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      1 namespace Eigen {
      2 
      3 namespace internal {
      4 
      5 template <typename Scalar>
      6 void rwupdt(
      7         Matrix< Scalar, Dynamic, Dynamic >  &r,
      8         const Matrix< Scalar, Dynamic, 1>  &w,
      9         Matrix< Scalar, Dynamic, 1>  &b,
     10         Scalar alpha)
     11 {
     12     typedef DenseIndex Index;
     13 
     14     const Index n = r.cols();
     15     eigen_assert(r.rows()>=n);
     16     std::vector<JacobiRotation<Scalar> > givens(n);
     17 
     18     /* Local variables */
     19     Scalar temp, rowj;
     20 
     21     /* Function Body */
     22     for (Index j = 0; j < n; ++j) {
     23         rowj = w[j];
     24 
     25         /* apply the previous transformations to */
     26         /* r(i,j), i=0,1,...,j-1, and to w(j). */
     27         for (Index i = 0; i < j; ++i) {
     28             temp = givens[i].c() * r(i,j) + givens[i].s() * rowj;
     29             rowj = -givens[i].s() * r(i,j) + givens[i].c() * rowj;
     30             r(i,j) = temp;
     31         }
     32 
     33         /* determine a givens rotation which eliminates w(j). */
     34         givens[j].makeGivens(-r(j,j), rowj);
     35 
     36         if (rowj == 0.)
     37             continue; // givens[j] is identity
     38 
     39         /* apply the current transformation to r(j,j), b(j), and alpha. */
     40         r(j,j) = givens[j].c() * r(j,j) + givens[j].s() * rowj;
     41         temp = givens[j].c() * b[j] + givens[j].s() * alpha;
     42         alpha = -givens[j].s() * b[j] + givens[j].c() * alpha;
     43         b[j] = temp;
     44     }
     45 }
     46 
     47 } // end namespace internal
     48 
     49 } // end namespace Eigen
     50