1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
|
SUBROUTINE CLATSP( UPLO, N, X, ISEED )
*
* -- LAPACK auxiliary test routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER N
* ..
* .. Array Arguments ..
INTEGER ISEED( * )
COMPLEX X( * )
* ..
*
* Purpose
* =======
*
* CLATSP generates a special test matrix for the complex symmetric
* (indefinite) factorization for packed matrices. The pivot blocks of
* the generated matrix will be in the following order:
* 2x2 pivot block, non diagonalizable
* 1x1 pivot block
* 2x2 pivot block, diagonalizable
* (cycle repeats)
* A row interchange is required for each non-diagonalizable 2x2 block.
*
* Arguments
* =========
*
* UPLO (input) CHARACTER
* Specifies whether the generated matrix is to be upper or
* lower triangular.
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (input) INTEGER
* The dimension of the matrix to be generated.
*
* X (output) COMPLEX array, dimension (N*(N+1)/2)
* The generated matrix in packed storage format. The matrix
* consists of 3x3 and 2x2 diagonal blocks which result in the
* pivot sequence given above. The matrix outside these
* diagonal blocks is zero.
*
* ISEED (input/output) INTEGER array, dimension (4)
* On entry, the seed for the random number generator. The last
* of the four integers must be odd. (modified on exit)
*
* =====================================================================
*
* .. Parameters ..
COMPLEX EYE
PARAMETER ( EYE = ( 0.0, 1.0 ) )
* ..
* .. Local Scalars ..
INTEGER J, JJ, N5
REAL ALPHA, ALPHA3, BETA
COMPLEX A, B, C, R
* ..
* .. External Functions ..
COMPLEX CLARND
EXTERNAL CLARND
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, SQRT
* ..
* .. Executable Statements ..
*
* Initialize constants
*
ALPHA = ( 1.+SQRT( 17. ) ) / 8.
BETA = ALPHA - 1. / 1000.
ALPHA3 = ALPHA*ALPHA*ALPHA
*
* Fill the matrix with zeros.
*
DO 10 J = 1, N*( N+1 ) / 2
X( J ) = 0.0
10 CONTINUE
*
* UPLO = 'U': Upper triangular storage
*
IF( UPLO.EQ.'U' ) THEN
N5 = N / 5
N5 = N - 5*N5 + 1
*
JJ = N*( N+1 ) / 2
DO 20 J = N, N5, -5
A = ALPHA3*CLARND( 5, ISEED )
B = CLARND( 5, ISEED ) / ALPHA
C = A - 2.*B*EYE
R = C / BETA
X( JJ ) = A
X( JJ-2 ) = B
JJ = JJ - J
X( JJ ) = CLARND( 2, ISEED )
X( JJ-1 ) = R
JJ = JJ - ( J-1 )
X( JJ ) = C
JJ = JJ - ( J-2 )
X( JJ ) = CLARND( 2, ISEED )
JJ = JJ - ( J-3 )
X( JJ ) = CLARND( 2, ISEED )
IF( ABS( X( JJ+( J-3 ) ) ).GT.ABS( X( JJ ) ) ) THEN
X( JJ+( J-4 ) ) = 2.0*X( JJ+( J-3 ) )
ELSE
X( JJ+( J-4 ) ) = 2.0*X( JJ )
END IF
JJ = JJ - ( J-4 )
20 CONTINUE
*
* Clean-up for N not a multiple of 5.
*
J = N5 - 1
IF( J.GT.2 ) THEN
A = ALPHA3*CLARND( 5, ISEED )
B = CLARND( 5, ISEED ) / ALPHA
C = A - 2.*B*EYE
R = C / BETA
X( JJ ) = A
X( JJ-2 ) = B
JJ = JJ - J
X( JJ ) = CLARND( 2, ISEED )
X( JJ-1 ) = R
JJ = JJ - ( J-1 )
X( JJ ) = C
JJ = JJ - ( J-2 )
J = J - 3
END IF
IF( J.GT.1 ) THEN
X( JJ ) = CLARND( 2, ISEED )
X( JJ-J ) = CLARND( 2, ISEED )
IF( ABS( X( JJ ) ).GT.ABS( X( JJ-J ) ) ) THEN
X( JJ-1 ) = 2.0*X( JJ )
ELSE
X( JJ-1 ) = 2.0*X( JJ-J )
END IF
JJ = JJ - J - ( J-1 )
J = J - 2
ELSE IF( J.EQ.1 ) THEN
X( JJ ) = CLARND( 2, ISEED )
J = J - 1
END IF
*
* UPLO = 'L': Lower triangular storage
*
ELSE
N5 = N / 5
N5 = N5*5
*
JJ = 1
DO 30 J = 1, N5, 5
A = ALPHA3*CLARND( 5, ISEED )
B = CLARND( 5, ISEED ) / ALPHA
C = A - 2.*B*EYE
R = C / BETA
X( JJ ) = A
X( JJ+2 ) = B
JJ = JJ + ( N-J+1 )
X( JJ ) = CLARND( 2, ISEED )
X( JJ+1 ) = R
JJ = JJ + ( N-J )
X( JJ ) = C
JJ = JJ + ( N-J-1 )
X( JJ ) = CLARND( 2, ISEED )
JJ = JJ + ( N-J-2 )
X( JJ ) = CLARND( 2, ISEED )
IF( ABS( X( JJ-( N-J-2 ) ) ).GT.ABS( X( JJ ) ) ) THEN
X( JJ-( N-J-2 )+1 ) = 2.0*X( JJ-( N-J-2 ) )
ELSE
X( JJ-( N-J-2 )+1 ) = 2.0*X( JJ )
END IF
JJ = JJ + ( N-J-3 )
30 CONTINUE
*
* Clean-up for N not a multiple of 5.
*
J = N5 + 1
IF( J.LT.N-1 ) THEN
A = ALPHA3*CLARND( 5, ISEED )
B = CLARND( 5, ISEED ) / ALPHA
C = A - 2.*B*EYE
R = C / BETA
X( JJ ) = A
X( JJ+2 ) = B
JJ = JJ + ( N-J+1 )
X( JJ ) = CLARND( 2, ISEED )
X( JJ+1 ) = R
JJ = JJ + ( N-J )
X( JJ ) = C
JJ = JJ + ( N-J-1 )
J = J + 3
END IF
IF( J.LT.N ) THEN
X( JJ ) = CLARND( 2, ISEED )
X( JJ+( N-J+1 ) ) = CLARND( 2, ISEED )
IF( ABS( X( JJ ) ).GT.ABS( X( JJ+( N-J+1 ) ) ) ) THEN
X( JJ+1 ) = 2.0*X( JJ )
ELSE
X( JJ+1 ) = 2.0*X( JJ+( N-J+1 ) )
END IF
JJ = JJ + ( N-J+1 ) + ( N-J )
J = J + 2
ELSE IF( J.EQ.N ) THEN
X( JJ ) = CLARND( 2, ISEED )
JJ = JJ + ( N-J+1 )
J = J + 1
END IF
END IF
*
RETURN
*
* End of CLATSP
*
END
|
