math/expressions/DVecNormExpr.h

//=================================================================================================
/*!
//  \file blaze/math/expressions/DVecNormExpr.h
//  \brief Header file for the dense vector norm expression
//
//  Copyright (C) 2012-2020 Klaus Iglberger - All Rights Reserved
//
//  This file is part of the Blaze library. You can redistribute it and/or modify it under
//  the terms of the New (Revised) BSD License. Redistribution and use in source and binary
//  forms, with or without modification, are permitted provided that the following conditions
//  are met:
//
//  1. Redistributions of source code must retain the above copyright notice, this list of
//     conditions and the following disclaimer.
//  2. Redistributions in binary form must reproduce the above copyright notice, this list
//     of conditions and the following disclaimer in the documentation and/or other materials
//     provided with the distribution.
//  3. Neither the names of the Blaze development group nor the names of its contributors
//     may be used to endorse or promote products derived from this software without specific
//     prior written permission.
//
//  THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
//  EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
//  OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
//  SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
//  INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED
//  TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
//  BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
//  CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
//  ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH
//  DAMAGE.
*/
//=================================================================================================

#ifndef _BLAZE_MATH_EXPRESSIONS_DVECNORMEXPR_H_
#define _BLAZE_MATH_EXPRESSIONS_DVECNORMEXPR_H_


//*************************************************************************************************
// Includes
//*************************************************************************************************

#include <utility>
#include <blaze/math/Aliases.h>
#include <blaze/math/expressions/DenseVector.h>
#include <blaze/math/functors/Abs.h>
#include <blaze/math/functors/Bind2nd.h>
#include <blaze/math/functors/Cbrt.h>
#include <blaze/math/functors/L1Norm.h>
#include <blaze/math/functors/L2Norm.h>
#include <blaze/math/functors/L3Norm.h>
#include <blaze/math/functors/L4Norm.h>
#include <blaze/math/functors/LpNorm.h>
#include <blaze/math/functors/Noop.h>
#include <blaze/math/functors/Pow.h>
#include <blaze/math/functors/Pow2.h>
#include <blaze/math/functors/Pow3.h>
#include <blaze/math/functors/Qdrt.h>
#include <blaze/math/functors/SqrAbs.h>
#include <blaze/math/functors/Sqrt.h>
#include <blaze/math/shims/Evaluate.h>
#include <blaze/math/shims/Invert.h>
#include <blaze/math/shims/IsZero.h>
#include <blaze/math/shims/PrevMultiple.h>
#include <blaze/math/SIMD.h>
#include <blaze/math/traits/MultTrait.h>
#include <blaze/math/typetraits/HasLoad.h>
#include <blaze/math/typetraits/HasSIMDAdd.h>
#include <blaze/math/typetraits/IsPadded.h>
#include <blaze/math/typetraits/IsSIMDEnabled.h>
#include <blaze/math/typetraits/UnderlyingBuiltin.h>
#include <blaze/system/Optimizations.h>
#include <blaze/util/algorithms/Min.h>
#include <blaze/util/Assert.h>
#include <blaze/util/FunctionTrace.h>
#include <blaze/util/IntegralConstant.h>
#include <blaze/util/mpl/And.h>
#include <blaze/util/mpl/If.h>
#include <blaze/util/StaticAssert.h>
#include <blaze/util/TypeList.h>
#include <blaze/util/Types.h>
#include <blaze/util/typetraits/HasMember.h>
#include <blaze/util/typetraits/RemoveCVRef.h>
#include <blaze/util/typetraits/RemoveReference.h>


namespace blaze {

//=================================================================================================
//
//  CLASS DEFINITION
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Auxiliary helper struct for the dense vector norms.
// \ingroup dense_vector
*/
template< typename VT       // Type of the dense vector
        , typename Abs      // Type of the abs operation
        , typename Power >  // Type of the power operation
struct DVecNormHelper
{
   //**Type definitions****************************************************************************
   //! Element type of the dense vector expression.
   using ET = ElementType_t<VT>;

