20 template<
typename T,
typename U,
22 bool NeedToTranspose = T::IsVectorAtCompileTime
23 && U::IsVectorAtCompileTime
24 && ((int(T::RowsAtCompileTime) == 1 && int(U::ColsAtCompileTime) == 1)
27 (
int(T::ColsAtCompileTime) == 1 && int(U::RowsAtCompileTime) == 1))
31 typedef typename scalar_product_traits<typename traits<T>::Scalar,
typename traits<U>::Scalar>::ReturnType ResScalar;
32 static inline ResScalar run(
const MatrixBase<T>& a,
const MatrixBase<U>& b)
34 return a.template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,
typename traits<U>::Scalar> >(b).sum();
38 template<
typename T,
typename U>
39 struct dot_nocheck<T, U, true>
41 typedef typename scalar_product_traits<typename traits<T>::Scalar,
typename traits<U>::Scalar>::ReturnType ResScalar;
42 static inline ResScalar run(
const MatrixBase<T>& a,
const MatrixBase<U>& b)
44 return a.transpose().template binaryExpr<scalar_conj_product_op<typename traits<T>::Scalar,
typename traits<U>::Scalar> >(b).sum();
60 template<
typename Derived>
61 template<
typename OtherDerived>
62 typename internal::scalar_product_traits<typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar>::ReturnType
65 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
66 EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
67 EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
68 typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
69 EIGEN_CHECK_BINARY_COMPATIBILIY(func,Scalar,
typename OtherDerived::Scalar);
71 eigen_assert(size() == other.size());
73 return internal::dot_nocheck<Derived,OtherDerived>::run(*
this, other);
86 template<
typename Derived>
87 template<
typename OtherDerived>
88 typename internal::traits<Derived>::Scalar
91 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
92 EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
93 EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
94 EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
95 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
97 eigen_assert(size() == other.size());
99 return internal::dot_nocheck<OtherDerived,Derived>::run(other,*this);
112 template<
typename Derived>
124 template<
typename Derived>
127 return internal::sqrt(squaredNorm());
136 template<
typename Derived>
140 typedef typename internal::nested<Derived>::type Nested;
141 typedef typename internal::remove_reference<Nested>::type _Nested;
142 _Nested n(derived());
152 template<
typename Derived>
162 template<
typename Derived,
int p>
163 struct lpNorm_selector
168 return pow(m.
cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
172 template<
typename Derived>
173 struct lpNorm_selector<Derived, 1>
175 static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
const MatrixBase<Derived>& m)
177 return m.cwiseAbs().sum();
181 template<
typename Derived>
182 struct lpNorm_selector<Derived, 2>
184 static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
const MatrixBase<Derived>& m)
190 template<
typename Derived>
191 struct lpNorm_selector<Derived,
Infinity>
193 static inline typename NumTraits<typename traits<Derived>::Scalar>::Real run(
const MatrixBase<Derived>& m)
195 return m.cwiseAbs().maxCoeff();
207 template<
typename Derived>
209 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
212 return internal::lpNorm_selector<Derived, p>::run(*
this);
223 template<
typename Derived>
224 template<
typename OtherDerived>
228 typename internal::nested<Derived,2>::type nested(derived());
229 typename internal::nested<OtherDerived,2>::type otherNested(other.derived());
230 return internal::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
244 template<
typename Derived>
247 typename Derived::Nested nested(derived());
248 for(
Index i = 0; i < cols(); ++i)
250 if(!internal::isApprox(nested.col(i).squaredNorm(),
static_cast<RealScalar
>(1), prec))
252 for(
Index j = 0; j < i; ++j)
253 if(!internal::isMuchSmallerThan(nested.col(i).dot(nested.col(j)), static_cast<Scalar>(1), prec))
261 #endif // EIGEN_DOT_H