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
|
SUBROUTINE CLATM1( MODE, COND, IRSIGN, IDIST, ISEED, D, N, INFO )
*
* -- LAPACK auxiliary test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER IDIST, INFO, IRSIGN, MODE, N
REAL COND
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
COMPLEX D( * )
* ..
*
* Purpose
* =======
*
* CLATM1 computes the entries of D(1..N) as specified by
* MODE, COND and IRSIGN. IDIST and ISEED determine the generation
* of random numbers. CLATM1 is called by CLATMR to generate
* random test matrices for LAPACK programs.
*
* Arguments
* =========
*
* 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:N)=1.0/COND
* MODE = 2 sets D(1:N-1)=1 and D(N)=1.0/COND
* MODE = 3 sets D(I)=COND**(-(I-1)/(N-1))
* 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 - REAL
* 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 random complex number
* uniformly distributed with absolute value 1
*
* IDIST - CHARACTER*1
* On entry, IDIST specifies the type of distribution to be
* used to generate a random matrix .
* 1 => real and imaginary parts each UNIFORM( 0, 1 )
* 2 => real and imaginary parts each UNIFORM( -1, 1 )
* 3 => real and imaginary parts each NORMAL( 0, 1 )
* 4 => complex number uniform in DISK( 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 CLATM1
* to continue the same random number sequence.
* Changed on exit.
*
* D - COMPLEX 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.
*
* 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 4
* -7 => if N negative
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER I
REAL ALPHA, TEMP
COMPLEX CTEMP
* ..
* .. External Functions ..
REAL SLARAN
COMPLEX CLARND
EXTERNAL SLARAN, CLARND
* ..
* .. External Subroutines ..
EXTERNAL CLARNV, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, EXP, LOG, REAL
* ..
* .. 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.4 ) ) THEN
INFO = -4
ELSE IF( N.LT.0 ) THEN
INFO = -7
END IF
*
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CLATM1', -INFO )
RETURN
END IF
*
* Compute D according to COND and MODE
*
IF( MODE.NE.0 ) THEN
GO TO ( 10, 30, 50, 70, 90, 110 )ABS( MODE )
*
* One large D value:
*
10 CONTINUE
DO 20 I = 1, N
D( I ) = ONE / COND
20 CONTINUE
D( 1 ) = ONE
GO TO 120
*
* One small D value:
*
30 CONTINUE
DO 40 I = 1, N
D( I ) = ONE
40 CONTINUE
D( N ) = ONE / COND
GO TO 120
*
* Exponentially distributed D values:
*
50 CONTINUE
D( 1 ) = ONE
IF( N.GT.1 ) THEN
ALPHA = COND**( -ONE / REAL( N-1 ) )
DO 60 I = 2, N
D( I ) = ALPHA**( I-1 )
60 CONTINUE
END IF
GO TO 120
*
* Arithmetically distributed D values:
*
70 CONTINUE
D( 1 ) = ONE
IF( N.GT.1 ) THEN
TEMP = ONE / COND
ALPHA = ( ONE-TEMP ) / REAL( N-1 )
DO 80 I = 2, N
D( I ) = REAL( N-I )*ALPHA + TEMP
80 CONTINUE
END IF
GO TO 120
*
* Randomly distributed D values on ( 1/COND , 1):
*
90 CONTINUE
ALPHA = LOG( ONE / COND )
DO 100 I = 1, N
D( I ) = EXP( ALPHA*SLARAN( ISEED ) )
100 CONTINUE
GO TO 120
*
* Randomly distributed D values from IDIST
*
110 CONTINUE
CALL CLARNV( IDIST, ISEED, N, D )
*
120 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 130 I = 1, N
CTEMP = CLARND( 3, ISEED )
D( I ) = D( I )*( CTEMP / ABS( CTEMP ) )
130 CONTINUE
END IF
*
* Reverse if MODE < 0
*
IF( MODE.LT.0 ) THEN
DO 140 I = 1, N / 2
CTEMP = D( I )
D( I ) = D( N+1-I )
D( N+1-I ) = CTEMP
140 CONTINUE
END IF
*
END IF
*
RETURN
*
* End of CLATM1
*
END
|