   //! Composite type of the dense vector expression.
   using CT = RemoveReference_t< CompositeType_t<VT> >;
   //**********************************************************************************************

   //**********************************************************************************************
   static constexpr bool value =
      ( useOptimizedKernels &&
        CT::simdEnabled &&
        If_t< HasSIMDEnabled_v<Abs> && HasSIMDEnabled_v<Power>
            , And_t< GetSIMDEnabled<Abs,ET>, GetSIMDEnabled<Power,ET> >
            , And_t< HasLoad<Abs>, HasLoad<Power> > >::value &&
        HasSIMDAdd_v< ElementType_t<CT>, ElementType_t<CT> > );
   //**********************************************************************************************
};
/*! \endcond */
//*************************************************************************************************


//=================================================================================================
//
//  GLOBAL FUNCTIONS
//
//=================================================================================================

//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Default backend implementation of the norm of a dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \param abs The functor for the abs operation.
// \param power The functor for the power operation.
// \param root The functor for the root operation.
// \return The norm of the given vector.
//
// This function implements the performance optimized norm of a dense vector. Due to the
// explicit application of the SFINAE principle, this function can only be selected by the
// compiler in case vectorization cannot be applied.
*/
template< typename VT      // Type of the dense vector
        , bool TF          // Transpose flag
        , typename Abs     // Type of the abs operation
        , typename Power   // Type of the power operation
        , typename Root >  // Type of the root operation
inline decltype(auto) norm_backend( const DenseVector<VT,TF>& dv, Abs abs, Power power, Root root, FalseType )
{
   using CT = CompositeType_t<VT>;
   using ET = ElementType_t<VT>;
   using PT = RemoveCVRef_t< decltype( power( abs( std::declval<ET>() ) ) ) >;
   using RT = RemoveCVRef_t< decltype( evaluate( root( std::declval<PT>() ) ) ) >;

   if( (*dv).size() == 0UL ) return RT{};

   CT tmp( *dv );

   const size_t N( tmp.size() );

   PT norm( power( abs( tmp[0UL] ) ) );
   size_t i( 1UL );

   for( ; (i+4UL) <= N; i+=4UL ) {
      norm += power( abs( tmp[i    ] ) ) + power( abs( tmp[i+1UL] ) ) +
              power( abs( tmp[i+2UL] ) ) + power( abs( tmp[i+3UL] ) );
   }
   for( ; (i+2UL) <= N; i+=2UL ) {
      norm += power( abs( tmp[i] ) ) + power( abs( tmp[i+1UL] ) );
   }
   for( ; i<N; ++i ) {
      norm += power( abs( tmp[i] ) );
   }

   return evaluate( root( norm ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief SIMD optimized backend implementation of the norm of a dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \param abs The functor for the abs operation.
// \param power The functor for the power operation.
// \param root The functor for the root operation.
// \return The norm of the given vector.
//
// This function implements the performance optimized norm of a dense vector. Due to the
// explicit application of the SFINAE principle, this function can only be selected by the
// compiler in case vectorization can be applied.
*/
template< typename VT      // Type of the dense vector
        , bool TF          // Transpose flag
        , typename Abs     // Type of the abs operation
        , typename Power   // Type of the power operation
        , typename Root >  // Type of the root operation
inline decltype(auto) norm_backend( const DenseVector<VT,TF>& dv, Abs abs, Power power, Root root, TrueType )
{
   using CT = CompositeType_t<VT>;
   using ET = ElementType_t<VT>;
   using RT = decltype( evaluate( root( std::declval<ET>() ) ) );

   static constexpr size_t SIMDSIZE = SIMDTrait<ET>::size;

   if( (*dv).size() == 0UL ) return RT{};

