1 SUBROUTINE SLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO )
2 *
3 * -- LAPACK auxiliary test routine (version 3.1)
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER INFO, KL, KU, LDA, M, N
9 * ..
10 * .. Array Arguments ..
11 INTEGER ISEED( 4 )
12 REAL A( LDA, * ), D( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * SLAGGE generates a real general m by n matrix A, by pre- and post-
19 * multiplying a real diagonal matrix D with random orthogonal matrices:
20 * A = U*D*V. The lower and upper bandwidths may then be reduced to
21 * kl and ku by additional orthogonal transformations.
22 *
23 * Arguments
24 * =========
25 *
26 * M (input) INTEGER
27 * The number of rows of the matrix A. M >= 0.
28 *
29 * N (input) INTEGER
30 * The number of columns of the matrix A. N >= 0.
31 *
32 * KL (input) INTEGER
33 * The number of nonzero subdiagonals within the band of A.
34 * 0 <= KL <= M-1.
35 *
36 * KU (input) INTEGER
37 * The number of nonzero superdiagonals within the band of A.
38 * 0 <= KU <= N-1.
39 *
40 * D (input) REAL array, dimension (min(M,N))
41 * The diagonal elements of the diagonal matrix D.
42 *
43 * A (output) REAL array, dimension (LDA,N)
44 * The generated m by n matrix A.
45 *
46 * LDA (input) INTEGER
47 * The leading dimension of the array A. LDA >= M.
48 *
49 * ISEED (input/output) INTEGER array, dimension (4)
50 * On entry, the seed of the random number generator; the array
51 * elements must be between 0 and 4095, and ISEED(4) must be
52 * odd.
53 * On exit, the seed is updated.
54 *
55 * WORK (workspace) REAL array, dimension (M+N)
56 *
57 * INFO (output) INTEGER
58 * = 0: successful exit
59 * < 0: if INFO = -i, the i-th argument had an illegal value
60 *
61 * =====================================================================
62 *
63 * .. Parameters ..
64 REAL ZERO, ONE
65 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
66 * ..
67 * .. Local Scalars ..
68 INTEGER I, J
69 REAL TAU, WA, WB, WN
70 * ..
71 * .. External Subroutines ..
72 EXTERNAL SGEMV, SGER, SLARNV, SSCAL, XERBLA
73 * ..
74 * .. Intrinsic Functions ..
75 INTRINSIC MAX, MIN, SIGN
76 * ..
77 * .. External Functions ..
78 REAL SNRM2
79 EXTERNAL SNRM2
80 * ..
81 * .. Executable Statements ..
82 *
83 * Test the input arguments
84 *
85 INFO = 0
86 IF( M.LT.0 ) THEN
87 INFO = -1
88 ELSE IF( N.LT.0 ) THEN
89 INFO = -2
90 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
91 INFO = -3
92 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
93 INFO = -4
94 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
95 INFO = -7
96 END IF
97 IF( INFO.LT.0 ) THEN
98 CALL XERBLA( 'SLAGGE', -INFO )
99 RETURN
100 END IF
101 *
102 * initialize A to diagonal matrix
103 *
104 DO 20 J = 1, N
105 DO 10 I = 1, M
106 A( I, J ) = ZERO
107 10 CONTINUE
108 20 CONTINUE
109 DO 30 I = 1, MIN( M, N )
110 A( I, I ) = D( I )
111 30 CONTINUE
112 *
113 * pre- and post-multiply A by random orthogonal matrices
114 *
115 DO 40 I = MIN( M, N ), 1, -1
116 IF( I.LT.M ) THEN
117 *
118 * generate random reflection
119 *
120 CALL SLARNV( 3, ISEED, M-I+1, WORK )
121 WN = SNRM2( M-I+1, WORK, 1 )
122 WA = SIGN( WN, WORK( 1 ) )
123 IF( WN.EQ.ZERO ) THEN
124 TAU = ZERO
125 ELSE
126 WB = WORK( 1 ) + WA
127 CALL SSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
128 WORK( 1 ) = ONE
129 TAU = WB / WA
130 END IF
131 *
132 * multiply A(i:m,i:n) by random reflection from the left
133 *
134 CALL SGEMV( 'Transpose', M-I+1, N-I+1, ONE, A( I, I ), LDA,
135 $ WORK, 1, ZERO, WORK( M+1 ), 1 )
136 CALL SGER( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
137 $ A( I, I ), LDA )
138 END IF
139 IF( I.LT.N ) THEN
140 *
141 * generate random reflection
142 *
143 CALL SLARNV( 3, ISEED, N-I+1, WORK )
144 WN = SNRM2( N-I+1, WORK, 1 )
145 WA = SIGN( WN, WORK( 1 ) )
146 IF( WN.EQ.ZERO ) THEN
147 TAU = ZERO
148 ELSE
149 WB = WORK( 1 ) + WA
150 CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
151 WORK( 1 ) = ONE
152 TAU = WB / WA
