[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2006-2008, 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #ifndef EIGEN_DOT_H
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| 11 | #define EIGEN_DOT_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | namespace internal {
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| 16 |
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| 17 | // helper function for dot(). The problem is that if we put that in the body of dot(), then upon calling dot
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| 18 | // with mismatched types, the compiler emits errors about failing to instantiate cwiseProduct BEFORE
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| 19 | // looking at the static assertions. Thus this is a trick to get better compile errors.
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| 20 | template<typename T, typename U,
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| 21 | // the NeedToTranspose condition here is taken straight from Assign.h
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| 22 | bool NeedToTranspose = T::IsVectorAtCompileTime
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| 23 | && U::IsVectorAtCompileTime
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| 24 | && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
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| 25 | | // FIXME | instead of || to please GCC 4.4.0 stupid warning "suggest parentheses around &&".
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| 26 | // revert to || as soon as not needed anymore.
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| 27 | (int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
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| 28 | >
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| 29 | struct dot_nocheck
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| 30 | {
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| 31 | typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
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| 32 | static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
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| 33 | {
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| 34 | return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
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| 35 | }
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| 36 | };
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| 37 |
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| 38 | template<typename T, typename U>
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| 39 | struct dot_nocheck<T, U, true>
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| 40 | {
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| 41 | typedef typename scalar_product_traits<typename traits<T>::Scalar,typename traits<U>::Scalar>::ReturnType ResScalar;
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| 42 | static inline ResScalar run(const MatrixBase<T>& a, const MatrixBase<U>& b)
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| 43 | {
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| 44 | return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,typename traits<U>::Scalar> >(b).sum();
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| 45 | }
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| 46 | };
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| 47 |
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| 48 | } // end namespace internal
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| 49 |
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| 50 | /** \returns the dot product of *this with other.
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| 51 | *
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| 52 | * \only_for_vectors
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| 53 | *
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| 54 | * \note If the scalar type is complex numbers, then this function returns the hermitian
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| 55 | * (sesquilinear) dot product, conjugate-linear in the first variable and linear in the
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| 56 | * second variable.
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| 57 | *
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| 58 | * \sa squaredNorm(), norm()
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| 59 | */
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| 60 | template<typename Derived>
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| 61 | template<typename OtherDerived>
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| 62 | inline typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,typename internal::traits<OtherDerived>::Scalar>::ReturnType
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| 63 | MatrixBase<Derived>::dot(const MatrixBase<OtherDerived>& other) const
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| 64 | {
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| 65 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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| 66 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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| 67 | EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
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| 68 | typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
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| 69 | EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,typename OtherDerived::Scalar);
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| 70 |
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| 71 | eigen_assert(size() == other.size());
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| 72 |
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| 73 | return internal::dot_nocheck<Derived,OtherDerived>::run(*this, other);
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| 74 | }
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| 75 |
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| 76 | #ifdef EIGEN2_SUPPORT
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| 77 | /** \returns the dot product of *this with other, with the Eigen2 convention that the dot product is linear in the first variable
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| 78 | * (conjugating the second variable). Of course this only makes a difference in the complex case.
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| 79 | *
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| 80 | * This method is only available in EIGEN2_SUPPORT mode.
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| 81 | *
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| 82 | * \only_for_vectors
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| 83 | *
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| 84 | * \sa dot()
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| 85 | */
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| 86 | template<typename Derived>
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| 87 | template<typename OtherDerived>
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| 88 | typename internal::traits<Derived>::Scalar
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| 89 | MatrixBase<Derived>::eigen2_dot(const MatrixBase<OtherDerived>& other) const
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| 90 | {
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| 91 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
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| 92 | EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
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| 93 | EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
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| 94 | EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
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| 95 | YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
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| 96 |
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| 97 | eigen_assert(size() == other.size());
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| 98 |
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| 99 | return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
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| 100 | }
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| 101 | #endif
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| 102 |
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| 103 |
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| 104 | //---------- implementation of L2 norm and related functions ----------
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| 105 |
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| 106 | /** \returns, for vectors, the squared \em l2 norm of \c *this, and for matrices the Frobenius norm.
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| 107 | * In both cases, it consists in the sum of the square of all the matrix entries.
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| 108 | * For vectors, this is also equals to the dot product of \c *this with itself.
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| 109 | *
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| 110 | * \sa dot(), norm()
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| 111 | */
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| 112 | template<typename Derived>
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| 113 | EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::squaredNorm() const
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| 114 | {
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| 115 | return numext::real((*this).cwiseAbs2().sum());
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| 116 | }
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| 117 |
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| 118 | /** \returns, for vectors, the \em l2 norm of \c *this, and for matrices the Frobenius norm.
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| 119 | * In both cases, it consists in the square root of the sum of the square of all the matrix entries.
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| 120 | * For vectors, this is also equals to the square root of the dot product of \c *this with itself.
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| 121 | *
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| 122 | * \sa dot(), squaredNorm()
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| 123 | */
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| 124 | template<typename Derived>
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| 125 | inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
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| 126 | {
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| 127 | using std::sqrt;
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| 128 | return sqrt(squaredNorm());
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| 129 | }
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| 130 |
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| 131 | /** \returns an expression of the quotient of *this by its own norm.
