License
C along with this program. If not, see
C <http://www.gnu.org/licenses/>.
C
C PURPOSE
C
C To compute the transformation of the symmetric matrix A by the
C matrix Z in the form
C
C A := op(Z)*A*op(Z)',
C
C where op(Z) is either Z or its transpose, Z'.
C
C ARGUMENTS
C
C Mode Parameters
C
C UPLO CHARACTER*1
C Specifies whether the upper or lower triangle of A
C is stored:
C = 'U': Upper triangle of A is stored;
C = 'L': Lower triangle of A is stored.
C
C TRANS CHARACTER*1
C Specifies whether op(Z) is Z or its transpose Z':
C = 'N': op(Z) = Z;
C = 'T': op(Z) = Z'.
C
C Input/Output Parameters
C
C M (input) INTEGER
C The order of the resulting symmetric matrix op(Z)*A*op(Z)'
C and the number of rows of the matrix Z, if TRANS = 'N',
C or the number of columns of the matrix Z, if TRANS = 'T'.
C M >= 0.
C
C N (input) INTEGER
C The order of the symmetric matrix A and the number of
C columns of the matrix Z, if TRANS = 'N', or the number of
C rows of the matrix Z, if TRANS = 'T'. N >= 0.
C
C A (input/output) DOUBLE PRECISION array, dimension
C (LDA,MAX(M,N))
C On entry, the leading N-by-N upper or lower triangular
C part of this array must contain the upper (UPLO = 'U')
C or lower (UPLO = 'L') triangular part of the symmetric
C matrix A.
C On exit, the leading M-by-M upper or lower triangular
C part of this array contains the upper (UPLO = 'U') or
C lower (UPLO = 'L') triangular part of the symmetric
C matrix op(Z)*A*op(Z)'.
C
C LDA INTEGER
C The leading dimension of the array A. LDA >= MAX(1,M,N).
C
C Z (input) DOUBLE PRECISION array, dimension (LDQ,K)
C where K = N if TRANS = 'N' and K = M if TRANS = 'T'.
C The leading M-by-N part, if TRANS = 'N', or N-by-M part,
C if TRANS = 'T', of this array contains the matrix Z.
C
C LDZ INTEGER
C The leading dimension of the array Z.
C LDZ >= MAX(1,M) if TRANS = 'N' and
C LDZ >= MAX(1,N) if TRANS = 'T'.
C
C Workspace
C
C DWORK DOUBLE PRECISION array, dimension (N)
C
C Error Indicator
C
C INFO INTEGER
C = 0: successful exit;
C < 0: if INFO = -i, the i-th argument had an illegal
C value.
C
C FURTHER COMMENTS
C
C This is a simpler, BLAS 2 version for MB01RD.
C
C CONTRIBUTOR
C
C A. Varga, DLR, Feb. 1995.
C
C REVISIONS
C
C April 1998 (T. Penzl).
C Sep. 1998 (V. Sima).
C
C ******************************************************************
C
C .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
C .. Scalar Arguments ..
CHARACTER TRANS, UPLO
INTEGER INFO, LDA, LDZ, M, N
C .. Array Arguments ..
DOUBLE PRECISION A(LDA,*), DWORK(*), Z(LDZ,*)
C .. Local Scalars ..
LOGICAL NOTTRA, UPPER
INTEGER I, J
C .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
C .. External Subroutines ..
EXTERNAL DCOPY, DGEMV, XERBLA
C .. Intrinsic Functions ..
INTRINSIC MAX
C
C .. Executable Statements
C
NOTTRA = LSAME( TRANS, 'N' )
UPPER = LSAME( UPLO, 'U' )
C
INFO = 0
IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L') ) ) THEN
INFO = -1
ELSE IF( .NOT.( NOTTRA .OR. LSAME( TRANS, 'T') ) ) THEN
INFO = -2
ELSE IF( M.LT.0 ) THEN
INFO = -3
ELSE IF( N.LT.0 ) THEN
INFO = -4
ELSE IF( LDA.LT.MAX( 1, M, N ) ) THEN
INFO = -6
ELSE IF( ( NOTTRA .AND. LDZ.LT.MAX( 1, M ) ) .OR.
