This repository has been archived by the owner on Nov 24, 2018. It is now read-only.
-
Notifications
You must be signed in to change notification settings - Fork 11
/
dormqr.go
167 lines (156 loc) · 4.52 KB
/
dormqr.go
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
// 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 native
import (
"github.com/gonum/blas"
"github.com/gonum/lapack"
)
// Dormqr multiplies an m×n matrix C by an orthogonal matrix Q as
// C = Q * C, if side == blas.Left and trans == blas.NoTrans,
// C = Q^T * C, if side == blas.Left and trans == blas.Trans,
// C = C * Q, if side == blas.Right and trans == blas.NoTrans,
// C = C * Q^T, if side == blas.Right and trans == blas.Trans,
// where Q is defined as the product of k elementary reflectors
// Q = H_0 * H_1 * ... * H_{k-1}.
//
// If side == blas.Left, A is an m×k matrix and 0 <= k <= m.
// If side == blas.Right, A is an n×k matrix and 0 <= k <= n.
// The ith column of A contains the vector which defines the elementary
// reflector H_i and tau[i] contains its scalar factor. tau must have length k
// and Dormqr will panic otherwise. Dgeqrf returns A and tau in the required
// form.
//
// work must have length at least max(1,lwork), and lwork must be at least n if
// side == blas.Left and at least m if side == blas.Right, otherwise Dormqr will
// panic.
//
// work is temporary storage, and lwork specifies the usable memory length. At
// minimum, lwork >= m if side == blas.Left and lwork >= n if side ==
// blas.Right, and this function will panic otherwise. Larger values of lwork
// will generally give better performance. On return, work[0] will contain the
// optimal value of lwork.
//
// If lwork is -1, instead of performing Dormqr, the optimal workspace size will
// be stored into work[0].
func (impl Implementation) Dormqr(side blas.Side, trans blas.Transpose, m, n, k int, a []float64, lda int, tau, c []float64, ldc int, work []float64, lwork int) {
var nq, nw int
switch side {
default:
panic(badSide)
case blas.Left:
nq = m
nw = n
case blas.Right:
nq = n
nw = m
}
switch {
case trans != blas.NoTrans && trans != blas.Trans:
panic(badTrans)
case m < 0 || n < 0:
panic(negDimension)
case k < 0 || nq < k:
panic("lapack: invalid value of k")
case len(work) < lwork:
panic(shortWork)
case lwork < max(1, nw) && lwork != -1:
panic(badWork)
}
if lwork != -1 {
checkMatrix(nq, k, a, lda)
checkMatrix(m, n, c, ldc)
if len(tau) != k {
panic(badTau)
}
}
if m == 0 || n == 0 || k == 0 {
work[0] = 1
return
}
const (
nbmax = 64
ldt = nbmax
tsize = nbmax * ldt
)
opts := string(side) + string(trans)
nb := min(nbmax, impl.Ilaenv(1, "DORMQR", opts, m, n, k, -1))
lworkopt := max(1, nw)*nb + tsize
if lwork == -1 {
work[0] = float64(lworkopt)
return
}
nbmin := 2
if 1 < nb && nb < k {
if lwork < nw*nb+tsize {
nb = (lwork - tsize) / nw
nbmin = max(2, impl.Ilaenv(2, "DORMQR", opts, m, n, k, -1))
}
}
if nb < nbmin || k <= nb {
// Call unblocked code.
impl.Dorm2r(side, trans, m, n, k, a, lda, tau, c, ldc, work)
work[0] = float64(lworkopt)
return
}
var (
ldwork = nb
left = side == blas.Left
notran = trans == blas.NoTrans
)
switch {
case left && notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m-i, n, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i*ldc:], ldc,
work[tsize:], ldwork)
}
case left && !notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, m-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m-i, n, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i*ldc:], ldc,
work[tsize:], ldwork)
}
case !left && notran:
for i := 0; i < k; i += nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, n-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m, n-i, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i:], ldc,
work[tsize:], ldwork)
}
case !left && !notran:
for i := ((k - 1) / nb) * nb; i >= 0; i -= nb {
ib := min(nb, k-i)
impl.Dlarft(lapack.Forward, lapack.ColumnWise, n-i, ib,
a[i*lda+i:], lda,
tau[i:],
work[:tsize], ldt)
impl.Dlarfb(side, trans, lapack.Forward, lapack.ColumnWise, m, n-i, ib,
a[i*lda+i:], lda,
work[:tsize], ldt,
c[i:], ldc,
work[tsize:], ldwork)
}
}
work[0] = float64(lworkopt)
}