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
|
*> \brief \b ZQRT13
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* .. Scalar Arguments ..
* INTEGER LDA, M, N, SCALE
* DOUBLE PRECISION NORMA
* ..
* .. Array Arguments ..
* INTEGER ISEED( 4 )
* COMPLEX*16 A( LDA, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZQRT13 generates a full-rank matrix that may be scaled to have large
*> or small norm.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] SCALE
*> \verbatim
*> SCALE is INTEGER
*> SCALE = 1: normally scaled matrix
*> SCALE = 2: matrix scaled up
*> SCALE = 3: matrix scaled down
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of rows of the matrix A.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of columns of A.
*> \endverbatim
*>
*> \param[out] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,N)
*> The M-by-N matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A.
*> \endverbatim
*>
*> \param[out] NORMA
*> \verbatim
*> NORMA is DOUBLE PRECISION
*> The one-norm of A.
*> \endverbatim
*>
*> \param[in,out] ISEED
*> \verbatim
*> ISEED is integer array, dimension (4)
*> Seed for random number generator
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complex16_lin
*
* =====================================================================
SUBROUTINE ZQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
*
* -- LAPACK test routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
INTEGER LDA, M, N, SCALE
DOUBLE PRECISION NORMA
* ..
* .. Array Arguments ..
INTEGER ISEED( 4 )
COMPLEX*16 A( LDA, * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D0 )
* ..
* .. Local Scalars ..
INTEGER INFO, J
DOUBLE PRECISION BIGNUM, SMLNUM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
EXTERNAL DLAMCH, DZASUM, ZLANGE
* ..
* .. External Subroutines ..
EXTERNAL ZLARNV, ZLASCL
* ..
* .. Intrinsic Functions ..
INTRINSIC DBLE, DCMPLX, SIGN
* ..
* .. Local Arrays ..
DOUBLE PRECISION DUMMY( 1 )
* ..
* .. Executable Statements ..
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* benign matrix
*
DO 10 J = 1, N
CALL ZLARNV( 2, ISEED, M, A( 1, J ) )
IF( J.LE.M ) THEN
A( J, J ) = A( J, J ) + DCMPLX( SIGN( DZASUM( M, A( 1, J ),
$ 1 ), DBLE( A( J, J ) ) ) )
END IF
10 CONTINUE
*
* scaled versions
*
IF( SCALE.NE.1 ) THEN
NORMA = ZLANGE( 'Max', M, N, A, LDA, DUMMY )
SMLNUM = DLAMCH( 'Safe minimum' )
BIGNUM = ONE / SMLNUM
SMLNUM = SMLNUM / DLAMCH( 'Epsilon' )
BIGNUM = ONE / SMLNUM
*
IF( SCALE.EQ.2 ) THEN
*
* matrix scaled up
*
CALL ZLASCL( 'General', 0, 0, NORMA, BIGNUM, M, N, A, LDA,
$ INFO )
ELSE IF( SCALE.EQ.3 ) THEN
*
* matrix scaled down
*
CALL ZLASCL( 'General', 0, 0, NORMA, SMLNUM, M, N, A, LDA,
$ INFO )
END IF
END IF
*
NORMA = ZLANGE( 'One-norm', M, N, A, LDA, DUMMY )
RETURN
*
* End of ZQRT13
*
END
|
