LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
zqrt13.f
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1 *> \brief \b ZQRT13
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 * Definition:
9 * ===========
10 *
11 * SUBROUTINE ZQRT13( SCALE, M, N, A, LDA, NORMA, ISEED )
12 *
13 * .. Scalar Arguments ..
14 * INTEGER LDA, M, N, SCALE
15 * DOUBLE PRECISION NORMA
16 * ..
17 * .. Array Arguments ..
18 * INTEGER ISEED( 4 )
19 * COMPLEX*16 A( LDA, * )
20 * ..
21 *
22 *
23 *> \par Purpose:
24 * =============
25 *>
26 *> \verbatim
27 *>
28 *> ZQRT13 generates a full-rank matrix that may be scaled to have large
29 *> or small norm.
30 *> \endverbatim
31 *
32 * Arguments:
33 * ==========
34 *
35 *> \param[in] SCALE
36 *> \verbatim
37 *> SCALE is INTEGER
38 *> SCALE = 1: normally scaled matrix
39 *> SCALE = 2: matrix scaled up
40 *> SCALE = 3: matrix scaled down
41 *> \endverbatim
42 *>
43 *> \param[in] M
44 *> \verbatim
45 *> M is INTEGER
46 *> The number of rows of the matrix A.
47 *> \endverbatim
48 *>
49 *> \param[in] N
50 *> \verbatim
51 *> N is INTEGER
52 *> The number of columns of A.
53 *> \endverbatim
54 *>
55 *> \param[out] A
56 *> \verbatim
57 *> A is COMPLEX*16 array, dimension (LDA,N)
58 *> The M-by-N matrix A.
59 *> \endverbatim
60 *>
61 *> \param[in] LDA
62 *> \verbatim
63 *> LDA is INTEGER
64 *> The leading dimension of the array A.
65 *> \endverbatim
66 *>
67 *> \param[out] NORMA
68 *> \verbatim
69 *> NORMA is DOUBLE PRECISION
70 *> The one-norm of A.
71 *> \endverbatim
72 *>
73 *> \param[in,out] ISEED
74 *> \verbatim
75 *> ISEED is integer array, dimension (4)
76 *> Seed for random number generator
77 *> \endverbatim
78 *
79 * Authors:
80 * ========
81 *
82 *> \author Univ. of Tennessee
83 *> \author Univ. of California Berkeley
84 *> \author Univ. of Colorado Denver
85 *> \author NAG Ltd.
86 *
87 *> \date December 2016
88 *
89 *> \ingroup complex16_lin
90 *
91 * =====================================================================
92  SUBROUTINE zqrt13( SCALE, M, N, A, LDA, NORMA, ISEED )
93 *
94 * -- LAPACK test routine (version 3.7.0) --
95 * -- LAPACK is a software package provided by Univ. of Tennessee, --
96 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
97 * December 2016
98 *
99 * .. Scalar Arguments ..
100  INTEGER LDA, M, N, SCALE
101  DOUBLE PRECISION NORMA
102 * ..
103 * .. Array Arguments ..
104  INTEGER ISEED( 4 )
105  COMPLEX*16 A( lda, * )
106 * ..
107 *
108 * =====================================================================
109 *
110 * .. Parameters ..
111  DOUBLE PRECISION ONE
112  parameter( one = 1.0d0 )
113 * ..
114 * .. Local Scalars ..
115  INTEGER INFO, J
116  DOUBLE PRECISION BIGNUM, SMLNUM
117 * ..
118 * .. External Functions ..
119  DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
120  EXTERNAL dlamch, dzasum, zlange
121 * ..
122 * .. External Subroutines ..
123  EXTERNAL dlabad, zlarnv, zlascl
124 * ..
125 * .. Intrinsic Functions ..
126  INTRINSIC dble, dcmplx, sign
127 * ..
128 * .. Local Arrays ..
129  DOUBLE PRECISION DUMMY( 1 )
130 * ..
131 * .. Executable Statements ..
132 *
133  IF( m.LE.0 .OR. n.LE.0 )
134  $ RETURN
135 *
136 * benign matrix
137 *
138  DO 10 j = 1, n
139  CALL zlarnv( 2, iseed, m, a( 1, j ) )
140  IF( j.LE.m ) THEN
141  a( j, j ) = a( j, j ) + dcmplx( sign( dzasum( m, a( 1, j ),
142  $ 1 ), dble( a( j, j ) ) ) )
143  END IF
144  10 CONTINUE
145 *
146 * scaled versions
147 *
148  IF( scale.NE.1 ) THEN
149  norma = zlange( 'Max', m, n, a, lda, dummy )
150  smlnum = dlamch( 'Safe minimum' )
151  bignum = one / smlnum
152  CALL dlabad( smlnum, bignum )
153  smlnum = smlnum / dlamch( 'Epsilon' )
154  bignum = one / smlnum
155 *
156  IF( scale.EQ.2 ) THEN
157 *
158 * matrix scaled up
159 *
160  CALL zlascl( 'General', 0, 0, norma, bignum, m, n, a, lda,
161  $ info )
162  ELSE IF( scale.EQ.3 ) THEN
163 *
164 * matrix scaled down
165 *
166  CALL zlascl( 'General', 0, 0, norma, smlnum, m, n, a, lda,
167  $ info )
168  END IF
169  END IF
170 *
171  norma = zlange( 'One-norm', m, n, a, lda, dummy )
172  RETURN
173 *
174 * End of ZQRT13
175 *
176  END
subroutine zlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: zlascl.f:145
subroutine dlabad(SMALL, LARGE)
DLABAD
Definition: dlabad.f:76
subroutine zqrt13(SCALE, M, N, A, LDA, NORMA, ISEED)
ZQRT13
Definition: zqrt13.f:93
subroutine zlarnv(IDIST, ISEED, N, X)
ZLARNV returns a vector of random numbers from a uniform or normal distribution.
Definition: zlarnv.f:101