35 #ifndef _BLAZE_MATH_EXPRESSIONS_DVECNORMEXPR_H_ 36 #define _BLAZE_MATH_EXPRESSIONS_DVECNORMEXPR_H_ 101 struct DVecNormHelper
105 using ET = ElementType_t<VT>;
108 using CT = RemoveReference_t< CompositeType_t<VT> >;
112 static constexpr
bool value =
113 ( useOptimizedKernels &&
115 If_t< HasSIMDEnabled_v<Abs> && HasSIMDEnabled_v<Power>
116 , And_t< GetSIMDEnabled<Abs,ET>, GetSIMDEnabled<Power,ET> >
117 , And_t< HasLoad<Abs>, HasLoad<Power> > >::value &&
118 HasSIMDAdd_v< ElementType_t<CT>, ElementType_t<CT> > );
148 template<
typename VT
153 inline decltype(
auto) norm_backend( const DenseVector<VT,TF>& dv, Abs
abs, Power power, Root root,
FalseType )
155 using CT = CompositeType_t<VT>;
156 using ET = ElementType_t<VT>;
157 using RT = decltype(
evaluate( root( std::declval<ET>() ) ) );
159 if( (~dv).
size() == 0UL )
return RT();
163 const size_t N( tmp.size() );
165 ET
norm( power(
abs( tmp[0UL] ) ) );
168 for( ; (i+4UL) <= N; i+=4UL ) {
169 norm += power(
abs( tmp[i ] ) ) + power(
abs( tmp[i+1UL] ) ) +
170 power(
abs( tmp[i+2UL] ) ) + power(
abs( tmp[i+3UL] ) );
172 for( ; (i+2UL) <= N; i+=2UL ) {
173 norm += power(
abs( tmp[i] ) ) + power(
abs( tmp[i+1UL] ) );
176 norm += power(
abs( tmp[i] ) );
200 template<
typename VT
205 inline decltype(
auto) norm_backend( const DenseVector<VT,TF>& dv, Abs
abs, Power power, Root root,
TrueType )
207 using CT = CompositeType_t<VT>;
208 using ET = ElementType_t<VT>;
209 using RT = decltype(
evaluate( root( std::declval<ET>() ) ) );
213 if( (~dv).
size() == 0UL )
return RT();
217 const size_t N( tmp.size() );
219 constexpr
bool remainder( !usePadding || !
IsPadded_v< RemoveReference_t<VT> > );
221 const size_t ipos( ( remainder )?( N &
size_t(-SIMDSIZE) ):( N ) );
224 SIMDTrait_t<ET> xmm1, xmm2, xmm3, xmm4;
227 for( ; (i+SIMDSIZE*3UL) < ipos; i+=SIMDSIZE*4UL ) {
228 xmm1 += power(
abs( tmp.load(i ) ) );
229 xmm2 += power(
abs( tmp.load(i+SIMDSIZE ) ) );
230 xmm3 += power(
abs( tmp.load(i+SIMDSIZE*2UL) ) );
231 xmm4 += power(
abs( tmp.load(i+SIMDSIZE*3UL) ) );
233 for( ; (i+SIMDSIZE) < ipos; i+=SIMDSIZE*2UL ) {
234 xmm1 += power(
abs( tmp.load(i ) ) );
235 xmm2 += power(
abs( tmp.load(i+SIMDSIZE) ) );
237 for( ; i<ipos; i+=SIMDSIZE ) {
238 xmm1 += power(
abs( tmp.load(i) ) );
241 ET
norm(
sum( xmm1 + xmm2 + xmm3 + xmm4 ) );
243 for( ; remainder && i<N; ++i ) {
244 norm += power(
abs( tmp[i] ) );
274 template<
typename VT
279 inline decltype(
auto) norm_backend( const DenseVector<VT,TF>& dv, Abs
abs, Power power, Root root )
281 return norm_backend( ~dv,
abs, power, root,
Bool_t< DVecNormHelper<VT,Abs,Power>::value >() );
302 template<
typename VT
328 template<
typename VT
354 template<
typename VT
380 template<
typename VT
406 template<
typename VT
432 template<
typename VT
463 template<
typename VT
474 return norm_backend( ~dv,
Abs(), UnaryPow(
Pow(), p ), UnaryPow(
Pow(),
inv( p ) ) );
506 using Norm =
typename TypeAt< Norms,
min( P-1UL, 4UL ) >::Type;
508 return Norm()( ~dv );
528 template<
typename VT
554 template<
typename VT
575 template<
typename VT
594 template<
typename VT
Header file for the Pow functor.
