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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra. Eigen itself is part of the KDE project.
//
// Copyright (C) 2006-2007 Benoit Jacob <jacob@math.jussieu.fr>
//
// Eigen is free software; you can redistribute it and/or modify it under the
// terms of the GNU General Public License as published by the Free Software
// Foundation; either version 2 or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
// details.
//
// You should have received a copy of the GNU General Public License along
// with Eigen; if not, write to the Free Software Foundation, Inc., 51
// Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
//
// As a special exception, if other files instantiate templates or use macros
// or functions from this file, or you compile this file and link it
// with other works to produce a work based on this file, this file does not
// by itself cause the resulting work to be covered by the GNU General Public
// License. This exception does not invalidate any other reasons why a work
// based on this file might be covered by the GNU General Public License.
#ifndef EIGEN_DOT_H
#define EIGEN_DOT_H
template<int Index, int Size, typename Derived1, typename Derived2>
struct DotUnroller
{
static void run(const Derived1 &v1, const Derived2& v2, typename Derived1::Scalar &dot)
{
DotUnroller<Index-1, Size, Derived1, Derived2>::run(v1, v2, dot);
dot += v1.coeff(Index) * conj(v2.coeff(Index));
}
};
template<int Size, typename Derived1, typename Derived2>
struct DotUnroller<0, Size, Derived1, Derived2>
{
static void run(const Derived1 &v1, const Derived2& v2, typename Derived1::Scalar &dot)
{
dot = v1.coeff(0) * conj(v2.coeff(0));
}
};
template<int Index, typename Derived1, typename Derived2>
struct DotUnroller<Index, Dynamic, Derived1, Derived2>
{
static void run(const Derived1&, const Derived2&, typename Derived1::Scalar&) {}
};
// prevent buggy user code from causing an infinite recursion
template<int Index, typename Derived1, typename Derived2>
struct DotUnroller<Index, 0, Derived1, Derived2>
{
static void run(const Derived1&, const Derived2&, typename Derived1::Scalar&) {}
};
/** \returns the dot product of *this with other.
*
* \only_for_vectors
*
* \note If the scalar type is complex numbers, then this function returns the hermitian
* (sesquilinear) dot product, linear in the first variable and anti-linear in the
* second variable.
*
* \sa norm2(), norm()
*/
template<typename Scalar, typename Derived>
template<typename OtherDerived>
Scalar MatrixBase<Scalar, Derived>::dot(const OtherDerived& other) const
{
assert(IsVectorAtCompileTime && OtherDerived::IsVectorAtCompileTime && size() == other.size());
Scalar res;
if(EIGEN_UNROLLED_LOOPS && SizeAtCompileTime != Dynamic && SizeAtCompileTime <= 16)
DotUnroller<SizeAtCompileTime-1, SizeAtCompileTime, Derived, OtherDerived>
::run(*static_cast<const Derived*>(this), other, res);
else
{
res = (*this).coeff(0) * conj(other.coeff(0));
for(int i = 1; i < size(); i++)
res += (*this).coeff(i)* conj(other.coeff(i));
}
return res;
}
/** \returns the squared norm of *this, i.e. the dot product of *this with itself.
*
* \only_for_vectors
*
* \sa dot(), norm()
*/
template<typename Scalar, typename Derived>
typename NumTraits<Scalar>::Real MatrixBase<Scalar, Derived>::norm2() const
{
return real(dot(*this));
}
/** \returns the norm of *this, i.e. the square root of the dot product of *this with itself.
*
* \only_for_vectors
*
* \sa dot(), norm2()
*/
template<typename Scalar, typename Derived>
typename NumTraits<Scalar>::Real MatrixBase<Scalar, Derived>::norm() const
{
return sqrt(norm2());
}
/** \returns an expression of the quotient of *this by its own norm.
*
* \only_for_vectors
*
* \sa norm()
*/
template<typename Scalar, typename Derived>
const ScalarMultiple<typename NumTraits<Scalar>::Real, Derived>
MatrixBase<Scalar, Derived>::normalized() const
{
return (*this) / norm();
}
template<typename Scalar, typename Derived>
template<typename OtherDerived>
bool MatrixBase<Scalar, Derived>::isOrtho
(const OtherDerived& other,
const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
{
return abs2(dot(other)) <= prec * prec * norm2() * other.norm2();
}
template<typename Scalar, typename Derived>
bool MatrixBase<Scalar, Derived>::isOrtho
(const typename NumTraits<Scalar>::Real& prec = precision<Scalar>()) const
{
for(int i = 0; i < cols(); i++)
{
if(!isApprox(col(i).norm2(), static_cast<Scalar>(1)))
return false;
for(int j = 0; j < i; j++)
if(!isMuchSmallerThan(col(i).dot(col(j)), static_cast<Scalar>(1)))
return false;
}
return true;
}
#endif // EIGEN_DOT_H
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