ScaLAPACK 2.1  2.1 ScaLAPACK: Scalable Linear Algebra PACKage
zlagsy.f
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1  SUBROUTINE zlagsy( N, K, 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, K, LDA, N
9 * ..
10 * .. Array Arguments ..
11  INTEGER ISEED( 4 )
12  DOUBLE PRECISION D( * )
13  COMPLEX*16 A( LDA, * ), WORK( * )
14 * ..
15 *
16 * Purpose
17 * =======
18 *
19 * ZLAGSY generates a complex symmetric matrix A, by pre- and post-
20 * multiplying a real diagonal matrix D with a random unitary matrix:
21 * A = U*D*U**T. The semi-bandwidth may then be reduced to k by
23 *
24 * Arguments
25 * =========
26 *
27 * N (input) INTEGER
28 * The order of the matrix A. N >= 0.
29 *
30 * K (input) INTEGER
31 * The number of nonzero subdiagonals within the band of A.
32 * 0 <= K <= N-1.
33 *
34 * D (input) DOUBLE PRECISION array, dimension (N)
35 * The diagonal elements of the diagonal matrix D.
36 *
37 * A (output) COMPLEX*16 array, dimension (LDA,N)
38 * The generated n by n symmetric matrix A (the full matrix is
39 * stored).
40 *
41 * LDA (input) INTEGER
42 * The leading dimension of the array A. LDA >= N.
43 *
44 * ISEED (input/output) INTEGER array, dimension (4)
45 * On entry, the seed of the random number generator; the array
46 * elements must be between 0 and 4095, and ISEED(4) must be
47 * odd.
48 * On exit, the seed is updated.
49 *
50 * WORK (workspace) COMPLEX*16 array, dimension (2*N)
51 *
52 * INFO (output) INTEGER
53 * = 0: successful exit
54 * < 0: if INFO = -i, the i-th argument had an illegal value
55 *
56 * =====================================================================
57 *
58 * .. Parameters ..
59  COMPLEX*16 ZERO, ONE, HALF
60  parameter( zero = ( 0.0d+0, 0.0d+0 ),
61  \$ one = ( 1.0d+0, 0.0d+0 ),
62  \$ half = ( 0.5d+0, 0.0d+0 ) )
63 * ..
64 * .. Local Scalars ..
65  INTEGER I, II, J, JJ
66  DOUBLE PRECISION WN
67  COMPLEX*16 ALPHA, TAU, WA, WB
68 * ..
69 * .. External Subroutines ..
70  EXTERNAL xerbla, zaxpy, zgemv, zgerc, zlacgv, zlarnv,
71  \$ zscal, zsymv
72 * ..
73 * .. External Functions ..
74  DOUBLE PRECISION DZNRM2
75  COMPLEX*16 ZDOTC
76  EXTERNAL dznrm2, zdotc
77 * ..
78 * .. Intrinsic Functions ..
79  INTRINSIC abs, dble, max
80 * ..
81 * .. Executable Statements ..
82 *
83 * Test the input arguments
84 *
85  info = 0
86  IF( n.LT.0 ) THEN
87  info = -1
88  ELSE IF( k.LT.0 .OR. k.GT.n-1 ) THEN
89  info = -2
90  ELSE IF( lda.LT.max( 1, n ) ) THEN
91  info = -5
92  END IF
93  IF( info.LT.0 ) THEN
94  CALL xerbla( 'ZLAGSY', -info )
95  RETURN
96  END IF
97 *
98 * initialize lower triangle of A to diagonal matrix
99 *
100  DO 20 j = 1, n
101  DO 10 i = j + 1, n
102  a( i, j ) = zero
103  10 CONTINUE
104  20 CONTINUE
105  DO 30 i = 1, n
106  a( i, i ) = d( i )
107  30 CONTINUE
108 *
109 * Generate lower triangle of symmetric matrix
110 *
111  DO 60 i = n - 1, 1, -1
112 *
113 * generate random reflection
114 *
115  CALL zlarnv( 3, iseed, n-i+1, work )
116  wn = dznrm2( n-i+1, work, 1 )
117  wa = ( wn / abs( work( 1 ) ) )*work( 1 )
118  IF( wn.EQ.zero ) THEN
119  tau = zero
120  ELSE
121  wb = work( 1 ) + wa
