| 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 |
