Attachment #445 for bug #774

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  // Eq. (39)
  VectorType S = VectorType::Ones(m);
  if (sigma.determinant()<0) S(m-1) = -1;

  // Eq. (40) and (43)
  if  ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 )
    S(m-1) = -1;

  Rt.block(0,0,m,m).noalias() =
    svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
    } else {
      const Scalar s = S(m-1); S(m-1) = -1;
      Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
      S(m-1) = s;
    }
  } else {
    Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
  }

  if (with_scaling)
  {

Return to bug 774

Lines 136-157 Link Here

(-)Umeyama.h.orig (-14 / +5 lines)
136		136
137	// Eq. (39)	137	// Eq. (39)
138	VectorType S = VectorType::Ones(m);	138	VectorType S = VectorType::Ones(m);
139	if (sigma.determinant()<0) S(m-1) = -1;
140		139
141	// Eq. (40) and (43)	140	// Eq. (40) and (43)
142	const VectorType& d = svd.singularValues();	141	if ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 )
143	Index rank = 0; for (Index i=0; i<m; ++i) if (!internal::isMuchSmallerThan(d.coeff(i),d.coeff(0))) ++rank;	142	S(m-1) = -1;
144	if (rank == m-1) {	143
145	if ( svd.matrixU().determinant() * svd.matrixV().determinant() > 0 ) {	144	Rt.block(0,0,m,m).noalias() =
146	Rt.block(0,0,m,m).noalias() = svd.matrixU()*svd.matrixV().transpose();	145	svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
147	} else {
148	const Scalar s = S(m-1); S(m-1) = -1;
149	Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
150	S(m-1) = s;
151	}
152	} else {
153	Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
154	}
155		146
156	if (with_scaling)	147	if (with_scaling)
157	{	148	{