1 SUBROUTINE CLAGGE( 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 D( * )
13 COMPLEX A( LDA, * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CLAGGE generates a complex general m by n matrix A, by pre- and post-
20 * multiplying a real diagonal matrix D with random unitary matrices:
21 * A = U*D*V. The lower and upper bandwidths may then be reduced to
22 * kl and ku by additional unitary transformations.
23 *
24 * Arguments
25 * =========
26 *
27 * M (input) INTEGER
28 * The number of rows of the matrix A. M >= 0.
29 *
30 * N (input) INTEGER
31 * The number of columns of the matrix A. N >= 0.
32 *
33 * KL (input) INTEGER
34 * The number of nonzero subdiagonals within the band of A.
35 * 0 <= KL <= M-1.
36 *
37 * KU (input) INTEGER
38 * The number of nonzero superdiagonals within the band of A.
39 * 0 <= KU <= N-1.
40 *
41 * D (input) REAL array, dimension (min(M,N))
42 * The diagonal elements of the diagonal matrix D.
43 *
44 * A (output) COMPLEX array, dimension (LDA,N)
45 * The generated m by n matrix A.
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= M.
49 *
50 * ISEED (input/output) INTEGER array, dimension (4)
51 * On entry, the seed of the random number generator; the array
52 * elements must be between 0 and 4095, and ISEED(4) must be
53 * odd.
54 * On exit, the seed is updated.
55 *
56 * WORK (workspace) COMPLEX array, dimension (M+N)
57 *
58 * INFO (output) INTEGER
59 * = 0: successful exit
60 * < 0: if INFO = -i, the i-th argument had an illegal value
61 *
62 * =====================================================================
63 *
64 * .. Parameters ..
65 COMPLEX ZERO, ONE
66 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
67 $ ONE = ( 1.0E+0, 0.0E+0 ) )
68 * ..
69 * .. Local Scalars ..
70 INTEGER I, J
71 REAL WN
72 COMPLEX TAU, WA, WB
73 * ..
74 * .. External Subroutines ..
75 EXTERNAL CGEMV, CGERC, CLACGV, CLARNV, CSCAL, XERBLA
76 * ..
77 * .. Intrinsic Functions ..
78 INTRINSIC ABS, MAX, MIN, REAL
79 * ..
80 * .. External Functions ..
81 REAL SCNRM2
82 EXTERNAL SCNRM2
83 * ..
84 * .. Executable Statements ..
85 *
86 * Test the input arguments
87 *
88 INFO = 0
89 IF( M.LT.0 ) THEN
90 INFO = -1
91 ELSE IF( N.LT.0 ) THEN
92 INFO = -2
93 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
94 INFO = -3
95 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
96 INFO = -4
97 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
98 INFO = -7
99 END IF
100 IF( INFO.LT.0 ) THEN
101 CALL XERBLA( 'CLAGGE', -INFO )
102 RETURN
103 END IF
104 *
105 * initialize A to diagonal matrix
106 *
107 DO 20 J = 1, N
108 DO 10 I = 1, M
109 A( I, J ) = ZERO
110 10 CONTINUE
111 20 CONTINUE
112 DO 30 I = 1, MIN( M, N )
113 A( I, I ) = D( I )
114 30 CONTINUE
115 *
116 * pre- and post-multiply A by random unitary matrices
117 *
118 DO 40 I = MIN( M, N ), 1, -1
119 IF( I.LT.M ) THEN
120 *
121 * generate random reflection
122 *
123 CALL CLARNV( 3, ISEED, M-I+1, WORK )
124 WN = SCNRM2( M-I+1, WORK, 1 )
125 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
126 IF( WN.EQ.ZERO ) THEN
127 TAU = ZERO
128 ELSE
129 WB = WORK( 1 ) + WA
130 CALL CSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
131 WORK( 1 ) = ONE
132 TAU = REAL( WB / WA )
133 END IF
134 *
135 * multiply A(i:m,i:n) by random reflection from the left
136 *
137 CALL CGEMV( 'Conjugate transpose', M-I+1, N-I+1, ONE,
138 $ A( I, I ), LDA, WORK, 1, ZERO, WORK( M+1 ), 1 )
139 CALL CGERC( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
140 $ A( I, I ), LDA )
141 END IF
142 IF( I.LT.N ) THEN
143 *
144 * generate random reflection
145 *
146 CALL CLARNV( 3, ISEED, N-I+1, WORK )
147 WN = SCNRM2( N-I+1, WORK, 1 )
148 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
149 IF( WN.EQ.ZERO ) THEN
150 TAU = ZERO
151 ELSE
152 WB = WORK( 1 ) + WA
153 CALL CSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
154 WORK( 1 ) = ONE
155 TAU = REAL( WB / WA )
156 END IF
157 *
158 * multiply A(i:m,i:n) by random reflection from the right
159 *
160 CALL CGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
161 $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
