1 SUBROUTINE SLATM7( MODE, COND, IRSIGN, IDIST, ISEED, D, N,
2 $ RANK, INFO )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Craig Lucas, University of Manchester / NAG Ltd.
6 * October, 2008
7 *
8 * .. Scalar Arguments ..
9 REAL COND
10 INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
11 * ..
12 * .. Array Arguments ..
13 REAL D( * )
14 INTEGER ISEED( 4 )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * SLATM7 computes the entries of D as specified by MODE
21 * COND and IRSIGN. IDIST and ISEED determine the generation
22 * of random numbers. SLATM7 is called by SLATMT to generate
23 * random test matrices.
24 *
25 * Arguments
26 * =========
27 *
28 * MODE - INTEGER
29 * On entry describes how D is to be computed:
30 * MODE = 0 means do not change D.
31 *
32 * MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND
33 * MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
34 * MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK
35 *
36 * MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
37 * MODE = 5 sets D to random numbers in the range
38 * ( 1/COND , 1 ) such that their logarithms
39 * are uniformly distributed.
40 * MODE = 6 set D to random numbers from same distribution
41 * as the rest of the matrix.
42 * MODE < 0 has the same meaning as ABS(MODE), except that
43 * the order of the elements of D is reversed.
44 * Thus if MODE is positive, D has entries ranging from
45 * 1 to 1/COND, if negative, from 1/COND to 1,
46 * Not modified.
47 *
48 * COND - REAL
49 * On entry, used as described under MODE above.
50 * If used, it must be >= 1. Not modified.
51 *
52 * IRSIGN - INTEGER
53 * On entry, if MODE neither -6, 0 nor 6, determines sign of
54 * entries of D
55 * 0 => leave entries of D unchanged
56 * 1 => multiply each entry of D by 1 or -1 with probability .5
57 *
58 * IDIST - CHARACTER*1
59 * On entry, IDIST specifies the type of distribution to be
60 * used to generate a random matrix .
61 * 1 => UNIFORM( 0, 1 )
62 * 2 => UNIFORM( -1, 1 )
63 * 3 => NORMAL( 0, 1 )
64 * Not modified.
65 *
66 * ISEED - INTEGER array, dimension ( 4 )
67 * On entry ISEED specifies the seed of the random number
68 * generator. The random number generator uses a
69 * linear congruential sequence limited to small
70 * integers, and so should produce machine independent
71 * random numbers. The values of ISEED are changed on
72 * exit, and can be used in the next call to SLATM7
73 * to continue the same random number sequence.
74 * Changed on exit.
75 *
76 * D - REAL array, dimension ( MIN( M , N ) )
77 * Array to be computed according to MODE, COND and IRSIGN.
78 * May be changed on exit if MODE is nonzero.
79 *
80 * N - INTEGER
81 * Number of entries of D. Not modified.
82 *
83 * RANK - INTEGER
84 * The rank of matrix to be generated for modes 1,2,3 only.
85 * D( RANK+1:N ) = 0.
86 * Not modified.
87 *
88 * INFO - INTEGER
89 * 0 => normal termination
90 * -1 => if MODE not in range -6 to 6
91 * -2 => if MODE neither -6, 0 nor 6, and
92 * IRSIGN neither 0 nor 1
93 * -3 => if MODE neither -6, 0 nor 6 and COND less than 1
94 * -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
95 * -7 => if N negative
96 *
97 * =====================================================================
98 *
99 * .. Parameters ..
100 REAL ONE
101 PARAMETER ( ONE = 1.0E0 )
102 REAL ZERO
103 PARAMETER ( ZERO = 0.0E0 )
104 REAL HALF
105 PARAMETER ( HALF = 0.5E0 )
106 * ..
107 * .. Local Scalars ..
108 REAL ALPHA, TEMP
109 INTEGER I
110 * ..
111 * .. External Functions ..
112 REAL SLARAN
113 EXTERNAL SLARAN
114 * ..
115 * .. External Subroutines ..
116 EXTERNAL SLARNV, XERBLA
117 * ..
118 * .. Intrinsic Functions ..
119 INTRINSIC ABS, EXP, LOG, REAL
120 * ..
121 * .. Executable Statements ..
122 *
123 * Decode and Test the input parameters. Initialize flags & seed.
