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
|
//
// $Id$
//
// Original author: Robert Burke <robert.burke@cshs.org>
//
// Copyright 2006 Louis Warschaw Prostate Cancer Center
// Cedars Sinai Medical Center, Los Angeles, California 90048
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
//
#ifndef _QR_HPP
#define _QR_HPP
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/matrix_proxy.hpp>
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/io.hpp>
namespace pwiz {
namespace math {
// Constructs a matrix to reflect a vector x onto ||x|| * e1.
//
// \param x vector to reflect
// \param F matrix object to construct reflector with
template<class matrix_type, class vector_type>
void Reflector(const vector_type& x, matrix_type& F)
{
using namespace boost::numeric::ublas;
typedef typename matrix_type::value_type value_type;
unit_vector<value_type> e1(x.size(), 0);
//v_k = -sgn( x(1) ) * inner_prod(x) * e1 + x;
double x_2 = norm_2(x);
boost::numeric::ublas::vector<value_type>
v_k((x(0) >= 0 ? x_2 : -1 * x_2) * e1 + x);
//v_k = v_k / norm_2(v_k);
double norm_vk = norm_2(v_k);
if (norm_vk != 0)
v_k /= norm_2(v_k);
// F = A(k:m,k:n) - 2 * outer_prod(v_k, v_k) * A(k:m,k:n)
identity_matrix<value_type> eye(v_k.size());
F = matrix_type(v_k.size(), v_k.size());
F = eye - 2. * outer_prod(v_k, v_k);
}
// Returns a matrix to reflect x onto ||x|| * e1.
//
// \param x vector to reflect
// \return Householder reflector for x
template<class matrix_type, class vector_type>
matrix_type Reflector(const vector_type& x)
{
using namespace boost::numeric::ublas;
matrix_type F(x.size(), x.size());
Reflector<matrix_type, vector_type>(x, F);
return F;
}
template<class matrix_type>
void qr(const matrix_type& A, matrix_type& Q, matrix_type& R)
{
using namespace boost::numeric::ublas;
typedef typename matrix_type::size_type size_type;
typedef typename matrix_type::value_type value_type;
// TODO resize Q and R to match the needed size.
int m=A.size1();
int n=A.size2();
identity_matrix<value_type> ident(m);
if (Q.size1() != ident.size1() || Q.size2() != ident.size2())
Q = matrix_type(m, m);
Q.assign(ident);
R.clear();
R = A;
for (size_type k=0; k< R.size1() && k<R.size2(); k++)
{
slice s1(k, 1, m - k);
slice s2(k, 0, m - k);
unit_vector<value_type> e1(m - k, 0);
// x = A(k:m, k);
matrix_vector_slice<matrix_type> x(R, s1, s2);
matrix_type F(x.size(), x.size());
Reflector(x, F);
matrix_type temp = subrange(R, k, m, k, n);
//F = prod(F, temp);
subrange(R, k, m, k, n) = prod(F, temp);
// <<---------------------------------------------->>
// forming Q
identity_matrix<value_type> iqk(A.size1());
matrix_type Q_k(iqk);
subrange(Q_k, Q_k.size1() - F.size1(), Q_k.size1(),
Q_k.size2() - F.size2(), Q_k.size2()) = F;
Q = prod(Q, Q_k);
}
}
}
}
#endif // _QR_HPP
|
