SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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◆ dlagge()

subroutine dlagge ( integer  m,
integer  n,
integer  kl,
integer  ku,
double precision, dimension( * )  d,
double precision, dimension( lda, * )  a,
integer  lda,
integer, dimension( 4 )  iseed,
double precision, dimension( * )  work,
integer  info 
)

Definition at line 1 of file dlagge.f.

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 DOUBLE PRECISION A( LDA, * ), D( * ), WORK( * )
13* ..
14*
15* Purpose
16* =======
17*
18* DLAGGE 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) DOUBLE PRECISION array, dimension (min(M,N))
41* The diagonal elements of the diagonal matrix D.
42*
43* A (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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 DOUBLE PRECISION ZERO, ONE
65 parameter( zero = 0.0d+0, one = 1.0d+0 )
66* ..
67* .. Local Scalars ..
68 INTEGER I, J
69 DOUBLE PRECISION TAU, WA, WB, WN
70* ..
71* .. External Subroutines ..
72 EXTERNAL dgemv, dger, dlarnv, dscal, xerbla
73* ..
74* .. Intrinsic Functions ..
75 INTRINSIC max, min, sign
76* ..
77* .. External Functions ..
78 DOUBLE PRECISION DNRM2
79 EXTERNAL dnrm2
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( 'DLAGGE', -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 dlarnv( 3, iseed, m-i+1, work )
121 wn = dnrm2( 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 dscal( 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 dgemv( 'Transpose', m-i+1, n-i+1, one, a( i, i ), lda,
135 $ work, 1, zero, work( m+1 ), 1 )
136 CALL dger( 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 dlarnv( 3, iseed, n-i+1, work )
144 wn = dnrm2( 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 dscal( 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 dgemv( 'No transpose', m-i+1, n-i+1, one, a( i, i ),
158 $ lda, work, 1, zero, work( n+1 ), 1 )
159 CALL dger( 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 = dnrm2( 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 dscal( 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 dgemv( '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 dger( 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 = dnrm2( 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 dscal( 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 dgemv( '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 dger( 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 = dnrm2( 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 dscal( 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 dgemv( '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 dger( 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 = dnrm2( 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 dscal( 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 dgemv( '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 dger( 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 DLAGGE
288*
max
#define max(A, B)
Definition pcgemr.c:180
min
#define min(A, B)
Definition pcgemr.c:181
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