153 END IF
154 *
155 * multiply A(i:m,i:n) by random reflection from the right
156 *
157 CALL SGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
158 $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
159 CALL SGER( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
160 $ A( I, I ), LDA )
161 END IF
162 40 CONTINUE
163 *
164 * Reduce number of subdiagonals to KL and number of superdiagonals
165 * to KU
166 *
167 DO 70 I = 1, MAX( M-1-KL, N-1-KU )
168 IF( KL.LE.KU ) THEN
169 *
170 * annihilate subdiagonal elements first (necessary if KL = 0)
171 *
172 IF( I.LE.MIN( M-1-KL, N ) ) THEN
173 *
174 * generate reflection to annihilate A(kl+i+1:m,i)
175 *
176 WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 )
177 WA = SIGN( WN, A( KL+I, I ) )
178 IF( WN.EQ.ZERO ) THEN
179 TAU = ZERO
180 ELSE
181 WB = A( KL+I, I ) + WA
182 CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
183 A( KL+I, I ) = ONE
184 TAU = WB / WA
185 END IF
186 *
187 * apply reflection to A(kl+i:m,i+1:n) from the left
188 *
189 CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
190 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
191 $ WORK, 1 )
192 CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
193 $ A( KL+I, I+1 ), LDA )
194 A( KL+I, I ) = -WA
195 END IF
196 *
197 IF( I.LE.MIN( N-1-KU, M ) ) THEN
198 *
199 * generate reflection to annihilate A(i,ku+i+1:n)
200 *
201 WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA )
202 WA = SIGN( WN, A( I, KU+I ) )
203 IF( WN.EQ.ZERO ) THEN
204 TAU = ZERO
205 ELSE
206 WB = A( I, KU+I ) + WA
207 CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
208 A( I, KU+I ) = ONE
209 TAU = WB / WA
210 END IF
211 *
212 * apply reflection to A(i+1:m,ku+i:n) from the right
213 *
214 CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
215 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
216 $ WORK, 1 )
217 CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
218 $ LDA, A( I+1, KU+I ), LDA )
219 A( I, KU+I ) = -WA
220 END IF
221 ELSE
222 *
223 * annihilate superdiagonal elements first (necessary if
224 * KU = 0)
225 *
226 IF( I.LE.MIN( N-1-KU, M ) ) THEN
227 *
228 * generate reflection to annihilate A(i,ku+i+1:n)
229 *
230 WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA )
231 WA = SIGN( WN, A( I, KU+I ) )
232 IF( WN.EQ.ZERO ) THEN
233 TAU = ZERO
234 ELSE
235 WB = A( I, KU+I ) + WA
236 CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
237 A( I, KU+I ) = ONE
238 TAU = WB / WA
239 END IF
240 *
241 * apply reflection to A(i+1:m,ku+i:n) from the right
242 *
243 CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
244 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
245 $ WORK, 1 )
246 CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
247 $ LDA, A( I+1, KU+I ), LDA )
248 A( I, KU+I ) = -WA
249 END IF
250 *
251 IF( I.LE.MIN( M-1-KL, N ) ) THEN
252 *
253 * generate reflection to annihilate A(kl+i+1:m,i)
254 *
255 WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 )
256 WA = SIGN( WN, A( KL+I, I ) )
257 IF( WN.EQ.ZERO ) THEN
258 TAU = ZERO
259 ELSE
260 WB = A( KL+I, I ) + WA
261 CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
262 A( KL+I, I ) = ONE
263 TAU = WB / WA
264 END IF
265 *
266 * apply reflection to A(kl+i:m,i+1:n) from the left
267 *
268 CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
269 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
270 $ WORK, 1 )
271 CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
272 $ A( KL+I, I+1 ), LDA )
273 A( KL+I, I ) = -WA
274 END IF
275 END IF
276 *
277 DO 50 J = KL + I + 1, M
278 A( J, I ) = ZERO
279 50 CONTINUE
280 *
281 DO 60 J = KU + I + 1, N
282 A( I, J ) = ZERO
283 60 CONTINUE
284 70 CONTINUE
285 RETURN
286 *
287 * End of SLAGGE
288 *
289 END
2 *
3 * -- LAPACK auxiliary test routine (version 3.1)
4 * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
5 * November 2006
6 *
7 * .. Scalar Arguments ..
8 INTEGER INFO, KL, KU, LDA, M, N
9 * ..
