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 | // TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
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6 | template <typename Scalar>
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7 | void qrsolv(
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8 | Matrix< Scalar, Dynamic, Dynamic > &s,
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9 | // TODO : use a PermutationMatrix once lmpar is no more:
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10 | const VectorXi &ipvt,
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11 | const Matrix< Scalar, Dynamic, 1 > &diag,
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12 | const Matrix< Scalar, Dynamic, 1 > &qtb,
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13 | Matrix< Scalar, Dynamic, 1 > &x,
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14 | Matrix< Scalar, Dynamic, 1 > &sdiag)
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15 |
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16 | {
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17 | typedef DenseIndex Index;
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18 |
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19 | /* Local variables */
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20 | Index i, j, k, l;
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21 | Scalar temp;
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22 | Index n = s.cols();
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23 | Matrix< Scalar, Dynamic, 1 > wa(n);
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24 | JacobiRotation<Scalar> givens;
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25 |
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26 | /* Function Body */
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27 | // the following will only change the lower triangular part of s, including
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28 | // the diagonal, though the diagonal is restored afterward
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29 |
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30 | /* copy r and (q transpose)*b to preserve input and initialize s. */
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31 | /* in particular, save the diagonal elements of r in x. */
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32 | x = s.diagonal();
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33 | wa = qtb;
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34 |
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35 | s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();
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36 |
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37 | /* eliminate the diagonal matrix d using a givens rotation. */
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38 | for (j = 0; j < n; ++j) {
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39 |
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40 | /* prepare the row of d to be eliminated, locating the */
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41 | /* diagonal element using p from the qr factorization. */
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42 | l = ipvt[j];
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43 | if (diag[l] == 0.)
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44 | break;
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45 | sdiag.tail(n-j).setZero();
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46 | sdiag[j] = diag[l];
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47 |
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48 | /* the transformations to eliminate the row of d */
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49 | /* modify only a single element of (q transpose)*b */
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50 | /* beyond the first n, which is initially zero. */
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51 | Scalar qtbpj = 0.;
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52 | for (k = j; k < n; ++k) {
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53 | /* determine a givens rotation which eliminates the */
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54 | /* appropriate element in the current row of d. */
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55 | givens.makeGivens(-s(k,k), sdiag[k]);
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56 |
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57 | /* compute the modified diagonal element of r and */
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58 | /* the modified element of ((q transpose)*b,0). */
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59 | s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];
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60 | temp = givens.c() * wa[k] + givens.s() * qtbpj;
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61 | qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
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62 | wa[k] = temp;
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63 |
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64 | /* accumulate the tranformation in the row of s. */
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65 | for (i = k+1; i<n; ++i) {
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66 | temp = givens.c() * s(i,k) + givens.s() * sdiag[i];
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67 | sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];
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68 | s(i,k) = temp;
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69 | }
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70 | }
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71 | }
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72 |
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73 | /* solve the triangular system for z. if the system is */
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74 | /* singular, then obtain a least squares solution. */
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75 | Index nsing;
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76 | for(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}
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77 |
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78 | wa.tail(n-nsing).setZero();
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79 | s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));
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80 |
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81 | // restore
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82 | sdiag = s.diagonal();
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83 | s.diagonal() = x;
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84 |
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85 | /* permute the components of z back to components of x. */
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86 | for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
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87 | }
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88 |
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89 | } // end namespace internal
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90 |
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91 | } // end namespace Eigen
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