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diff --git a/third_party/eigen3/Eigen/src/Core/StableNorm.h b/third_party/eigen3/Eigen/src/Core/StableNorm.h
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-// 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)
-{
- using std::max;
- 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
- {
- scale = maxCoeff;
- invScale = tmp;
- }
- }
-
- // 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 Derived>
-inline typename NumTraits<typename traits<Derived>::Scalar>::Real
-blueNorm_impl(const EigenBase<Derived>& _vec)
-{
- typedef typename Derived::RealScalar RealScalar;
- typedef typename Derived::Index Index;
- using std::pow;
- using std::sqrt;
- using std::abs;
- const Derived& vec(_vec.derived());
- static bool initialized = false;
- static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
- if(!initialized)
- {
- int ibeta, it, iemin, iemax, iexp;
- RealScalar eps;
- // 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
- ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers
- it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa
- iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent
- iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent
- rbig = (std::numeric_limits<RealScalar>::max)(); // largest floating-point number
-
- iexp = -((1-iemin)/2);
- b1 = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // lower boundary of midrange
- iexp = (iemax + 1 - it)/2;
- b2 = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // upper boundary of midrange
-
- iexp = (2-iemin)/2;
- s1m = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // scaling factor for lower range
- iexp = - ((iemax+it)/2);
- s2m = RealScalar(pow(RealScalar(ibeta),RealScalar(iexp))); // scaling factor for upper range
-
- overfl = rbig*s2m; // overflow boundary for abig
- eps = RealScalar(pow(double(ibeta), 1-it));
- relerr = sqrt(eps); // tolerance for neglecting asml
- initialized = true;
- }
- Index n = vec.size();
- RealScalar ab2 = b2 / RealScalar(n);
- RealScalar asml = RealScalar(0);
- RealScalar amed = RealScalar(0);
- RealScalar abig = RealScalar(0);
- for(typename Derived::InnerIterator it(vec, 0); it; ++it)
- {
- RealScalar ax = abs(it.value());
- if(ax > ab2) abig += numext::abs2(ax*s2m);
- else if(ax < b1) asml += numext::abs2(ax*s1m);
- else amed += numext::abs2(ax);
- }
- if(abig > RealScalar(0))
- {
- abig = sqrt(abig);
- if(abig > overfl)
- {
- return rbig;
- }
- 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
-{
- using std::sqrt;
- const Index blockSize = 4096;
- RealScalar scale(0);
- RealScalar invScale(1);
- RealScalar ssq(0); // sum of square
- enum {
- Alignment = (int(Flags)&DirectAccessBit) || (int(Flags)&AlignedBit) ? 1 : 0
- };
- Index n = size();
- Index bi = internal::first_aligned(derived());
- if (bi>0)
- internal::stable_norm_kernel(this->head(bi), ssq, scale, invScale);
- for (; bi<n; bi+=blockSize)
- internal::stable_norm_kernel(this->segment(bi,numext::mini(blockSize, n - bi)).template forceAlignedAccessIf<Alignment>(), ssq, scale, invScale);
- return scale * sqrt(ssq);
-}
-
-/** \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
-{
- return this->cwiseAbs().redux(internal::scalar_hypot_op<RealScalar>());
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_STABLENORM_H
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