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
294
295
296
297
|
*> \brief \b DLATM7
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
* RANK, INFO )
*
* .. Scalar Arguments ..
* DOUBLE PRECISION COND
* INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
* ..
* .. Array Arguments ..
* DOUBLE PRECISION D( * )
* INTEGER ISEED( 4 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLATM7 computes the entries of D as specified by MODE
*> COND and IRSIGN. IDIST and ISEED determine the generation
*> of random numbers. DLATM7 is called by DLATMT to generate
*> random test matrices.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \verbatim
*> MODE - INTEGER
*> On entry describes how D is to be computed:
*> MODE = 0 means do not change D.
*>
*> MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND
*> MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
*> MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK
*>
*> MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
*> MODE = 5 sets D to random numbers in the range
*> ( 1/COND , 1 ) such that their logarithms
*> are uniformly distributed.
*> MODE = 6 set D to random numbers from same distribution
*> as the rest of the matrix.
*> MODE < 0 has the same meaning as ABS(MODE), except that
*> the order of the elements of D is reversed.
*> Thus if MODE is positive, D has entries ranging from
*> 1 to 1/COND, if negative, from 1/COND to 1,
*> Not modified.
*>
*> COND - DOUBLE PRECISION
*> On entry, used as described under MODE above.
*> If used, it must be >= 1. Not modified.
*>
*> IRSIGN - INTEGER
*> On entry, if MODE neither -6, 0 nor 6, determines sign of
*> entries of D
*> 0 => leave entries of D unchanged
*> 1 => multiply each entry of D by 1 or -1 with probability .5
*>
*> IDIST - CHARACTER*1
*> On entry, IDIST specifies the type of distribution to be
*> used to generate a random matrix .
*> 1 => UNIFORM( 0, 1 )
*> 2 => UNIFORM( -1, 1 )
*> 3 => NORMAL( 0, 1 )
*> Not modified.
*>
*> ISEED - INTEGER array, dimension ( 4 )
*> On entry ISEED specifies the seed of the random number
*> generator. The random number generator uses a
*> linear congruential sequence limited to small
*> integers, and so should produce machine independent
*> random numbers. The values of ISEED are changed on
*> exit, and can be used in the next call to DLATM7
*> to continue the same random number sequence.
*> Changed on exit.
*>
*> D - DOUBLE PRECISION array, dimension ( MIN( M , N ) )
*> Array to be computed according to MODE, COND and IRSIGN.
*> May be changed on exit if MODE is nonzero.
*>
*> N - INTEGER
*> Number of entries of D. Not modified.
*>
*> RANK - INTEGER
*> The rank of matrix to be generated for modes 1,2,3 only.
*> D( RANK+1:N ) = 0.
*> Not modified.
*>
*> INFO - INTEGER
*> 0 => normal termination
*> -1 => if MODE not in range -6 to 6
*> -2 => if MODE neither -6, 0 nor 6, and
*> IRSIGN neither 0 nor 1
*> -3 => if MODE neither -6, 0 nor 6 and COND less than 1
*> -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
*> -7 => if N negative
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_matgen
*
* =====================================================================
SUBROUTINE DLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
$ RANK, INFO )
*
* -- LAPACK computational routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
DOUBLE PRECISION COND
INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
* ..
* .. Array Arguments ..
DOUBLE PRECISION D( * )
INTEGER ISEED( 4 )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D0 )
DOUBLE PRECISION HALF
PARAMETER ( HALF = 0.5D0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION ALPHA, TEMP
INTEGER I
* ..
* .. External Functions ..
DOUBLE PRECISION DLARAN
EXTERNAL DLARAN
* ..
* .. External Subroutines ..
EXTERNAL DLARNV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, EXP, LOG
* ..
* .. Executable Statements ..
*
* Decode and Test the input parameters. Initialize flags & seed.
*
INFO = 0
*
* Quick return if possible
*
IF( N.EQ.0 )
$ RETURN
*
* Set INFO if an error
*
IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN
INFO = -1
ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
$ ( IRSIGN.NE.0 .AND. IRSIGN.NE.1 ) ) THEN
INFO = -2
ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
$ COND.LT.ONE ) THEN
INFO = -3
ELSE IF( ( MODE.EQ.6 .OR. MODE.EQ.-6 ) .AND.
$ ( IDIST.LT.1 .OR. IDIST.GT.3 ) ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -7
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLATM7', -INFO )
RETURN
END IF
*
* Compute D according to COND and MODE
*
IF( MODE.NE.0 ) THEN
GO TO ( 100, 130, 160, 190, 210, 230 )ABS( MODE )
*
* One large D value:
*
100 CONTINUE
DO 110 I = 2, RANK
D( I ) = ONE / COND
110 CONTINUE
DO 120 I = RANK + 1, N
D( I ) = ZERO
120 CONTINUE
D( 1 ) = ONE
GO TO 240
*
* One small D value:
*
130 CONTINUE
DO 140 I = 1, RANK - 1
D( I ) = ONE
140 CONTINUE
DO 150 I = RANK + 1, N
D( I ) = ZERO
150 CONTINUE
D( RANK ) = ONE / COND
GO TO 240
*
* Exponentially distributed D values:
*
160 CONTINUE
D( 1 ) = ONE
IF( N.GT.1 .AND. RANK.GT.1 ) THEN
ALPHA = COND**( -ONE / DBLE( RANK-1 ) )
DO 170 I = 2, RANK
D( I ) = ALPHA**( I-1 )
170 CONTINUE
DO 180 I = RANK + 1, N
D( I ) = ZERO
180 CONTINUE
END IF
GO TO 240
*
* Arithmetically distributed D values:
*
190 CONTINUE
D( 1 ) = ONE
IF( N.GT.1 ) THEN
TEMP = ONE / COND
ALPHA = ( ONE-TEMP ) / DBLE( N-1 )
DO 200 I = 2, N
D( I ) = DBLE( N-I )*ALPHA + TEMP
200 CONTINUE
END IF
GO TO 240
*
* Randomly distributed D values on ( 1/COND , 1):
*
210 CONTINUE
ALPHA = LOG( ONE / COND )
DO 220 I = 1, N
D( I ) = EXP( ALPHA*DLARAN( ISEED ) )
220 CONTINUE
GO TO 240
*
* Randomly distributed D values from IDIST
*
230 CONTINUE
CALL DLARNV( IDIST, ISEED, N, D )
*
240 CONTINUE
*
* If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
* random signs to D
*
IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
$ IRSIGN.EQ.1 ) THEN
DO 250 I = 1, N
TEMP = DLARAN( ISEED )
IF( TEMP.GT.HALF )
$ D( I ) = -D( I )
250 CONTINUE
END IF
*
* Reverse if MODE < 0
*
IF( MODE.LT.0 ) THEN
DO 260 I = 1, N / 2
TEMP = D( I )
D( I ) = D( N+1-I )
D( N+1-I ) = TEMP
260 CONTINUE
END IF
*
END IF
*
RETURN
*
* End of DLATM7
*
END
|