10 * .. Array Arguments ..
11 INTEGER ISEED( 4 )
12 REAL A( LDA, * ), D( * ), WORK( * )
13 * ..
14 *
15 * Purpose
16 * =======
17 *
18 * SLAGGE generates a real general m by n matrix A, by pre- and post-
19 * multiplying a real diagonal matrix D with random orthogonal matrices:
20 * A = U*D*V. The lower and upper bandwidths may then be reduced to
21 * kl and ku by additional orthogonal transformations.
22 *
23 * Arguments
24 * =========
25 *
26 * M (input) INTEGER
27 * The number of rows of the matrix A. M >= 0.
28 *
29 * N (input) INTEGER
30 * The number of columns of the matrix A. N >= 0.
31 *
32 * KL (input) INTEGER
33 * The number of nonzero subdiagonals within the band of A.
34 * 0 <= KL <= M-1.
35 *
36 * KU (input) INTEGER
37 * The number of nonzero superdiagonals within the band of A.
38 * 0 <= KU <= N-1.
39 *
40 * D (input) REAL array, dimension (min(M,N))
41 * The diagonal elements of the diagonal matrix D.
42 *
43 * A (output) REAL array, dimension (LDA,N)
44 * The generated m by n matrix A.
45 *
46 * LDA (input) INTEGER
47 * The leading dimension of the array A. LDA >= M.
48 *
49 * ISEED (input/output) INTEGER array, dimension (4)
50 * On entry, the seed of the random number generator; the array
51 * elements must be between 0 and 4095, and ISEED(4) must be
52 * odd.
53 * On exit, the seed is updated.
54 *
55 * WORK (workspace) REAL array, dimension (M+N)
56 *
57 * INFO (output) INTEGER
58 * = 0: successful exit
59 * < 0: if INFO = -i, the i-th argument had an illegal value
60 *
61 * =====================================================================
62 *
63 * .. Parameters ..
64 REAL ZERO, ONE
65 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
66 * ..
67 * .. Local Scalars ..
68 INTEGER I, J
69 REAL TAU, WA, WB, WN
70 * ..
71 * .. External Subroutines ..
72 EXTERNAL SGEMV, SGER, SLARNV, SSCAL, XERBLA
73 * ..
74 * .. Intrinsic Functions ..
75 INTRINSIC MAX, MIN, SIGN
76 * ..
77 * .. External Functions ..
78 REAL SNRM2
79 EXTERNAL SNRM2
80 * ..
81 * .. Executable Statements ..
82 *
83 * Test the input arguments
84 *
85 INFO = 0
86 IF( M.LT.0 ) THEN
87 INFO = -1
88 ELSE IF( N.LT.0 ) THEN
89 INFO = -2
90 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
91 INFO = -3
92 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
93 INFO = -4
94 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
95 INFO = -7
96 END IF
97 IF( INFO.LT.0 ) THEN
98 CALL XERBLA( 'SLAGGE', -INFO )
99 RETURN
100 END IF
101 *
102 * initialize A to diagonal matrix
103 *
104 DO 20 J = 1, N
105 DO 10 I = 1, M
106 A( I, J ) = ZERO
107 10 CONTINUE
108 20 CONTINUE
109 DO 30 I = 1, MIN( M, N )
110 A( I, I ) = D( I )
111 30 CONTINUE
112 *
113 * pre- and post-multiply A by random orthogonal matrices
114 *
115 DO 40 I = MIN( M, N ), 1, -1
116 IF( I.LT.M ) THEN
117 *
118 * generate random reflection
119 *
120 CALL SLARNV( 3, ISEED, M-I+1, WORK )
121 WN = SNRM2( M-I+1, WORK, 1 )
122 WA = SIGN( WN, WORK( 1 ) )
123 IF( WN.EQ.ZERO ) THEN
124 TAU = ZERO
125 ELSE
126 WB = WORK( 1 ) + WA
127 CALL SSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
128 WORK( 1 ) = ONE
129 TAU = WB / WA
130 END IF
131 *
132 * multiply A(i:m,i:n) by random reflection from the left
133 *
134 CALL SGEMV( 'Transpose', M-I+1, N-I+1, ONE, A( I, I ), LDA,
135 $ WORK, 1, ZERO, WORK( M+1 ), 1 )
136 CALL SGER( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
137 $ A( I, I ), LDA )
138 END IF
139 IF( I.LT.N ) THEN
140 *
141 * generate random reflection
142 *
143 CALL SLARNV( 3, ISEED, N-I+1, WORK )
144 WN = SNRM2( N-I+1, WORK, 1 )
145 WA = SIGN( WN, WORK( 1 ) )
146 IF( WN.EQ.ZERO ) THEN
147 TAU = ZERO
148 ELSE
149 WB = WORK( 1 ) + WA
150 CALL SSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
151 WORK( 1 ) = ONE