   CT tmp( *dv );

   const size_t N( tmp.size() );

   constexpr bool remainder( !IsPadded_v< RemoveReference_t<VT> > );

   const size_t ipos( remainder ? prevMultiple( N, SIMDSIZE ) : N );
   BLAZE_INTERNAL_ASSERT( ipos <= N, "Invalid end calculation" );

   size_t i( 0UL );
   ET norm{};

   if( SIMDSIZE*3UL < ipos )
   {
      SIMDTrait_t<ET> xmm1{}, xmm2{}, xmm3{}, xmm4{};

      for( ; (i+SIMDSIZE*3UL) < ipos; i+=SIMDSIZE*4UL ) {
         xmm1 += power( abs( tmp.load(i             ) ) );
         xmm2 += power( abs( tmp.load(i+SIMDSIZE    ) ) );
         xmm3 += power( abs( tmp.load(i+SIMDSIZE*2UL) ) );
         xmm4 += power( abs( tmp.load(i+SIMDSIZE*3UL) ) );
      }
      for( ; (i+SIMDSIZE) < ipos; i+=SIMDSIZE*2UL ) {
         xmm1 += power( abs( tmp.load(i         ) ) );
         xmm2 += power( abs( tmp.load(i+SIMDSIZE) ) );
      }
      for( ; i<ipos; i+=SIMDSIZE ) {
         xmm1 += power( abs( tmp.load(i) ) );
      }

      norm = sum( xmm1 + xmm2 + xmm3 + xmm4 );
   }
   else if( SIMDSIZE < ipos )
   {
      SIMDTrait_t<ET> xmm1{}, xmm2{};

      for( ; (i+SIMDSIZE) < ipos; i+=SIMDSIZE*2UL ) {
         xmm1 += power( abs( tmp.load(i         ) ) );
         xmm2 += power( abs( tmp.load(i+SIMDSIZE) ) );
      }
      for( ; i<ipos; i+=SIMDSIZE ) {
         xmm1 += power( abs( tmp.load(i) ) );
      }

      norm = sum( xmm1 + xmm2 );
   }
   else
   {
      SIMDTrait_t<ET> xmm1{};

      for( ; i<ipos; i+=SIMDSIZE ) {
         xmm1 += power( abs( tmp.load(i) ) );
      }

      norm = sum( xmm1 );
   }

   for( ; remainder && i<N; ++i ) {
      norm += power( abs( tmp[i] ) );
   }

   return evaluate( root( norm ) );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*! \cond BLAZE_INTERNAL */
/*!\brief Computes a custom norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \param abs The functor for the abs operation.
// \param power The functor for the power operation.
// \param root The functor for the root operation.
// \return The norm of the given dense vector.
//
// This function computes a custom norm of the given dense vector by means of the given functors.
// The following example demonstrates the computation of the L2 norm by means of the blaze::Noop,
// blaze::Pow2 and blaze::Sqrt functors:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l2 = norm( a, blaze::Noop(), blaze::Pow2(), blaze::Sqrt() );
   \endcode
*/
template< typename VT      // Type of the dense vector
        , bool TF          // Transpose flag
        , typename Abs     // Type of the abs operation
        , typename Power   // Type of the power operation
        , typename Root >  // Type of the root operation
inline decltype(auto) norm_backend( const DenseVector<VT,TF>& dv, Abs abs, Power power, Root root )
{
   return norm_backend( *dv, abs, power, root, Bool_t< DVecNormHelper<VT,Abs,Power>::value >() );
}
/*! \endcond */
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the L2 norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The L2 norm of the given dense vector.
//
// This function computes the L2 norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l2 = norm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) norm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return norm_backend( *dv, SqrAbs(), Noop(), Sqrt() );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the squared L2 norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The squared L2 norm of the given dense vector.
//
// This function computes the squared L2 norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l2 = sqrNorm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) sqrNorm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return norm_backend( *dv, SqrAbs(), Noop(), Noop() );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the L1 norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The L1 norm of the given dense vector.
//
// This function computes the L1 norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l1 = l1Norm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) l1Norm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return norm_backend( *dv, Abs(), Noop(), Noop() );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the L2 norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The L2 norm of the given dense vector.
//
// This function computes the L2 norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l2 = l2Norm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) l2Norm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return norm_backend( *dv, SqrAbs(), Noop(), Sqrt() );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the L3 norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The L3 norm of the given dense vector.
//
// This function computes the L3 norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l3 = l3Norm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) l3Norm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return norm_backend( *dv, Abs(), Pow3(), Cbrt() );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the L4 norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The L4 norm of the given dense vector.
//
// This function computes the L4 norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double l4 = l4Norm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) l4Norm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return norm_backend( *dv, SqrAbs(), Pow2(), Qdrt() );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the Lp norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \param p The norm parameter (p > 0).
// \return The Lp norm of the given dense vector.
//
// This function computes the Lp norm of the given dense vector, where the norm is specified by
// the runtime argument \a p:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double lp = lpNorm( a, 2.3 );
   \endcode

