r1updt.h

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

namespace internal {

template <typename Scalar>
void r1updt(Matrix<Scalar, Dynamic, Dynamic> &s, const Matrix<Scalar, Dynamic, 1> &u,
            std::vector<JacobiRotation<Scalar> > &v_givens, std::vector<JacobiRotation<Scalar> > &w_givens,
            Matrix<Scalar, Dynamic, 1> &v, Matrix<Scalar, Dynamic, 1> &w, bool *sing) {
  typedef DenseIndex Index;
  const JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1, 0);

  /* Local variables */
  const Index m = s.rows();
  const Index n = s.cols();
  Index i, j = 1;
  Scalar temp;
  JacobiRotation<Scalar> givens;

  // r1updt had a broader usecase, but we don't use it here. And, more
  // importantly, we can not test it.
  eigen_assert(m == n);
  eigen_assert(u.size() == m);
  eigen_assert(v.size() == n);
  eigen_assert(w.size() == n);

  /* move the nontrivial part of the last column of s into w. */
  w[n - 1] = s(n - 1, n - 1);

  /* rotate the vector v into a multiple of the n-th unit vector */
  /* in such a way that a spike is introduced into w. */
  for (j = n - 2; j >= 0; --j) {
    w[j] = 0.;
    if (v[j] != 0.) {
      /* determine a givens rotation which eliminates the */
      /* j-th element of v. */
      givens.makeGivens(-v[n - 1], v[j]);

      /* apply the transformation to v and store the information */
      /* necessary to recover the givens rotation. */
      v[n - 1] = givens.s() * v[j] + givens.c() * v[n - 1];
      v_givens[j] = givens;

      /* apply the transformation to s and extend the spike in w. */
      for (i = j; i < m; ++i) {
        temp = givens.c() * s(j, i) - givens.s() * w[i];
        w[i] = givens.s() * s(j, i) + givens.c() * w[i];
        s(j, i) = temp;
      }
    } else
      v_givens[j] = IdentityRotation;
  }

  /* add the spike from the rank 1 update to w. */
  w += v[n - 1] * u;

  /* eliminate the spike. */
  *sing = false;
  for (j = 0; j < n - 1; ++j) {
    if (w[j] != 0.) {
      /* determine a givens rotation which eliminates the */
      /* j-th element of the spike. */
      givens.makeGivens(-s(j, j), w[j]);

      /* apply the transformation to s and reduce the spike in w. */
      for (i = j; i < m; ++i) {
        temp = givens.c() * s(j, i) + givens.s() * w[i];
        w[i] = -givens.s() * s(j, i) + givens.c() * w[i];
        s(j, i) = temp;
      }

      /* store the information necessary to recover the */
      /* givens rotation. */
      w_givens[j] = givens;
    } else
      w_givens[j] = IdentityRotation;

    /* test for zero diagonal elements in the output s. */
    if (s(j, j) == 0.) {
      *sing = true;
    }
  }
  /* move w back into the last column of the output s. */
  s(n - 1, n - 1) = w[n - 1];

  if (s(j, j) == 0.) {
    *sing = true;
  }
  return;
}

}  // end namespace internal

}  // end namespace Eigen