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
|
namespace Eigen {
namespace internal {
template <typename Scalar>
void r1updt(
Matrix< Scalar, Dynamic, Dynamic > &s,
const Matrix< Scalar, Dynamic, 1> &u,
std::vector<JacobiRotation<Scalar> > &v_givens,
std::vector<JacobiRotation<Scalar> > &w_givens,
Matrix< Scalar, Dynamic, 1> &v,
Matrix< Scalar, Dynamic, 1> &w,
bool *sing)
{
typedef DenseIndex Index;
const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0);
/* Local variables */
const Index m = s.rows();
const Index n = s.cols();
Index i, j=1;
Scalar temp;
JacobiRotation<Scalar> givens;
// r1updt had a broader usecase, but we don't use it here. And, more
// importantly, we can not test it.
eigen_assert(m==n);
eigen_assert(u.size()==m);
eigen_assert(v.size()==n);
eigen_assert(w.size()==n);
/* move the nontrivial part of the last column of s into w. */
w[n-1] = s(n-1,n-1);
/* rotate the vector v into a multiple of the n-th unit vector */
/* in such a way that a spike is introduced into w. */
for (j=n-2; j>=0; --j) {
w[j] = 0.;
if (v[j] != 0.) {
/* determine a givens rotation which eliminates the */
/* j-th element of v. */
givens.makeGivens(-v[n-1], v[j]);
/* apply the transformation to v and store the information */
/* necessary to recover the givens rotation. */
v[n-1] = givens.s() * v[j] + givens.c() * v[n-1];
v_givens[j] = givens;
/* apply the transformation to s and extend the spike in w. */
for (i = j; i < m; ++i) {
temp = givens.c() * s(j,i) - givens.s() * w[i];
w[i] = givens.s() * s(j,i) + givens.c() * w[i];
s(j,i) = temp;
}
} else
v_givens[j] = IdentityRotation;
}
/* add the spike from the rank 1 update to w. */
w += v[n-1] * u;
/* eliminate the spike. */
*sing = false;
for (j = 0; j < n-1; ++j) {
if (w[j] != 0.) {
/* determine a givens rotation which eliminates the */
/* j-th element of the spike. */
givens.makeGivens(-s(j,j), w[j]);
/* apply the transformation to s and reduce the spike in w. */
for (i = j; i < m; ++i) {
temp = givens.c() * s(j,i) + givens.s() * w[i];
w[i] = -givens.s() * s(j,i) + givens.c() * w[i];
s(j,i) = temp;
}
/* store the information necessary to recover the */
/* givens rotation. */
w_givens[j] = givens;
} else
v_givens[j] = IdentityRotation;
/* test for zero diagonal elements in the output s. */
if (s(j,j) == 0.) {
*sing = true;
}
}
/* move w back into the last column of the output s. */
s(n-1,n-1) = w[n-1];
if (s(j,j) == 0.) {
*sing = true;
}
return;
}
} // end namespace internal
} // end namespace Eigen
|