// \note The norm parameter \a p is expected to be larger than 0. This precondition is only checked
// by a user assertion.
*/
template< typename VT    // Type of the dense vector
        , bool TF        // Transpose flag
        , typename ST >  // Type of the norm parameter
inline decltype(auto) lpNorm( const DenseVector<VT,TF>& dv, ST p )
{
   BLAZE_FUNCTION_TRACE;

   BLAZE_USER_ASSERT( !isZero( p ), "Invalid p for Lp norm detected" );

   using ScalarType = MultTrait_t< UnderlyingBuiltin_t<VT>, decltype( inv( p ) ) >;
   using UnaryPow = Bind2nd<Pow,ScalarType>;
   return norm_backend( *dv, Abs(), UnaryPow( Pow(), p ), UnaryPow( Pow(), inv( p ) ) );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the Lp norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The Lp norm of the given dense vector.
//
// This function computes the Lp norm of the given dense vector, where the norm is specified by
// the runtime argument \a P:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double lp = lpNorm<2>( a );
   \endcode

// \note The norm parameter \a P is expected to be larger than 0. A value of 0 results in a
// compile time error!.
*/
template< size_t P     // Compile time norm parameter
        , typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) lpNorm( const DenseVector<VT,TF>& dv )
{
   BLAZE_STATIC_ASSERT_MSG( P > 0UL, "Invalid norm parameter detected" );

   using Norms = TypeList< L1Norm, L2Norm, L3Norm, L4Norm, LpNorm<P> >;
   using Norm  = typename TypeAt< Norms, min( P-1UL, 4UL ) >::Type;

   return Norm()( *dv );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the infinity norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The infinity norm of the given dense vector.
//
// This function computes the infinity norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double linf = linfNorm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) linfNorm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return max( abs( *dv ) );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Computes the maximum norm for the given dense vector.
// \ingroup dense_vector
//
// \param dv The given dense vector for the norm computation.
// \return The maximum norm of the given dense vector.
//
// This function computes the maximum norm of the given dense vector:

   \code
   blaze::DynamicVector<double> a;
   // ... Resizing and initialization
   const double max = maxNorm( a );
   \endcode
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) maxNorm( const DenseVector<VT,TF>& dv )
{
   BLAZE_FUNCTION_TRACE;

   return linfNorm( *dv );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Calculation of the square length (magnitude) of the dense vector \f$|\vec{a}|^2\f$.
// \ingroup dense_vector
//
// \param dv The given dense vector.
// \return The square length (magnitude) of the dense vector.
//
// This function calculates the actual square length (magnitude) of the dense vector. The
// function has the same effect as calling the \a sqrNorm() function on the dense vector.
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) sqrLength( const DenseVector<VT,TF>& dv )
{
   return sqrNorm( *dv );
}
//*************************************************************************************************


//*************************************************************************************************
/*!\brief Calculation of the length (magnitude) of the dense vector \f$|\vec{a}|\f$.
// \ingroup dense_vector
//
// \param dv The given dense vector.
// \return The length (magnitude) of the dense vector.
//
// This function calculates the actual length (magnitude) of the dense vector. The function has
// the same effect as calling the \a norm() function on the dense vector.
*/
template< typename VT  // Type of the dense vector
        , bool TF >    // Transpose flag
inline decltype(auto) length( const DenseVector<VT,TF>& dv )
{
   return norm( *dv );
}
//*************************************************************************************************

} // namespace blaze

#endif