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Fix bug #314:

Browse Source 
- remove most of the metaprogramming kung fu in MathFunctions.h (only keep functions that differs from the std)
- remove the overloads for array expression that were in the std namespace
This commit is contained in:
Gael Guennebaud 2012-11-06 15:25:50 +01:00
parent 959ef37006
commit a76fbbf397
88 changed files with 496 additions and 468 deletions
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1
Eigen/src/Cholesky/LDLT.h
View File

@ -248,6 +248,7 @@ template<> struct ldlt_inplace<Lower>
template<typename MatrixType, typename TranspositionType, typename Workspace>
static bool unblocked(MatrixType& mat, TranspositionType& transpositions, Workspace& temp, int* sign=0)
{
using std::abs;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;

2
Eigen/src/Cholesky/LLT.h
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@ -190,6 +190,7 @@ template<typename Scalar, int UpLo> struct llt_inplace;
template<typename MatrixType, typename VectorType>
static typename MatrixType::Index llt_rank_update_lower(MatrixType& mat, const VectorType& vec, const typename MatrixType::RealScalar& sigma)
{
using std::sqrt;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
typedef typename MatrixType::Index Index;
@ -263,6 +264,7 @@ template<typename Scalar> struct llt_inplace<Scalar, Lower>
template<typename MatrixType>
static typename MatrixType::Index unblocked(MatrixType& mat)
{
using std::sqrt;
typedef typename MatrixType::Index Index;
eigen_assert(mat.rows()==mat.cols());

3
Eigen/src/Core/DiagonalMatrix.h
View File

@ -286,11 +286,12 @@ MatrixBase<Derived>::asDiagonal() const
template<typename Derived>
bool MatrixBase<Derived>::isDiagonal(const RealScalar& prec) const
{
using std::abs;
if(cols() != rows()) return false;
RealScalar maxAbsOnDiagonal = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
{
RealScalar absOnDiagonal = internal::abs(coeff(j,j));
RealScalar absOnDiagonal = abs(coeff(j,j));
if(absOnDiagonal > maxAbsOnDiagonal) maxAbsOnDiagonal = absOnDiagonal;
}
for(Index j = 0; j < cols(); ++j)

3
Eigen/src/Core/Dot.h
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@ -124,7 +124,8 @@ EIGEN_STRONG_INLINE typename NumTraits<typename internal::traits<Derived>::Scala
template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real MatrixBase<Derived>::norm() const
{
return internal::sqrt(squaredNorm());
using std::sqrt;
return sqrt(squaredNorm());
}
/** \returns an expression of the quotient of *this by its own norm.

20
Eigen/src/Core/Functors.h
View File

@ -287,7 +287,7 @@ struct functor_traits<scalar_opposite_op<Scalar> >
template<typename Scalar> struct scalar_abs_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_abs_op)
typedef typename NumTraits<Scalar>::Real result_type;
EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { return internal::abs(a); }
EIGEN_STRONG_INLINE const result_type operator() (const Scalar& a) const { using std::abs; return abs(a); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const
{ return internal::pabs(a); }
@ -325,7 +325,7 @@ struct functor_traits<scalar_abs2_op<Scalar> >
*/
template<typename Scalar> struct scalar_conjugate_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_conjugate_op)
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { return internal::conj(a); }
EIGEN_STRONG_INLINE const Scalar operator() (const Scalar& a) const { using internal::conj; return conj(a); }
template<typename Packet>
EIGEN_STRONG_INLINE const Packet packetOp(const Packet& a) const { return internal::pconj(a); }
};
@ -421,7 +421,7 @@ struct functor_traits<scalar_imag_ref_op<Scalar> >
*/
template<typename Scalar> struct scalar_exp_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_exp_op)
inline const Scalar operator() (const Scalar& a) const { return internal::exp(a); }
inline const Scalar operator() (const Scalar& a) const { using std::exp; return exp(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pexp(a); }
};
@ -437,7 +437,7 @@ struct functor_traits<scalar_exp_op<Scalar> >
*/
template<typename Scalar> struct scalar_log_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_log_op)
inline const Scalar operator() (const Scalar& a) const { return internal::log(a); }
inline const Scalar operator() (const Scalar& a) const { using std::log; return log(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::plog(a); }
};
@ -674,7 +674,7 @@ struct functor_traits<scalar_add_op<Scalar> >
*/
template<typename Scalar> struct scalar_sqrt_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_sqrt_op)
inline const Scalar operator() (const Scalar& a) const { return internal::sqrt(a); }
inline const Scalar operator() (const Scalar& a) const { using std::sqrt; return sqrt(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::psqrt(a); }
};
@ -692,7 +692,7 @@ struct functor_traits<scalar_sqrt_op<Scalar> >
*/
template<typename Scalar> struct scalar_cos_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_cos_op)
inline Scalar operator() (const Scalar& a) const { return internal::cos(a); }
inline Scalar operator() (const Scalar& a) const { using std::cos; return cos(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pcos(a); }
};
@ -711,7 +711,7 @@ struct functor_traits<scalar_cos_op<Scalar> >
*/
template<typename Scalar> struct scalar_sin_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_sin_op)
inline const Scalar operator() (const Scalar& a) const { return internal::sin(a); }
inline const Scalar operator() (const Scalar& a) const { using std::sin; return sin(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::psin(a); }
};
@ -731,7 +731,7 @@ struct functor_traits<scalar_sin_op<Scalar> >
*/
template<typename Scalar> struct scalar_tan_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_tan_op)
inline const Scalar operator() (const Scalar& a) const { return internal::tan(a); }
inline const Scalar operator() (const Scalar& a) const { using std::tan; return tan(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::ptan(a); }
};
@ -750,7 +750,7 @@ struct functor_traits<scalar_tan_op<Scalar> >
*/
template<typename Scalar> struct scalar_acos_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_acos_op)
inline const Scalar operator() (const Scalar& a) const { return internal::acos(a); }
inline const Scalar operator() (const Scalar& a) const { using std::acos; return acos(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pacos(a); }
};
@ -769,7 +769,7 @@ struct functor_traits<scalar_acos_op<Scalar> >
*/
template<typename Scalar> struct scalar_asin_op {
EIGEN_EMPTY_STRUCT_CTOR(scalar_asin_op)
inline const Scalar operator() (const Scalar& a) const { return internal::asin(a); }
inline const Scalar operator() (const Scalar& a) const { using std::asin; return asin(a); }
typedef typename packet_traits<Scalar>::type Packet;
inline Packet packetOp(const Packet& a) const { return internal::pasin(a); }
};

25
Eigen/src/Core/GenericPacketMath.h
View File

@ -130,7 +130,7 @@ pmax(const Packet& a,
/** \internal \returns the absolute value of \a a */
template<typename Packet> inline Packet
pabs(const Packet& a) { return abs(a); }
pabs(const Packet& a) { using std::abs; return abs(a); }
/** \internal \returns the bitwise and of \a a and \a b */
template<typename Packet> inline Packet
@ -215,7 +215,12 @@ template<typename Packet> inline Packet preverse(const Packet& a)
/** \internal \returns \a a with real and imaginary part flipped (for complex type only) */
template<typename Packet> inline Packet pcplxflip(const Packet& a)
{ return Packet(imag(a),real(a)); }
{
// FIXME: uncomment the following in case we drop the internal imag and real functions.
// using std::imag;
// using std::real;
return Packet(imag(a),real(a));
}
/**************************
* Special math functions
@ -223,35 +228,35 @@ template<typename Packet> inline Packet pcplxflip(const Packet& a)
/** \internal \returns the sine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet psin(const Packet& a) { return sin(a); }
Packet psin(const Packet& a) { using std::sin; return sin(a); }
/** \internal \returns the cosine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pcos(const Packet& a) { return cos(a); }
Packet pcos(const Packet& a) { using std::cos; return cos(a); }
/** \internal \returns the tan of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet ptan(const Packet& a) { return tan(a); }
Packet ptan(const Packet& a) { using std::tan; return tan(a); }
/** \internal \returns the arc sine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pasin(const Packet& a) { return asin(a); }
Packet pasin(const Packet& a) { using std::asin; return asin(a); }
/** \internal \returns the arc cosine of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pacos(const Packet& a) { return acos(a); }
Packet pacos(const Packet& a) { using std::acos; return acos(a); }
/** \internal \returns the exp of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet pexp(const Packet& a) { return exp(a); }
Packet pexp(const Packet& a) { using std::exp; return exp(a); }
/** \internal \returns the log of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet plog(const Packet& a) { return log(a); }
Packet plog(const Packet& a) { using std::log; return log(a); }
/** \internal \returns the square-root of \a a (coeff-wise) */
template<typename Packet> EIGEN_DECLARE_FUNCTION_ALLOWING_MULTIPLE_DEFINITIONS
Packet psqrt(const Packet& a) { return sqrt(a); }
Packet psqrt(const Packet& a) { using std::sqrt; return sqrt(a); }
/***************************************************************************
* The following functions might not have to be overwritten for vectorized types

44
Eigen/src/Core/GlobalFunctions.h
View File

@ -1,7 +1,7 @@
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010-2012 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
@ -11,7 +11,7 @@
#ifndef EIGEN_GLOBAL_FUNCTIONS_H
#define EIGEN_GLOBAL_FUNCTIONS_H
#define EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(NAME,FUNCTOR) \
#define EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(NAME,FUNCTOR) \
template<typename Derived> \
inline const Eigen::CwiseUnaryOp<Eigen::internal::FUNCTOR<typename Derived::Scalar>, const Derived> \
NAME(const Eigen::ArrayBase<Derived>& x) { \
@ -35,20 +35,20 @@
};
namespace std
namespace Eigen
{
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(real,scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(imag,scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(sin,scalar_sin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(cos,scalar_cos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(asin,scalar_asin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(acos,scalar_acos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(tan,scalar_tan_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(exp,scalar_exp_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(log,scalar_log_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(abs,scalar_abs_op)
EIGEN_ARRAY_DECLARE_GLOBAL_STD_UNARY(sqrt,scalar_sqrt_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(real,scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(imag,scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sin,scalar_sin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(cos,scalar_cos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(asin,scalar_asin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(acos,scalar_acos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(tan,scalar_tan_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(exp,scalar_exp_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(log,scalar_log_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(abs,scalar_abs_op)
EIGEN_ARRAY_DECLARE_GLOBAL_UNARY(sqrt,scalar_sqrt_op)
template<typename Derived>
inline const Eigen::CwiseUnaryOp<Eigen::internal::scalar_pow_op<typename Derived::Scalar>, const Derived>
pow(const Eigen::ArrayBase<Derived>& x, const typename Derived::Scalar& exponent) {
@ -64,10 +64,7 @@ namespace std
exponents.derived()
);
}
}
namespace Eigen
{
/**
* \brief Component-wise division of a scalar by array elements.
**/
@ -85,16 +82,7 @@ namespace Eigen
{
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(real,scalar_real_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(imag,scalar_imag_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(sin,scalar_sin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(cos,scalar_cos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(asin,scalar_asin_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(acos,scalar_acos_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(tan,scalar_tan_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(exp,scalar_exp_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(log,scalar_log_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs,scalar_abs_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(abs2,scalar_abs2_op)
EIGEN_ARRAY_DECLARE_GLOBAL_EIGEN_UNARY(sqrt,scalar_sqrt_op)
}
}

147
Eigen/src/Core/MathFunctions.h
View File

@ -250,33 +250,6 @@ inline EIGEN_MATHFUNC_RETVAL(conj, Scalar) conj(const Scalar& x)
return EIGEN_MATHFUNC_IMPL(conj, Scalar)::run(x);
}
/****************************************************************************
* Implementation of abs *
****************************************************************************/
template<typename Scalar>
struct abs_impl
{
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x)
{
using std::abs;
return abs(x);
}
};
template<typename Scalar>
struct abs_retval
{
typedef typename NumTraits<Scalar>::Real type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(abs, Scalar) abs(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(abs, Scalar)::run(x);
}
/****************************************************************************
* Implementation of abs2 *
****************************************************************************/
@ -322,6 +295,7 @@ struct norm1_default_impl
typedef typename NumTraits<Scalar>::Real RealScalar;
static inline RealScalar run(const Scalar& x)
{
using std::abs;
return abs(real(x)) + abs(imag(x));
}
};
@ -331,6 +305,7 @@ struct norm1_default_impl<Scalar, false>
{
static inline Scalar run(const Scalar& x)
{
using std::abs;
return abs(x);
}
};
@ -362,6 +337,7 @@ struct hypot_impl
{
using std::max;
using std::min;
using std::abs;
RealScalar _x = abs(x);
RealScalar _y = abs(y);
RealScalar p = (max)(_x, _y);
@ -404,121 +380,6 @@ inline NewType cast(const OldType& x)
return cast_impl<OldType, NewType>::run(x);
}
/****************************************************************************
* Implementation of sqrt *
****************************************************************************/
template<typename Scalar, bool IsInteger>
struct sqrt_default_impl
{
static inline Scalar run(const Scalar& x)
{
using std::sqrt;
return sqrt(x);
}
};
template<typename Scalar>
struct sqrt_default_impl<Scalar, true>
{
static inline Scalar run(const Scalar&)
{
#ifdef EIGEN2_SUPPORT
eigen_assert(!NumTraits<Scalar>::IsInteger);
#else
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
#endif
return Scalar(0);
}
};
template<typename Scalar>
struct sqrt_impl : sqrt_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct sqrt_retval
{
typedef Scalar type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(sqrt, Scalar) sqrt(const Scalar& x)
{
return EIGEN_MATHFUNC_IMPL(sqrt, Scalar)::run(x);
}
/****************************************************************************
* Implementation of standard unary real functions (exp, log, sin, cos, ... *
****************************************************************************/
// This macro instanciate all the necessary template mechanism which is common to all unary real functions.
#define EIGEN_MATHFUNC_STANDARD_REAL_UNARY(NAME) \
template<typename Scalar, bool IsInteger> struct NAME##_default_impl { \
static inline Scalar run(const Scalar& x) { using std::NAME; return NAME(x); } \
}; \
template<typename Scalar> struct NAME##_default_impl<Scalar, true> { \
static inline Scalar run(const Scalar&) { \
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar) \
return Scalar(0); \
} \
}; \
template<typename Scalar> struct NAME##_impl \
: NAME##_default_impl<Scalar, NumTraits<Scalar>::IsInteger> \
{}; \
template<typename Scalar> struct NAME##_retval { typedef Scalar type; }; \
template<typename Scalar> \
inline EIGEN_MATHFUNC_RETVAL(NAME, Scalar) NAME(const Scalar& x) { \
return EIGEN_MATHFUNC_IMPL(NAME, Scalar)::run(x); \
}
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(exp)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(log)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(sin)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(cos)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(tan)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(asin)
EIGEN_MATHFUNC_STANDARD_REAL_UNARY(acos)
/****************************************************************************
* Implementation of atan2 *
****************************************************************************/
template<typename Scalar, bool IsInteger>
struct atan2_default_impl
{
typedef Scalar retval;
static inline Scalar run(const Scalar& x, const Scalar& y)
{
using std::atan2;
return atan2(x, y);
}
};
template<typename Scalar>
struct atan2_default_impl<Scalar, true>
{
static inline Scalar run(const Scalar&, const Scalar&)
{
EIGEN_STATIC_ASSERT_NON_INTEGER(Scalar)
return Scalar(0);
}
};
template<typename Scalar>
struct atan2_impl : atan2_default_impl<Scalar, NumTraits<Scalar>::IsInteger> {};
template<typename Scalar>
struct atan2_retval
{
typedef Scalar type;
};
template<typename Scalar>
inline EIGEN_MATHFUNC_RETVAL(atan2, Scalar) atan2(const Scalar& x, const Scalar& y)
{
return EIGEN_MATHFUNC_IMPL(atan2, Scalar)::run(x, y);
}
/****************************************************************************
* Implementation of atanh2 *
****************************************************************************/
@ -765,11 +626,13 @@ struct scalar_fuzzy_default_impl<Scalar, false, false>
template<typename OtherScalar>
static inline bool isMuchSmallerThan(const Scalar& x, const OtherScalar& y, const RealScalar& prec)
{
using std::abs;
return abs(x) <= abs(y) * prec;
}
static inline bool isApprox(const Scalar& x, const Scalar& y, const RealScalar& prec)
{
using std::min;
using std::abs;
return abs(x - y) <= (min)(abs(x), abs(y)) * prec;
}
static inline bool isApproxOrLessThan(const Scalar& x, const Scalar& y, const RealScalar& prec)

