OpenRadioss 2025.1.11
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slagge.f
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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.LT. IF( IN ) 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.EQ. IF( WNZERO ) 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.LE. IF( KLKU ) THEN
169*
170* annihilate subdiagonal elements first (necessary if KL = 0)
171*
172.LE. IF( IMIN( 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.EQ. IF( WNZERO ) 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.LE. IF( IMIN( 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.EQ. IF( WNZERO ) 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.LE. IF( IMIN( 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.EQ. IF( WNZERO ) 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.LE. IF( IMIN( 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.EQ. IF( WNZERO ) 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
slarnv
subroutine slarnv(idist, iseed, n, x)
SLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition slarnv.f:97
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
sscal
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
sgemv
subroutine sgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
SGEMV
Definition sgemv.f:156
sger
subroutine sger(m, n, alpha, x, incx, y, incy, a, lda)
SGER
Definition sger.f:130
min
#define min(a, b)
Definition macros.h:20
max
#define max(a, b)
Definition macros.h:21
slagge
subroutine slagge(m, n, kl, ku, d, a, lda, iseed, work, info)
Definition slagge.f:2