| 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 dogleg(
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| 7 | const Matrix< Scalar, Dynamic, Dynamic > &qrfac,
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| 8 | const Matrix< Scalar, Dynamic, 1 > &diag,
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| 9 | const Matrix< Scalar, Dynamic, 1 > &qtb,
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| 10 | Scalar delta,
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| 11 | Matrix< Scalar, Dynamic, 1 > &x)
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| 12 | {
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| 13 | using std::abs;
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| 14 | using std::sqrt;
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| 15 |
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| 16 | typedef DenseIndex Index;
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| 17 |
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| 18 | /* Local variables */
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| 19 | Index i, j;
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| 20 | Scalar sum, temp, alpha, bnorm;
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| 21 | Scalar gnorm, qnorm;
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| 22 | Scalar sgnorm;
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| 23 |
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| 24 | /* Function Body */
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| 25 | const Scalar epsmch = NumTraits<Scalar>::epsilon();
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| 26 | const Index n = qrfac.cols();
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| 27 | eigen_assert(n==qtb.size());
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| 28 | eigen_assert(n==x.size());
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| 29 | eigen_assert(n==diag.size());
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| 30 | Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);
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| 31 |
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| 32 | /* first, calculate the gauss-newton direction. */
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| 33 | for (j = n-1; j >=0; --j) {
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| 34 | temp = qrfac(j,j);
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| 35 | if (temp == 0.) {
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| 36 | temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();
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| 37 | if (temp == 0.)
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| 38 | temp = epsmch;
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| 39 | }
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| 40 | if (j==n-1)
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| 41 | x[j] = qtb[j] / temp;
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| 42 | else
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| 43 | x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;
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| 44 | }
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| 45 |
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| 46 | /* test whether the gauss-newton direction is acceptable. */
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| 47 | qnorm = diag.cwiseProduct(x).stableNorm();
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| 48 | if (qnorm <= delta)
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| 49 | return;
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| 50 |
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| 51 | // TODO : this path is not tested by Eigen unit tests
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| 52 |
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| 53 | /* the gauss-newton direction is not acceptable. */
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| 54 | /* next, calculate the scaled gradient direction. */
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| 55 |
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| 56 | wa1.fill(0.);
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| 57 | for (j = 0; j < n; ++j) {
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| 58 | wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j];
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| 59 | wa1[j] /= diag[j];
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| 60 | }
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| 61 |
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| 62 | /* calculate the norm of the scaled gradient and test for */
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| 63 | /* the special case in which the scaled gradient is zero. */
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| 64 | gnorm = wa1.stableNorm();
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| 65 | sgnorm = 0.;
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| 66 | alpha = delta / qnorm;
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| 67 | if (gnorm == 0.)
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| 68 | goto algo_end;
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| 69 |
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| 70 | /* calculate the point along the scaled gradient */
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| 71 | /* at which the quadratic is minimized. */
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| 72 | wa1.array() /= (diag*gnorm).array();
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| 73 | // TODO : once unit tests cover this part,:
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| 74 | // wa2 = qrfac.template triangularView<Upper>() * wa1;
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| 75 | for (j = 0; j < n; ++j) {
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| 76 | sum = 0.;
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| 77 | for (i = j; i < n; ++i) {
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| 78 | sum += qrfac(j,i) * wa1[i];
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| 79 | }
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| 80 | wa2[j] = sum;
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| 81 | }
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| 82 | temp = wa2.stableNorm();
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| 83 | sgnorm = gnorm / temp / temp;
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| 84 |
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| 85 | /* test whether the scaled gradient direction is acceptable. */
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| 86 | alpha = 0.;
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| 87 | if (sgnorm >= delta)
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| 88 | goto algo_end;
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| 89 |
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| 90 | /* the scaled gradient direction is not acceptable. */
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| 91 | /* finally, calculate the point along the dogleg */
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| 92 | /* at which the quadratic is minimized. */
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| 93 | bnorm = qtb.stableNorm();
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| 94 | temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
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| 95 | temp = temp - delta / qnorm * numext::abs2(sgnorm / delta) + sqrt(numext::abs2(temp - delta / qnorm) + (1.-numext::abs2(delta / qnorm)) * (1.-numext::abs2(sgnorm / delta)));
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| 96 | alpha = delta / qnorm * (1. - numext::abs2(sgnorm / delta)) / temp;
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| 97 | algo_end:
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| 98 |
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| 99 | /* form appropriate convex combination of the gauss-newton */
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| 100 | /* direction and the scaled gradient direction. */
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| 101 | temp = (1.-alpha) * (std::min)(sgnorm,delta);
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| 102 | x = temp * wa1 + alpha * x;
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| 103 | }
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| 104 |
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| 105 | } // end namespace internal
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| 106 |
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| 107 | } // end namespace Eigen
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