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| 132 | *
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| 133 | * \only_for_vectors
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| 134 | *
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| 135 | * \sa norm(), normalize()
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| 136 | */
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| 137 | template<typename Derived>
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| 138 | inline const typename MatrixBase<Derived>::PlainObject
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| 139 | MatrixBase<Derived>::normalized() const
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| 140 | {
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| 141 | typedef typename internal::nested<Derived>::type Nested;
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| 142 | typedef typename internal::remove_reference<Nested>::type _Nested;
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| 143 | _Nested n(derived());
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| 144 | return n / n.norm();
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| 145 | }
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| 146 |
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| 147 | /** Normalizes the vector, i.e. divides it by its own norm.
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| 148 | *
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| 149 | * \only_for_vectors
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| 150 | *
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| 151 | * \sa norm(), normalized()
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| 152 | */
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| 153 | template<typename Derived>
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| 154 | inline void MatrixBase<Derived>::normalize()
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| 155 | {
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| 156 | *this /= norm();
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| 157 | }
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| 158 |
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| 159 | //---------- implementation of other norms ----------
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| 160 |
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| 161 | namespace internal {
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| 162 |
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| 163 | template<typename Derived, int p>
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| 164 | struct lpNorm_selector
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| 165 | {
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| 166 | typedef typename NumTraits<typename traits<Derived>::Scalar>::Real RealScalar;
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| 167 | static inline RealScalar run(const MatrixBase<Derived>& m)
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| 168 | {
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| 169 | using std::pow;
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| 170 | return pow(m.cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
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| 171 | }
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| 172 | };
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| 173 |
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| 174 | template<typename Derived>
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| 175 | struct lpNorm_selector<Derived, 1>
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| 176 | {
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| 177 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
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| 178 | {
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| 179 | return m.cwiseAbs().sum();
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| 180 | }
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| 181 | };
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| 182 |
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| 183 | template<typename Derived>
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| 184 | struct lpNorm_selector<Derived, 2>
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| 185 | {
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| 186 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
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| 187 | {
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| 188 | return m.norm();
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| 189 | }
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| 190 | };
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| 191 |
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| 192 | template<typename Derived>
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| 193 | struct lpNorm_selector<Derived, Infinity>
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| 194 | {
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| 195 | static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(const MatrixBase<Derived>& m)
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| 196 | {
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| 197 | return m.cwiseAbs().maxCoeff();
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| 198 | }
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| 199 | };
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| 200 |
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| 201 | } // end namespace internal
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| 202 |
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| 203 | /** \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
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| 204 | * of the coefficients of *this. If \a p is the special value \a Eigen::Infinity, this function returns the \f$ \ell^\infty \f$
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| 205 | * norm, that is the maximum of the absolute values of the coefficients of *this.
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| 206 | *
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| 207 | * \sa norm()
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| 208 | */
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| 209 | template<typename Derived>
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| 210 | template<int p>
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| 211 | inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
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| 212 | MatrixBase<Derived>::lpNorm() const
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| 213 | {
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| 214 | return internal::lpNorm_selector<Derived, p>::run(*this);
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| 215 | }
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| 216 |
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| 217 | //---------- implementation of isOrthogonal / isUnitary ----------
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| 218 |
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| 219 | /** \returns true if *this is approximately orthogonal to \a other,
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| 220 | * within the precision given by \a prec.
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| 221 | *
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| 222 | * Example: \include MatrixBase_isOrthogonal.cpp
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| 223 | * Output: \verbinclude MatrixBase_isOrthogonal.out
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| 224 | */
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| 225 | template<typename Derived>
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| 226 | template<typename OtherDerived>
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| 227 | bool MatrixBase<Derived>::isOrthogonal
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| 228 | (const MatrixBase<OtherDerived>& other, const RealScalar& prec) const
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| 229 | {
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| 230 | typename internal::nested<Derived,2>::type nested(derived());
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| 231 | typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
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| 232 | return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
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| 233 | }
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| 234 |
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| 235 | /** \returns true if *this is approximately an unitary matrix,
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| 236 | * within the precision given by \a prec. In the case where the \a Scalar
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| 237 | * type is real numbers, a unitary matrix is an orthogonal matrix, whence the name.
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| 238 | *
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| 239 | * \note This can be used to check whether a family of vectors forms an orthonormal basis.
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| 240 | * Indeed, \c m.isUnitary() returns true if and only if the columns (equivalently, the rows) of m form an
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| 241 | * orthonormal basis.
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| 242 | *
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| 243 | * Example: \include MatrixBase_isUnitary.cpp
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| 244 | * Output: \verbinclude MatrixBase_isUnitary.out
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| 245 | */
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| 246 | template<typename Derived>
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| 247 | bool MatrixBase<Derived>::isUnitary(const RealScalar& prec) const
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| 248 | {
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| 249 | typename Derived::Nested nested(derived());
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| 250 | for(Index i = 0; i < cols(); ++i)
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| 251 | {
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| 252 | if(!internal::isApprox(nested.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
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| 253 | return false;
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| 254 | for(Index j = 0; j < i; ++j)
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| 255 | if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
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| 256 | return false;
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| 257 | }
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| 258 | return true;
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| 259 | }
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| 260 |
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| 261 | } // end namespace Eigen
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| 262 |
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| 263 | #endif // EIGEN_DOT_H
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