23
Eigen/src/Core/StableNorm.h
View File

@ -44,6 +44,7 @@ inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
MatrixBase<Derived>::stableNorm() const
{
using std::min;
using std::sqrt;
const Index blockSize = 4096;
RealScalar scale(0);
RealScalar invScale(1);
@ -57,7 +58,7 @@ MatrixBase<Derived>::stableNorm() const
internal::stable_norm_kernel(this->head(bi), ssq, scale, invScale);
for (; bi<n; bi+=blockSize)
internal::stable_norm_kernel(this->segment(bi,(min)(blockSize, n - bi)).template forceAlignedAccessIf<Alignment>(), ssq, scale, invScale);
return scale * internal::sqrt(ssq);
return scale * sqrt(ssq);
}
/** \returns the \em l2 norm of \c *this using the Blue's algorithm.
@ -76,6 +77,8 @@ MatrixBase<Derived>::blueNorm() const
using std::pow;
using std::min;
using std::max;
using std::sqrt;
using std::abs;
static Index nmax = -1;
static RealScalar b1, b2, s1m, s2m, overfl, rbig, relerr;
if(nmax <= 0)
@ -109,7 +112,7 @@ MatrixBase<Derived>::blueNorm() const
overfl = rbig*s2m; // overflow boundary for abig
eps = RealScalar(pow(double(ibeta), 1-it));
relerr = internal::sqrt(eps); // tolerance for neglecting asml
relerr = sqrt(eps); // tolerance for neglecting asml
abig = RealScalar(1.0/eps - 1.0);
if (RealScalar(nbig)>abig) nmax = int(abig); // largest safe n
else nmax = nbig;
@ -121,14 +124,14 @@ MatrixBase<Derived>::blueNorm() const
RealScalar abig = RealScalar(0);
for(Index j=0; j<n; ++j)
{
RealScalar ax = internal::abs(coeff(j));
RealScalar ax = abs(coeff(j));
if(ax > ab2) abig += internal::abs2(ax*s2m);
else if(ax < b1) asml += internal::abs2(ax*s1m);
else amed += internal::abs2(ax);
}
if(abig > RealScalar(0))
{
abig = internal::sqrt(abig);
abig = sqrt(abig);
if(abig > overfl)
{
return rbig;
@ -136,7 +139,7 @@ MatrixBase<Derived>::blueNorm() const
if(amed > RealScalar(0))
{
abig = abig/s2m;
amed = internal::sqrt(amed);
amed = sqrt(amed);
}
else
return abig/s2m;
@ -145,20 +148,20 @@ MatrixBase<Derived>::blueNorm() const
{
if (amed > RealScalar(0))
{
abig = internal::sqrt(amed);
amed = internal::sqrt(asml) / s1m;
abig = sqrt(amed);
amed = sqrt(asml) / s1m;
}
else
return internal::sqrt(asml)/s1m;
return sqrt(asml)/s1m;
}
else
return internal::sqrt(amed);
return sqrt(amed);
asml = (min)(abig, amed);
abig = (max)(abig, amed);
if(asml <= abig*relerr)
return abig;
else
return abig * internal::sqrt(RealScalar(1) + internal::abs2(asml/abig));
return abig * sqrt(RealScalar(1) + internal::abs2(asml/abig));
}
/** \returns the \em l2 norm of \c *this avoiding undeflow and overflow.

10
Eigen/src/Core/TriangularMatrix.h
View File

@ -781,20 +781,21 @@ MatrixBase<Derived>::triangularView() const
template<typename Derived>
bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
{
using std::abs;
RealScalar maxAbsOnUpperPart = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
{
Index maxi = (std::min)(j, rows()-1);
for(Index i = 0; i <= maxi; ++i)
{
RealScalar absValue = internal::abs(coeff(i,j));
RealScalar absValue = abs(coeff(i,j));
if(absValue > maxAbsOnUpperPart) maxAbsOnUpperPart = absValue;
}
}
RealScalar threshold = maxAbsOnUpperPart * prec;
for(Index j = 0; j < cols(); ++j)
for(Index i = j+1; i < rows(); ++i)
if(internal::abs(coeff(i, j)) > threshold) return false;
if(abs(coeff(i, j)) > threshold) return false;
return true;
}
@ -806,11 +807,12 @@ bool MatrixBase<Derived>::isUpperTriangular(const RealScalar& prec) const
template<typename Derived>
bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
{
using std::abs;
RealScalar maxAbsOnLowerPart = static_cast<RealScalar>(-1);
for(Index j = 0; j < cols(); ++j)
for(Index i = j; i < rows(); ++i)
{
RealScalar absValue = internal::abs(coeff(i,j));
RealScalar absValue = abs(coeff(i,j));
if(absValue > maxAbsOnLowerPart) maxAbsOnLowerPart = absValue;
}
RealScalar threshold = maxAbsOnLowerPart * prec;
@ -818,7 +820,7 @@ bool MatrixBase<Derived>::isLowerTriangular(const RealScalar& prec) const
{
Index maxi = (std::min)(j, rows()-1);
for(Index i = 0; i < maxi; ++i)
if(internal::abs(coeff(i, j)) > threshold) return false;
if(abs(coeff(i, j)) > threshold) return false;
}
return true;
}

14
Eigen/src/Eigen2Support/MathFunctions.h
View File

@ -15,14 +15,14 @@ namespace Eigen {
template<typename T> inline typename NumTraits<T>::Real ei_real(const T& x) { return internal::real(x); }
template<typename T> inline typename NumTraits<T>::Real ei_imag(const T& x) { return internal::imag(x); }
template<typename T> inline T ei_conj(const T& x) { return internal::conj(x); }
template<typename T> inline typename NumTraits<T>::Real ei_abs (const T& x) { return internal::abs(x); }
template<typename T> inline typename NumTraits<T>::Real ei_abs (const T& x) { using std::abs; return abs(x); }
template<typename T> inline typename NumTraits<T>::Real ei_abs2(const T& x) { return internal::abs2(x); }
template<typename T> inline T ei_sqrt(const T& x) { return internal::sqrt(x); }
template<typename T> inline T ei_exp (const T& x) { return internal::exp(x); }
template<typename T> inline T ei_log (const T& x) { return internal::log(x); }
template<typename T> inline T ei_sin (const T& x) { return internal::sin(x); }
template<typename T> inline T ei_cos (const T& x) { return internal::cos(x); }
template<typename T> inline T ei_atan2(const T& x,const T& y) { return internal::atan2(x,y); }
template<typename T> inline T ei_sqrt(const T& x) { using std::sqrt; return sqrt(x); }
template<typename T> inline T ei_exp (const T& x) { using std::exp; return exp(x); }
template<typename T> inline T ei_log (const T& x) { using std::log; return log(x); }
template<typename T> inline T ei_sin (const T& x) { using std::sin; return sin(x); }
template<typename T> inline T ei_cos (const T& x) { using std::cos; return cos(x); }
template<typename T> inline T ei_atan2(const T& x,const T& y) { using std::atan2; return atan2(x,y); }
template<typename T> inline T ei_pow (const T& x,const T& y) { return internal::pow(x,y); }
template<typename T> inline T ei_random () { return internal::random<T>(); }
template<typename T> inline T ei_random (const T& x, const T& y) { return internal::random(x, y); }

3
Eigen/src/Eigenvalues/ComplexSchur.h
View File

@ -258,10 +258,11 @@ inline bool ComplexSchur<MatrixType>::subdiagonalEntryIsNeglegible(Index i)
template<typename MatrixType>
typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::computeShift(Index iu, Index iter)
{
using std::abs;
if (iter == 10 || iter == 20)
{
// exceptional shift, taken from http://www.netlib.org/eispack/comqr.f
return internal::abs(internal::real(m_matT.coeff(iu,iu-1))) + internal::abs(internal::real(m_matT.coeff(iu-1,iu-2)));
return abs(internal::real(m_matT.coeff(iu,iu-1))) + abs(internal::real(m_matT.coeff(iu-1,iu-2)));
}
// compute the shift as one of the eigenvalues of t, the 2x2

20
Eigen/src/Eigenvalues/EigenSolver.h
View File

@ -364,6 +364,8 @@ template<typename MatrixType>
EigenSolver<MatrixType>&
EigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
{
using std::sqrt;
using std::abs;
assert(matrix.cols() == matrix.rows());
// Reduce to real Schur form.
@ -388,7 +390,7 @@ EigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvect
else
{
Scalar p = Scalar(0.5) * (m_matT.coeff(i, i) - m_matT.coeff(i+1, i+1));
Scalar z = internal::sqrt(internal::abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));
Scalar z = sqrt(abs(p * p + m_matT.coeff(i+1, i) * m_matT.coeff(i, i+1)));
m_eivalues.coeffRef(i) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, z);
m_eivalues.coeffRef(i+1) = ComplexScalar(m_matT.coeff(i+1, i+1) + p, -z);
i += 2;
@ -410,8 +412,9 @@ EigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvect
template<typename Scalar>
std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)
{
using std::abs;
Scalar r,d;
if (internal::abs(yr) > internal::abs(yi))
if (abs(yr) > abs(yi))
{
r = yi/yr;
d = yr + r*yi;
@ -429,6 +432,7 @@ std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)
template<typename MatrixType>
void EigenSolver<MatrixType>::doComputeEigenvectors()
{
using std::abs;
const Index size = m_eivec.cols();
const Scalar eps = NumTraits<Scalar>::epsilon();
@ -484,14 +488,14 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
Scalar denom = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag();
Scalar t = (x * lastr - lastw * r) / denom;
m_matT.coeffRef(i,n) = t;
if (internal::abs(x) > internal::abs(lastw))
if (abs(x) > abs(lastw))
m_matT.coeffRef(i+1,n) = (-r - w * t) / x;
else
m_matT.coeffRef(i+1,n) = (-lastr - y * t) / lastw;
}
// Overflow control
Scalar t = internal::abs(m_matT.coeff(i,n));
Scalar t = abs(m_matT.coeff(i,n));
if ((eps * t) * t > Scalar(1))
m_matT.col(n).tail(size-i) /= t;
}
@ -503,7 +507,7 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
Index l = n-1;
// Last vector component imaginary so matrix is triangular
if (internal::abs(m_matT.coeff(n,n-1)) > internal::abs(m_matT.coeff(n-1,n)))
if (abs(m_matT.coeff(n,n-1)) > abs(m_matT.coeff(n-1,n)))
{
m_matT.coeffRef(n-1,n-1) = q / m_matT.coeff(n,n-1);
m_matT.coeffRef(n-1,n) = -(m_matT.coeff(n,n) - p) / m_matT.coeff(n,n-1);
@ -545,12 +549,12 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
Scalar vr = (m_eivalues.coeff(i).real() - p) * (m_eivalues.coeff(i).real() - p) + m_eivalues.coeff(i).imag() * m_eivalues.coeff(i).imag() - q * q;
Scalar vi = (m_eivalues.coeff(i).real() - p) * Scalar(2) * q;
if ((vr == 0.0) && (vi == 0.0))
vr = eps * norm * (internal::abs(w) + internal::abs(q) + internal::abs(x) + internal::abs(y) + internal::abs(lastw));
vr = eps * norm * (abs(w) + abs(q) + abs(x) + abs(y) + abs(lastw));
std::complex<Scalar> cc = cdiv(x*lastra-lastw*ra+q*sa,x*lastsa-lastw*sa-q*ra,vr,vi);
m_matT.coeffRef(i,n-1) = internal::real(cc);
m_matT.coeffRef(i,n) = internal::imag(cc);
if (internal::abs(x) > (internal::abs(lastw) + internal::abs(q)))
if (abs(x) > (abs(lastw) + abs(q)))
{
m_matT.coeffRef(i+1,n-1) = (-ra - w * m_matT.coeff(i,n-1) + q * m_matT.coeff(i,n)) / x;
m_matT.coeffRef(i+1,n) = (-sa - w * m_matT.coeff(i,n) - q * m_matT.coeff(i,n-1)) / x;
@ -565,7 +569,7 @@ void EigenSolver<MatrixType>::doComputeEigenvectors()
// Overflow control
using std::max;
Scalar t = (max)(internal::abs(m_matT.coeff(i,n-1)),internal::abs(m_matT.coeff(i,n)));
Scalar t = (max)(abs(m_matT.coeff(i,n-1)),abs(m_matT.coeff(i,n)));
if ((eps * t) * t > Scalar(1))
m_matT.block(i, n-1, size-i, 2) /= t;

