qrsolv.h

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

namespace Eigen {

namespace internal {

// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt
template <typename Scalar>
void qrsolv(Matrix<Scalar, Dynamic, Dynamic> &s,
            // TODO : use a PermutationMatrix once lmpar is no more:
            const VectorXi &ipvt, const Matrix<Scalar, Dynamic, 1> &diag, const Matrix<Scalar, Dynamic, 1> &qtb,
            Matrix<Scalar, Dynamic, 1> &x, Matrix<Scalar, Dynamic, 1> &sdiag)

{
  typedef DenseIndex Index;

  /* Local variables */
  Index i, j, k, l;
  Scalar temp;
  Index n = s.cols();
  Matrix<Scalar, Dynamic, 1> wa(n);
  JacobiRotation<Scalar> givens;

  /* Function Body */
  // the following will only change the lower triangular part of s, including
  // the diagonal, though the diagonal is restored afterward

  /*     copy r and (q transpose)*b to preserve input and initialize s. */
  /*     in particular, save the diagonal elements of r in x. */
  x = s.diagonal();
  wa = qtb;

  s.topLeftCorner(n, n).template triangularView<StrictlyLower>() = s.topLeftCorner(n, n).transpose();

  /*     eliminate the diagonal matrix d using a givens rotation. */
  for (j = 0; j < n; ++j) {
    /*        prepare the row of d to be eliminated, locating the */
    /*        diagonal element using p from the qr factorization. */
    l = ipvt[j];
    if (diag[l] == 0.) break;
    sdiag.tail(n - j).setZero();
    sdiag[j] = diag[l];

    /*        the transformations to eliminate the row of d */
    /*        modify only a single element of (q transpose)*b */
    /*        beyond the first n, which is initially zero. */
    Scalar qtbpj = 0.;
    for (k = j; k < n; ++k) {
      /*           determine a givens rotation which eliminates the */
      /*           appropriate element in the current row of d. */
      givens.makeGivens(-s(k, k), sdiag[k]);

      /*           compute the modified diagonal element of r and */
      /*           the modified element of ((q transpose)*b,0). */
      s(k, k) = givens.c() * s(k, k) + givens.s() * sdiag[k];
      temp = givens.c() * wa[k] + givens.s() * qtbpj;
      qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;
      wa[k] = temp;

      /*           accumulate the transformation in the row of s. */
      for (i = k + 1; i < n; ++i) {
        temp = givens.c() * s(i, k) + givens.s() * sdiag[i];
        sdiag[i] = -givens.s() * s(i, k) + givens.c() * sdiag[i];
        s(i, k) = temp;
      }
    }
  }

  /*     solve the triangular system for z. if the system is */
  /*     singular, then obtain a least squares solution. */
  Index nsing;
  for (nsing = 0; nsing < n && sdiag[nsing] != 0; nsing++) {
  }

  wa.tail(n - nsing).setZero();
  s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));

  // restore
  sdiag = s.diagonal();
  s.diagonal() = x;

  /*     permute the components of z back to components of x. */
  for (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];
}

}  // end namespace internal

}  // end namespace Eigen