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
|
SUBROUTINE ZLARFG( N, ALPHA, X, INCX, TAU )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* September 30, 1994
*
* .. Scalar Arguments ..
INTEGER INCX, N
COMPLEX*16 ALPHA, TAU
* ..
* .. Array Arguments ..
COMPLEX*16 X( * )
* ..
*
* Purpose
* =======
*
* ZLARFG generates a complex elementary reflector H of order n, such
* that
*
* H' * ( alpha ) = ( beta ), 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' ) ,
* ( 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 .
*
* Arguments
* =========
*
* N (input) INTEGER
* The order of the elementary reflector.
*
* ALPHA (input/output) COMPLEX*16
* On entry, the value alpha.
* On exit, it is overwritten with the value beta.
*
* X (input/output) COMPLEX*16 array, dimension
* (1+(N-2)*abs(INCX))
* On entry, the vector x.
* On exit, it is overwritten with the vector v.
*
* INCX (input) INTEGER
* The increment between elements of X. INCX > 0.
*
* TAU (output) COMPLEX*16
* The value tau.
*
* =====================================================================
*
* .. 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
*
IF( ABS( BETA ).LT.SAFMIN ) THEN
*
* XNORM, BETA may be inaccurate; scale X and recompute them
*
KNT = 0
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 )
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
*
ALPHA = BETA
DO 20 J = 1, KNT
ALPHA = ALPHA*SAFMIN
20 CONTINUE
ELSE
TAU = DCMPLX( ( BETA-ALPHR ) / BETA, -ALPHI / BETA )
ALPHA = ZLADIV( DCMPLX( ONE ), ALPHA-BETA )
CALL ZSCAL( N-1, ALPHA, X, INCX )
ALPHA = BETA
END IF
END IF
*
RETURN
*
* End of ZLARFG
*
END
|