4
Eigen/src/Eigenvalues/GeneralizedEigenSolver.h
View File

@ -290,6 +290,8 @@ template<typename MatrixType>
GeneralizedEigenSolver<MatrixType>&
GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixType& B, bool computeEigenvectors)
{
using std::sqrt;
using std::abs;
eigen_assert(A.cols() == A.rows() && B.cols() == A.rows() && B.cols() == B.rows());
// Reduce to generalized real Schur form:
@ -317,7 +319,7 @@ GeneralizedEigenSolver<MatrixType>::compute(const MatrixType& A, const MatrixTyp
else
{
Scalar p = Scalar(0.5) * (m_matS.coeff(i, i) - m_matS.coeff(i+1, i+1));
Scalar z = internal::sqrt(internal::abs(p * p + m_matS.coeff(i+1, i) * m_matS.coeff(i, i+1)));
Scalar z = sqrt(abs(p * p + m_matS.coeff(i+1, i) * m_matS.coeff(i, i+1)));
m_alphas.coeffRef(i) = ComplexScalar(m_matS.coeff(i+1, i+1) + p, z);
m_alphas.coeffRef(i+1) = ComplexScalar(m_matS.coeff(i+1, i+1) + p, -z);

3
Eigen/src/Eigenvalues/MatrixBaseEigenvalues.h
View File

@ -121,10 +121,11 @@ template<typename Derived>
inline typename MatrixBase<Derived>::RealScalar
MatrixBase<Derived>::operatorNorm() const
{
using std::sqrt;
typename Derived::PlainObject m_eval(derived());
// FIXME if it is really guaranteed that the eigenvalues are already sorted,
// then we don't need to compute a maxCoeff() here, comparing the 1st and last ones is enough.
return internal::sqrt((m_eval*m_eval.adjoint())
return sqrt((m_eval*m_eval.adjoint())
.eval()
.template selfadjointView<Lower>()
.eigenvalues()

20
Eigen/src/Eigenvalues/RealQZ.h
View File

@ -278,13 +278,14 @@ namespace Eigen {
template<typename MatrixType>
inline typename MatrixType::Index RealQZ<MatrixType>::findSmallSubdiagEntry(Index iu)
{
using std::abs;
Index res = iu;
while (res > 0)
{
Scalar s = internal::abs(m_S.coeff(res-1,res-1)) + internal::abs(m_S.coeff(res,res));
Scalar s = abs(m_S.coeff(res-1,res-1)) + abs(m_S.coeff(res,res));
if (s == Scalar(0.0))
s = m_normOfS;
if (internal::abs(m_S.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
if (abs(m_S.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
break;
res--;
}
@ -295,9 +296,10 @@ namespace Eigen {
template<typename MatrixType>
inline typename MatrixType::Index RealQZ<MatrixType>::findSmallDiagEntry(Index f, Index l)
{
using std::abs;
Index res = l;
while (res >= f) {
if (internal::abs(m_T.coeff(res,res)) <= NumTraits<Scalar>::epsilon() * m_normOfT)
if (abs(m_T.coeff(res,res)) <= NumTraits<Scalar>::epsilon() * m_normOfT)
break;
res--;
}
@ -308,8 +310,10 @@ namespace Eigen {
template<typename MatrixType>
inline void RealQZ<MatrixType>::splitOffTwoRows(Index i)
{
using std::abs;
using std::sqrt;
const Index dim=m_S.cols();
if (internal::abs(m_S.coeff(i+1,i)==Scalar(0)))
if (abs(m_S.coeff(i+1,i)==Scalar(0)))
return;
Index z = findSmallDiagEntry(i,i+1);
if (z==i-1)
@ -320,7 +324,7 @@ namespace Eigen {
Scalar p = Scalar(0.5)*(STi(0,0)-STi(1,1));
Scalar q = p*p + STi(1,0)*STi(0,1);
if (q>=0) {
Scalar z = internal::sqrt(q);
Scalar z = sqrt(q);
// one QR-like iteration for ABi - lambda I
// is enough - when we know exact eigenvalue in advance,
// convergence is immediate
@ -393,7 +397,9 @@ namespace Eigen {
/** \internal QR-like iterative step for block f..l */
template<typename MatrixType>
inline void RealQZ<MatrixType>::step(Index f, Index l, Index iter) {
inline void RealQZ<MatrixType>::step(Index f, Index l, Index iter)
{
using std::abs;
const Index dim = m_S.cols();
// x, y, z
@ -411,7 +417,7 @@ namespace Eigen {
a98=m_S.coeff(l-0,l-1),
b77i=Scalar(1.0)/m_T.coeff(l-2,l-2),
b88i=Scalar(1.0)/m_T.coeff(l-1,l-1);
Scalar ss = internal::abs(a87*b77i) + internal::abs(a98*b88i),
Scalar ss = abs(a87*b77i) + abs(a98*b88i),
lpl = Scalar(1.5)*ss,
ll = ss*ss;
x = ll + a11*a11*b11i*b11i - lpl*a11*b11i + a12*a21*b11i*b22i

22
Eigen/src/Eigenvalues/RealSchur.h
View File

@ -345,13 +345,14 @@ inline typename MatrixType::Scalar RealSchur<MatrixType>::computeNormOfT()
template<typename MatrixType>
inline typename MatrixType::Index RealSchur<MatrixType>::findSmallSubdiagEntry(Index iu, Scalar norm)
{
using std::abs;
Index res = iu;
while (res > 0)
{
Scalar s = internal::abs(m_matT.coeff(res-1,res-1)) + internal::abs(m_matT.coeff(res,res));
Scalar s = abs(m_matT.coeff(res-1,res-1)) + abs(m_matT.coeff(res,res));
if (s == 0.0)
s = norm;
if (internal::abs(m_matT.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
if (abs(m_matT.coeff(res,res-1)) < NumTraits<Scalar>::epsilon() * s)
break;
res--;
}
@ -362,6 +363,8 @@ inline typename MatrixType::Index RealSchur<MatrixType>::findSmallSubdiagEntry(I
template<typename MatrixType>
inline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, Scalar exshift)
{
using std::sqrt;
using std::abs;
const Index size = m_matT.cols();
// The eigenvalues of the 2x2 matrix [a b; c d] are
@ -373,7 +376,7 @@ inline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, Scal
if (q >= Scalar(0)) // Two real eigenvalues
{
Scalar z = internal::sqrt(internal::abs(q));
Scalar z = sqrt(abs(q));
JacobiRotation<Scalar> rot;
if (p >= Scalar(0))
rot.makeGivens(p + z, m_matT.coeff(iu, iu-1));
@ -395,6 +398,8 @@ inline void RealSchur<MatrixType>::splitOffTwoRows(Index iu, bool computeU, Scal
template<typename MatrixType>
inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& exshift, Vector3s& shiftInfo)
{
using std::sqrt;
using std::abs;
shiftInfo.coeffRef(0) = m_matT.coeff(iu,iu);
shiftInfo.coeffRef(1) = m_matT.coeff(iu-1,iu-1);
shiftInfo.coeffRef(2) = m_matT.coeff(iu,iu-1) * m_matT.coeff(iu-1,iu);
@ -405,7 +410,7 @@ inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& ex
exshift += shiftInfo.coeff(0);
for (Index i = 0; i <= iu; ++i)
m_matT.coeffRef(i,i) -= shiftInfo.coeff(0);
Scalar s = internal::abs(m_matT.coeff(iu,iu-1)) + internal::abs(m_matT.coeff(iu-1,iu-2));
Scalar s = abs(m_matT.coeff(iu,iu-1)) + abs(m_matT.coeff(iu-1,iu-2));
shiftInfo.coeffRef(0) = Scalar(0.75) * s;
shiftInfo.coeffRef(1) = Scalar(0.75) * s;
shiftInfo.coeffRef(2) = Scalar(-0.4375) * s * s;
@ -418,7 +423,7 @@ inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& ex
s = s * s + shiftInfo.coeff(2);
if (s > Scalar(0))
{
s = internal::sqrt(s);
s = sqrt(s);
if (shiftInfo.coeff(1) < shiftInfo.coeff(0))
s = -s;
s = s + (shiftInfo.coeff(1) - shiftInfo.coeff(0)) / Scalar(2.0);
@ -435,6 +440,7 @@ inline void RealSchur<MatrixType>::computeShift(Index iu, Index iter, Scalar& ex
template<typename MatrixType>
inline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const Vector3s& shiftInfo, Index& im, Vector3s& firstHouseholderVector)
{
using std::abs;
Vector3s& v = firstHouseholderVector; // alias to save typing
for (im = iu-2; im >= il; --im)
@ -448,9 +454,9 @@ inline void RealSchur<MatrixType>::initFrancisQRStep(Index il, Index iu, const V
if (im == il) {
break;
}
const Scalar lhs = m_matT.coeff(im,im-1) * (internal::abs(v.coeff(1)) + internal::abs(v.coeff(2)));
const Scalar rhs = v.coeff(0) * (internal::abs(m_matT.coeff(im-1,im-1)) + internal::abs(Tmm) + internal::abs(m_matT.coeff(im+1,im+1)));
if (internal::abs(lhs) < NumTraits<Scalar>::epsilon() * rhs)
const Scalar lhs = m_matT.coeff(im,im-1) * (abs(v.coeff(1)) + abs(v.coeff(2)));
const Scalar rhs = v.coeff(0) * (abs(m_matT.coeff(im-1,im-1)) + abs(Tmm) + abs(m_matT.coeff(im+1,im+1)));
if (abs(lhs) < NumTraits<Scalar>::epsilon() * rhs)
{
break;
}

5
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
View File

@ -384,6 +384,7 @@ template<typename MatrixType>
SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
::compute(const MatrixType& matrix, int options)
{
using std::abs;
eigen_assert(matrix.cols() == matrix.rows());
eigen_assert((options&~(EigVecMask|GenEigMask))==0
&& (options&EigVecMask)!=EigVecMask
@ -421,7 +422,7 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
while (end>0)
{
for (Index i = start; i<end; ++i)
if (internal::isMuchSmallerThan(internal::abs(m_subdiag[i]),(internal::abs(diag[i])+internal::abs(diag[i+1]))))
if (internal::isMuchSmallerThan(abs(m_subdiag[i]),(abs(diag[i])+abs(diag[i+1]))))
m_subdiag[i] = 0;
// find the largest unreduced block
@ -675,6 +676,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,2
static inline void run(SolverType& solver, const MatrixType& mat, int options)
{
using std::sqrt;
eigen_assert(mat.cols() == 2 && mat.cols() == mat.rows());
eigen_assert((options&~(EigVecMask|GenEigMask))==0
&& (options&EigVecMask)!=EigVecMask
@ -736,6 +738,7 @@ namespace internal {
template<int StorageOrder,typename RealScalar, typename Scalar, typename Index>
static void tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n)
{
using std::abs;
RealScalar td = (diag[end-1] - diag[end])*RealScalar(0.5);
RealScalar e = subdiag[end-1];
// Note that thanks to scaling, e^2 or td^2 cannot overflow, however they can still

2
Eigen/src/Eigenvalues/Tridiagonalization.h
View File

@ -345,6 +345,7 @@ namespace internal {
template<typename MatrixType, typename CoeffVectorType>
void tridiagonalization_inplace(MatrixType& matA, CoeffVectorType& hCoeffs)
{
using internal::conj;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
@ -467,6 +468,7 @@ struct tridiagonalization_inplace_selector<MatrixType,3,false>
template<typename DiagonalType, typename SubDiagonalType>
static void run(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)
{
using std::sqrt;
diag[0] = mat(0,0);
RealScalar v1norm2 = abs2(mat(2,0));
if(v1norm2 == RealScalar(0))

4
Eigen/src/Geometry/AlignedBox.h
View File

@ -248,14 +248,14 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
*/
template<typename Derived>
inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
{ return internal::sqrt(NonInteger(squaredExteriorDistance(p))); }
{ using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(p))); }
/** \returns the distance between the boxes \a b and \c *this,
* and zero if the boxes intersect.
* \sa squaredExteriorDistance()
*/
inline NonInteger exteriorDistance(const AlignedBox& b) const
{ return internal::sqrt(NonInteger(squaredExteriorDistance(b))); }
{ using std::sqrt; return sqrt(NonInteger(squaredExteriorDistance(b))); }
/** \returns \c *this with scalar type casted to \a NewScalarType
*

9
Eigen/src/Geometry/AngleAxis.h
View File

@ -161,6 +161,7 @@ AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived
using std::acos;
using std::min;
using std::max;
using std::sqrt;
Scalar n2 = q.vec().squaredNorm();
if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision())
{
@ -170,7 +171,7 @@ AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived
else
{
m_angle = Scalar(2)*acos((min)((max)(Scalar(-1),q.w()),Scalar(1)));
m_axis = q.vec() / internal::sqrt(n2);
m_axis = q.vec() / sqrt(n2);
}
return *this;
}
@ -202,9 +203,11 @@ template<typename Scalar>
typename AngleAxis<Scalar>::Matrix3
AngleAxis<Scalar>::toRotationMatrix(void) const
{
using std::sin;
using std::cos;
Matrix3 res;
Vector3 sin_axis = internal::sin(m_angle) * m_axis;
Scalar c = internal::cos(m_angle);
Vector3 sin_axis = sin(m_angle) * m_axis;
Scalar c = cos(m_angle);
Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
Scalar tmp;

17
Eigen/src/Geometry/EulerAngles.h
View File

@ -32,6 +32,7 @@ template<typename Derived>
inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
{
using std::atan2;
/* Implemented from Graphics Gems IV */
EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
@ -47,31 +48,31 @@ MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
if (a0==a2)
{
Scalar s = Vector2(coeff(j,i) , coeff(k,i)).norm();
res[1] = internal::atan2(s, coeff(i,i));
res[1] = atan2(s, coeff(i,i));
if (s > epsilon)
{
res[0] = internal::atan2(coeff(j,i), coeff(k,i));
res[2] = internal::atan2(coeff(i,j),-coeff(i,k));
res[0] = atan2(coeff(j,i), coeff(k,i));
res[2] = atan2(coeff(i,j),-coeff(i,k));
}
else
{
res[0] = Scalar(0);
res[2] = (coeff(i,i)>0?1:-1)*internal::atan2(-coeff(k,j), coeff(j,j));
res[2] = (coeff(i,i)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
}
}
else
{
Scalar c = Vector2(coeff(i,i) , coeff(i,j)).norm();
res[1] = internal::atan2(-coeff(i,k), c);
res[1] = atan2(-coeff(i,k), c);
if (c > epsilon)
{
res[0] = internal::atan2(coeff(j,k), coeff(k,k));
res[2] = internal::atan2(coeff(i,j), coeff(i,i));
res[0] = atan2(coeff(j,k), coeff(k,k));
res[2] = atan2(coeff(i,j), coeff(i,i));
}
else
{
res[0] = Scalar(0);
res[2] = (coeff(i,k)>0?1:-1)*internal::atan2(-coeff(k,j), coeff(j,j));
res[2] = (coeff(i,k)>0?1:-1)*atan2(-coeff(k,j), coeff(j,j));
}
}
if (!odd)

