aboutsummaryrefslogtreecommitdiffhomepage
path: root/lapack/zlarfg.f
blob: a90ae9f745cbb13dff9f16efa0216ab78e4bc090 (plain)
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
*> \brief \b ZLARFG
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*> \htmlonly
*> Download ZLARFG + dependencies 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlarfg.f"> 
*> [TGZ]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlarfg.f"> 
*> [ZIP]</a> 
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarfg.f"> 
*> [TXT]</a>
*> \endhtmlonly 
*
*  Definition:
*  ===========
*
*       SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
* 
*       .. Scalar Arguments ..
*       INTEGER            INCX, N
*       COMPLEX*16         ALPHA, TAU
*       ..
*       .. Array Arguments ..
*       COMPLEX*16         X( * )
*       ..
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> ZLARFG generates a complex elementary reflector H of order n, such
*> that
*>
*>       H**H * ( alpha ) = ( beta ),   H**H * H = I.
*>              (   x   )   (   0  )
*>
*> where alpha and beta are scalars, with beta real, and x is an
*> (n-1)-element complex vector. H is represented in the form
*>
*>       H = I - tau * ( 1 ) * ( 1 v**H ) ,
*>                     ( v )
*>
*> where tau is a complex scalar and v is a complex (n-1)-element
*> vector. Note that H is not hermitian.
*>
*> If the elements of x are all zero and alpha is real, then tau = 0
*> and H is taken to be the unit matrix.
*>
*> Otherwise  1 <= real(tau) <= 2  and  abs(tau-1) <= 1 .
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the elementary reflector.
*> \endverbatim
*>
*> \param[in,out] ALPHA
*> \verbatim
*>          ALPHA is COMPLEX*16
*>          On entry, the value alpha.
*>          On exit, it is overwritten with the value beta.
*> \endverbatim
*>
*> \param[in,out] X
*> \verbatim
*>          X is COMPLEX*16 array, dimension
*>                         (1+(N-2)*abs(INCX))
*>          On entry, the vector x.
*>          On exit, it is overwritten with the vector v.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*>          INCX is INTEGER
*>          The increment between elements of X. INCX > 0.
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*>          TAU is COMPLEX*16
*>          The value tau.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee 
*> \author Univ. of California Berkeley 
*> \author Univ. of Colorado Denver 
*> \author NAG Ltd. 
*
*> \date November 2011
*
*> \ingroup complex16OTHERauxiliary
*
*  =====================================================================
      SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
*
*  -- LAPACK auxiliary routine (version 3.4.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     November 2011
*
*     .. Scalar Arguments ..
      INTEGER            INCX, N
      COMPLEX*16         ALPHA, TAU
*     ..
*     .. Array Arguments ..
      COMPLEX*16         X( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            J, KNT
      DOUBLE PRECISION   ALPHI, ALPHR, BETA, RSAFMN, SAFMIN, XNORM
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLAPY3, DZNRM2
      COMPLEX*16         ZLADIV
      EXTERNAL           DLAMCH, DLAPY3, DZNRM2, ZLADIV
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          ABS, DBLE, DCMPLX, DIMAG, SIGN
*     ..
*     .. External Subroutines ..
      EXTERNAL           ZDSCAL, ZSCAL
*     ..
*     .. Executable Statements ..
*
      IF( N.LE.0 ) THEN
         TAU = ZERO
         RETURN
      END IF
*
      XNORM = DZNRM2( N-1, X, INCX )
      ALPHR = DBLE( ALPHA )
      ALPHI = DIMAG( ALPHA )
*
      IF( XNORM.EQ.ZERO .AND. ALPHI.EQ.ZERO ) THEN
*
*        H  =  I
*
         TAU = ZERO
      ELSE
*
*        general case
*
         BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )
         SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )
         RSAFMN = ONE / SAFMIN
*
         KNT = 0
         IF( ABS( BETA ).LT.SAFMIN ) THEN
*
*           XNORM, BETA may be inaccurate; scale X and recompute them
*
   10       CONTINUE
            KNT = KNT + 1
            CALL ZDSCAL( N-1, RSAFMN, X, INCX )
            BETA = BETA*RSAFMN
            ALPHI = ALPHI*RSAFMN
            ALPHR = ALPHR*RSAFMN
            IF( ABS( BETA ).LT.SAFMIN )
     $         GO TO 10
*
*           New BETA is at most 1, at least SAFMIN
*
            XNORM = DZNRM2( N-1, X, INCX )
            ALPHA = DCMPLX( ALPHR, ALPHI )
            BETA = -SIGN( DLAPY3( ALPHR, ALPHI, XNORM ), ALPHR )
         END IF
         TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )
         ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA )
         CALL ZSCAL( N-1, ALPHA, X, INCX )
*
*        If ALPHA is subnormal, it may lose relative accuracy
*
         DO 20 J = 1, KNT
            BETA = BETA*SAFMIN
 20      CONTINUE
         ALPHA = BETA
      END IF
*
      RETURN
*
*     End of ZLARFG
*
      END