Dot.h

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
#ifndef EIGEN_DOT_H
#define EIGEN_DOT_H
 
namespace Eigen { 
 
namespace internal {
 
// helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
// with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
// looking at the static assertions. Thus this is a trick to get better compile errors.
template<typename T, typename U,
// the NeedToTranspose condition here is taken straight from Assign.h
         bool NeedToTranspose = T::IsVectorAtCompileTime
                && U::IsVectorAtCompileTime
                && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
                      |  // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
                         // revert to || as soon as not needed anymore.
                    (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
>
struct dot_nocheck
{
  typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
  static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
  {
    return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
  }
};
 
template<typename T, typename U>
struct dot_nocheck<T, U, true>
{
  typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
  static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
  {
    return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
  }
};
 
} // end namespace internal

template<typename Derived>
template<typename OtherDerived>
inline typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
  typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
  EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
 
  eigen_assert(size() == other.size());
 
  return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
}
 
#ifdef EIGEN2_SUPPORT
template<typename Derived>
template<typename OtherDerived>
typename internal::traits<Derived>::Scalar
MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
{
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
  EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
  EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
 
  eigen_assert(size() == other.size());
 
  return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
}
#endif
 
 
//---------- implementation of L2 norm and related functions ----------

template<typename Derived>
EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
{
  return numext::real((*this).cwiseAbs2().sum());
}

template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
{
  using std::sqrt;
  return sqrt(squaredNorm());
}

template<typename Derived>
inline const typename MatrixBase<Derived>::PlainObject
MatrixBase<Derived>::normalized() const
{
  typedef typename internal::nested<Derived>::type Nested;
  typedef typename internal::remove_reference<Nested>::type _Nested;
  _Nested n(derived());
  return n / n.norm();
}

template<typename Derived>
inline void MatrixBase<Derived>::normalize()
{
  *this /= norm();
}
 
//---------- implementation of other norms ----------
 
namespace internal {
 
template<typename Derived, int p>
struct lpNorm_selector
{
  typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
  static inline RealScalar run(const MatrixBase<Derived>& m)
  {
    using std::pow;
    return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
  }
};
 
template<typename Derived>
struct lpNorm_selector<Derived, 1>
{
  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
  {
    return m.cwiseAbs().sum();
  }
};
 
template<typename Derived>
struct lpNorm_selector<Derived, 2>
{
  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
  {
    return m.norm();
  }
};
 
template<typename Derived>
struct lpNorm_selector<Derived, Infinity>
{
  static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
  {
    return m.cwiseAbs().maxCoeff();
  }
};
 
} // end namespace internal

/** \returns the \f$ \ell^p \f$ norm of *this, that is, returns the p-th root of the sum of the p-th powers of the absolute values
  *          of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
  *          norm, that is the maximum of the absolute values of the coefficients of *this.
  *
  * \sa norm()
  */
template<typename Derived>
template<int p>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::lpNorm() const
{
  return internal::lpNorm_selector<Derived, p>::run(*this);
}
 
//---------- implementation of isOrthogonal / isUnitary ----------

template<typename Derived>
template<typename OtherDerived>
bool MatrixBase<Derived>::isOrthogonal
(const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
{
  typename internal::nested<Derived,2>::type nested(derived());
  typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
  return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
}

template<typename Derived>
bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
{
  typename Derived::Nested nested(derived());
  for(Index i = 0; i < cols(); ++i)
  {
    if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
      return false;
    for(Index j = 0; j < i; ++j)
      if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
        return false;
  }
  return true;
}
 
} // end namespace Eigen
 
#endif // EIGEN_DOT_H