5
Eigen/src/Geometry/Hyperplane.h
View File

@ -135,7 +135,7 @@ public:
/** \returns the absolute distance between the plane \c *this and a point \a p.
* \sa signedDistance()
*/
inline Scalar absDistance(const VectorType& p) const { return internal::abs(signedDistance(p)); }
inline Scalar absDistance(const VectorType& p) const { using std::abs; return abs(signedDistance(p)); }
/** \returns the projection of a point \a p onto the plane \c *this.
*/
@ -178,13 +178,14 @@ public:
*/
VectorType intersection(const Hyperplane& other) const
{
using std::abs;
EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
// since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
// whether the two lines are approximately parallel.
if(internal::isMuchSmallerThan(det, Scalar(1)))
{ // special case where the two lines are approximately parallel. Pick any point on the first line.
if(internal::abs(coeffs().coeff(1))>internal::abs(coeffs().coeff(0)))
if(abs(coeffs().coeff(1))>abs(coeffs().coeff(0)))
return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
else
return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));

2
Eigen/src/Geometry/ParametrizedLine.h
View File

@ -87,7 +87,7 @@ public:
/** \returns the distance of a point \a p to its projection onto the line \c *this.
* \sa squaredDistance()
*/
RealScalar distance(const VectorType& p) const { return internal::sqrt(squaredDistance(p)); }
RealScalar distance(const VectorType& p) const { using std::sqrt; return sqrt(squaredDistance(p)); }
/** \returns the projection of a point \a p onto the line \c *this. */
VectorType projection(const VectorType& p) const

27
Eigen/src/Geometry/Quaternion.h
View File

@ -505,9 +505,11 @@ EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const Quaternion
template<class Derived>
EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
{
using std::cos;
using std::sin;
Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
this->w() = internal::cos(ha);
this->vec() = internal::sin(ha) * aa.axis();
this->w() = cos(ha);
this->vec() = sin(ha) * aa.axis();
return derived();
}
@ -581,6 +583,7 @@ template<typename Derived1, typename Derived2>
inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
{
using std::max;
using std::sqrt;
Vector3 v0 = a.normalized();
Vector3 v1 = b.normalized();
Scalar c = v1.dot(v0);
@ -601,12 +604,12 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri
Vector3 axis = svd.matrixV().col(2);
Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
this->w() = internal::sqrt(w2);
this->vec() = axis * internal::sqrt(Scalar(1) - w2);
this->w() = sqrt(w2);
this->vec() = axis * sqrt(Scalar(1) - w2);
return derived();
}
Vector3 axis = v0.cross(v1);
Scalar s = internal::sqrt((Scalar(1)+c)*Scalar(2));
Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
Scalar invs = Scalar(1)/s;
this->vec() = axis * invs;
this->w() = s * Scalar(0.5);
@ -677,7 +680,8 @@ inline typename internal::traits<Derived>::Scalar
QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
{
using std::acos;
double d = internal::abs(this->dot(other));
using std::abs;
double d = abs(this->dot(other));
if (d>=1.0)
return Scalar(0);
return static_cast<Scalar>(2 * acos(d));
@ -692,9 +696,11 @@ Quaternion<typename internal::traits<Derived>::Scalar>
QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const
{
using std::acos;
using std::sin;
using std::abs;
static const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
Scalar d = this->dot(other);
Scalar absD = internal::abs(d);
Scalar absD = abs(d);
Scalar scale0;
Scalar scale1;
@ -708,10 +714,10 @@ QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& oth
{
// theta is the angle between the 2 quaternions
Scalar theta = acos(absD);
Scalar sinTheta = internal::sin(theta);
Scalar sinTheta = sin(theta);
scale0 = internal::sin( ( Scalar(1) - t ) * theta) / sinTheta;
scale1 = internal::sin( ( t * theta) ) / sinTheta;
scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
scale1 = sin( ( t * theta) ) / sinTheta;
}
if(d<0) scale1 = -scale1;
@ -728,6 +734,7 @@ struct quaternionbase_assign_impl<Other,3,3>
typedef DenseIndex Index;
template<class Derived> static inline void run(QuaternionBase<Derived>& q, const Other& mat)
{
using std::sqrt;
// This algorithm comes from "Quaternion Calculus and Fast Animation",
// Ken Shoemake, 1987 SIGGRAPH course notes
Scalar t = mat.trace();

9
Eigen/src/Geometry/Rotation2D.h
View File

@ -133,8 +133,9 @@ template<typename Scalar>
template<typename Derived>
Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
{
using std::atan2;
EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
m_angle = internal::atan2(mat.coeff(1,0), mat.coeff(0,0));
m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
return *this;
}
@ -144,8 +145,10 @@ template<typename Scalar>
typename Rotation2D<Scalar>::Matrix2
Rotation2D<Scalar>::toRotationMatrix(void) const
{
Scalar sinA = internal::sin(m_angle);
Scalar cosA = internal::cos(m_angle);
using std::sin;
using std::cos;
Scalar sinA = sin(m_angle);
Scalar cosA = cos(m_angle);
return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
}

7
Eigen/src/Householder/Householder.h
View File

@ -67,6 +67,9 @@ void MatrixBase<Derived>::makeHouseholder(
Scalar& tau,
RealScalar& beta) const
{
using std::sqrt;
using internal::conj;
EIGEN_STATIC_ASSERT_VECTOR_ONLY(EssentialPart)
VectorBlock<const Derived, EssentialPart::SizeAtCompileTime> tail(derived(), 1, size()-1);
@ -81,11 +84,11 @@ void MatrixBase<Derived>::makeHouseholder(
}
else
{
beta = internal::sqrt(internal::abs2(c0) + tailSqNorm);
beta = sqrt(internal::abs2(c0) + tailSqNorm);
if (internal::real(c0)>=RealScalar(0))
beta = -beta;
essential = tail / (c0 - beta);
tau = internal::conj((beta - c0) / beta);
tau = conj((beta - c0) / beta);
}
}

49
Eigen/src/Jacobi/Jacobi.h
View File

@ -50,15 +50,16 @@ template<typename Scalar> class JacobiRotation
/** Concatenates two planar rotation */
JacobiRotation operator*(const JacobiRotation& other)
{
return JacobiRotation(m_c * other.m_c - internal::conj(m_s) * other.m_s,
internal::conj(m_c * internal::conj(other.m_s) + internal::conj(m_s) * internal::conj(other.m_c)));
using internal::conj;
return JacobiRotation(m_c * other.m_c - conj(m_s) * other.m_s,
conj(m_c * conj(other.m_s) + conj(m_s) * conj(other.m_c)));
}
/** Returns the transposed transformation */
JacobiRotation transpose() const { return JacobiRotation(m_c, -internal::conj(m_s)); }
JacobiRotation transpose() const { using internal::conj; return JacobiRotation(m_c, -conj(m_s)); }
/** Returns the adjoint transformation */
JacobiRotation adjoint() const { return JacobiRotation(internal::conj(m_c), -m_s); }
JacobiRotation adjoint() const { using internal::conj; return JacobiRotation(conj(m_c), -m_s); }
template<typename Derived>
bool makeJacobi(const MatrixBase<Derived>&, typename Derived::Index p, typename Derived::Index q);
@ -81,6 +82,8 @@ template<typename Scalar> class JacobiRotation
template<typename Scalar>
bool JacobiRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
{
using std::sqrt;
using std::abs;
typedef typename NumTraits<Scalar>::Real RealScalar;
if(y == Scalar(0))
{
@ -90,8 +93,8 @@ bool JacobiRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
}
else
{
RealScalar tau = (x-z)/(RealScalar(2)*internal::abs(y));
RealScalar w = internal::sqrt(internal::abs2(tau) + RealScalar(1));
RealScalar tau = (x-z)/(RealScalar(2)*abs(y));
RealScalar w = sqrt(internal::abs2(tau) + RealScalar(1));
RealScalar t;
if(tau>RealScalar(0))
{
@ -102,8 +105,8 @@ bool JacobiRotation<Scalar>::makeJacobi(RealScalar x, Scalar y, RealScalar z)
t = RealScalar(1) / (tau - w);
}
RealScalar sign_t = t > RealScalar(0) ? RealScalar(1) : RealScalar(-1);
RealScalar n = RealScalar(1) / internal::sqrt(internal::abs2(t)+RealScalar(1));
m_s = - sign_t * (internal::conj(y) / internal::abs(y)) * internal::abs(t) * n;
RealScalar n = RealScalar(1) / sqrt(internal::abs2(t)+RealScalar(1));
m_s = - sign_t * (internal::conj(y) / abs(y)) * abs(t) * n;
m_c = n;
return true;
}
@ -152,6 +155,10 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
template<typename Scalar>
void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::true_type)
{
using std::sqrt;
using std::abs;
using internal::conj;
if(q==Scalar(0))
{
m_c = internal::real(p)<0 ? Scalar(-1) : Scalar(1);
@ -161,8 +168,8 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
else if(p==Scalar(0))
{
m_c = 0;
m_s = -q/internal::abs(q);
if(r) *r = internal::abs(q);
m_s = -q/abs(q);
if(r) *r = abs(q);
}
else
{
@ -175,12 +182,12 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
Scalar qs = q / p1;
RealScalar q2 = internal::abs2(qs);
RealScalar u = internal::sqrt(RealScalar(1) + q2/p2);
RealScalar u = sqrt(RealScalar(1) + q2/p2);
if(internal::real(p)<RealScalar(0))
u = -u;
m_c = Scalar(1)/u;
m_s = -qs*internal::conj(ps)*(m_c/p2);
m_s = -qs*conj(ps)*(m_c/p2);
if(r) *r = p * u;
}
else
@ -190,14 +197,14 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
Scalar qs = q / q1;
RealScalar q2 = internal::abs2(qs);
RealScalar u = q1 * internal::sqrt(p2 + q2);
RealScalar u = q1 * sqrt(p2 + q2);
if(internal::real(p)<RealScalar(0))
u = -u;
p1 = internal::abs(p);
p1 = abs(p);
ps = p/p1;
m_c = p1/u;
m_s = -internal::conj(ps) * (q/u);
m_s = -conj(ps) * (q/u);
if(r) *r = ps * u;
}
}
@ -207,22 +214,24 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
template<typename Scalar>
void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar* r, internal::false_type)
{
using std::sqrt;
using std::abs;
if(q==Scalar(0))
{
m_c = p<Scalar(0) ? Scalar(-1) : Scalar(1);
m_s = Scalar(0);
if(r) *r = internal::abs(p);
if(r) *r = abs(p);
}
else if(p==Scalar(0))
{
m_c = Scalar(0);
m_s = q<Scalar(0) ? Scalar(1) : Scalar(-1);
if(r) *r = internal::abs(q);
if(r) *r = abs(q);
}
else if(internal::abs(p) > internal::abs(q))
else if(abs(p) > abs(q))
{
Scalar t = q/p;
Scalar u = internal::sqrt(Scalar(1) + internal::abs2(t));
Scalar u = sqrt(Scalar(1) + internal::abs2(t));
if(p<Scalar(0))
u = -u;
m_c = Scalar(1)/u;
@ -232,7 +241,7 @@ void JacobiRotation<Scalar>::makeGivens(const Scalar& p, const Scalar& q, Scalar
else
{
Scalar t = p/q;
Scalar u = internal::sqrt(Scalar(1) + internal::abs2(t));
Scalar u = sqrt(Scalar(1) + internal::abs2(t));
if(q<Scalar(0))
u = -u;
m_s = -Scalar(1)/u;

7
Eigen/src/LU/FullPivLU.h
View File

@ -293,11 +293,12 @@ template<typename _MatrixType> class FullPivLU
*/
inline Index rank() const
{
using std::abs;
eigen_assert(m_isInitialized && "LU is not initialized.");
RealScalar premultiplied_threshold = internal::abs(m_maxpivot) * threshold();
RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
Index result = 0;
for(Index i = 0; i < m_nonzero_pivots; ++i)
result += (internal::abs(m_lu.coeff(i,i)) > premultiplied_threshold);
result += (abs(m_lu.coeff(i,i)) > premultiplied_threshold);
return result;
}
@ -547,6 +548,7 @@ struct kernel_retval<FullPivLU<_MatrixType> >
template<typename Dest> void evalTo(Dest& dst) const
{
using std::abs;
const Index cols = dec().matrixLU().cols(), dimker = cols - rank();
if(dimker == 0)
{
@ -632,6 +634,7 @@ struct image_retval<FullPivLU<_MatrixType> >
template<typename Dest> void evalTo(Dest& dst) const
{
using std::abs;
if(rank() == 0)
{
// The Image is just {0}, so it doesn't have a basis properly speaking, but let's

4
Eigen/src/LU/Inverse.h
View File

@ -55,6 +55,7 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
bool& invertible
)
{
using std::abs;
determinant = matrix.coeff(0,0);
invertible = abs(determinant) > absDeterminantThreshold;
if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant;
@ -98,6 +99,7 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
bool& invertible
)
{
using std::abs;
typedef typename ResultType::Scalar Scalar;
determinant = matrix.determinant();
invertible = abs(determinant) > absDeterminantThreshold;
@ -167,6 +169,7 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
bool& invertible
)
{
using std::abs;
typedef typename ResultType::Scalar Scalar;
Matrix<Scalar,3,1> cofactors_col0;
cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
@ -251,6 +254,7 @@ struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
bool& invertible
)
{
using std::abs;
determinant = matrix.determinant();
invertible = abs(determinant) > absDeterminantThreshold;
if(invertible) compute_inverse<MatrixType, ResultType>::run(matrix, inverse);

11
Eigen/src/QR/ColPivHouseholderQR.h
View File

@ -181,11 +181,12 @@ template<typename _MatrixType> class ColPivHouseholderQR
*/
inline Index rank() const
{
using std::abs;
eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
RealScalar premultiplied_threshold = internal::abs(m_maxpivot) * threshold();
RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
Index result = 0;
for(Index i = 0; i < m_nonzero_pivots; ++i)
result += (internal::abs(m_qr.coeff(i,i)) > premultiplied_threshold);
result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
return result;
}
@ -342,9 +343,10 @@ template<typename _MatrixType> class ColPivHouseholderQR
template<typename MatrixType>
typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::absDeterminant() const
{
using std::abs;
eigen_assert(m_isInitialized && "ColPivHouseholderQR is not initialized.");
eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
return internal::abs(m_qr.diagonal().prod());
return abs(m_qr.diagonal().prod());
}
template<typename MatrixType>
@ -358,6 +360,7 @@ typename MatrixType::RealScalar ColPivHouseholderQR<MatrixType>::logAbsDetermina
template<typename MatrixType>
ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
{
using std::abs;
Index rows = matrix.rows();
Index cols = matrix.cols();
Index size = matrix.diagonalSize();
@ -426,7 +429,7 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const
m_qr.coeffRef(k,k) = beta;
// remember the maximum absolute value of diagonal coefficients
if(internal::abs(beta) > m_maxpivot) m_maxpivot = internal::abs(beta);
if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
// apply the householder transformation
m_qr.bottomRightCorner(rows-k, cols-k-1)

