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 covar(
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7 | Matrix< Scalar, Dynamic, Dynamic > &r,
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8 | const VectorXi &ipvt,
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9 | Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
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10 | {
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11 | using std::abs;
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12 | typedef DenseIndex Index;
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13 |
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14 | /* Local variables */
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15 | Index i, j, k, l, ii, jj;
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16 | bool sing;
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17 | Scalar temp;
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18 |
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19 | /* Function Body */
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20 | const Index n = r.cols();
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21 | const Scalar tolr = tol * abs(r(0,0));
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22 | Matrix< Scalar, Dynamic, 1 > wa(n);
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23 | eigen_assert(ipvt.size()==n);
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24 |
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25 | /* form the inverse of r in the full upper triangle of r. */
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26 | l = -1;
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27 | for (k = 0; k < n; ++k)
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28 | if (abs(r(k,k)) > tolr) {
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29 | r(k,k) = 1. / r(k,k);
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30 | for (j = 0; j <= k-1; ++j) {
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31 | temp = r(k,k) * r(j,k);
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32 | r(j,k) = 0.;
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33 | r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;
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34 | }
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35 | l = k;
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36 | }
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37 |
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38 | /* form the full upper triangle of the inverse of (r transpose)*r */
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39 | /* in the full upper triangle of r. */
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40 | for (k = 0; k <= l; ++k) {
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41 | for (j = 0; j <= k-1; ++j)
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42 | r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);
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43 | r.col(k).head(k+1) *= r(k,k);
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44 | }
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45 |
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46 | /* form the full lower triangle of the covariance matrix */
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47 | /* in the strict lower triangle of r and in wa. */
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48 | for (j = 0; j < n; ++j) {
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49 | jj = ipvt[j];
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50 | sing = j > l;
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51 | for (i = 0; i <= j; ++i) {
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52 | if (sing)
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53 | r(i,j) = 0.;
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54 | ii = ipvt[i];
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55 | if (ii > jj)
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56 | r(ii,jj) = r(i,j);
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57 | if (ii < jj)
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58 | r(jj,ii) = r(i,j);
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59 | }
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60 | wa[jj] = r(j,j);
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61 | }
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62 |
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63 | /* symmetrize the covariance matrix in r. */
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64 | r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();
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65 | r.diagonal() = wa;
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66 | }
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67 |
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68 | } // end namespace internal
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69 |
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70 | } // end namespace Eigen
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