124 *
125 INFO = 0
126 *
127 * Quick return if possible
128 *
129 IF( N.EQ.0 )
130 $ RETURN
131 *
132 * Set INFO if an error
133 *
134 IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN
135 INFO = -1
136 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
137 $ ( IRSIGN.NE.0 .AND. IRSIGN.NE.1 ) ) THEN
138 INFO = -2
139 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
140 $ COND.LT.ONE ) THEN
141 INFO = -3
142 ELSE IF( ( MODE.EQ.6 .OR. MODE.EQ.-6 ) .AND.
143 $ ( IDIST.LT.1 .OR. IDIST.GT.3 ) ) THEN
144 INFO = -4
145 ELSE IF( N.LT.0 ) THEN
146 INFO = -7
147 END IF
148 *
149 IF( INFO.NE.0 ) THEN
150 CALL XERBLA( 'SLATM7', -INFO )
151 RETURN
152 END IF
153 *
154 * Compute D according to COND and MODE
155 *
156 IF( MODE.NE.0 ) THEN
157 GO TO ( 100, 130, 160, 190, 210, 230 )ABS( MODE )
158 *
159 * One large D value:
160 *
161 100 CONTINUE
162 DO 110 I = 2, RANK
163 D( I ) = ONE / COND
164 110 CONTINUE
165 DO 120 I = RANK + 1, N
166 D( I ) = ZERO
167 120 CONTINUE
168 D( 1 ) = ONE
169 GO TO 240
170 *
171 * One small D value:
172 *
173 130 CONTINUE
174 DO 140 I = 1, RANK - 1
175 D( I ) = ONE
176 140 CONTINUE
177 DO 150 I = RANK + 1, N
178 D( I ) = ZERO
179 150 CONTINUE
180 D( RANK ) = ONE / COND
181 GO TO 240
182 *
183 * Exponentially distributed D values:
184 *
185 160 CONTINUE
186 D( 1 ) = ONE
187 IF( N.GT.1 ) THEN
188 ALPHA = COND**( -ONE / REAL( RANK-1 ) )
189 DO 170 I = 2, RANK
190 D( I ) = ALPHA**( I-1 )
191 170 CONTINUE
192 DO 180 I = RANK + 1, N
193 D( I ) = ZERO
194 180 CONTINUE
195 END IF
196 GO TO 240
197 *
198 * Arithmetically distributed D values:
199 *
200 190 CONTINUE
201 D( 1 ) = ONE
202 IF( N.GT.1 ) THEN
203 TEMP = ONE / COND
204 ALPHA = ( ONE-TEMP ) / REAL( N-1 )
205 DO 200 I = 2, N
206 D( I ) = REAL( N-I )*ALPHA + TEMP
207 200 CONTINUE
208 END IF
209 GO TO 240
210 *
211 * Randomly distributed D values on ( 1/COND , 1):
212 *
213 210 CONTINUE
214 ALPHA = LOG( ONE / COND )
215 DO 220 I = 1, N
216 D( I ) = EXP( ALPHA*SLARAN( ISEED ) )
217 220 CONTINUE
218 GO TO 240
219 *
220 * Randomly distributed D values from IDIST
221 *
222 230 CONTINUE
223 CALL SLARNV( IDIST, ISEED, N, D )
224 *
225 240 CONTINUE
226 *
227 * If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
228 * random signs to D
229 *
230 IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
231 $ IRSIGN.EQ.1 ) THEN
232 DO 250 I = 1, N
233 TEMP = SLARAN( ISEED )
234 IF( TEMP.GT.HALF )
235 $ D( I ) = -D( I )
236 250 CONTINUE
237 END IF
238 *
239 * Reverse if MODE < 0
240 *
241 IF( MODE.LT.0 ) THEN
242 DO 260 I = 1, N / 2
243 TEMP = D( I )
244 D( I ) = D( N+1-I )
245 D( N+1-I ) = TEMP
246 260 CONTINUE
247 END IF
248 *
249 END IF
250 *
251 RETURN
252 *
253 * End of SLATM7
254 *
255 END
2 $ RANK, INFO )
3 *
4 * -- LAPACK test routine (version 3.1) --
5 * Craig Lucas, University of Manchester / NAG Ltd.
6 * October, 2008
7 *
8 * .. Scalar Arguments ..
9 REAL COND
10 INTEGER IDIST, INFO, IRSIGN, MODE, N, RANK
11 * ..
12 * .. Array Arguments ..