5
Eigen/src/QR/ColPivHouseholderQR_MKL.h
View File

@ -47,6 +47,7 @@ ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynami
const Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic>& matrix) \
\
{ \
using std::abs; \
typedef Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynamic> MatrixType; \
typedef MatrixType::Scalar Scalar; \
typedef MatrixType::RealScalar RealScalar; \
@ -71,10 +72,10 @@ ColPivHouseholderQR<Matrix<EIGTYPE, Dynamic, Dynamic, EIGCOLROW, Dynamic, Dynami
m_isInitialized = true; \
m_maxpivot=m_qr.diagonal().cwiseAbs().maxCoeff(); \
m_hCoeffs.adjointInPlace(); \
RealScalar premultiplied_threshold = internal::abs(m_maxpivot) * threshold(); \
RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold(); \
lapack_int *perm = m_colsPermutation.indices().data(); \
for(i=0;i<size;i++) { \
m_nonzero_pivots += (internal::abs(m_qr.coeff(i,i)) > premultiplied_threshold);\
m_nonzero_pivots += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);\
} \
for(i=0;i<cols;i++) perm[i]--;\
\

14
Eigen/src/QR/FullPivHouseholderQR.h
View File

@ -201,11 +201,12 @@ template<typename _MatrixType> class FullPivHouseholderQR
*/
inline Index rank() const
{
using std::abs;
eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
RealScalar premultiplied_threshold = internal::abs(m_maxpivot) * threshold();
RealScalar premultiplied_threshold = abs(m_maxpivot) * threshold();
Index result = 0;
for(Index i = 0; i < m_nonzero_pivots; ++i)
result += (internal::abs(m_qr.coeff(i,i)) > premultiplied_threshold);
result += (abs(m_qr.coeff(i,i)) > premultiplied_threshold);
return result;
}
@ -362,9 +363,10 @@ template<typename _MatrixType> class FullPivHouseholderQR
template<typename MatrixType>
typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::absDeterminant() const
{
using std::abs;
eigen_assert(m_isInitialized && "FullPivHouseholderQR is not initialized.");
eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
return internal::abs(m_qr.diagonal().prod());
return abs(m_qr.diagonal().prod());
}
template<typename MatrixType>
@ -378,6 +380,7 @@ typename MatrixType::RealScalar FullPivHouseholderQR<MatrixType>::logAbsDetermin
template<typename MatrixType>
FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(const MatrixType& matrix)
{
using std::abs;
Index rows = matrix.rows();
Index cols = matrix.cols();
Index size = (std::min)(rows,cols);
@ -439,7 +442,7 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons
m_qr.coeffRef(k,k) = beta;
// remember the maximum absolute value of diagonal coefficients
if(internal::abs(beta) > m_maxpivot) m_maxpivot = internal::abs(beta);
if(abs(beta) > m_maxpivot) m_maxpivot = abs(beta);
m_qr.bottomRightCorner(rows-k, cols-k-1)
.applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), m_hCoeffs.coeffRef(k), &m_temp.coeffRef(k+1));
@ -544,6 +547,7 @@ public:
template <typename ResultType>
void evalTo(ResultType& result, WorkVectorType& workspace) const
{
using internal::conj;
// compute the product H'_0 H'_1 ... H'_n-1,
// where H_k is the k-th Householder transformation I - h_k v_k v_k'
// and v_k is the k-th Householder vector [1,m_qr(k+1,k), m_qr(k+2,k), ...]
@ -555,7 +559,7 @@ public:
for (Index k = size-1; k >= 0; k--)
{
result.block(k, k, rows-k, rows-k)
.applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), internal::conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));
.applyHouseholderOnTheLeft(m_qr.col(k).tail(rows-k-1), conj(m_hCoeffs.coeff(k)), &workspace.coeffRef(k));
result.row(k).swap(result.row(m_rowsTranspositions.coeff(k)));
}
}

3
Eigen/src/QR/HouseholderQR.h
View File

@ -181,9 +181,10 @@ template<typename _MatrixType> class HouseholderQR
template<typename MatrixType>
typename MatrixType::RealScalar HouseholderQR<MatrixType>::absDeterminant() const
{
using std::abs;
eigen_assert(m_isInitialized && "HouseholderQR is not initialized.");
eigen_assert(m_qr.rows() == m_qr.cols() && "You can't take the determinant of a non-square matrix!");
return internal::abs(m_qr.diagonal().prod());
return abs(m_qr.diagonal().prod());
}
template<typename MatrixType>

11
Eigen/src/SVD/JacobiSVD.h
View File

@ -359,6 +359,7 @@ struct svd_precondition_2x2_block_to_be_real<MatrixType, QRPreconditioner, true>
typedef typename SVD::Index Index;
static void run(typename SVD::WorkMatrixType& work_matrix, SVD& svd, Index p, Index q)
{
using std::sqrt;
Scalar z;
JacobiRotation<Scalar> rot;
RealScalar n = sqrt(abs2(work_matrix.coeff(p,p)) + abs2(work_matrix.coeff(q,p)));
@ -398,6 +399,7 @@ void real_2x2_jacobi_svd(const MatrixType& matrix, Index p, Index q,
JacobiRotation<RealScalar> *j_left,
JacobiRotation<RealScalar> *j_right)
{
using std::sqrt;
Matrix<RealScalar,2,2> m;
m << real(matrix.coeff(p,p)), real(matrix.coeff(p,q)),
real(matrix.coeff(q,p)), real(matrix.coeff(q,q));
@ -727,6 +729,7 @@ template<typename MatrixType, int QRPreconditioner>
JacobiSVD<MatrixType, QRPreconditioner>&
JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsigned int computationOptions)
{
using std::abs;
allocate(matrix.rows(), matrix.cols(), computationOptions);
// currently we stop when we reach precision 2*epsilon as the last bit of precision can require an unreasonable number of iterations,
@ -764,9 +767,9 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
// notice that this comparison will evaluate to false if any NaN is involved, ensuring that NaN's don't
// keep us iterating forever. Similarly, small denormal numbers are considered zero.
using std::max;
RealScalar threshold = (max)(considerAsZero, precision * (max)(internal::abs(m_workMatrix.coeff(p,p)),
internal::abs(m_workMatrix.coeff(q,q))));
if((max)(internal::abs(m_workMatrix.coeff(p,q)),internal::abs(m_workMatrix.coeff(q,p))) > threshold)
RealScalar threshold = (max)(considerAsZero, precision * (max)(abs(m_workMatrix.coeff(p,p)),
abs(m_workMatrix.coeff(q,q))));
if((max)(abs(m_workMatrix.coeff(p,q)),abs(m_workMatrix.coeff(q,p))) > threshold)
{
finished = false;
@ -790,7 +793,7 @@ JacobiSVD<MatrixType, QRPreconditioner>::compute(const MatrixType& matrix, unsig
for(Index i = 0; i < m_diagSize; ++i)
{
RealScalar a = internal::abs(m_workMatrix.coeff(i,i));
RealScalar a = abs(m_workMatrix.coeff(i,i));
m_singularValues.coeffRef(i) = a;
if(computeU() && (a!=RealScalar(0))) m_matrixU.col(i) *= m_workMatrix.coeff(i,i)/a;
}

4
Eigen/src/SparseCholesky/SimplicialCholesky.h
View File

@ -746,6 +746,8 @@ template<typename Derived>
template<bool DoLDLT>
void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType& ap)
{
using std::sqrt;
eigen_assert(m_analysisIsOk && "You must first call analyzePattern()");
eigen_assert(ap.rows()==ap.cols());
const Index size = ap.rows();
@ -830,7 +832,7 @@ void SimplicialCholeskyBase<Derived>::factorize_preordered(const CholMatrixType&
ok = false; /* failure, matrix is not positive definite */
break;
}
Lx[p] = internal::sqrt(d) ;
Lx[p] = sqrt(d) ;
}
}

8
Eigen/src/SparseCore/AmbiVector.h
View File

@ -291,6 +291,7 @@ class AmbiVector<_Scalar,_Index>::Iterator
Iterator(const AmbiVector& vec, RealScalar epsilon = 0)
: m_vector(vec)
{
using std::abs;
m_epsilon = epsilon;
m_isDense = m_vector.m_mode==IsDense;
if (m_isDense)
@ -304,7 +305,7 @@ class AmbiVector<_Scalar,_Index>::Iterator
{
ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);
m_currentEl = m_vector.m_llStart;
while (m_currentEl>=0 && internal::abs(llElements[m_currentEl].value)<=m_epsilon)
while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<=m_epsilon)
m_currentEl = llElements[m_currentEl].next;
if (m_currentEl<0)
{
@ -326,11 +327,12 @@ class AmbiVector<_Scalar,_Index>::Iterator
Iterator& operator++()
{
using std::abs;
if (m_isDense)
{
do {
++m_cachedIndex;
} while (m_cachedIndex<m_vector.m_end && internal::abs(m_vector.m_buffer[m_cachedIndex])<m_epsilon);
} while (m_cachedIndex<m_vector.m_end && abs(m_vector.m_buffer[m_cachedIndex])<m_epsilon);
if (m_cachedIndex<m_vector.m_end)
m_cachedValue = m_vector.m_buffer[m_cachedIndex];
else
@ -341,7 +343,7 @@ class AmbiVector<_Scalar,_Index>::Iterator
ListEl* EIGEN_RESTRICT llElements = reinterpret_cast<ListEl*>(m_vector.m_buffer);
do {
m_currentEl = llElements[m_currentEl].next;
} while (m_currentEl>=0 && internal::abs(llElements[m_currentEl].value)<m_epsilon);
} while (m_currentEl>=0 && abs(llElements[m_currentEl].value)<m_epsilon);
if (m_currentEl<0)
{
m_cachedIndex = -1;

3
Eigen/src/SparseCore/SparseDot.h
View File

@ -86,7 +86,8 @@ template<typename Derived>
inline typename NumTraits<typename internal::traits<Derived>::Scalar>::Real
SparseMatrixBase<Derived>::norm() const
{
return internal::sqrt(squaredNorm());
using std::sqrt;
return sqrt(squaredNorm());
}
} // end namespace Eigen

3
Eigen/src/SparseCore/SparseProduct.h
View File

@ -107,7 +107,8 @@ class SparseSparseProduct : internal::no_assignment_operator,
SparseSparseProduct pruned(const Scalar& reference = 0, const RealScalar& epsilon = NumTraits<RealScalar>::dummy_precision()) const
{
return SparseSparseProduct(m_lhs,m_rhs,internal::abs(reference)*epsilon);
using std::abs;
return SparseSparseProduct(m_lhs,m_rhs,abs(reference)*epsilon);
}
template<typename Dest>

19
blas/level1_impl.h
View File

@ -75,6 +75,9 @@ int EIGEN_CAT(EIGEN_CAT(i,SCALAR_SUFFIX),amin_)(int *n, RealScalar *px, int *inc
int EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealScalar *ps)
{
using std::sqrt;
using std::abs;
Scalar& a = *reinterpret_cast<Scalar*>(pa);
Scalar& b = *reinterpret_cast<Scalar*>(pb);
RealScalar* c = pc;
@ -82,8 +85,8 @@ int EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealSc
#if !ISCOMPLEX
Scalar r,z;
Scalar aa = internal::abs(a);
Scalar ab = internal::abs(b);
Scalar aa = abs(a);
Scalar ab = abs(b);
if((aa+ab)==Scalar(0))
{
*c = 1;
@ -93,7 +96,7 @@ int EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealSc
}
else
{
r = internal::sqrt(a*a + b*b);
r = sqrt(a*a + b*b);
Scalar amax = aa>ab ? a : b;
r = amax>0 ? r : -r;
*c = a/r;
@ -108,7 +111,7 @@ int EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealSc
#else
Scalar alpha;
RealScalar norm,scale;
if(internal::abs(a)==RealScalar(0))
if(abs(a)==RealScalar(0))
{
*c = RealScalar(0);
*s = Scalar(1);
@ -116,10 +119,10 @@ int EIGEN_BLAS_FUNC(rotg)(RealScalar *pa, RealScalar *pb, RealScalar *pc, RealSc
}
else
{
scale = internal::abs(a) + internal::abs(b);
norm = scale*internal::sqrt((internal::abs2(a/scale))+ (internal::abs2(b/scale)));
alpha = a/internal::abs(a);
*c = internal::abs(a)/norm;
scale = abs(a) + abs(b);
norm = scale*sqrt((internal::abs2(a/scale))+ (internal::abs2(b/scale)));
alpha = a/abs(a);
*c = abs(a)/norm;
*s = alpha*internal::conj(b)/norm;
a = alpha*norm;
}

3
test/adjoint.cpp
View File

@ -16,6 +16,7 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
/* this test covers the following files:
Transpose.h Conjugate.h Dot.h
*/
using std::abs;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -63,7 +64,7 @@ template<typename MatrixType> void adjoint(const MatrixType& m)
VERIFY_IS_APPROX(v3, v1.normalized());
VERIFY_IS_APPROX(v3.norm(), RealScalar(1));
}
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(vzero.dot(v1)), static_cast<RealScalar>(1));
VERIFY_IS_MUCH_SMALLER_THAN(abs(vzero.dot(v1)), static_cast<RealScalar>(1));
// check compatibility of dot and adjoint

