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
|
SUBROUTINE SLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
*
* -- LAPACK routine (version 3.3.1) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* -- April 2011 --
*
* .. Scalar Arguments ..
CHARACTER SIDE
INTEGER INCV, L, LDC, M, N
REAL TAU
* ..
* .. Array Arguments ..
REAL C( LDC, * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SLARZ applies a real elementary reflector H to a real M-by-N
* matrix C, from either the left or the right. H is represented in the
* form
*
* H = I - tau * v * v**T
*
* where tau is a real scalar and v is a real vector.
*
* If tau = 0, then H is taken to be the unit matrix.
*
*
* H is a product of k elementary reflectors as returned by STZRZF.
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'L': form H * C
* = 'R': form C * H
*
* M (input) INTEGER
* The number of rows of the matrix C.
*
* N (input) INTEGER
* The number of columns of the matrix C.
*
* L (input) INTEGER
* The number of entries of the vector V containing
* the meaningful part of the Householder vectors.
* If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
*
* V (input) REAL array, dimension (1+(L-1)*abs(INCV))
* The vector v in the representation of H as returned by
* STZRZF. V is not used if TAU = 0.
*
* INCV (input) INTEGER
* The increment between elements of v. INCV <> 0.
*
* TAU (input) REAL
* The value tau in the representation of H.
*
* C (input/output) REAL array, dimension (LDC,N)
* On entry, the M-by-N matrix C.
* On exit, C is overwritten by the matrix H * C if SIDE = 'L',
* or C * H if SIDE = 'R'.
*
* LDC (input) INTEGER
* The leading dimension of the array C. LDC >= max(1,M).
*
* WORK (workspace) REAL array, dimension
* (N) if SIDE = 'L'
* or (M) if SIDE = 'R'
*
* Further Details
* ===============
*
* Based on contributions by
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. External Subroutines ..
EXTERNAL SAXPY, SCOPY, SGEMV, SGER
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. Executable Statements ..
*
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form H * C
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:n ) = C( 1, 1:n )
*
CALL SCOPY( N, C, LDC, WORK, 1 )
*
* w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )**T * v( 1:l )
*
CALL SGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
$ INCV, ONE, WORK, 1 )
*
* C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
*
CALL SAXPY( N, -TAU, WORK, 1, C, LDC )
*
* C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
* tau * v( 1:l ) * w( 1:n )**T
*
CALL SGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
$ LDC )
END IF
*
ELSE
*
* Form C * H
*
IF( TAU.NE.ZERO ) THEN
*
* w( 1:m ) = C( 1:m, 1 )
*
CALL SCOPY( M, C, 1, WORK, 1 )
*
* w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
*
CALL SGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
$ V, INCV, ONE, WORK, 1 )
*
* C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
*
CALL SAXPY( M, -TAU, WORK, 1, C, 1 )
*
* C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
* tau * w( 1:m ) * v( 1:l )**T
*
CALL SGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
$ LDC )
*
END IF
*
END IF
*
RETURN
*
* End of SLARZ
*
END
|