decltype(auto) sqrNorm(const DenseMatrix< MT, SO > &dm)
Computes the squared L2 norm for the given dense matrix.
Definition: DMatNormExpr.h:495
BoolConstant< false > FalseType
Type/value traits base class.The FalseType class is used as base class for type traits and value trai...
Definition: IntegralConstant.h:121
Header file for the Sqrt functor.
Header file for auxiliary alias declarations.
Headerfile for the generic min algorithm.
#define BLAZE_USER_ASSERT(expr, msg)
Run time assertion macro for user checks.In case of an invalid run time expression,...
Definition: Assert.h:117
Generic wrapper for the cbrt() function.
Definition: Cbrt.h:81
Generic wrapper for the squared abs() function.
Definition: SqrAbs.h:85
Header file for the HasLoad type trait.
Header file for basic type definitions.
decltype(auto) l3Norm(const DenseMatrix< MT, SO > &dm)
Computes the L3 norm for the given dense matrix.
Definition: DMatNormExpr.h:573
Header file for the Pow2 functor.
decltype(auto) l2Norm(const DenseMatrix< MT, SO > &dm)
Computes the L2 norm for the given dense matrix.
Definition: DMatNormExpr.h:547
decltype(auto) l4Norm(const DenseMatrix< MT, SO > &dm)
Computes the L4 norm for the given dense matrix.
Definition: DMatNormExpr.h:599
Header file for the isZero shim.
Header file for the Bind2nd functor.
Header file for the And_t alias template.
Header file for the DenseVector base class.
decltype(auto) lpNorm(const DenseMatrix< MT, SO > &dm, ST p)
Computes the Lp norm for the given dense matrix.
Definition: DMatNormExpr.h:631
Header file for the invert shim.
Generic wrapper for the qdrt() function.
Definition: Qdrt.h:82
BoolConstant< true > TrueType
Type traits base class.The TrueType class is used as base class for type traits and value traits that...
Definition: IntegralConstant.h:132
System settings for performance optimizations.
#define BLAZE_STATIC_ASSERT_MSG(expr, msg)
Compile time assertion macro.In case of an invalid compile time expression, a compilation error is cr...
Definition: StaticAssert.h:123
const MT::ResultType evaluate(const Matrix< MT, SO > &matrix)
Evaluates the given matrix expression.
Definition: Matrix.h:912
Header file for the Cbrt functor.
Header file for the LpNorm functor.
bool isZero(const DiagonalProxy< MT > &proxy)
Returns whether the represented element is 0.
Definition: DiagonalProxy.h:677
Generic wrapper for the abs() function.
Definition: Abs.h:83
Generic wrapper for the sqrt() function.
Definition: Sqrt.h:83
Header file for the multiplication trait.
Namespace of the Blaze C++ math library.
Definition: Blaze.h:58
Header file for the L4Norm functor.
Header file for the If class template.
Header file for the SqrAbs functor.
Header file for the UnderlyingBuiltin type trait.
decltype(auto) l1Norm(const DenseMatrix< MT, SO > &dm)
Computes the L1 norm for the given dense matrix.
Definition: DMatNormExpr.h:521
decltype(auto) min(const DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
Computes the componentwise minimum of the dense matrices lhs and rhs.
Definition: DMatDMatMapExpr.h:1162
decltype(auto) sum(const DenseMatrix< MT, SO > &dm)
Reduces the given dense matrix by means of addition.
