File: MA02ID.f

package info (click to toggle)
dynare 4.3.0-2
  • links: PTS, VCS
  • area: main
  • in suites: wheezy
  • size: 40,640 kB
  • sloc: fortran: 82,231; cpp: 72,734; ansic: 28,874; pascal: 13,241; sh: 4,300; objc: 3,281; yacc: 2,833; makefile: 1,288; lex: 1,162; python: 162; lisp: 54; xml: 8
file content (293 lines) | stat: -rw-r--r-- 9,139 bytes parent folder | download
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
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
      DOUBLE PRECISION FUNCTION MA02ID( TYP, NORM, N, A, LDA, QG,
     $                                  LDQG, DWORK )
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 value of the one norm, or the Frobenius norm, or
C     the infinity norm, or the element of largest absolute value
C     of a real skew-Hamiltonian matrix
C
C                   [  A   G  ]          T         T
C             X  =  [       T ],   G = -G,   Q = -Q,
C                   [  Q   A  ]
C
C     or of a real Hamiltonian matrix
C
C                   [  A   G  ]          T         T
C             X  =  [       T ],   G =  G,   Q =  Q,
C                   [  Q  -A  ]
C
C     where A, G and Q are real n-by-n matrices.
C
C     Note that for this kind of matrices the infinity norm is equal
C     to the one norm.
C
C     FUNCTION VALUE
C
C     MA02ID  DOUBLE PRECISION
C             The computed norm.
C
C     ARGUMENTS
C
C     Mode Parameters
C
C     TYP     CHARACTER*1
C             Specifies the type of the input matrix X:
C             = 'S':         X is skew-Hamiltonian;
C             = 'H':         X is Hamiltonian.
C
C     NORM    CHARACTER*1
C             Specifies the value to be returned in MA02ID:
C             = '1' or 'O':  one norm of X;
C             = 'F' or 'E':  Frobenius norm of X;
C             = 'I':         infinity norm of X;
C             = 'M':         max(abs(X(i,j)).
C
C     Input/Output Parameters
C
C     N       (input) INTEGER
C             The order of the matrix A.  N >= 0.
C
C     A       (input) DOUBLE PRECISION array, dimension (LDA,N)
C             On entry, the leading N-by-N part of this array must
C             contain the matrix A.
C
C     LDA     INTEGER
C             The leading dimension of the array A.  LDA >= MAX(1,N).
C
C     QG      (input) DOUBLE PRECISION array, dimension (LDQG,N+1)
C             On entry, the leading N-by-N+1 part of this array must
C             contain in columns 1:N the lower triangular part of the
C             matrix Q and in columns 2:N+1 the upper triangular part
C             of the matrix G. If TYP = 'S', the parts containing the
C             diagonal and the first supdiagonal of this array are not
C             referenced.
C
C     LDQG    INTEGER
C             The leading dimension of the array QG.  LDQG >= MAX(1,N).
C
C     Workspace
C
C
C     DWORK   DOUBLE PRECISION array, dimension (LDWORK)
C             where LDWORK >= 2*N when NORM = '1', NORM = 'I' or
C             NORM = 'O'; otherwise, DWORK is not referenced.
C
C     CONTRIBUTORS
C
C     D. Kressner, Technical Univ. Berlin, Germany, and
C     P. Benner, Technical Univ. Chemnitz, Germany, December 2003.
C
C     REVISIONS
C
C     V. Sima, June 2008 (SLICOT version of the HAPACK routine DLANHA).
C
C     KEYWORDS
C
C     Elementary matrix operations, Hamiltonian matrix, skew-Hamiltonian
C     matrix.
C
C     ******************************************************************
C
C     .. Parameters ..
      DOUBLE PRECISION   ONE, TWO, ZERO
      PARAMETER          ( ONE = 1.0D+0, TWO = 2.0D+0, ZERO = 0.0D+0 )
C     .. Scalar Arguments ..
      CHARACTER          NORM, TYP
      INTEGER            LDA, LDQG, N
C     .. Array Arguments ..
      DOUBLE PRECISION   A(LDA,*), DWORK(*), QG(LDQG,*)
C     .. Local Scalars ..
      LOGICAL            LSH
      INTEGER            I, J
      DOUBLE PRECISION   DSCL, DSUM, SCALE, SUM, TEMP, VALUE
C     .. External Functions ..
      LOGICAL            LSAME
      DOUBLE PRECISION   DLANGE, DLAPY2
      EXTERNAL           DLANGE, DLAPY2, LSAME
C     .. External Subroutines ..
      EXTERNAL           DLASSQ
C     .. Intrinsic Functions ..
      INTRINSIC          ABS, MAX, SQRT
C
C     .. Executable Statements ..
C
      LSH = LSAME( TYP, 'S' )
C
      IF ( N.EQ.0 ) THEN
         VALUE = ZERO
C
      ELSE IF ( LSAME( NORM, 'M' ) .AND. LSH ) THEN
C
C        Find max(abs(A(i,j))).
C
         VALUE = DLANGE( 'MaxElement', N, N, A, LDA, DWORK )
         IF ( N.GT.1 ) THEN
            DO 30  J = 1, N+1
               DO 10  I = 1, J-2
                  VALUE = MAX( VALUE, ABS( QG(I,J) ) )
   10          CONTINUE
               DO 20  I = J+1, N
                  VALUE = MAX( VALUE, ABS( QG(I,J) ) )
   20          CONTINUE
   30       CONTINUE
         END IF
C
      ELSE IF ( LSAME( NORM, 'M' ) ) THEN
C
C        Find max( abs( A(i,j) ), abs( QG(i,j) ) ).
