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 scalar_conj_product_op<typename traits<T>::Scalar,
typename traits<U>::Scalar> conj_prod;
32 typedef typename conj_prod::result_type ResScalar;
35 static ResScalar run(
const MatrixBase<T>& a,
const MatrixBase<U>& b)
37 return a.template binaryExpr<conj_prod>(b).sum();
41 template<
typename T,
typename U>
42 struct dot_nocheck<T, U, true>
44 typedef scalar_conj_product_op<typename traits<T>::Scalar,
typename traits<U>::Scalar> conj_prod;
45 typedef typename conj_prod::result_type ResScalar;
48 static ResScalar run(
const MatrixBase<T>& a,
const MatrixBase<U>& b)
50 return a.transpose().template binaryExpr<conj_prod>(b).sum();
67 template<
typename Derived>
68 template<
typename OtherDerived>
71 typename ScalarBinaryOpTraits<typename internal::traits<Derived>::Scalar,
typename internal::traits<OtherDerived>::Scalar>::ReturnType
74 EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
75 EIGEN_STATIC_ASSERT_VECTOR_ONLY(OtherDerived)
76 EIGEN_STATIC_ASSERT_SAME_VECTOR_SIZE(Derived,OtherDerived)
77 #if !(defined(EIGEN_NO_STATIC_ASSERT) && defined(EIGEN_NO_DEBUG)) 78 typedef internal::scalar_conj_product_op<Scalar,typename OtherDerived::Scalar> func;
79 EIGEN_CHECK_BINARY_COMPATIBILIY(func,
Scalar,
typename OtherDerived::Scalar);
82 eigen_assert(size() == other.
size());
84 return internal::dot_nocheck<Derived,OtherDerived>::run(*
this, other);
95 template<
typename Derived>
98 return numext::real((*this).cwiseAbs2().sum());
107 template<
typename Derived>
110 return numext::sqrt(squaredNorm());
122 template<
typename Derived>
123 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const typename MatrixBase<Derived>::PlainObject
126 typedef typename internal::nested_eval<Derived,2>::type _Nested;
127 _Nested n(derived());
128 RealScalar z = n.squaredNorm();
131 return n / numext::sqrt(z);
144 template<
typename Derived>
147 RealScalar z = squaredNorm();
150 derived() /= numext::sqrt(z);
165 template<
typename Derived>
166 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE
const typename MatrixBase<Derived>::PlainObject
169 typedef typename internal::nested_eval<Derived,3>::type _Nested;
170 _Nested n(derived());
171 RealScalar w = n.cwiseAbs().maxCoeff();
172 RealScalar z = (n/w).squaredNorm();
174 return n / (numext::sqrt(z)*w);
190 template<
typename Derived>
193 RealScalar w = cwiseAbs().maxCoeff();
194 RealScalar z = (derived()/w).squaredNorm();
196 derived() /= numext::sqrt(z)*w;
203 template<
typename Derived,
int p>
204 struct lpNorm_selector
211 return pow(m.
cwiseAbs().array().pow(p).sum(), RealScalar(1)/p);
215 template<
typename Derived>
216 struct lpNorm_selector<Derived, 1>
225 template<
typename Derived>
226 struct lpNorm_selector<Derived, 2>
235 template<
typename Derived>
236 struct lpNorm_selector<Derived, Infinity>
242 if(Derived::SizeAtCompileTime==0 || (Derived::SizeAtCompileTime==
Dynamic && m.
size()==0))
243 return RealScalar(0);
260 template<
typename Derived>
262 #ifndef EIGEN_PARSED_BY_DOXYGEN 265 EIGEN_DEVICE_FUNC MatrixBase<Derived>::RealScalar
269 return internal::lpNorm_selector<Derived, p>::run(*
this);
280 template<
typename Derived>
281 template<
typename OtherDerived>
285 typename internal::nested_eval<Derived,2>::type nested(derived());
286 typename internal::nested_eval<OtherDerived,2>::type otherNested(other.
derived());
287 return numext::abs2(nested.dot(otherNested)) <= prec * prec * nested.squaredNorm() * otherNested.squaredNorm();
301 template<
typename Derived>
304 typename internal::nested_eval<Derived,1>::type
self(derived());
305 for(
Index i = 0; i < cols(); ++i)
307 if(!internal::isApprox(
self.col(i).squaredNorm(), static_cast<RealScalar>(1), prec))
309 for(
Index j = 0; j < i; ++j)
310 if(!internal::isMuchSmallerThan(
self.col(i).dot(
self.col(j)), static_cast<Scalar>(1), prec))
318 #endif // EIGEN_DOT_H internal::traits< Solve< Decomposition, RhsType > >::Scalar Scalar
Definition: DenseBase.h:66
bool isUnitary(const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Dot.h:302
Namespace containing all symbols from the Eigen library.
Definition: Core:141
Holds information about the various numeric (i.e. scalar) types allowed by Eigen. ...
Definition: NumTraits.h:232
const PlainObject normalized() const
Definition: Dot.h:124
Derived & derived()
Definition: EigenBase.h:46
EIGEN_CONSTEXPR Index size() const EIGEN_NOEXCEPT
Definition: EigenBase.h:67
void normalize()
Definition: Dot.h:145
RealScalar norm() const
Definition: Dot.h:108
void stableNormalize()
Definition: Dot.h:191
RealScalar squaredNorm() const
Definition: Dot.h:96
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const PlainObject stableNormalized() const
Definition: Dot.h:167
Definition: Eigen_Colamd.h:50
ScalarBinaryOpTraits< typename internal::traits< Derived >::Scalar, typename internal::traits< OtherDerived >::Scalar >::ReturnType dot(const MatrixBase< OtherDerived > &other) const
Definition: Dot.h:72
RealScalar lpNorm() const
Definition: Dot.h:267
bool isOrthogonal(const MatrixBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Dot.h:283
const int Dynamic
Definition: Constants.h:22
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
const CwiseAbsReturnType cwiseAbs() const
Definition: MatrixBase.h:34