cart-elc

StableNorm.h (8700B)

---

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 #ifndef EIGEN_STABLENORM_H
 #define EIGEN_STABLENORM_H
 
 namespace Eigen { 
 
 namespace internal {
 
 template<typename ExpressionType, typename Scalar>
 inline void stable_norm_kernel(const ExpressionType& bl, Scalar& ssq, Scalar& scale, Scalar& invScale)
 {
   Scalar maxCoeff = bl.cwiseAbs().maxCoeff();
   
   if(maxCoeff>scale)
   {
     ssq = ssq * numext::abs2(scale/maxCoeff);
     Scalar tmp = Scalar(1)/maxCoeff;
     if(tmp > NumTraits<Scalar>::highest())
     {
       invScale = NumTraits<Scalar>::highest();
       scale = Scalar(1)/invScale;
     }
     else if(maxCoeff>NumTraits<Scalar>::highest()) // we got a INF
     {
       invScale = Scalar(1);
       scale = maxCoeff;
     }
     else
     {
       scale = maxCoeff;
       invScale = tmp;
     }
   }
   else if(maxCoeff!=maxCoeff) // we got a NaN
   {
     scale = maxCoeff;
   }
   
   // TODO if the maxCoeff is much much smaller than the current scale,
   // then we can neglect this sub vector
   if(scale>Scalar(0)) // if scale==0, then bl is 0 
     ssq += (bl*invScale).squaredNorm();
 }
 
 template<typename VectorType, typename RealScalar>
 void stable_norm_impl_inner_step(const VectorType &vec, RealScalar& ssq, RealScalar& scale, RealScalar& invScale)
 {
   typedef typename VectorType::Scalar Scalar;
   const Index blockSize = 4096;
   
   typedef typename internal::nested_eval<VectorType,2>::type VectorTypeCopy;
   typedef typename internal::remove_all<VectorTypeCopy>::type VectorTypeCopyClean;
   const VectorTypeCopy copy(vec);
   
   enum {
     CanAlign = (   (int(VectorTypeCopyClean::Flags)&DirectAccessBit)
                 || (int(internal::evaluator<VectorTypeCopyClean>::Alignment)>0) // FIXME Alignment)>0 might not be enough
                ) && (blockSize*sizeof(Scalar)*2<EIGEN_STACK_ALLOCATION_LIMIT)
                  && (EIGEN_MAX_STATIC_ALIGN_BYTES>0) // if we cannot allocate on the stack, then let's not bother about this optimization
   };
   typedef typename internal::conditional<CanAlign, Ref<const Matrix<Scalar,Dynamic,1,0,blockSize,1>, internal::evaluator<VectorTypeCopyClean>::Alignment>,
                                                    typename VectorTypeCopyClean::ConstSegmentReturnType>::type SegmentWrapper;
   Index n = vec.size();
   
   Index bi = internal::first_default_aligned(copy);
   if (bi>0)
     internal::stable_norm_kernel(copy.head(bi), ssq, scale, invScale);
   for (; bi<n; bi+=blockSize)
     internal::stable_norm_kernel(SegmentWrapper(copy.segment(bi,numext::mini(blockSize, n - bi))), ssq, scale, invScale);
 }
 
 template<typename VectorType>
 typename VectorType::RealScalar
 stable_norm_impl(const VectorType &vec, typename enable_if<VectorType::IsVectorAtCompileTime>::type* = 0 )
 {
   using std::sqrt;
   using std::abs;
 
   Index n = vec.size();
 
   if(n==1)
     return abs(vec.coeff(0));
 
   typedef typename VectorType::RealScalar RealScalar;
   RealScalar scale(0);
   RealScalar invScale(1);
   RealScalar ssq(0); // sum of squares
 
   stable_norm_impl_inner_step(vec, ssq, scale, invScale);
   
   return scale * sqrt(ssq);
 }
 
 template<typename MatrixType>
 typename MatrixType::RealScalar
 stable_norm_impl(const MatrixType &mat, typename enable_if<!MatrixType::IsVectorAtCompileTime>::type* = 0 )
 {
   using std::sqrt;
 
   typedef typename MatrixType::RealScalar RealScalar;
   RealScalar scale(0);
   RealScalar invScale(1);
   RealScalar ssq(0); // sum of squares
 
   for(Index j=0; j<mat.outerSize(); ++j)
     stable_norm_impl_inner_step(mat.innerVector(j), ssq, scale, invScale);
   return scale * sqrt(ssq);
 }
 
 template<typename Derived>
 inline typename NumTraits<typename traits<Derived>::Scalar>::Real
 blueNorm_impl(const EigenBase<Derived>& _vec)
 {
   typedef typename Derived::RealScalar RealScalar;  
   using std::pow;
   using std::sqrt;
   using std::abs;
 