13 REAL D( * )
14 INTEGER ISEED( 4 )
15 * ..
16 *
17 * Purpose
18 * =======
19 *
20 * SLATM7 computes the entries of D as specified by MODE
21 * COND and IRSIGN. IDIST and ISEED determine the generation
22 * of random numbers. SLATM7 is called by SLATMT to generate
23 * random test matrices.
24 *
25 * Arguments
26 * =========
27 *
28 * MODE - INTEGER
29 * On entry describes how D is to be computed:
30 * MODE = 0 means do not change D.
31 *
32 * MODE = 1 sets D(1)=1 and D(2:RANK)=1.0/COND
33 * MODE = 2 sets D(1:RANK-1)=1 and D(RANK)=1.0/COND
34 * MODE = 3 sets D(I)=COND**(-(I-1)/(RANK-1)) I=1:RANK
35 *
36 * MODE = 4 sets D(i)=1 - (i-1)/(N-1)*(1 - 1/COND)
37 * MODE = 5 sets D to random numbers in the range
38 * ( 1/COND , 1 ) such that their logarithms
39 * are uniformly distributed.
40 * MODE = 6 set D to random numbers from same distribution
41 * as the rest of the matrix.
42 * MODE < 0 has the same meaning as ABS(MODE), except that
43 * the order of the elements of D is reversed.
44 * Thus if MODE is positive, D has entries ranging from
45 * 1 to 1/COND, if negative, from 1/COND to 1,
46 * Not modified.
47 *
48 * COND - REAL
49 * On entry, used as described under MODE above.
50 * If used, it must be >= 1. Not modified.
51 *
52 * IRSIGN - INTEGER
53 * On entry, if MODE neither -6, 0 nor 6, determines sign of
54 * entries of D
55 * 0 => leave entries of D unchanged
56 * 1 => multiply each entry of D by 1 or -1 with probability .5
57 *
58 * IDIST - CHARACTER*1
59 * On entry, IDIST specifies the type of distribution to be
60 * used to generate a random matrix .
61 * 1 => UNIFORM( 0, 1 )
62 * 2 => UNIFORM( -1, 1 )
63 * 3 => NORMAL( 0, 1 )
64 * Not modified.
65 *
66 * ISEED - INTEGER array, dimension ( 4 )
67 * On entry ISEED specifies the seed of the random number
68 * generator. The random number generator uses a
69 * linear congruential sequence limited to small
70 * integers, and so should produce machine independent
71 * random numbers. The values of ISEED are changed on
72 * exit, and can be used in the next call to SLATM7
73 * to continue the same random number sequence.
74 * Changed on exit.
75 *
76 * D - REAL array, dimension ( MIN( M , N ) )
77 * Array to be computed according to MODE, COND and IRSIGN.
78 * May be changed on exit if MODE is nonzero.
79 *
80 * N - INTEGER
81 * Number of entries of D. Not modified.
82 *
83 * RANK - INTEGER
84 * The rank of matrix to be generated for modes 1,2,3 only.
85 * D( RANK+1:N ) = 0.
86 * Not modified.
87 *
88 * INFO - INTEGER
89 * 0 => normal termination
90 * -1 => if MODE not in range -6 to 6
91 * -2 => if MODE neither -6, 0 nor 6, and
92 * IRSIGN neither 0 nor 1
93 * -3 => if MODE neither -6, 0 nor 6 and COND less than 1
94 * -4 => if MODE equals 6 or -6 and IDIST not in range 1 to 3
95 * -7 => if N negative
96 *
97 * =====================================================================
98 *
99 * .. Parameters ..
100 REAL ONE
101 PARAMETER ( ONE = 1.0E0 )
102 REAL ZERO
103 PARAMETER ( ZERO = 0.0E0 )
104 REAL HALF
105 PARAMETER ( HALF = 0.5E0 )
106 * ..
107 * .. Local Scalars ..
108 REAL ALPHA, TEMP
109 INTEGER I
110 * ..
111 * .. External Functions ..
112 REAL SLARAN
113 EXTERNAL SLARAN
114 * ..
115 * .. External Subroutines ..
116 EXTERNAL SLARNV, XERBLA
117 * ..
118 * .. Intrinsic Functions ..
119 INTRINSIC ABS, EXP, LOG, REAL
120 * ..
121 * .. Executable Statements ..
122 *
123 * Decode and Test the input parameters. Initialize flags & seed.