122  CALL zscal( n-i, one / wb, work( 2 ), 1 )
123  work( 1 ) = one
124  tau = dble( wb / wa )
125  END IF
126 *
127 * apply random reflection to A(i:n,i:n) from the left
128 * and the right
129 *
130 * compute y := tau * A * conjg(u)
131 *
132  CALL zlacgv( n-i+1, work, 1 )
133  CALL zsymv( 'Lower', n-i+1, tau, a( i, i ), lda, work, 1, zero,
134  \$ work( n+1 ), 1 )
135  CALL zlacgv( n-i+1, work, 1 )
136 *
137 * compute v := y - 1/2 * tau * ( u, y ) * u
138 *
139  alpha = -half*tau*zdotc( n-i+1, work, 1, work( n+1 ), 1 )
140  CALL zaxpy( n-i+1, alpha, work, 1, work( n+1 ), 1 )
141 *
142 * apply the transformation as a rank-2 update to A(i:n,i:n)
143 *
144 * CALL ZSYR2( 'Lower', N-I+1, -ONE, WORK, 1, WORK( N+1 ), 1,
145 * \$ A( I, I ), LDA )
146 *
147  DO 50 jj = i, n
148  DO 40 ii = jj, n
149  a( ii, jj ) = a( ii, jj ) -
150  \$ work( ii-i+1 )*work( n+jj-i+1 ) -
151  \$ work( n+ii-i+1 )*work( jj-i+1 )
152  40 CONTINUE
153  50 CONTINUE
154  60 CONTINUE
155 *
156 * Reduce number of subdiagonals to K
157 *
158  DO 100 i = 1, n - 1 - k
159 *
160 * generate reflection to annihilate A(k+i+1:n,i)
161 *
162  wn = dznrm2( n-k-i+1, a( k+i, i ), 1 )
163  wa = ( wn / abs( a( k+i, i ) ) )*a( k+i, i )
164  IF( wn.EQ.zero ) THEN
165  tau = zero
166  ELSE
167  wb = a( k+i, i ) + wa
168  CALL zscal( n-k-i, one / wb, a( k+i+1, i ), 1 )
169  a( k+i, i ) = one
170  tau = dble( wb / wa )
171  END IF
172 *
173 * apply reflection to A(k+i:n,i+1:k+i-1) from the left
174 *
175  CALL zgemv( 'Conjugate transpose', n-k-i+1, k-1, one,
176  \$ a( k+i, i+1 ), lda, a( k+i, i ), 1, zero, work, 1 )
177  CALL zgerc( n-k-i+1, k-1, -tau, a( k+i, i ), 1, work, 1,
178  \$ a( k+i, i+1 ), lda )
179 *
180 * apply reflection to A(k+i:n,k+i:n) from the left and the right
181 *
182 * compute y := tau * A * conjg(u)
183 *
184  CALL zlacgv( n-k-i+1, a( k+i, i ), 1 )
185  CALL zsymv( 'Lower', n-k-i+1, tau, a( k+i, k+i ), lda,
186  \$ a( k+i, i ), 1, zero, work, 1 )
187  CALL zlacgv( n-k-i+1, a( k+i, i ), 1 )
188 *
189 * compute v := y - 1/2 * tau * ( u, y ) * u
190 *
191  alpha = -half*tau*zdotc( n-k-i+1, a( k+i, i ), 1, work, 1 )
192  CALL zaxpy( n-k-i+1, alpha, a( k+i, i ), 1, work, 1 )
193 *
194 * apply symmetric rank-2 update to A(k+i:n,k+i:n)
195 *
196 * CALL ZSYR2( 'Lower', N-K-I+1, -ONE, A( K+I, I ), 1, WORK, 1,
197 * \$ A( K+I, K+I ), LDA )
198 *
199  DO 80 jj = k + i, n
200  DO 70 ii = jj, n
201  a( ii, jj ) = a( ii, jj ) - a( ii, i )*work( jj-k-i+1 ) -
202  \$ work( ii-k-i+1 )*a( jj, i )
203  70 CONTINUE
204  80 CONTINUE
205 *
206  a( k+i, i ) = -wa
207  DO 90 j = k + i + 1, n
208  a( j, i ) = zero
209  90 CONTINUE
210  100 CONTINUE
211 *
212 * Store full symmetric matrix
213 *
214  DO 120 j = 1, n
215  DO 110 i = j + 1, n
216  a( j, i ) = a( i, j )
217  110 CONTINUE
218  120 CONTINUE
219  RETURN
220 *
221 * End of ZLAGSY
222 *
223  END
max
#define max(A, B)
Definition: pcgemr.c:180
zlagsy
subroutine zlagsy(N, K, D, A, LDA, ISEED, WORK, INFO)
Definition: zlagsy.f:2
zsymv
subroutine zsymv(UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
Definition: zsymv.f:2
zlarnv
subroutine zlarnv(IDIST, ISEED, N, X)
Definition: zlarnv.f:2