62
test/array.cpp
View File

@ -83,6 +83,7 @@ template<typename ArrayType> void array(const ArrayType& m)
template<typename ArrayType> void comparisons(const ArrayType& m)
{
using std::abs;
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -120,7 +121,7 @@ template<typename ArrayType> void comparisons(const ArrayType& m)
Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
for (int j=0; j<cols; ++j)
for (int i=0; i<rows; ++i)
m3(i,j) = internal::abs(m1(i,j))<mid ? 0 : m1(i,j);
m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
.select(ArrayType::Zero(rows,cols),m1), m3);
// shorter versions:
@ -149,6 +150,7 @@ template<typename ArrayType> void comparisons(const ArrayType& m)
template<typename ArrayType> void array_real(const ArrayType& m)
{
using std::abs;
typedef typename ArrayType::Index Index;
typedef typename ArrayType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -163,49 +165,49 @@ template<typename ArrayType> void array_real(const ArrayType& m)
Scalar s1 = internal::random<Scalar>();
// these tests are mostly to check possible compilation issues.
VERIFY_IS_APPROX(m1.sin(), std::sin(m1));
VERIFY_IS_APPROX(m1.sin(), internal::sin(m1));
VERIFY_IS_APPROX(m1.cos(), std::cos(m1));
VERIFY_IS_APPROX(m1.cos(), internal::cos(m1));
VERIFY_IS_APPROX(m1.asin(), std::asin(m1));
VERIFY_IS_APPROX(m1.asin(), internal::asin(m1));
VERIFY_IS_APPROX(m1.acos(), std::acos(m1));
VERIFY_IS_APPROX(m1.acos(), internal::acos(m1));
VERIFY_IS_APPROX(m1.tan(), std::tan(m1));
VERIFY_IS_APPROX(m1.tan(), internal::tan(m1));
// VERIFY_IS_APPROX(m1.sin(), std::sin(m1));
VERIFY_IS_APPROX(m1.sin(), sin(m1));
// VERIFY_IS_APPROX(m1.cos(), std::cos(m1));
VERIFY_IS_APPROX(m1.cos(), cos(m1));
// VERIFY_IS_APPROX(m1.asin(), std::asin(m1));
VERIFY_IS_APPROX(m1.asin(), asin(m1));
// VERIFY_IS_APPROX(m1.acos(), std::acos(m1));
VERIFY_IS_APPROX(m1.acos(), acos(m1));
// VERIFY_IS_APPROX(m1.tan(), std::tan(m1));
VERIFY_IS_APPROX(m1.tan(), tan(m1));
VERIFY_IS_APPROX(internal::cos(m1+RealScalar(3)*m2), internal::cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(std::cos(m1+RealScalar(3)*m2), std::cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
// VERIFY_IS_APPROX(std::cos(m1+RealScalar(3)*m2), std::cos((m1+RealScalar(3)*m2).eval()));
VERIFY_IS_APPROX(m1.abs().sqrt(), std::sqrt(std::abs(m1)));
VERIFY_IS_APPROX(m1.abs().sqrt(), internal::sqrt(internal::abs(m1)));
VERIFY_IS_APPROX(m1.abs(), internal::sqrt(internal::abs2(m1)));
// VERIFY_IS_APPROX(m1.abs().sqrt(), std::sqrt(std::abs(m1)));
VERIFY_IS_APPROX(m1.abs().sqrt(), sqrt(abs(m1)));
VERIFY_IS_APPROX(m1.abs(), sqrt(internal::abs2(m1)));
VERIFY_IS_APPROX(internal::abs2(internal::real(m1)) + internal::abs2(internal::imag(m1)), internal::abs2(m1));
VERIFY_IS_APPROX(internal::abs2(std::real(m1)) + internal::abs2(std::imag(m1)), internal::abs2(m1));
VERIFY_IS_APPROX(internal::abs2(real(m1)) + internal::abs2(imag(m1)), internal::abs2(m1));
if(!NumTraits<Scalar>::IsComplex)
VERIFY_IS_APPROX(internal::real(m1), m1);
VERIFY_IS_APPROX(m1.abs().log(), std::log(std::abs(m1)));
VERIFY_IS_APPROX(m1.abs().log(), internal::log(internal::abs(m1)));
//VERIFY_IS_APPROX(m1.abs().log(), std::log(std::abs(m1)));
VERIFY_IS_APPROX(m1.abs().log(), log(abs(m1)));
VERIFY_IS_APPROX(m1.exp(), std::exp(m1));
VERIFY_IS_APPROX(m1.exp() * m2.exp(), std::exp(m1+m2));
VERIFY_IS_APPROX(m1.exp(), internal::exp(m1));
VERIFY_IS_APPROX(m1.exp() / m2.exp(), std::exp(m1-m2));
// VERIFY_IS_APPROX(m1.exp(), std::exp(m1));
VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
VERIFY_IS_APPROX(m1.exp(), exp(m1));
VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
VERIFY_IS_APPROX(m1.pow(2), m1.square());
VERIFY_IS_APPROX(std::pow(m1,2), m1.square());
VERIFY_IS_APPROX(pow(m1,2), m1.square());
ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
VERIFY_IS_APPROX(std::pow(m1,exponents), m1.square());
VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
m3 = m1.abs();
VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(std::pow(m3,RealScalar(0.5)), m3.sqrt());
VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
// scalar by array division
const RealScalar tiny = std::sqrt(std::numeric_limits<RealScalar>::epsilon());
const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
s1 += Scalar(tiny);
m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
@ -223,11 +225,11 @@ template<typename ArrayType> void array_complex(const ArrayType& m)
for (Index i = 0; i < m.rows(); ++i)
for (Index j = 0; j < m.cols(); ++j)
m2(i,j) = std::sqrt(m1(i,j));
m2(i,j) = sqrt(m1(i,j));
VERIFY_IS_APPROX(m1.sqrt(), m2);
VERIFY_IS_APPROX(m1.sqrt(), std::sqrt(m1));
VERIFY_IS_APPROX(m1.sqrt(), internal::sqrt(m1));
// VERIFY_IS_APPROX(m1.sqrt(), std::sqrt(m1));
VERIFY_IS_APPROX(m1.sqrt(), Eigen::sqrt(m1));
}
template<typename ArrayType> void min_max(const ArrayType& m)

6
test/array_for_matrix.cpp
View File

@ -73,6 +73,7 @@ template<typename MatrixType> void array_for_matrix(const MatrixType& m)
template<typename MatrixType> void comparisons(const MatrixType& m)
{
using std::abs;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -110,7 +111,7 @@ template<typename MatrixType> void comparisons(const MatrixType& m)
Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
for (int j=0; j<cols; ++j)
for (int i=0; i<rows; ++i)
m3(i,j) = internal::abs(m1(i,j))<mid ? 0 : m1(i,j);
m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
VERIFY_IS_APPROX( (m1.array().abs()<MatrixType::Constant(rows,cols,mid).array())
.select(MatrixType::Zero(rows,cols),m1), m3);
// shorter versions:
@ -133,11 +134,12 @@ template<typename MatrixType> void comparisons(const MatrixType& m)
template<typename VectorType> void lpNorm(const VectorType& v)
{
using std::sqrt;
VectorType u = VectorType::Random(v.size());
VERIFY_IS_APPROX(u.template lpNorm<Infinity>(), u.cwiseAbs().maxCoeff());
VERIFY_IS_APPROX(u.template lpNorm<1>(), u.cwiseAbs().sum());
VERIFY_IS_APPROX(u.template lpNorm<2>(), internal::sqrt(u.array().abs().square().sum()));
VERIFY_IS_APPROX(u.template lpNorm<2>(), sqrt(u.array().abs().square().sum()));
VERIFY_IS_APPROX(internal::pow(u.template lpNorm<5>(), typename VectorType::RealScalar(5)), u.array().abs().pow(5).sum());
}

4
test/eigen2support.cpp
View File

@ -43,7 +43,9 @@ template<typename MatrixType> void eigen2support(const MatrixType& m)
VERIFY_IS_EQUAL((m1.col(0).end(1)), (m1.col(0).segment(rows-1,1)));
VERIFY_IS_EQUAL((m1.col(0).template end<1>()), (m1.col(0).segment(rows-1,1)));
using namespace internal;
using std::cos;
using internal::real;
using internal::abs2;
VERIFY_IS_EQUAL(ei_cos(s1), cos(s1));
VERIFY_IS_EQUAL(ei_real(s1), real(s1));
VERIFY_IS_EQUAL(ei_abs2(s1), abs2(s1));

2
test/geo_alignedbox.cpp
View File

@ -109,7 +109,7 @@ void specificTest1()
VERIFY_IS_APPROX( 14.0f, box.volume() );
VERIFY_IS_APPROX( 53.0f, box.diagonal().squaredNorm() );
VERIFY_IS_APPROX( internal::sqrt( 53.0f ), box.diagonal().norm() );
VERIFY_IS_APPROX( std::sqrt( 53.0f ), box.diagonal().norm() );
VERIFY_IS_APPROX( m, box.corner( BoxType::BottomLeft ) );
VERIFY_IS_APPROX( M, box.corner( BoxType::TopRight ) );

3
test/geo_hyperplane.cpp
View File

@ -79,6 +79,7 @@ template<typename HyperplaneType> void hyperplane(const HyperplaneType& _plane)
template<typename Scalar> void lines()
{
using std::abs;
typedef Hyperplane<Scalar, 2> HLine;
typedef ParametrizedLine<Scalar, 2> PLine;
typedef Matrix<Scalar,2,1> Vector;
@ -90,7 +91,7 @@ template<typename Scalar> void lines()
Vector u = Vector::Random();
Vector v = Vector::Random();
Scalar a = internal::random<Scalar>();
while (internal::abs(a-1) < 1e-4) a = internal::random<Scalar>();
while (abs(a-1) < 1e-4) a = internal::random<Scalar>();
while (u.norm() < 1e-4) u = Vector::Random();
while (v.norm() < 1e-4) v = Vector::Random();

3
test/geo_parametrizedline.cpp
View File

@ -18,6 +18,7 @@ template<typename LineType> void parametrizedline(const LineType& _line)
/* this test covers the following files:
ParametrizedLine.h
*/
using std::abs;
typedef typename LineType::Index Index;
const Index dim = _line.dim();
typedef typename LineType::Scalar Scalar;
@ -35,7 +36,7 @@ template<typename LineType> void parametrizedline(const LineType& _line)
LineType l0(p0, d0);
Scalar s0 = internal::random<Scalar>();
Scalar s1 = internal::abs(internal::random<Scalar>());
Scalar s1 = abs(internal::random<Scalar>());
VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0), RealScalar(1) );
VERIFY_IS_MUCH_SMALLER_THAN( l0.distance(p0+s0*d0), RealScalar(1) );

13
test/geo_quaternion.cpp
View File

@ -23,6 +23,7 @@ template<typename T> T bounded_acos(T v)
template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType& q1)
{
using std::abs;
typedef typename QuatType::Scalar Scalar;
typedef Matrix<Scalar,3,1> VectorType;
typedef AngleAxis<Scalar> AA;
@ -36,9 +37,9 @@ template<typename QuatType> void check_slerp(const QuatType& q0, const QuatType&
{
QuatType q = q0.slerp(t,q1);
Scalar theta = AA(q*q0.inverse()).angle();
VERIFY(internal::abs(q.norm() - 1) < largeEps);
VERIFY(abs(q.norm() - 1) < largeEps);
if(theta_tot==0) VERIFY(theta_tot==0);
else VERIFY(internal::abs(theta/theta_tot - t) < largeEps);
else VERIFY(abs(theta/theta_tot - t) < largeEps);
}
}
@ -47,7 +48,7 @@ template<typename Scalar, int Options> void quaternion(void)
/* this test covers the following files:
Quaternion.h
*/
using std::abs;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,3,1> Vector3;
typedef Matrix<Scalar,4,1> Vector4;
@ -82,13 +83,13 @@ template<typename Scalar, int Options> void quaternion(void)
q2 = AngleAxisx(a, v1.normalized());
// angular distance
Scalar refangle = internal::abs(AngleAxisx(q1.inverse()*q2).angle());
Scalar refangle = abs(AngleAxisx(q1.inverse()*q2).angle());
if (refangle>Scalar(M_PI))
refangle = Scalar(2)*Scalar(M_PI) - refangle;
if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps)
{
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(q1.angularDistance(q2) - refangle), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(abs(q1.angularDistance(q2) - refangle), Scalar(1));
}
// rotation matrix conversion
@ -109,7 +110,7 @@ template<typename Scalar, int Options> void quaternion(void)
// Do not execute the test if the rotation angle is almost zero, or
// the rotation axis and v1 are almost parallel.
if (internal::abs(aa.angle()) > 5*test_precision<Scalar>()
if (abs(aa.angle()) > 5*test_precision<Scalar>()
&& (aa.axis() - v1.normalized()).norm() < 1.99
&& (aa.axis() + v1.normalized()).norm() < 1.99)
{

8
test/geo_transformations.cpp
View File

@ -88,6 +88,8 @@ template<typename Scalar, int Mode, int Options> void transformations()
/* this test covers the following files:
Cross.h Quaternion.h, Transform.cpp
*/
using std::cos;
using std::abs;
typedef Matrix<Scalar,2,2> Matrix2;
typedef Matrix<Scalar,3,3> Matrix3;
typedef Matrix<Scalar,4,4> Matrix4;
@ -115,7 +117,7 @@ template<typename Scalar, int Mode, int Options> void transformations()
VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
VERIFY_IS_APPROX(internal::cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
@ -155,7 +157,7 @@ template<typename Scalar, int Mode, int Options> void transformations()
// Transform
// TODO complete the tests !
a = 0;
while (internal::abs(a)<Scalar(0.1))
while (abs(a)<Scalar(0.1))
a = internal::random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
q1 = AngleAxisx(a, v0.normalized());
Transform3 t0, t1, t2;
@ -249,7 +251,7 @@ template<typename Scalar, int Mode, int Options> void transformations()
Vector2 v20 = Vector2::Random();
Vector2 v21 = Vector2::Random();
for (int k=0; k<2; ++k)
if (internal::abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
if (abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
t21.setIdentity();
t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),

3
test/inverse.cpp
View File

@ -13,6 +13,7 @@
template<typename MatrixType> void inverse(const MatrixType& m)
{
using std::abs;
typedef typename MatrixType::Index Index;
/* this test covers the following files:
Inverse.h
@ -63,7 +64,7 @@ template<typename MatrixType> void inverse(const MatrixType& m)
MatrixType m3 = v3*v3.transpose(), m4(rows,cols);
m3.computeInverseAndDetWithCheck(m4, det, invertible);
VERIFY( rows==1 ? invertible : !invertible );
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(det-m3.determinant()), RealScalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(abs(det-m3.determinant()), RealScalar(1));
m3.computeInverseWithCheck(m4, invertible);
VERIFY( rows==1 ? invertible : !invertible );
#endif

3
test/linearstructure.cpp
View File

@ -11,6 +11,7 @@
template<typename MatrixType> void linearStructure(const MatrixType& m)
{
using std::abs;
/* this test covers the following files:
CwiseUnaryOp.h, CwiseBinaryOp.h, SelfCwiseBinaryOp.h
*/
@ -27,7 +28,7 @@ template<typename MatrixType> void linearStructure(const MatrixType& m)
m3(rows, cols);
Scalar s1 = internal::random<Scalar>();
while (internal::abs(s1)<1e-3) s1 = internal::random<Scalar>();
while (abs(s1)<1e-3) s1 = internal::random<Scalar>();
Index r = internal::random<Index>(0, rows-1),
c = internal::random<Index>(0, cols-1);