162 CALL CGERC( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
163 $ A( I, I ), LDA )
164 END IF
165 40 CONTINUE
166 *
167 * Reduce number of subdiagonals to KL and number of superdiagonals
168 * to KU
169 *
170 DO 70 I = 1, MAX( M-1-KL, N-1-KU )
171 IF( KL.LE.KU ) THEN
172 *
173 * annihilate subdiagonal elements first (necessary if KL = 0)
174 *
175 IF( I.LE.MIN( M-1-KL, N ) ) THEN
176 *
177 * generate reflection to annihilate A(kl+i+1:m,i)
178 *
179 WN = SCNRM2( M-KL-I+1, A( KL+I, I ), 1 )
180 WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
181 IF( WN.EQ.ZERO ) THEN
182 TAU = ZERO
183 ELSE
184 WB = A( KL+I, I ) + WA
185 CALL CSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
186 A( KL+I, I ) = ONE
187 TAU = REAL( WB / WA )
188 END IF
189 *
190 * apply reflection to A(kl+i:m,i+1:n) from the left
191 *
192 CALL CGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
193 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
194 $ WORK, 1 )
195 CALL CGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
196 $ 1, A( KL+I, I+1 ), LDA )
197 A( KL+I, I ) = -WA
198 END IF
199 *
200 IF( I.LE.MIN( N-1-KU, M ) ) THEN
201 *
202 * generate reflection to annihilate A(i,ku+i+1:n)
203 *
204 WN = SCNRM2( N-KU-I+1, A( I, KU+I ), LDA )
205 WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
206 IF( WN.EQ.ZERO ) THEN
207 TAU = ZERO
208 ELSE
209 WB = A( I, KU+I ) + WA
210 CALL CSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
211 A( I, KU+I ) = ONE
212 TAU = REAL( WB / WA )
213 END IF
214 *
215 * apply reflection to A(i+1:m,ku+i:n) from the right
216 *
217 CALL CLACGV( N-KU-I+1, A( I, KU+I ), LDA )
218 CALL CGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
219 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
220 $ WORK, 1 )
221 CALL CGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
222 $ LDA, A( I+1, KU+I ), LDA )
223 A( I, KU+I ) = -WA
224 END IF
225 ELSE
226 *
227 * annihilate superdiagonal elements first (necessary if
228 * KU = 0)
229 *
230 IF( I.LE.MIN( N-1-KU, M ) ) THEN
231 *
232 * generate reflection to annihilate A(i,ku+i+1:n)
233 *
234 WN = SCNRM2( N-KU-I+1, A( I, KU+I ), LDA )
235 WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
236 IF( WN.EQ.ZERO ) THEN
237 TAU = ZERO
238 ELSE
239 WB = A( I, KU+I ) + WA
240 CALL CSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
241 A( I, KU+I ) = ONE
242 TAU = REAL( WB / WA )
243 END IF
244 *
245 * apply reflection to A(i+1:m,ku+i:n) from the right
246 *
247 CALL CLACGV( N-KU-I+1, A( I, KU+I ), LDA )
248 CALL CGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
249 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
250 $ WORK, 1 )
251 CALL CGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
252 $ LDA, A( I+1, KU+I ), LDA )
253 A( I, KU+I ) = -WA
254 END IF
255 *
256 IF( I.LE.MIN( M-1-KL, N ) ) THEN
257 *
258 * generate reflection to annihilate A(kl+i+1:m,i)
259 *
260 WN = SCNRM2( M-KL-I+1, A( KL+I, I ), 1 )
261 WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
262 IF( WN.EQ.ZERO ) THEN
263 TAU = ZERO
264 ELSE
265 WB = A( KL+I, I ) + WA
266 CALL CSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
267 A( KL+I, I ) = ONE
268 TAU = REAL( WB / WA )
269 END IF
270 *
271 * apply reflection to A(kl+i:m,i+1:n) from the left
272 *
273 CALL CGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
274 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
275 $ WORK, 1 )
276 CALL CGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
277 $ 1, A( KL+I, I+1 ), LDA )
278 A( KL+I, I ) = -WA
279 END IF
280 END IF
281 *
282 DO 50 J = KL + I + 1, M
283 A( J, I ) = ZERO
284 50 CONTINUE
285 *
286 DO 60 J = KU + I + 1, N
287 A( I, J ) = ZERO
288 60 CONTINUE
289 70 CONTINUE
290 RETURN
291 *
292 * End of CLAGGE
293 *
294 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 D( * )
13 COMPLEX A( LDA, * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * CLAGGE generates a complex general m by n matrix A, by pre- and post-
20 * multiplying a real diagonal matrix D with random unitary matrices:
21 * A = U*D*V. The lower and upper bandwidths may then be reduced to
22 * kl and ku by additional unitary transformations.