152 TAU = WB / WA
153 END IF
154 *
155 * multiply A(i:m,i:n) by random reflection from the right
156 *
157 CALL SGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
158 $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
159 CALL SGER( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
160 $ A( I, I ), LDA )
161 END IF
162 40 CONTINUE
163 *
164 * Reduce number of subdiagonals to KL and number of superdiagonals
165 * to KU
166 *
167 DO 70 I = 1, MAX( M-1-KL, N-1-KU )
168 IF( KL.LE.KU ) THEN
169 *
170 * annihilate subdiagonal elements first (necessary if KL = 0)
171 *
172 IF( I.LE.MIN( M-1-KL, N ) ) THEN
173 *
174 * generate reflection to annihilate A(kl+i+1:m,i)
175 *
176 WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 )
177 WA = SIGN( WN, A( KL+I, I ) )
178 IF( WN.EQ.ZERO ) THEN
179 TAU = ZERO
180 ELSE
181 WB = A( KL+I, I ) + WA
182 CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
183 A( KL+I, I ) = ONE
184 TAU = WB / WA
185 END IF
186 *
187 * apply reflection to A(kl+i:m,i+1:n) from the left
188 *
189 CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
190 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
191 $ WORK, 1 )
192 CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
193 $ A( KL+I, I+1 ), LDA )
194 A( KL+I, I ) = -WA
195 END IF
196 *
197 IF( I.LE.MIN( N-1-KU, M ) ) THEN
198 *
199 * generate reflection to annihilate A(i,ku+i+1:n)
200 *
201 WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA )
202 WA = SIGN( WN, A( I, KU+I ) )
203 IF( WN.EQ.ZERO ) THEN
204 TAU = ZERO
205 ELSE
206 WB = A( I, KU+I ) + WA
207 CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
208 A( I, KU+I ) = ONE
209 TAU = WB / WA
210 END IF
211 *
212 * apply reflection to A(i+1:m,ku+i:n) from the right
213 *
214 CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
215 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
216 $ WORK, 1 )
217 CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
218 $ LDA, A( I+1, KU+I ), LDA )
219 A( I, KU+I ) = -WA
220 END IF
221 ELSE
222 *
223 * annihilate superdiagonal elements first (necessary if
224 * KU = 0)
225 *
226 IF( I.LE.MIN( N-1-KU, M ) ) THEN
227 *
228 * generate reflection to annihilate A(i,ku+i+1:n)
229 *
230 WN = SNRM2( N-KU-I+1, A( I, KU+I ), LDA )
231 WA = SIGN( WN, A( I, KU+I ) )
232 IF( WN.EQ.ZERO ) THEN
233 TAU = ZERO
234 ELSE
235 WB = A( I, KU+I ) + WA
236 CALL SSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
237 A( I, KU+I ) = ONE
238 TAU = WB / WA
239 END IF
240 *
241 * apply reflection to A(i+1:m,ku+i:n) from the right
242 *
243 CALL SGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
244 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
245 $ WORK, 1 )
246 CALL SGER( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
247 $ LDA, A( I+1, KU+I ), LDA )
248 A( I, KU+I ) = -WA
249 END IF
250 *
251 IF( I.LE.MIN( M-1-KL, N ) ) THEN
252 *
253 * generate reflection to annihilate A(kl+i+1:m,i)
254 *
255 WN = SNRM2( M-KL-I+1, A( KL+I, I ), 1 )
256 WA = SIGN( WN, A( KL+I, I ) )
257 IF( WN.EQ.ZERO ) THEN
258 TAU = ZERO
259 ELSE
260 WB = A( KL+I, I ) + WA
261 CALL SSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
262 A( KL+I, I ) = ONE
263 TAU = WB / WA
264 END IF
265 *
266 * apply reflection to A(kl+i:m,i+1:n) from the left
267 *
268 CALL SGEMV( 'Transpose', M-KL-I+1, N-I, ONE,
269 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
270 $ WORK, 1 )
271 CALL SGER( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, 1,
272 $ A( KL+I, I+1 ), LDA )
273 A( KL+I, I ) = -WA
274 END IF
275 END IF
276 *
277 DO 50 J = KL + I + 1, M
278 A( J, I ) = ZERO
279 50 CONTINUE
280 *
281 DO 60 J = KU + I + 1, N
282 A( I, J ) = ZERO
283 60 CONTINUE
284 70 CONTINUE
285 RETURN
286 *
287 * End of SLAGGE
288 *
289 END