2
test/meta.cpp
View File

@ -56,7 +56,7 @@ void test_meta()
VERIFY(( internal::is_same<float,internal::remove_pointer<float* const >::type >::value));
VERIFY(internal::meta_sqrt<1>::ret == 1);
#define VERIFY_META_SQRT(X) VERIFY(internal::meta_sqrt<X>::ret == int(internal::sqrt(double(X))))
#define VERIFY_META_SQRT(X) VERIFY(internal::meta_sqrt<X>::ret == int(std::sqrt(double(X))))
VERIFY_META_SQRT(2);
VERIFY_META_SQRT(3);
VERIFY_META_SQRT(4);

22
test/packetmath.cpp
View File

@ -99,6 +99,7 @@ struct packet_helper<false,Packet>
template<typename Scalar> void packetmath()
{
using std::abs;
typedef typename internal::packet_traits<Scalar>::type Packet;
const int PacketSize = internal::packet_traits<Scalar>::size;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -113,7 +114,7 @@ template<typename Scalar> void packetmath()
{
data1[i] = internal::random<Scalar>()/RealScalar(PacketSize);
data2[i] = internal::random<Scalar>()/RealScalar(PacketSize);
refvalue = (std::max)(refvalue,internal::abs(data1[i]));
refvalue = (std::max)(refvalue,abs(data1[i]));
}
internal::pstore(data2, internal::pload<Packet>(data1));
@ -207,6 +208,7 @@ template<typename Scalar> void packetmath()
template<typename Scalar> void packetmath_real()
{
using std::abs;
typedef typename internal::packet_traits<Scalar>::type Packet;
const int PacketSize = internal::packet_traits<Scalar>::size;
@ -220,32 +222,32 @@ template<typename Scalar> void packetmath_real()
data1[i] = internal::random<Scalar>(-1e3,1e3);
data2[i] = internal::random<Scalar>(-1e3,1e3);
}
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSin, internal::sin, internal::psin);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasCos, internal::cos, internal::pcos);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasTan, internal::tan, internal::ptan);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSin, std::sin, internal::psin);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasCos, std::cos, internal::pcos);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasTan, std::tan, internal::ptan);
for (int i=0; i<size; ++i)
{
data1[i] = internal::random<Scalar>(-1,1);
data2[i] = internal::random<Scalar>(-1,1);
}
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasASin, internal::asin, internal::pasin);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasACos, internal::acos, internal::pacos);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasASin, std::asin, internal::pasin);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasACos, std::acos, internal::pacos);
for (int i=0; i<size; ++i)
{
data1[i] = internal::random<Scalar>(-87,88);
data2[i] = internal::random<Scalar>(-87,88);
}
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasExp, internal::exp, internal::pexp);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasExp, std::exp, internal::pexp);
for (int i=0; i<size; ++i)
{
data1[i] = internal::random<Scalar>(0,1e6);
data2[i] = internal::random<Scalar>(0,1e6);
}
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLog, internal::log, internal::plog);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSqrt, internal::sqrt, internal::psqrt);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasLog, std::log, internal::plog);
CHECK_CWISE1_IF(internal::packet_traits<Scalar>::HasSqrt, std::sqrt, internal::psqrt);
ref[0] = data1[0];
for (int i=0; i<PacketSize; ++i)
@ -254,7 +256,7 @@ template<typename Scalar> void packetmath_real()
CHECK_CWISE2((std::min), internal::pmin);
CHECK_CWISE2((std::max), internal::pmax);
CHECK_CWISE1(internal::abs, internal::pabs);
CHECK_CWISE1(abs, internal::pabs);
ref[0] = data1[0];
for (int i=0; i<PacketSize; ++i)

2
test/pastix_support.cpp
View File

@ -41,4 +41,4 @@ void test_pastix_support()
CALL_SUBTEST_2(test_pastix_T<double>());
CALL_SUBTEST_3( (test_pastix_T_LU<std::complex<float> >()) );
CALL_SUBTEST_4(test_pastix_T_LU<std::complex<double> >());
}
}

3
test/prec_inverse_4x4.cpp
View File

@ -29,6 +29,7 @@ template<typename MatrixType> void inverse_permutation_4x4()
template<typename MatrixType> void inverse_general_4x4(int repeat)
{
using std::abs;
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
double error_sum = 0., error_max = 0.;
@ -38,7 +39,7 @@ template<typename MatrixType> void inverse_general_4x4(int repeat)
RealScalar absdet;
do {
m = MatrixType::Random();
absdet = internal::abs(m.determinant());
absdet = abs(m.determinant());
} while(absdet < NumTraits<Scalar>::epsilon());
MatrixType inv = m.inverse();
double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / NumTraits<Scalar>::epsilon() );

6
test/qr.cpp
View File

@ -53,6 +53,8 @@ template<typename MatrixType, int Cols2> void qr_fixedsize()
template<typename MatrixType> void qr_invertible()
{
using std::log;
using std::abs;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
@ -76,12 +78,12 @@ template<typename MatrixType> void qr_invertible()
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = internal::abs(m1.diagonal().prod());
RealScalar absdet = abs(m1.diagonal().prod());
m3 = qr.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()

6
test/qr_colpivoting.cpp
View File

@ -72,6 +72,8 @@ template<typename MatrixType, int Cols2> void qr_fixedsize()
template<typename MatrixType> void qr_invertible()
{
using std::log;
using std::abs;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
@ -95,12 +97,12 @@ template<typename MatrixType> void qr_invertible()
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = internal::abs(m1.diagonal().prod());
RealScalar absdet = abs(m1.diagonal().prod());
m3 = qr.householderQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()

6
test/qr_fullpivoting.cpp
View File

@ -51,6 +51,8 @@ template<typename MatrixType> void qr()
template<typename MatrixType> void qr_invertible()
{
using std::log;
using std::abs;
typedef typename NumTraits<typename MatrixType::Scalar>::Real RealScalar;
typedef typename MatrixType::Scalar Scalar;
@ -78,12 +80,12 @@ template<typename MatrixType> void qr_invertible()
// now construct a matrix with prescribed determinant
m1.setZero();
for(int i = 0; i < size; i++) m1(i,i) = internal::random<Scalar>();
RealScalar absdet = internal::abs(m1.diagonal().prod());
RealScalar absdet = abs(m1.diagonal().prod());
m3 = qr.matrixQ(); // get a unitary
m1 = m3 * m1 * m3;
qr.compute(m1);
VERIFY_IS_APPROX(absdet, qr.absDeterminant());
VERIFY_IS_APPROX(internal::log(absdet), qr.logAbsDeterminant());
VERIFY_IS_APPROX(log(absdet), qr.logAbsDeterminant());
}
template<typename MatrixType> void qr_verify_assert()

8
test/real_qz.cpp
View File

@ -16,7 +16,7 @@ template<typename MatrixType> void real_qz(const MatrixType& m)
/* this test covers the following files:
RealQZ.h
*/
using std::abs;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -36,11 +36,11 @@ template<typename MatrixType> void real_qz(const MatrixType& m)
bool all_zeros = true;
for (Index i=0; i<A.cols(); i++)
for (Index j=0; j<i; j++) {
if (internal::abs(qz.matrixT()(i,j))!=Scalar(0.0))
if (abs(qz.matrixT()(i,j))!=Scalar(0.0))
all_zeros = false;
if (j<i-1 && internal::abs(qz.matrixS()(i,j))!=Scalar(0.0))
if (j<i-1 && abs(qz.matrixS()(i,j))!=Scalar(0.0))
all_zeros = false;
if (j==i-1 && j>0 && internal::abs(qz.matrixS()(i,j))!=Scalar(0.0) && internal::abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
if (j==i-1 && j>0 && abs(qz.matrixS()(i,j))!=Scalar(0.0) && abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
all_zeros = false;
}
VERIFY_IS_EQUAL(all_zeros, true);

7
test/redux.cpp
View File

@ -61,6 +61,7 @@ template<typename MatrixType> void matrixRedux(const MatrixType& m)
template<typename VectorType> void vectorRedux(const VectorType& w)
{
using std::abs;
typedef typename VectorType::Index Index;
typedef typename VectorType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -80,7 +81,7 @@ template<typename VectorType> void vectorRedux(const VectorType& w)
minc = (std::min)(minc, internal::real(v[j]));
maxc = (std::max)(maxc, internal::real(v[j]));
}
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(s - v.head(i).sum()), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.head(i).sum()), Scalar(1));
VERIFY_IS_APPROX(p, v_for_prod.head(i).prod());
VERIFY_IS_APPROX(minc, v.real().head(i).minCoeff());
VERIFY_IS_APPROX(maxc, v.real().head(i).maxCoeff());
@ -97,7 +98,7 @@ template<typename VectorType> void vectorRedux(const VectorType& w)
minc = (std::min)(minc, internal::real(v[j]));
maxc = (std::max)(maxc, internal::real(v[j]));
}
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(s - v.tail(size-i).sum()), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.tail(size-i).sum()), Scalar(1));
VERIFY_IS_APPROX(p, v_for_prod.tail(size-i).prod());
VERIFY_IS_APPROX(minc, v.real().tail(size-i).minCoeff());
VERIFY_IS_APPROX(maxc, v.real().tail(size-i).maxCoeff());
@ -114,7 +115,7 @@ template<typename VectorType> void vectorRedux(const VectorType& w)
minc = (std::min)(minc, internal::real(v[j]));
maxc = (std::max)(maxc, internal::real(v[j]));
}
VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(s - v.segment(i, size-2*i).sum()), Scalar(1));
VERIFY_IS_MUCH_SMALLER_THAN(abs(s - v.segment(i, size-2*i).sum()), Scalar(1));
VERIFY_IS_APPROX(p, v_for_prod.segment(i, size-2*i).prod());
VERIFY_IS_APPROX(minc, v.real().segment(i, size-2*i).minCoeff());
VERIFY_IS_APPROX(maxc, v.real().segment(i, size-2*i).maxCoeff());

2
test/sparselu.cpp
View File

@ -40,4 +40,4 @@ void test_sparselu()
CALL_SUBTEST_2(test_sparselu_T<double>());
CALL_SUBTEST_3(test_sparselu_T<std::complex<float> >());
CALL_SUBTEST_4(test_sparselu_T<std::complex<double> >());
}
}

24
test/stable_norm.cpp
View File

@ -32,6 +32,8 @@ template<typename MatrixType> void stable_norm(const MatrixType& m)
/* this test covers the following files:
StableNorm.h
*/
using std::sqrt;
using std::abs;
typedef typename MatrixType::Index Index;
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
@ -73,21 +75,21 @@ template<typename MatrixType> void stable_norm(const MatrixType& m)
// test isFinite
VERIFY(!isFinite( std::numeric_limits<RealScalar>::infinity()));
VERIFY(!isFinite(internal::sqrt(-internal::abs(big))));
VERIFY(!isFinite(sqrt(-abs(big))));
// test overflow
VERIFY(isFinite(internal::sqrt(size)*internal::abs(big)));
VERIFY_IS_NOT_APPROX(internal::sqrt(copy(vbig.squaredNorm())), internal::abs(internal::sqrt(size)*big)); // here the default norm must fail
VERIFY_IS_APPROX(vbig.stableNorm(), internal::sqrt(size)*internal::abs(big));
VERIFY_IS_APPROX(vbig.blueNorm(), internal::sqrt(size)*internal::abs(big));
VERIFY_IS_APPROX(vbig.hypotNorm(), internal::sqrt(size)*internal::abs(big));
VERIFY(isFinite(sqrt(size)*abs(big)));
VERIFY_IS_NOT_APPROX(sqrt(copy(vbig.squaredNorm())), abs(sqrt(size)*big)); // here the default norm must fail
VERIFY_IS_APPROX(vbig.stableNorm(), sqrt(size)*abs(big));
VERIFY_IS_APPROX(vbig.blueNorm(), sqrt(size)*abs(big));
VERIFY_IS_APPROX(vbig.hypotNorm(), sqrt(size)*abs(big));
// test underflow
VERIFY(isFinite(internal::sqrt(size)*internal::abs(small)));
VERIFY_IS_NOT_APPROX(internal::sqrt(copy(vsmall.squaredNorm())), internal::abs(internal::sqrt(size)*small)); // here the default norm must fail
VERIFY_IS_APPROX(vsmall.stableNorm(), internal::sqrt(size)*internal::abs(small));
VERIFY_IS_APPROX(vsmall.blueNorm(), internal::sqrt(size)*internal::abs(small));
VERIFY_IS_APPROX(vsmall.hypotNorm(), internal::sqrt(size)*internal::abs(small));
VERIFY(isFinite(sqrt(size)*abs(small)));
VERIFY_IS_NOT_APPROX(sqrt(copy(vsmall.squaredNorm())), abs(sqrt(size)*small)); // here the default norm must fail
VERIFY_IS_APPROX(vsmall.stableNorm(), sqrt(size)*abs(small));
VERIFY_IS_APPROX(vsmall.blueNorm(), sqrt(size)*abs(small));
VERIFY_IS_APPROX(vsmall.hypotNorm(), sqrt(size)*abs(small));
// Test compilation of cwise() version
VERIFY_IS_APPROX(vrand.colwise().stableNorm(), vrand.colwise().norm());

6
test/umeyama.cpp
View File

@ -93,13 +93,14 @@ Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> randMatrixSpecialUnitary(int si
template <typename MatrixType>
void run_test(int dim, int num_elements)
{
using std::abs;
typedef typename internal::traits<MatrixType>::Scalar Scalar;
typedef Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic> MatrixX;
typedef Matrix<Scalar, Eigen::Dynamic, 1> VectorX;
// MUST be positive because in any other case det(cR_t) may become negative for
// odd dimensions!
const Scalar c = internal::abs(internal::random<Scalar>());
const Scalar c = abs(internal::random<Scalar>());
MatrixX R = randMatrixSpecialUnitary<Scalar>(dim);
VectorX t = Scalar(50)*VectorX::Random(dim,1);
@ -122,6 +123,7 @@ void run_test(int dim, int num_elements)
template<typename Scalar, int Dimension>
void run_fixed_size_test(int num_elements)
{
using std::abs;
typedef Matrix<Scalar, Dimension+1, Dynamic> MatrixX;
typedef Matrix<Scalar, Dimension+1, Dimension+1> HomMatrix;
typedef Matrix<Scalar, Dimension, Dimension> FixedMatrix;
@ -131,7 +133,7 @@ void run_fixed_size_test(int num_elements)
// MUST be positive because in any other case det(cR_t) may become negative for
// odd dimensions!
const Scalar c = internal::abs(internal::random<Scalar>());
const Scalar c = abs(internal::random<Scalar>());
FixedMatrix R = randMatrixSpecialUnitary<Scalar>(dim);
FixedVector t = Scalar(50)*FixedVector::Random(dim,1);

3
unsupported/Eigen/AlignedVector3
View File

@ -167,7 +167,8 @@ template<typename _Scalar> class AlignedVector3
inline Scalar norm() const
{
return internal::sqrt(squaredNorm());
using std::sqrt;
return sqrt(squaredNorm());
}
inline AlignedVector3 cross(const AlignedVector3& other) const