23 *
24 * Arguments
25 * =========
26 *
27 * M (input) INTEGER
28 * The number of rows of the matrix A. M >= 0.
29 *
30 * N (input) INTEGER
31 * The number of columns of the matrix A. N >= 0.
32 *
33 * KL (input) INTEGER
34 * The number of nonzero subdiagonals within the band of A.
35 * 0 <= KL <= M-1.
36 *
37 * KU (input) INTEGER
38 * The number of nonzero superdiagonals within the band of A.
39 * 0 <= KU <= N-1.
40 *
41 * D (input) REAL array, dimension (min(M,N))
42 * The diagonal elements of the diagonal matrix D.
43 *
44 * A (output) COMPLEX array, dimension (LDA,N)
45 * The generated m by n matrix A.
46 *
47 * LDA (input) INTEGER
48 * The leading dimension of the array A. LDA >= M.
49 *
50 * ISEED (input/output) INTEGER array, dimension (4)
51 * On entry, the seed of the random number generator; the array
52 * elements must be between 0 and 4095, and ISEED(4) must be
53 * odd.
54 * On exit, the seed is updated.
55 *
56 * WORK (workspace) COMPLEX array, dimension (M+N)
57 *
58 * INFO (output) INTEGER
59 * = 0: successful exit
60 * < 0: if INFO = -i, the i-th argument had an illegal value
61 *
62 * =====================================================================
63 *
64 * .. Parameters ..
65 COMPLEX ZERO, ONE
66 PARAMETER ( ZERO = ( 0.0E+0, 0.0E+0 ),
67 $ ONE = ( 1.0E+0, 0.0E+0 ) )
68 * ..
69 * .. Local Scalars ..
70 INTEGER I, J
71 REAL WN
72 COMPLEX TAU, WA, WB
73 * ..
74 * .. External Subroutines ..
75 EXTERNAL CGEMV, CGERC, CLACGV, CLARNV, CSCAL, XERBLA
76 * ..
77 * .. Intrinsic Functions ..
78 INTRINSIC ABS, MAX, MIN, REAL
79 * ..
80 * .. External Functions ..
81 REAL SCNRM2
82 EXTERNAL SCNRM2
83 * ..
84 * .. Executable Statements ..
85 *
86 * Test the input arguments
87 *
88 INFO = 0
89 IF( M.LT.0 ) THEN
90 INFO = -1
91 ELSE IF( N.LT.0 ) THEN
92 INFO = -2
93 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN
94 INFO = -3
95 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN
96 INFO = -4
97 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
98 INFO = -7
99 END IF
100 IF( INFO.LT.0 ) THEN
101 CALL XERBLA( 'CLAGGE', -INFO )
102 RETURN
103 END IF
104 *
105 * initialize A to diagonal matrix
106 *
107 DO 20 J = 1, N
108 DO 10 I = 1, M
109 A( I, J ) = ZERO
110 10 CONTINUE
111 20 CONTINUE
112 DO 30 I = 1, MIN( M, N )
113 A( I, I ) = D( I )
114 30 CONTINUE
115 *
116 * pre- and post-multiply A by random unitary matrices
117 *
118 DO 40 I = MIN( M, N ), 1, -1
119 IF( I.LT.M ) THEN
120 *
121 * generate random reflection
122 *
123 CALL CLARNV( 3, ISEED, M-I+1, WORK )
124 WN = SCNRM2( M-I+1, WORK, 1 )
125 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
126 IF( WN.EQ.ZERO ) THEN
127 TAU = ZERO
128 ELSE
129 WB = WORK( 1 ) + WA
130 CALL CSCAL( M-I, ONE / WB, WORK( 2 ), 1 )
131 WORK( 1 ) = ONE
132 TAU = REAL( WB / WA )
133 END IF
134 *
135 * multiply A(i:m,i:n) by random reflection from the left
136 *
137 CALL CGEMV( 'Conjugate transpose', M-I+1, N-I+1, ONE,
138 $ A( I, I ), LDA, WORK, 1, ZERO, WORK( M+1 ), 1 )
139 CALL CGERC( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1,
140 $ A( I, I ), LDA )
141 END IF
142 IF( I.LT.N ) THEN
143 *
144 * generate random reflection
145 *
146 CALL CLARNV( 3, ISEED, N-I+1, WORK )
147 WN = SCNRM2( N-I+1, WORK, 1 )
148 WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 )
149 IF( WN.EQ.ZERO ) THEN
150 TAU = ZERO
151 ELSE
152 WB = WORK( 1 ) + WA
153 CALL CSCAL( N-I, ONE / WB, WORK( 2 ), 1 )
154 WORK( 1 ) = ONE
155 TAU = REAL( WB / WA )
156 END IF
157 *
158 * multiply A(i:m,i:n) by random reflection from the right
159 *
160 CALL CGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ),
161 $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 )
162 CALL CGERC( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1,
