SCALAPACK 2.2.2
LAPACK: Linear Algebra PACKage
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◆ slagsy()

subroutine slagsy ( integer  n,
integer  k,
real, dimension( * )  d,
real, dimension( lda, * )  a,
integer  lda,
integer, dimension( 4 )  iseed,
real, dimension( * )  work,
integer  info 
)

Definition at line 1 of file slagsy.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, K, LDA, N
9* ..
10* .. Array Arguments ..
11 INTEGER ISEED( 4 )
12 REAL A( LDA, * ), D( * ), WORK( * )
13* ..
14*
15* Purpose
16* =======
17*
18* SLAGSY generates a real symmetric matrix A, by pre- and post-
19* multiplying a real diagonal matrix D with a random orthogonal matrix:
20* A = U*D*U'. The semi-bandwidth may then be reduced to k by additional
21* orthogonal transformations.
22*
23* Arguments
24* =========
25*
26* N (input) INTEGER
27* The order of the matrix A. N >= 0.
28*
29* K (input) INTEGER
30* The number of nonzero subdiagonals within the band of A.
31* 0 <= K <= N-1.
32*
33* D (input) REAL array, dimension (N)
34* The diagonal elements of the diagonal matrix D.
35*
36* A (output) REAL array, dimension (LDA,N)
37* The generated n by n symmetric matrix A (the full matrix is
38* stored).
39*
40* LDA (input) INTEGER
41* The leading dimension of the array A. LDA >= N.
42*
43* ISEED (input/output) INTEGER array, dimension (4)
44* On entry, the seed of the random number generator; the array
45* elements must be between 0 and 4095, and ISEED(4) must be
46* odd.
47* On exit, the seed is updated.
48*
49* WORK (workspace) REAL array, dimension (2*N)
50*
51* INFO (output) INTEGER
52* = 0: successful exit
53* < 0: if INFO = -i, the i-th argument had an illegal value
54*
55* =====================================================================
56*
57* .. Parameters ..
58 REAL ZERO, ONE, HALF
59 parameter( zero = 0.0e+0, one = 1.0e+0, half = 0.5e+0 )
60* ..
61* .. Local Scalars ..
62 INTEGER I, J
63 REAL ALPHA, TAU, WA, WB, WN
64* ..
65* .. External Subroutines ..
66 EXTERNAL saxpy, sgemv, sger, slarnv, sscal, ssymv,
67 $ ssyr2, xerbla
68* ..
69* .. External Functions ..
70 REAL SDOT, SNRM2
71 EXTERNAL sdot, snrm2
72* ..
73* .. Intrinsic Functions ..
74 INTRINSIC max, sign
75* ..
76* .. Executable Statements ..
77*
78* Test the input arguments
79*
80 info = 0
81 IF( n.LT.0 ) THEN
82 info = -1
83 ELSE IF( k.LT.0 .OR. k.GT.n-1 ) THEN
84 info = -2
85 ELSE IF( lda.LT.max( 1, n ) ) THEN
86 info = -5
87 END IF
88 IF( info.LT.0 ) THEN
89 CALL xerbla( 'SLAGSY', -info )
90 RETURN
91 END IF
92*
93* initialize lower triangle of A to diagonal matrix
94*
95 DO 20 j = 1, n
96 DO 10 i = j + 1, n
97 a( i, j ) = zero
98 10 CONTINUE
99 20 CONTINUE
100 DO 30 i = 1, n
101 a( i, i ) = d( i )
102 30 CONTINUE
103*
104* Generate lower triangle of symmetric matrix
105*
106 DO 40 i = n - 1, 1, -1
107*
108* generate random reflection
109*
110 CALL slarnv( 3, iseed, n-i+1, work )
111 wn = snrm2( n-i+1, work, 1 )
112 wa = sign( wn, work( 1 ) )
113 IF( wn.EQ.zero ) THEN
114 tau = zero
115 ELSE
116 wb = work( 1 ) + wa
117 CALL sscal( n-i, one / wb, work( 2 ), 1 )
118 work( 1 ) = one
119 tau = wb / wa
120 END IF
121*
122* apply random reflection to A(i:n,i:n) from the left
123* and the right
124*
125* compute y := tau * A * u
126*
127 CALL ssymv( 'Lower', n-i+1, tau, a( i, i ), lda, work, 1, zero,
128 $ work( n+1 ), 1 )
129*
130* compute v := y - 1/2 * tau * ( y, u ) * u
131*
132 alpha = -half*tau*sdot( n-i+1, work( n+1 ), 1, work, 1 )
133 CALL saxpy( n-i+1, alpha, work, 1, work( n+1 ), 1 )
134*
135* apply the transformation as a rank-2 update to A(i:n,i:n)
136*
137 CALL ssyr2( 'Lower', n-i+1, -one, work, 1, work( n+1 ), 1,
138 $ a( i, i ), lda )
139 40 CONTINUE
140*
141* Reduce number of subdiagonals to K
142*
143 DO 60 i = 1, n - 1 - k
144*
145* generate reflection to annihilate A(k+i+1:n,i)
146*
147 wn = snrm2( n-k-i+1, a( k+i, i ), 1 )
148 wa = sign( wn, a( k+i, i ) )
149 IF( wn.EQ.zero ) THEN
150 tau = zero
151 ELSE
152 wb = a( k+i, i ) + wa
153 CALL sscal( n-k-i, one / wb, a( k+i+1, i ), 1 )
154 a( k+i, i ) = one
155 tau = wb / wa
156 END IF
157*
158* apply reflection to A(k+i:n,i+1:k+i-1) from the left
159*
160 CALL sgemv( 'Transpose', n-k-i+1, k-1, one, a( k+i, i+1 ), lda,
161 $ a( k+i, i ), 1, zero, work, 1 )
162 CALL sger( n-k-i+1, k-1, -tau, a( k+i, i ), 1, work, 1,
163 $ a( k+i, i+1 ), lda )
164*
165* apply reflection to A(k+i:n,k+i:n) from the left and the right
166*
167* compute y := tau * A * u
168*
169 CALL ssymv( 'Lower', n-k-i+1, tau, a( k+i, k+i ), lda,
170 $ a( k+i, i ), 1, zero, work, 1 )
171*
172* compute v := y - 1/2 * tau * ( y, u ) * u
173*
174 alpha = -half*tau*sdot( n-k-i+1, work, 1, a( k+i, i ), 1 )
175 CALL saxpy( n-k-i+1, alpha, a( k+i, i ), 1, work, 1 )
176*
177* apply symmetric rank-2 update to A(k+i:n,k+i:n)
178*
179 CALL ssyr2( 'Lower', n-k-i+1, -one, a( k+i, i ), 1, work, 1,
180 $ a( k+i, k+i ), lda )
181*
182 a( k+i, i ) = -wa
183 DO 50 j = k + i + 1, n
184 a( j, i ) = zero
185 50 CONTINUE
186 60 CONTINUE
187*
188* Store full symmetric matrix
189*
190 DO 80 j = 1, n
191 DO 70 i = j + 1, n
192 a( j, i ) = a( i, j )
193 70 CONTINUE
194 80 CONTINUE
195 RETURN
196*
197* End of SLAGSY
198*
max
#define max(A, B)
Definition pcgemr.c:180
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