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
|
// Copyright ©2015 The Gonum Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
package gonum
import (
"gonum.org/v1/gonum/blas"
"gonum.org/v1/gonum/blas/blas64"
"gonum.org/v1/gonum/lapack"
)
// Dlarft forms the triangular factor T of a block reflector H, storing the answer
// in t.
//
// H = I - V * T * Vᵀ if store == lapack.ColumnWise
// H = I - Vᵀ * T * V if store == lapack.RowWise
//
// H is defined by a product of the elementary reflectors where
//
// H = H_0 * H_1 * ... * H_{k-1} if direct == lapack.Forward
// H = H_{k-1} * ... * H_1 * H_0 if direct == lapack.Backward
//
// t is a k×k triangular matrix. t is upper triangular if direct = lapack.Forward
// and lower triangular otherwise. This function will panic if t is not of
// sufficient size.
//
// store describes the storage of the elementary reflectors in v. See
// Dlarfb for a description of layout.
//
// tau contains the scalar factors of the elementary reflectors H_i.
//
// Dlarft is an internal routine. It is exported for testing purposes.
func (Implementation) Dlarft(direct lapack.Direct, store lapack.StoreV, n, k int, v []float64, ldv int, tau []float64, t []float64, ldt int) {
mv, nv := n, k
if store == lapack.RowWise {
mv, nv = k, n
}
switch {
case direct != lapack.Forward && direct != lapack.Backward:
panic(badDirect)
case store != lapack.RowWise && store != lapack.ColumnWise:
panic(badStoreV)
case n < 0:
panic(nLT0)
case k < 1:
panic(kLT1)
case ldv < max(1, nv):
panic(badLdV)
case len(tau) < k:
panic(shortTau)
case ldt < max(1, k):
panic(shortT)
}
if n == 0 {
return
}
switch {
case len(v) < (mv-1)*ldv+nv:
panic(shortV)
case len(t) < (k-1)*ldt+k:
panic(shortT)
}
bi := blas64.Implementation()
// TODO(btracey): There are a number of minor obvious loop optimizations here.
// TODO(btracey): It may be possible to rearrange some of the code so that
// index of 1 is more common in the Dgemv.
if direct == lapack.Forward {
prevlastv := n - 1
for i := 0; i < k; i++ {
prevlastv = max(i, prevlastv)
if tau[i] == 0 {
for j := 0; j <= i; j++ {
t[j*ldt+i] = 0
}
continue
}
var lastv int
if store == lapack.ColumnWise {
// skip trailing zeros
for lastv = n - 1; lastv >= i+1; lastv-- {
if v[lastv*ldv+i] != 0 {
break
}
}
for j := 0; j < i; j++ {
t[j*ldt+i] = -tau[i] * v[i*ldv+j]
}
j := min(lastv, prevlastv)
bi.Dgemv(blas.Trans, j-i, i,
-tau[i], v[(i+1)*ldv:], ldv, v[(i+1)*ldv+i:], ldv,
1, t[i:], ldt)
} else {
for lastv = n - 1; lastv >= i+1; lastv-- {
if v[i*ldv+lastv] != 0 {
break
}
}
for j := 0; j < i; j++ {
t[j*ldt+i] = -tau[i] * v[j*ldv+i]
}
j := min(lastv, prevlastv)
bi.Dgemv(blas.NoTrans, i, j-i,
-tau[i], v[i+1:], ldv, v[i*ldv+i+1:], 1,
1, t[i:], ldt)
}
bi.Dtrmv(blas.Upper, blas.NoTrans, blas.NonUnit, i, t, ldt, t[i:], ldt)
t[i*ldt+i] = tau[i]
if i > 1 {
prevlastv = max(prevlastv, lastv)
} else {
prevlastv = lastv
}
}
return
}
prevlastv := 0
for i := k - 1; i >= 0; i-- {
if tau[i] == 0 {
for j := i; j < k; j++ {
t[j*ldt+i] = 0
}
continue
}
var lastv int
if i < k-1 {
if store == lapack.ColumnWise {
for lastv = 0; lastv < i; lastv++ {
if v[lastv*ldv+i] != 0 {
break
}
}
for j := i + 1; j < k; j++ {
t[j*ldt+i] = -tau[i] * v[(n-k+i)*ldv+j]
}
j := max(lastv, prevlastv)
bi.Dgemv(blas.Trans, n-k+i-j, k-i-1,
-tau[i], v[j*ldv+i+1:], ldv, v[j*ldv+i:], ldv,
1, t[(i+1)*ldt+i:], ldt)
} else {
for lastv = 0; lastv < i; lastv++ {
if v[i*ldv+lastv] != 0 {
break
}
}
for j := i + 1; j < k; j++ {
t[j*ldt+i] = -tau[i] * v[j*ldv+n-k+i]
}
j := max(lastv, prevlastv)
bi.Dgemv(blas.NoTrans, k-i-1, n-k+i-j,
-tau[i], v[(i+1)*ldv+j:], ldv, v[i*ldv+j:], 1,
1, t[(i+1)*ldt+i:], ldt)
}
bi.Dtrmv(blas.Lower, blas.NoTrans, blas.NonUnit, k-i-1,
t[(i+1)*ldt+i+1:], ldt,
t[(i+1)*ldt+i:], ldt)
if i > 0 {
prevlastv = min(prevlastv, lastv)
} else {
prevlastv = lastv
}
}
t[i*ldt+i] = tau[i]
}
}
|