   // This program calculates the machine-dependent constants
   // bl, b2, slm, s2m, relerr overfl
   // from the "basic" machine-dependent numbers
   // nbig, ibeta, it, iemin, iemax, rbig.
   // The following define the basic machine-dependent constants.
   // For portability, the PORT subprograms "ilmaeh" and "rlmach"
   // are used. For any specific computer, each of the assignment
   // statements can be replaced
   static const int ibeta = std::numeric_limits<RealScalar>::radix;  // base for floating-point numbers
   static const int it    = NumTraits<RealScalar>::digits();  // number of base-beta digits in mantissa
   static const int iemin = NumTraits<RealScalar>::min_exponent();  // minimum exponent
   static const int iemax = NumTraits<RealScalar>::max_exponent();  // maximum exponent
   static const RealScalar rbig   = NumTraits<RealScalar>::highest();  // largest floating-point number
   static const RealScalar b1     = RealScalar(pow(RealScalar(ibeta),RealScalar(-((1-iemin)/2))));  // lower boundary of midrange
   static const RealScalar b2     = RealScalar(pow(RealScalar(ibeta),RealScalar((iemax + 1 - it)/2)));  // upper boundary of midrange
   static const RealScalar s1m    = RealScalar(pow(RealScalar(ibeta),RealScalar((2-iemin)/2)));  // scaling factor for lower range
   static const RealScalar s2m    = RealScalar(pow(RealScalar(ibeta),RealScalar(- ((iemax+it)/2))));  // scaling factor for upper range
   static const RealScalar eps    = RealScalar(pow(double(ibeta), 1-it));
   static const RealScalar relerr = sqrt(eps);  // tolerance for neglecting asml
 
   const Derived& vec(_vec.derived());
   Index n = vec.size();
   RealScalar ab2 = b2 / RealScalar(n);
   RealScalar asml = RealScalar(0);
   RealScalar amed = RealScalar(0);
   RealScalar abig = RealScalar(0);
 
   for(Index j=0; j<vec.outerSize(); ++j)
   {
     for(typename Derived::InnerIterator iter(vec, j); iter; ++iter)
     {
       RealScalar ax = abs(iter.value());
       if(ax > ab2)     abig += numext::abs2(ax*s2m);
       else if(ax < b1) asml += numext::abs2(ax*s1m);
       else             amed += numext::abs2(ax);
     }
   }
   if(amed!=amed)
     return amed;  // we got a NaN
   if(abig > RealScalar(0))
   {
     abig = sqrt(abig);
     if(abig > rbig) // overflow, or *this contains INF values
       return abig;  // return INF
     if(amed > RealScalar(0))
     {
       abig = abig/s2m;
       amed = sqrt(amed);
     }
     else
       return abig/s2m;
   }
   else if(asml > RealScalar(0))
   {
     if (amed > RealScalar(0))
     {
       abig = sqrt(amed);
       amed = sqrt(asml) / s1m;
     }
     else
       return sqrt(asml)/s1m;
   }
   else
     return sqrt(amed);
   asml = numext::mini(abig, amed);
   abig = numext::maxi(abig, amed);
   if(asml <= abig*relerr)
     return abig;
   else
     return abig * sqrt(RealScalar(1) + numext::abs2(asml/abig));
 }
 
 } // end namespace internal
 
 /** \returns the \em l2 norm of \c *this avoiding underflow and overflow.
   * This version use a blockwise two passes algorithm:
   *  1 - find the absolute largest coefficient \c s
   *  2 - compute \f$ s \Vert \frac{*this}{s} \Vert \f$ in a standard way
   *
   * For architecture/scalar types supporting vectorization, this version
   * is faster than blueNorm(). Otherwise the blueNorm() is much faster.
   *
   * \sa norm(), blueNorm(), hypotNorm()
   */
 template<typename Derived>
 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
 MatrixBase<Derived>::stableNorm() const
 {
   return internal::stable_norm_impl(derived());
 }
 
 /** \returns the \em l2 norm of \c *this using the Blue's algorithm.
   * A Portable Fortran Program to Find the Euclidean Norm of a Vector,
   * ACM TOMS, Vol 4, Issue 1, 1978.
   *
   * For architecture/scalar types without vectorization, this version
   * is much faster than stableNorm(). Otherwise the stableNorm() is faster.
   *
   * \sa norm(), stableNorm(), hypotNorm()
   */
 template<typename Derived>
 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
 MatrixBase<Derived>::blueNorm() const
 {
   return internal::blueNorm_impl(*this);
 }
 
 /** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.
   * This version use a concatenation of hypot() calls, and it is very slow.
   *
   * \sa norm(), stableNorm()
   */
 template<typename Derived>
 inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
 MatrixBase<Derived>::hypotNorm() const
 {
   if(size()==1)
     return numext::abs(coeff(0,0));
   else
     return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
 }
 
 } // end namespace Eigen
 
 #endif // EIGEN_STABLENORM_H