163 $ A( I, I ), LDA )
164 END IF
165 40 CONTINUE
166 *
167 * Reduce number of subdiagonals to KL and number of superdiagonals
168 * to KU
169 *
170 DO 70 I = 1, MAX( M-1-KL, N-1-KU )
171 IF( KL.LE.KU ) THEN
172 *
173 * annihilate subdiagonal elements first (necessary if KL = 0)
174 *
175 IF( I.LE.MIN( M-1-KL, N ) ) THEN
176 *
177 * generate reflection to annihilate A(kl+i+1:m,i)
178 *
179 WN = SCNRM2( M-KL-I+1, A( KL+I, I ), 1 )
180 WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
181 IF( WN.EQ.ZERO ) THEN
182 TAU = ZERO
183 ELSE
184 WB = A( KL+I, I ) + WA
185 CALL CSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
186 A( KL+I, I ) = ONE
187 TAU = REAL( WB / WA )
188 END IF
189 *
190 * apply reflection to A(kl+i:m,i+1:n) from the left
191 *
192 CALL CGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
193 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
194 $ WORK, 1 )
195 CALL CGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
196 $ 1, A( KL+I, I+1 ), LDA )
197 A( KL+I, I ) = -WA
198 END IF
199 *
200 IF( I.LE.MIN( N-1-KU, M ) ) THEN
201 *
202 * generate reflection to annihilate A(i,ku+i+1:n)
203 *
204 WN = SCNRM2( N-KU-I+1, A( I, KU+I ), LDA )
205 WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
206 IF( WN.EQ.ZERO ) THEN
207 TAU = ZERO
208 ELSE
209 WB = A( I, KU+I ) + WA
210 CALL CSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
211 A( I, KU+I ) = ONE
212 TAU = REAL( WB / WA )
213 END IF
214 *
215 * apply reflection to A(i+1:m,ku+i:n) from the right
216 *
217 CALL CLACGV( N-KU-I+1, A( I, KU+I ), LDA )
218 CALL CGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
219 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
220 $ WORK, 1 )
221 CALL CGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
222 $ LDA, A( I+1, KU+I ), LDA )
223 A( I, KU+I ) = -WA
224 END IF
225 ELSE
226 *
227 * annihilate superdiagonal elements first (necessary if
228 * KU = 0)
229 *
230 IF( I.LE.MIN( N-1-KU, M ) ) THEN
231 *
232 * generate reflection to annihilate A(i,ku+i+1:n)
233 *
234 WN = SCNRM2( N-KU-I+1, A( I, KU+I ), LDA )
235 WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I )
236 IF( WN.EQ.ZERO ) THEN
237 TAU = ZERO
238 ELSE
239 WB = A( I, KU+I ) + WA
240 CALL CSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA )
241 A( I, KU+I ) = ONE
242 TAU = REAL( WB / WA )
243 END IF
244 *
245 * apply reflection to A(i+1:m,ku+i:n) from the right
246 *
247 CALL CLACGV( N-KU-I+1, A( I, KU+I ), LDA )
248 CALL CGEMV( 'No transpose', M-I, N-KU-I+1, ONE,
249 $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO,
250 $ WORK, 1 )
251 CALL CGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ),
252 $ LDA, A( I+1, KU+I ), LDA )
253 A( I, KU+I ) = -WA
254 END IF
255 *
256 IF( I.LE.MIN( M-1-KL, N ) ) THEN
257 *
258 * generate reflection to annihilate A(kl+i+1:m,i)
259 *
260 WN = SCNRM2( M-KL-I+1, A( KL+I, I ), 1 )
261 WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I )
262 IF( WN.EQ.ZERO ) THEN
263 TAU = ZERO
264 ELSE
265 WB = A( KL+I, I ) + WA
266 CALL CSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 )
267 A( KL+I, I ) = ONE
268 TAU = REAL( WB / WA )
269 END IF
270 *
271 * apply reflection to A(kl+i:m,i+1:n) from the left
272 *
273 CALL CGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE,
274 $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO,
275 $ WORK, 1 )
276 CALL CGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK,
277 $ 1, A( KL+I, I+1 ), LDA )
278 A( KL+I, I ) = -WA
279 END IF
280 END IF
281 *
282 DO 50 J = KL + I + 1, M
283 A( J, I ) = ZERO
284 50 CONTINUE
285 *
286 DO 60 J = KU + I + 1, N
287 A( I, J ) = ZERO
288 60 CONTINUE
289 70 CONTINUE
290 RETURN
291 *
292 * End of CLAGGE
293 *
294 END