124 *
125 INFO = 0
126 *
127 * Quick return if possible
128 *
129 IF( N.EQ.0 )
130 $ RETURN
131 *
132 * Set INFO if an error
133 *
134 IF( MODE.LT.-6 .OR. MODE.GT.6 ) THEN
135 INFO = -1
136 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
137 $ ( IRSIGN.NE.0 .AND. IRSIGN.NE.1 ) ) THEN
138 INFO = -2
139 ELSE IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
140 $ COND.LT.ONE ) THEN
141 INFO = -3
142 ELSE IF( ( MODE.EQ.6 .OR. MODE.EQ.-6 ) .AND.
143 $ ( IDIST.LT.1 .OR. IDIST.GT.3 ) ) THEN
144 INFO = -4
145 ELSE IF( N.LT.0 ) THEN
146 INFO = -7
147 END IF
148 *
149 IF( INFO.NE.0 ) THEN
150 CALL XERBLA( 'SLATM7', -INFO )
151 RETURN
152 END IF
153 *
154 * Compute D according to COND and MODE
155 *
156 IF( MODE.NE.0 ) THEN
157 GO TO ( 100, 130, 160, 190, 210, 230 )ABS( MODE )
158 *
159 * One large D value:
160 *
161 100 CONTINUE
162 DO 110 I = 2, RANK
163 D( I ) = ONE / COND
164 110 CONTINUE
165 DO 120 I = RANK + 1, N
166 D( I ) = ZERO
167 120 CONTINUE
168 D( 1 ) = ONE
169 GO TO 240
170 *
171 * One small D value:
172 *
173 130 CONTINUE
174 DO 140 I = 1, RANK - 1
175 D( I ) = ONE
176 140 CONTINUE
177 DO 150 I = RANK + 1, N
178 D( I ) = ZERO
179 150 CONTINUE
180 D( RANK ) = ONE / COND
181 GO TO 240
182 *
183 * Exponentially distributed D values:
184 *
185 160 CONTINUE
186 D( 1 ) = ONE
187 IF( N.GT.1 ) THEN
188 ALPHA = COND**( -ONE / REAL( RANK-1 ) )
189 DO 170 I = 2, RANK
190 D( I ) = ALPHA**( I-1 )
191 170 CONTINUE
192 DO 180 I = RANK + 1, N
193 D( I ) = ZERO
194 180 CONTINUE
195 END IF
196 GO TO 240
197 *
198 * Arithmetically distributed D values:
199 *
200 190 CONTINUE
201 D( 1 ) = ONE
202 IF( N.GT.1 ) THEN
203 TEMP = ONE / COND
204 ALPHA = ( ONE-TEMP ) / REAL( N-1 )
205 DO 200 I = 2, N
206 D( I ) = REAL( N-I )*ALPHA + TEMP
207 200 CONTINUE
208 END IF
209 GO TO 240
210 *
211 * Randomly distributed D values on ( 1/COND , 1):
212 *
213 210 CONTINUE
214 ALPHA = LOG( ONE / COND )
215 DO 220 I = 1, N
216 D( I ) = EXP( ALPHA*SLARAN( ISEED ) )
217 220 CONTINUE
218 GO TO 240
219 *
220 * Randomly distributed D values from IDIST
221 *
222 230 CONTINUE
223 CALL SLARNV( IDIST, ISEED, N, D )
224 *
225 240 CONTINUE
226 *
227 * If MODE neither -6 nor 0 nor 6, and IRSIGN = 1, assign
228 * random signs to D
229 *
230 IF( ( MODE.NE.-6 .AND. MODE.NE.0 .AND. MODE.NE.6 ) .AND.
231 $ IRSIGN.EQ.1 ) THEN
232 DO 250 I = 1, N
233 TEMP = SLARAN( ISEED )
234 IF( TEMP.GT.HALF )
235 $ D( I ) = -D( I )
236 250 CONTINUE
237 END IF
238 *
239 * Reverse if MODE < 0
240 *
241 IF( MODE.LT.0 ) THEN
242 DO 260 I = 1, N / 2
243 TEMP = D( I )
244 D( I ) = D( N+1-I )
245 D( N+1-I ) = TEMP
246 260 CONTINUE
247 END IF
248 *
249 END IF
250 *
251 RETURN
252 *
253 * End of SLATM7
254 *
255 END