source: pacpussensors/trunk/Vislab/lib3dv-1.2.0/lib3dv/eigen/lapack/dlarfg.f

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1*> \brief \b DLARFG
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLARFG + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlarfg.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlarfg.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlarfg.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
22*
23* .. Scalar Arguments ..
24* INTEGER INCX, N
25* DOUBLE PRECISION ALPHA, TAU
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION X( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DLARFG generates a real elementary reflector H of order n, such
38*> that
39*>
40*> H * ( alpha ) = ( beta ), H**T * H = I.
41*> ( x ) ( 0 )
42*>
43*> where alpha and beta are scalars, and x is an (n-1)-element real
44*> vector. H is represented in the form
45*>
46*> H = I - tau * ( 1 ) * ( 1 v**T ) ,
47*> ( v )
48*>
49*> where tau is a real scalar and v is a real (n-1)-element
50*> vector.
51*>
52*> If the elements of x are all zero, then tau = 0 and H is taken to be
53*> the unit matrix.
54*>
55*> Otherwise 1 <= tau <= 2.
56*> \endverbatim
57*
58* Arguments:
59* ==========
60*
61*> \param[in] N
62*> \verbatim
63*> N is INTEGER
64*> The order of the elementary reflector.
65*> \endverbatim
66*>
67*> \param[in,out] ALPHA
68*> \verbatim
69*> ALPHA is DOUBLE PRECISION
70*> On entry, the value alpha.
71*> On exit, it is overwritten with the value beta.
72*> \endverbatim
73*>
74*> \param[in,out] X
75*> \verbatim
76*> X is DOUBLE PRECISION array, dimension
77*> (1+(N-2)*abs(INCX))
78*> On entry, the vector x.
79*> On exit, it is overwritten with the vector v.
80*> \endverbatim
81*>
82*> \param[in] INCX
83*> \verbatim
84*> INCX is INTEGER
85*> The increment between elements of X. INCX > 0.
86*> \endverbatim
87*>
88*> \param[out] TAU
89*> \verbatim
90*> TAU is DOUBLE PRECISION
91*> The value tau.
92*> \endverbatim
93*
94* Authors:
95* ========
96*
97*> \author Univ. of Tennessee
98*> \author Univ. of California Berkeley
99*> \author Univ. of Colorado Denver
100*> \author NAG Ltd.
101*
102*> \date November 2011
103*
104*> \ingroup doubleOTHERauxiliary
105*
106* =====================================================================
107 SUBROUTINE DLARFG( N, ALPHA, X, INCX, TAU )
108*
109* -- LAPACK auxiliary routine (version 3.4.0) --
110* -- LAPACK is a software package provided by Univ. of Tennessee, --
111* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
112* November 2011
113*
114* .. Scalar Arguments ..
115 INTEGER INCX, N
116 DOUBLE PRECISION ALPHA, TAU
117* ..
118* .. Array Arguments ..
119 DOUBLE PRECISION X( * )
120* ..
121*
122* =====================================================================
123*
124* .. Parameters ..
125 DOUBLE PRECISION ONE, ZERO
126 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
127* ..
128* .. Local Scalars ..
129 INTEGER J, KNT
130 DOUBLE PRECISION BETA, RSAFMN, SAFMIN, XNORM
131* ..
132* .. External Functions ..
133 DOUBLE PRECISION DLAMCH, DLAPY2, DNRM2
134 EXTERNAL DLAMCH, DLAPY2, DNRM2
135* ..
136* .. Intrinsic Functions ..
137 INTRINSIC ABS, SIGN
138* ..
139* .. External Subroutines ..
140 EXTERNAL DSCAL
141* ..
142* .. Executable Statements ..
143*
144 IF( N.LE.1 ) THEN
145 TAU = ZERO
146 RETURN
147 END IF
148*
149 XNORM = DNRM2( N-1, X, INCX )
150*
151 IF( XNORM.EQ.ZERO ) THEN
152*
153* H = I
154*
155 TAU = ZERO
156 ELSE
157*
158* general case
159*
160 BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
161 SAFMIN = DLAMCH( 'S' ) / DLAMCH( 'E' )
162 KNT = 0
163 IF( ABS( BETA ).LT.SAFMIN ) THEN
164*
165* XNORM, BETA may be inaccurate; scale X and recompute them
166*
167 RSAFMN = ONE / SAFMIN
168 10 CONTINUE
169 KNT = KNT + 1
170 CALL DSCAL( N-1, RSAFMN, X, INCX )
171 BETA = BETA*RSAFMN
172 ALPHA = ALPHA*RSAFMN
173 IF( ABS( BETA ).LT.SAFMIN )
174 $ GO TO 10
175*
176* New BETA is at most 1, at least SAFMIN
177*
178 XNORM = DNRM2( N-1, X, INCX )
179 BETA = -SIGN( DLAPY2( ALPHA, XNORM ), ALPHA )
180 END IF
181 TAU = ( BETA-ALPHA ) / BETA
182 CALL DSCAL( N-1, ONE / ( ALPHA-BETA ), X, INCX )
183*
184* If ALPHA is subnormal, it may lose relative accuracy
185*
186 DO 20 J = 1, KNT
187 BETA = BETA*SAFMIN
188 20 CONTINUE
189 ALPHA = BETA
190 END IF
191*
192 RETURN
193*
194* End of DLARFG
195*
196 END
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