Definition: DMatReduceExpr.h:2147
Header file for the HasSIMDAdd type trait.
decltype(auto) inv(const DenseMatrix< MT, SO > &dm)
Calculation of the inverse of the given dense matrix.
Definition: DMatInvExpr.h:423
Header file for all SIMD functionality.
Base class for N-dimensional dense vectors.The DenseVector class is a base class for all arbitrarily ...
Definition: DenseVector.h:76
Header file for the L2Norm functor.
Implementation of a type list.The TypeList class template represents a list of data types of arbitrar...
Definition: TypeList.h:119
Generic wrapper for the null function.
Definition: Noop.h:60
decltype(auto) max(const DenseMatrix< MT1, SO1 > &lhs, const DenseMatrix< MT2, SO2 > &rhs)
Computes the componentwise maximum of the dense matrices lhs and rhs.
Definition: DMatDMatMapExpr.h:1198
IntegralConstant< bool, B > Bool_t
Compile time integral constant wrapper for bool.The Bool_t alias template represents an integral wrap...
Definition: IntegralConstant.h:153
Header file for the Abs functor.
Header file for the IsPadded type trait.
decltype(auto) abs(const DenseMatrix< MT, SO > &dm)
Applies the abs() function to each single element of the dense matrix dm.
Definition: DMatMapExpr.h:1156
decltype(auto) maxNorm(const DenseMatrix< MT, SO > &dm)
Computes the maximum norm for the given dense matrix.
Definition: DMatNormExpr.h:721
typename MultTrait< T1, T2 >::Type MultTrait_t
Auxiliary alias declaration for the MultTrait class template.The MultTrait_t alias declaration provid...
Definition: MultTrait.h:240
Header file for the evaluate shim.
Header file for the IsSIMDEnabled type trait.
Generic wrapper for the pow2() function.
Definition: Pow2.h:78
constexpr bool IsPadded_v
Auxiliary variable template for the IsPadded type trait.The IsPadded_v variable template provides a c...
Definition: IsPadded.h:134
decltype(auto) length(const DenseVector< VT, TF > &dv)
Calculation of the length (magnitude) of the dense vector .
Definition: DVecNormExpr.h:596
Header file for run time assertion macros.
Generic wrapper for the pow() function.
Definition: Pow.h:63
Indexing a type list.The TypeAt class can be used to access a type list at a specified position to qu...
Definition: TypeAt.h:75
Header file for the Unique class template.
#define BLAZE_FUNCTION_TRACE
Function trace macro.This macro can be used to reliably trace function calls. In case function tracin...
Definition: FunctionTrace.h:94
Generic wrapper for a binary operation with fixed 2nd argument.
Definition: Bind2nd.h:65
constexpr size_t size(const Matrix< MT, SO > &matrix) noexcept
Returns the total number of elements of the matrix.
Definition: Matrix.h:530
Header file for the HasMember type traits.
Header file for the Noop functor.
Header file for the RemoveReference type trait.
decltype(auto) norm(const DenseMatrix< MT, SO > &dm)
Computes the L2 norm for the given dense matrix.
Definition: DMatNormExpr.h:469
decltype(auto) linfNorm(const DenseMatrix< MT, SO > &dm)
Computes the infinity norm for the given dense matrix.
Definition: DMatNormExpr.h:695
Generic wrapper for the pow3() function.
Definition: Pow3.h:78
Header file for the L3Norm functor.
Header file for the IntegralConstant class template.
decltype(auto) sqrLength(const DenseVector< VT, TF > &dv)
Calculation of the square length (magnitude) of the dense vector .
Definition: DVecNormExpr.h:577
Header file for the L1Norm functor.
Header file for the Qdrt functor.
#define BLAZE_INTERNAL_ASSERT(expr, msg)
Run time assertion macro for internal checks.In case of an invalid run time expression,...
Definition: Assert.h:101
Header file for the Pow3 functor.
Header file for the function trace functionality.