1 | namespace Eigen {
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2 |
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3 | namespace internal {
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4 |
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5 | template <typename Scalar>
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6 | void r1updt(
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7 | Matrix< Scalar, Dynamic, Dynamic > &s,
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8 | const Matrix< Scalar, Dynamic, 1> &u,
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9 | std::vector<JacobiRotation<Scalar> > &v_givens,
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10 | std::vector<JacobiRotation<Scalar> > &w_givens,
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11 | Matrix< Scalar, Dynamic, 1> &v,
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12 | Matrix< Scalar, Dynamic, 1> &w,
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13 | bool *sing)
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14 | {
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15 | typedef DenseIndex Index;
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16 | const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0);
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17 |
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18 | /* Local variables */
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19 | const Index m = s.rows();
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20 | const Index n = s.cols();
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21 | Index i, j=1;
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22 | Scalar temp;
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23 | JacobiRotation<Scalar> givens;
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24 |
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25 | // r1updt had a broader usecase, but we dont use it here. And, more
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26 | // importantly, we can not test it.
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27 | eigen_assert(m==n);
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28 | eigen_assert(u.size()==m);
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29 | eigen_assert(v.size()==n);
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30 | eigen_assert(w.size()==n);
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31 |
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32 | /* move the nontrivial part of the last column of s into w. */
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33 | w[n-1] = s(n-1,n-1);
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34 |
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35 | /* rotate the vector v into a multiple of the n-th unit vector */
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36 | /* in such a way that a spike is introduced into w. */
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37 | for (j=n-2; j>=0; --j) {
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38 | w[j] = 0.;
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39 | if (v[j] != 0.) {
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40 | /* determine a givens rotation which eliminates the */
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41 | /* j-th element of v. */
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42 | givens.makeGivens(-v[n-1], v[j]);
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43 |
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44 | /* apply the transformation to v and store the information */
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45 | /* necessary to recover the givens rotation. */
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46 | v[n-1] = givens.s() * v[j] + givens.c() * v[n-1];
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47 | v_givens[j] = givens;
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48 |
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49 | /* apply the transformation to s and extend the spike in w. */
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50 | for (i = j; i < m; ++i) {
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51 | temp = givens.c() * s(j,i) - givens.s() * w[i];
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52 | w[i] = givens.s() * s(j,i) + givens.c() * w[i];
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53 | s(j,i) = temp;
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54 | }
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55 | } else
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56 | v_givens[j] = IdentityRotation;
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57 | }
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58 |
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59 | /* add the spike from the rank 1 update to w. */
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60 | w += v[n-1] * u;
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61 |
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62 | /* eliminate the spike. */
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63 | *sing = false;
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64 | for (j = 0; j < n-1; ++j) {
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65 | if (w[j] != 0.) {
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66 | /* determine a givens rotation which eliminates the */
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67 | /* j-th element of the spike. */
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68 | givens.makeGivens(-s(j,j), w[j]);
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69 |
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70 | /* apply the transformation to s and reduce the spike in w. */
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71 | for (i = j; i < m; ++i) {
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72 | temp = givens.c() * s(j,i) + givens.s() * w[i];
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73 | w[i] = -givens.s() * s(j,i) + givens.c() * w[i];
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74 | s(j,i) = temp;
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75 | }
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76 |
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77 | /* store the information necessary to recover the */
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78 | /* givens rotation. */
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79 | w_givens[j] = givens;
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80 | } else
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81 | v_givens[j] = IdentityRotation;
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82 |
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83 | /* test for zero diagonal elements in the output s. */
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84 | if (s(j,j) == 0.) {
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85 | *sing = true;
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86 | }
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87 | }
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88 | /* move w back into the last column of the output s. */
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89 | s(n-1,n-1) = w[n-1];
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90 |
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91 | if (s(j,j) == 0.) {
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92 | *sing = true;
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93 | }
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94 | return;
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95 | }
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96 |
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97 | } // end namespace internal
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98 |
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99 | } // end namespace Eigen
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