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 SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
IMPLICIT NONE
*
* -- LAPACK auxiliary 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, LDC, M, N
REAL TAU
* ..
* .. Array Arguments ..
REAL C( LDC, * ), V( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* SLARF 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.
*
* 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.
*
* V (input) REAL array, dimension
* (1 + (M-1)*abs(INCV)) if SIDE = 'L'
* or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
* The vector v in the representation of H. 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'
*
* =====================================================================
*
* .. Parameters ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
LOGICAL APPLYLEFT
INTEGER I, LASTV, LASTC
* ..
* .. External Subroutines ..
EXTERNAL SGEMV, SGER
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ILASLR, ILASLC
EXTERNAL LSAME, ILASLR, ILASLC
* ..
* .. Executable Statements ..
*
APPLYLEFT = LSAME( SIDE, 'L' )
LASTV = 0
LASTC = 0
IF( TAU.NE.ZERO ) THEN
! Set up variables for scanning V. LASTV begins pointing to the end
! of V.
IF( APPLYLEFT ) THEN
LASTV = M
ELSE
LASTV = N
END IF
IF( INCV.GT.0 ) THEN
I = 1 + (LASTV-1) * INCV
ELSE
I = 1
END IF
! Look for the last non-zero row in V.
DO WHILE( LASTV.GT.0 .AND. V( I ).EQ.ZERO )
LASTV = LASTV - 1
I = I - INCV
END DO
IF( APPLYLEFT ) THEN
! Scan for the last non-zero column in C(1:lastv,:).
LASTC = ILASLC(LASTV, N, C, LDC)
ELSE
! Scan for the last non-zero row in C(:,1:lastv).
LASTC = ILASLR(M, LASTV, C, LDC)
END IF
END IF
! Note that lastc.eq.0 renders the BLAS operations null; no special
! case is needed at this level.
IF( APPLYLEFT ) THEN
*
* Form H * C
*
IF( LASTV.GT.0 ) THEN
*
* w(1:lastc,1) := C(1:lastv,1:lastc)**T * v(1:lastv,1)
*
CALL SGEMV( 'Transpose', LASTV, LASTC, ONE, C, LDC, V, INCV,
$ ZERO, WORK, 1 )
*
* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**T
*
CALL SGER( LASTV, LASTC, -TAU, V, INCV, WORK, 1, C, LDC )
END IF
ELSE
*
* Form C * H
*
IF( LASTV.GT.0 ) THEN
*
* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
*
CALL SGEMV( 'No transpose', LASTC, LASTV, ONE, C, LDC,
$ V, INCV, ZERO, WORK, 1 )
*
* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**T
*
CALL SGER( LASTC, LASTV, -TAU, WORK, 1, V, INCV, C, LDC )
END IF
END IF
RETURN
*
* End of SLARF
*
END
|