$ ( .NOT.NOTTRA .AND. LDZ.LT.MAX( 1, N ) ) ) THEN
INFO = -8
END IF
C
IF ( INFO.NE.0 ) THEN
CALL XERBLA( 'MB01RW', -INFO )
RETURN
END IF
C
C Quick return if possible.
C
IF( N.EQ.0 .OR. M.EQ.0 )
$ RETURN
C
IF ( NOTTRA ) THEN
C
C Compute Z*A*Z'.
C
IF ( UPPER ) THEN
C
C Compute Z*A in A (M-by-N).
C
DO 10 J = 1, N
CALL DCOPY( J-1, A(1,J), 1, DWORK, 1 )
CALL DCOPY( N-J+1, A(J,J), LDA, DWORK(J), 1 )
CALL DGEMV( TRANS, M, N, ONE, Z, LDZ, DWORK, 1, ZERO,
$ A(1,J), 1 )
10 CONTINUE
C
C Compute A*Z' in the upper triangular part of A.
C
DO 20 I = 1, M
CALL DCOPY( N, A(I,1), LDA, DWORK, 1 )
CALL DGEMV( TRANS, M-I+1, N, ONE, Z(I,1), LDZ, DWORK, 1,
$ ZERO, A(I,I), LDA )
20 CONTINUE
C
ELSE
C
C Compute A*Z' in A (N-by-M).
C
DO 30 I = 1, N
CALL DCOPY( I-1, A(I,1), LDA, DWORK, 1 )
CALL DCOPY( N-I+1, A(I,I), 1, DWORK(I), 1 )
CALL DGEMV( TRANS, M, N, ONE, Z, LDZ, DWORK, 1, ZERO,
$ A(I,1), LDA )
30 CONTINUE
C
C Compute Z*A in the lower triangular part of A.
C
DO 40 J = 1, M
CALL DCOPY( N, A(1,J), 1, DWORK, 1 )
CALL DGEMV( TRANS, M-J+1, N, ONE, Z(J,1), LDZ, DWORK, 1,
$ ZERO, A(J,J), 1 )
40 CONTINUE
C
END IF
ELSE
C
C Compute Z'*A*Z.
C
IF ( UPPER ) THEN
C
C Compute Z'*A in A (M-by-N).
C
DO 50 J = 1, N
CALL DCOPY( J-1, A(1,J), 1, DWORK, 1 )
CALL DCOPY( N-J+1, A(J,J), LDA, DWORK(J), 1 )
CALL DGEMV( TRANS, N, M, ONE, Z, LDZ, DWORK, 1, ZERO,
$ A(1,J), 1 )
50 CONTINUE
C
C Compute A*Z in the upper triangular part of A.
C
DO 60 I = 1, M
CALL DCOPY( N, A(I,1), LDA, DWORK, 1 )
CALL DGEMV( TRANS, N, M-I+1, ONE, Z(1,I), LDZ, DWORK, 1,
$ ZERO, A(I,I), LDA )
60 CONTINUE
C
ELSE
C
C Compute A*Z in A (N-by-M).
C
DO 70 I = 1, N
CALL DCOPY( I-1, A(I,1), LDA, DWORK, 1 )
CALL DCOPY( N-I+1, A(I,I), 1, DWORK(I), 1 )
CALL DGEMV( TRANS, N, M, ONE, Z, LDZ, DWORK, 1, ZERO,
$ A(I,1), LDA )
70 CONTINUE
C
C Compute Z'*A in the lower triangular part of A.
C
DO 80 J = 1, M
CALL DCOPY( N, A(1,J), 1, DWORK, 1 )
CALL DGEMV( TRANS, N, M-J+1, ONE, Z(1,J), LDZ, DWORK, 1,
$ ZERO, A(J,J), 1 )
80 CONTINUE
C
END IF
END IF
C
RETURN
C *** Last line of MB01RW ***
END
|
