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
22 * additional unitary transformations.
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
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
22 * additional unitary transformations.
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