C
         VALUE = MAX( DLANGE( 'MaxElement', N, N, A, LDA, DWORK ),
     $                DLANGE( 'MaxElement', N, N+1, QG, LDQG,
     $                        DWORK ) )
C
      ELSE IF ( ( LSAME( NORM, 'O' ) .OR. ( NORM.EQ.'1' ) .OR.
     $            LSAME( NORM, 'I' ) ) .AND. LSH ) THEN
C
C        Find the column and row sums of A (in one pass).
C
         VALUE = ZERO
         DO 40 I = 1, N
            DWORK(I) = ZERO
   40    CONTINUE
C
         DO 60 J = 1, N
            SUM = ZERO
            DO 50 I = 1, N
               TEMP = ABS( A(I,J) )
               SUM  = SUM + TEMP
               DWORK(I) = DWORK(I) + TEMP
   50       CONTINUE
            DWORK(N+J) = SUM
   60    CONTINUE
C
C        Compute the maximal absolute column sum.
C
         DO 90 J = 1, N+1
            DO 70  I = 1, J-2
               TEMP = ABS( QG(I,J) )
               DWORK(I) = DWORK(I) + TEMP
               DWORK(J-1) = DWORK(J-1) + TEMP
   70       CONTINUE
            IF ( J.LT.N+1 ) THEN
               SUM = DWORK(N+J)
               DO 80  I = J+1, N
                  TEMP = ABS( QG(I,J) )
                  SUM  = SUM + TEMP
                  DWORK(N+I) = DWORK(N+I) + TEMP
   80          CONTINUE
               VALUE = MAX( VALUE, SUM )
            END IF
   90    CONTINUE
         DO 100 I = 1, N
            VALUE = MAX( VALUE, DWORK(I) )
  100    CONTINUE
C
      ELSE IF ( LSAME( NORM, 'O' ) .OR. ( NORM.EQ.'1' ) .OR.
     $          LSAME( NORM, 'I' ) ) THEN
C
C        Find the column and row sums of A (in one pass).
C
         VALUE = ZERO
         DO 110 I = 1, N
            DWORK(I) = ZERO
  110   CONTINUE
C
         DO 130 J = 1, N
            SUM = ZERO
            DO 120 I = 1, N
               TEMP = ABS( A(I,J) )
               SUM  = SUM + TEMP
               DWORK(I) = DWORK(I) + TEMP
  120       CONTINUE
            DWORK(N+J) = SUM
  130    CONTINUE
C
C        Compute the maximal absolute column sum.
C
         DO 160 J = 1, N+1
            DO 140  I = 1, J-2
               TEMP = ABS( QG(I,J) )
               DWORK(I) = DWORK(I) + TEMP
               DWORK(J-1) = DWORK(J-1) + TEMP
  140       CONTINUE
            IF ( J.GT.1 )
     $         DWORK(J-1) = DWORK(J-1) + ABS( QG(J-1,J) )
            IF ( J.LT.N+1 ) THEN
               SUM = DWORK(N+J) + ABS( QG(J,J) )
               DO 150 I = J+1, N
                  TEMP = ABS( QG(I,J) )
                  SUM  = SUM + TEMP
                  DWORK(N+I) = DWORK(N+I) + TEMP
  150          CONTINUE
               VALUE = MAX( VALUE, SUM )
            END IF
  160    CONTINUE
         DO 170 I = 1, N
            VALUE = MAX( VALUE, DWORK(I) )
  170    CONTINUE
C
      ELSE IF ( ( LSAME( NORM, 'F' ) .OR.
     $            LSAME( NORM, 'E' ) ) .AND. LSH ) THEN
C
C        Find normF(A).
C
         SCALE = ZERO
         SUM = ONE
         DO 180 J = 1, N
            CALL DLASSQ( N, A(1,J), 1, SCALE, SUM )
  180    CONTINUE
C
C        Add normF(G) and normF(Q).
C
         DO 190 J = 1, N+1
            IF ( J.GT.2 )
     $         CALL DLASSQ( J-2, QG(1,J), 1, SCALE, SUM )
            IF ( J.LT.N )
     $         CALL DLASSQ( N-J, QG(J+1,J), 1, SCALE, SUM )
  190    CONTINUE
         VALUE = SQRT( TWO )*SCALE*SQRT( SUM )
      ELSE IF ( LSAME( NORM, 'F' ) .OR. LSAME( NORM, 'E' ) ) THEN
         SCALE = ZERO
         SUM = ONE
         DO 200 J = 1, N
            CALL DLASSQ( N, A(1,J), 1, SCALE, SUM )
  200    CONTINUE
         DSCL = ZERO
         DSUM = ONE
         DO 210 J = 1, N+1
            IF ( J.GT.1 ) THEN
               CALL DLASSQ( J-2, QG(1,J), 1, SCALE, SUM )
               CALL DLASSQ( 1, QG(J-1,J), 1, DSCL, DSUM )
            END IF
            IF ( J.LT.N+1 ) THEN
               CALL DLASSQ( 1, QG(J,J), 1, DSCL, DSUM )
               CALL DLASSQ( N-J, QG(J+1,J), 1, SCALE, SUM )
            END IF
  210    CONTINUE
         VALUE = DLAPY2( SQRT( TWO )*SCALE*SQRT( SUM ),
     $                   DSCL*SQRT( DSUM ) )
      END IF
C
      MA02ID = VALUE
      RETURN
C *** Last line of MA02ID ***
      END