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107 lines
3.2 KiB
107 lines
3.2 KiB
namespace Eigen {
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namespace internal {
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template <typename Scalar>
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void dogleg(
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const Matrix< Scalar, Dynamic, Dynamic > &qrfac,
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const Matrix< Scalar, Dynamic, 1 > &diag,
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const Matrix< Scalar, Dynamic, 1 > &qtb,
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Scalar delta,
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Matrix< Scalar, Dynamic, 1 > &x)
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{
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using std::abs;
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using std::sqrt;
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typedef DenseIndex Index;
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/* Local variables */
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Index i, j;
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Scalar sum, temp, alpha, bnorm;
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Scalar gnorm, qnorm;
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Scalar sgnorm;
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/* Function Body */
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const Scalar epsmch = NumTraits<Scalar>::epsilon();
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const Index n = qrfac.cols();
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eigen_assert(n==qtb.size());
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eigen_assert(n==x.size());
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eigen_assert(n==diag.size());
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Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);
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/* first, calculate the gauss-newton direction. */
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for (j = n-1; j >=0; --j) {
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temp = qrfac(j,j);
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if (temp == 0.) {
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temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();
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if (temp == 0.)
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temp = epsmch;
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}
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if (j==n-1)
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x[j] = qtb[j] / temp;
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else
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x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;
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}
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/* test whether the gauss-newton direction is acceptable. */
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qnorm = diag.cwiseProduct(x).stableNorm();
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if (qnorm <= delta)
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return;
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// TODO : this path is not tested by Eigen unit tests
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/* the gauss-newton direction is not acceptable. */
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/* next, calculate the scaled gradient direction. */
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wa1.fill(0.);
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for (j = 0; j < n; ++j) {
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wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j];
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wa1[j] /= diag[j];
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}
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/* calculate the norm of the scaled gradient and test for */
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/* the special case in which the scaled gradient is zero. */
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gnorm = wa1.stableNorm();
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sgnorm = 0.;
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alpha = delta / qnorm;
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if (gnorm == 0.)
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goto algo_end;
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/* calculate the point along the scaled gradient */
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/* at which the quadratic is minimized. */
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wa1.array() /= (diag*gnorm).array();
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// TODO : once unit tests cover this part,:
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// wa2 = qrfac.template triangularView<Upper>() * wa1;
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for (j = 0; j < n; ++j) {
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sum = 0.;
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for (i = j; i < n; ++i) {
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sum += qrfac(j,i) * wa1[i];
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}
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wa2[j] = sum;
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}
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temp = wa2.stableNorm();
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sgnorm = gnorm / temp / temp;
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/* test whether the scaled gradient direction is acceptable. */
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alpha = 0.;
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if (sgnorm >= delta)
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goto algo_end;
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/* the scaled gradient direction is not acceptable. */
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/* finally, calculate the point along the dogleg */
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/* at which the quadratic is minimized. */
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bnorm = qtb.stableNorm();
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temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);
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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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alpha = delta / qnorm * (1. - numext::abs2(sgnorm / delta)) / temp;
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algo_end:
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/* form appropriate convex combination of the gauss-newton */
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/* direction and the scaled gradient direction. */
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temp = (1.-alpha) * (std::min)(sgnorm,delta);
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x = temp * wa1 + alpha * x;
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}
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} // end namespace internal
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} // end namespace Eigen
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