2
unsupported/Eigen/src/FFT/ei_kissfft_impl.h
View File

@ -28,6 +28,7 @@ struct kiss_cpx_fft
inline
void make_twiddles(int nfft,bool inverse)
{
using std::acos;
m_inverse = inverse;
m_twiddles.resize(nfft);
Scalar phinc = (inverse?2:-2)* acos( (Scalar) -1) / nfft;
@ -399,6 +400,7 @@ struct kissfft_impl
inline
Complex * real_twiddles(int ncfft2)
{
using std::acos;
std::vector<Complex> & twidref = m_realTwiddles[ncfft2];// creates new if not there
if ( (int)twidref.size() != ncfft2 ) {
twidref.resize(ncfft2);

3
unsupported/Eigen/src/IterativeSolvers/IncompleteCholesky.h
View File

@ -116,6 +116,7 @@ template<typename Scalar, int _UpLo, typename OrderingType>
template<typename _MatrixType>
void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType& mat)
{
using std::sqrt;
eigen_assert(m_analysisIsOk && "analyzePattern() should be called first");
// FIXME Stability: We should probably compute the scaling factors and the shifts that are needed to ensure a succesful LLT factorization and an efficient preconditioner.
@ -182,7 +183,7 @@ void IncompleteCholesky<Scalar,_UpLo, OrderingType>::factorize(const _MatrixType
m_info = NumericalIssue;
return;
}
RealScalar rdiag = internal::sqrt(RealScalar(diag));
RealScalar rdiag = sqrt(RealScalar(diag));
Scalar scal = Scalar(1)/rdiag;
vals[colPtr[j]] = rdiag;
// Insert the largest p elements in the matrix and scale them meanwhile

3
unsupported/Eigen/src/IterativeSolvers/IterationController.h
View File

@ -129,7 +129,8 @@ class IterationController
bool converged() const { return m_res <= m_rhsn * m_resmax; }
bool converged(double nr)
{
m_res = internal::abs(nr);
using std::abs;
m_res = abs(nr);
m_resminreach = (std::min)(m_resminreach, m_res);
return converged();
}

1
unsupported/Eigen/src/IterativeSolvers/MINRES.h
View File

@ -32,6 +32,7 @@ namespace Eigen {
const Preconditioner& precond, int& iters,
typename Dest::RealScalar& tol_error)
{
using std::sqrt;
typedef typename Dest::RealScalar RealScalar;
typedef typename Dest::Scalar Scalar;
typedef Matrix<Scalar,Dynamic,1> VectorType;

17
unsupported/Eigen/src/MatrixFunctions/MatrixFunction.h
View File

@ -235,6 +235,7 @@ void MatrixFunction<MatrixType,AtomicType,1>::computeSchurDecomposition()
template <typename MatrixType, typename AtomicType>
void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
{
using std::abs;
const Index rows = m_T.rows();
VectorType diag = m_T.diagonal(); // contains eigenvalues of A
@ -251,14 +252,14 @@ void MatrixFunction<MatrixType,AtomicType,1>::partitionEigenvalues()
// Look for other element to add to the set
for (Index j=i+1; j<rows; ++j) {
if (internal::abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {
typename ListOfClusters::iterator qj = findCluster(diag(j));
if (qj == m_clusters.end()) {
qi->push_back(diag(j));
} else {
qi->insert(qi->end(), qj->begin(), qj->end());
m_clusters.erase(qj);
}
if (abs(diag(j) - diag(i)) <= separation() && std::find(qi->begin(), qi->end(), diag(j)) == qi->end()) {
typename ListOfClusters::iterator qj = findCluster(diag(j));
if (qj == m_clusters.end()) {
qi->push_back(diag(j));
} else {
qi->insert(qi->end(), qj->begin(), qj->end());
m_clusters.erase(qj);
}
}
}
}

3
unsupported/Eigen/src/MatrixFunctions/MatrixLogarithm.h
View File

@ -125,6 +125,7 @@ void MatrixLogarithmAtomic<MatrixType>::compute2x2(const MatrixType& A, MatrixTy
template <typename MatrixType>
void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixType& result)
{
using std::pow;
int numberOfSquareRoots = 0;
int numberOfExtraSquareRoots = 0;
int degree;
@ -141,7 +142,7 @@ void MatrixLogarithmAtomic<MatrixType>::computeBig(const MatrixType& A, MatrixTy
degree = getPadeDegree(normTminusI);
int degree2 = getPadeDegree(normTminusI / RealScalar(2));
if ((degree - degree2 <= 1) || (numberOfExtraSquareRoots == 1))
break;
break;
++numberOfExtraSquareRoots;
}
MatrixType sqrtT;

6
unsupported/Eigen/src/MatrixFunctions/MatrixSquareRoot.h
View File

@ -99,11 +99,12 @@ template <typename MatrixType>
void MatrixSquareRootQuasiTriangular<MatrixType>::computeDiagonalPartOfSqrt(MatrixType& sqrtT,
const MatrixType& T)
{
using std::sqrt;
const Index size = m_A.rows();
for (Index i = 0; i < size; i++) {
if (i == size - 1 || T.coeff(i+1, i) == 0) {
eigen_assert(T(i,i) > 0);
sqrtT.coeffRef(i,i) = internal::sqrt(T.coeff(i,i));
sqrtT.coeffRef(i,i) = sqrt(T.coeff(i,i));
}
else {
compute2x2diagonalBlock(sqrtT, T, i);
@ -289,6 +290,7 @@ template <typename MatrixType>
template <typename ResultType>
void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
{
using std::sqrt;
// Compute Schur decomposition of m_A
const ComplexSchur<MatrixType> schurOfA(m_A);
const MatrixType& T = schurOfA.matrixT();
@ -299,7 +301,7 @@ void MatrixSquareRootTriangular<MatrixType>::compute(ResultType &result)
result.resize(m_A.rows(), m_A.cols());
typedef typename MatrixType::Index Index;
for (Index i = 0; i < m_A.rows(); i++) {
result.coeffRef(i,i) = internal::sqrt(T.coeff(i,i));
result.coeffRef(i,i) = sqrt(T.coeff(i,i));
}
for (Index j = 1; j < m_A.cols(); j++) {
for (Index i = j-1; i >= 0; i--) {

15
unsupported/Eigen/src/NonLinearOptimization/HybridNonLinearSolver.h
View File

@ -52,7 +52,7 @@ public:
Parameters()
: factor(Scalar(100.))
, maxfev(1000)
, xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
, xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
, nb_of_subdiagonals(-1)
, nb_of_superdiagonals(-1)
, epsfcn(Scalar(0.)) {}
@ -70,7 +70,7 @@ public:
HybridNonLinearSolverSpace::Status hybrj1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
HybridNonLinearSolverSpace::Status solveInit(FVectorType &x);
@ -79,7 +79,7 @@ public:
HybridNonLinearSolverSpace::Status hybrd1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType &x);
@ -185,6 +185,8 @@ template<typename FunctorType, typename Scalar>
HybridNonLinearSolverSpace::Status
HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)
{
using std::abs;
assert(x.size()==n); // check the caller is not cheating us
Index j;
@ -276,7 +278,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)
++ncsuc;
if (ratio >= Scalar(.5) || ncsuc > 1)
delta = (std::max)(delta, pnorm / Scalar(.5));
if (internal::abs(ratio - 1.) <= Scalar(.1)) {
if (abs(ratio - 1.) <= Scalar(.1)) {
delta = pnorm / Scalar(.5);
}
}
@ -423,6 +425,9 @@ template<typename FunctorType, typename Scalar>
HybridNonLinearSolverSpace::Status
HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType &x)
{
using std::sqrt;
using std::abs;
assert(x.size()==n); // check the caller is not cheating us
Index j;
@ -516,7 +521,7 @@ HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType
++ncsuc;
if (ratio >= Scalar(.5) || ncsuc > 1)
delta = (std::max)(delta, pnorm / Scalar(.5));
if (internal::abs(ratio - 1.) <= Scalar(.1)) {
if (abs(ratio - 1.) <= Scalar(.1)) {
delta = pnorm / Scalar(.5);
}
}

36
unsupported/Eigen/src/NonLinearOptimization/LevenbergMarquardt.h
View File

@ -55,8 +55,8 @@ public:
Parameters()
: factor(Scalar(100.))
, maxfev(400)
, ftol(internal::sqrt(NumTraits<Scalar>::epsilon()))
, xtol(internal::sqrt(NumTraits<Scalar>::epsilon()))
, ftol(std::sqrt(NumTraits<Scalar>::epsilon()))
, xtol(std::sqrt(NumTraits<Scalar>::epsilon()))
, gtol(Scalar(0.))
, epsfcn(Scalar(0.)) {}
Scalar factor;
@ -72,7 +72,7 @@ public:
LevenbergMarquardtSpace::Status lmder1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
LevenbergMarquardtSpace::Status minimize(FVectorType &x);
@ -83,12 +83,12 @@ public:
FunctorType &functor,
FVectorType &x,
Index *nfev,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
LevenbergMarquardtSpace::Status lmstr1(
FVectorType &x,
const Scalar tol = internal::sqrt(NumTraits<Scalar>::epsilon())
const Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())
);
LevenbergMarquardtSpace::Status minimizeOptimumStorage(FVectorType &x);
@ -206,6 +206,9 @@ template<typename FunctorType, typename Scalar>
LevenbergMarquardtSpace::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
{
using std::abs;
using std::sqrt;
assert(x.size()==n); // check the caller is not cheating us
/* calculate the jacobian matrix. */
@ -249,7 +252,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
if (fnorm != 0.)
for (Index j = 0; j < n; ++j)
if (wa2[permutation.indices()[j]] != 0.)
gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (gnorm <= parameters.gtol)
@ -288,7 +291,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
/* the scaled directional derivative. */
wa3 = fjac.template triangularView<Upper>() * (qrfac.colsPermutation().inverse() *wa1);
temp1 = internal::abs2(wa3.stableNorm() / fnorm);
temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
temp2 = internal::abs2(sqrt(par) * pnorm / fnorm);
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
@ -326,9 +329,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
}
/* tests for convergence. */
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::RelativeReductionTooSmall;
if (delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@ -336,7 +339,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOneStep(FVectorType &x)
/* tests for termination and stringent tolerances. */
if (nfev >= parameters.maxfev)
return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::FtolTooSmall;
if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
return LevenbergMarquardtSpace::XtolTooSmall;
@ -423,6 +426,9 @@ template<typename FunctorType, typename Scalar>
LevenbergMarquardtSpace::Status
LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorType &x)
{
using std::abs;
using std::sqrt;
assert(x.size()==n); // check the caller is not cheating us
Index i, j;
@ -496,7 +502,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
if (fnorm != 0.)
for (j = 0; j < n; ++j)
if (wa2[permutation.indices()[j]] != 0.)
gnorm = (std::max)(gnorm, internal::abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
gnorm = (std::max)(gnorm, abs( fjac.col(j).head(j+1).dot(qtf.head(j+1)/fnorm) / wa2[permutation.indices()[j]]));
/* test for convergence of the gradient norm. */
if (gnorm <= parameters.gtol)
@ -535,7 +541,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
/* the scaled directional derivative. */
wa3 = fjac.topLeftCorner(n,n).template triangularView<Upper>() * (permutation.inverse() * wa1);
temp1 = internal::abs2(wa3.stableNorm() / fnorm);
temp2 = internal::abs2(internal::sqrt(par) * pnorm / fnorm);
temp2 = internal::abs2(sqrt(par) * pnorm / fnorm);
prered = temp1 + temp2 / Scalar(.5);
dirder = -(temp1 + temp2);
@ -573,9 +579,9 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
}
/* tests for convergence. */
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1. && delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;
if (internal::abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= parameters.ftol && prered <= parameters.ftol && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::RelativeReductionTooSmall;
if (delta <= parameters.xtol * xnorm)
return LevenbergMarquardtSpace::RelativeErrorTooSmall;
@ -583,7 +589,7 @@ LevenbergMarquardt<FunctorType,Scalar>::minimizeOptimumStorageOneStep(FVectorTyp
/* tests for termination and stringent tolerances. */
if (nfev >= parameters.maxfev)
return LevenbergMarquardtSpace::TooManyFunctionEvaluation;
if (internal::abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
if (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)
return LevenbergMarquardtSpace::FtolTooSmall;
if (delta <= NumTraits<Scalar>::epsilon() * xnorm)
return LevenbergMarquardtSpace::XtolTooSmall;

4
unsupported/Eigen/src/NonLinearOptimization/chkder.h
View File

@ -16,6 +16,10 @@ void chkder(
Matrix< Scalar, Dynamic, 1 > &err
)
{
using std::sqrt;
using std::abs;
using std::log;
typedef DenseIndex Index;
const Scalar eps = sqrt(NumTraits<Scalar>::epsilon());

3
unsupported/Eigen/src/NonLinearOptimization/covar.h
View File

@ -6,8 +6,9 @@ template <typename Scalar>
void covar(
Matrix< Scalar, Dynamic, Dynamic > &r,
const VectorXi &ipvt,
Scalar tol = sqrt(NumTraits<Scalar>::epsilon()) )
Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )
{
using std::abs;
typedef DenseIndex Index;
/* Local variables */

3
unsupported/Eigen/src/NonLinearOptimization/dogleg.h
View File

@ -10,6 +10,9 @@ void dogleg(
Scalar delta,
Matrix< Scalar, Dynamic, 1 > &x)
{
using std::abs;
using std::sqrt;
typedef DenseIndex Index;
/* Local variables */

3
unsupported/Eigen/src/NonLinearOptimization/fdjac1.h
View File

@ -11,6 +11,9 @@ DenseIndex fdjac1(
DenseIndex ml, DenseIndex mu,
Scalar epsfcn)
{
using std::sqrt;
using std::abs;
typedef DenseIndex Index;
/* Local variables */

4
unsupported/Eigen/src/NonLinearOptimization/lmpar.h
View File

@ -12,6 +12,8 @@ void lmpar(
Scalar &par,
Matrix< Scalar, Dynamic, 1 > &x)
{
using std::abs;
using std::sqrt;
typedef DenseIndex Index;
/* Local variables */
@ -168,6 +170,8 @@ void lmpar2(
Matrix< Scalar, Dynamic, 1 > &x)
{
using std::sqrt;
using std::abs;
typedef DenseIndex Index;
/* Local variables */

6
unsupported/Eigen/src/NumericalDiff/NumericalDiff.h
View File

@ -63,11 +63,13 @@ public:
*/
int df(const InputType& _x, JacobianType &jac) const
{
using std::sqrt;
using std::abs;
/* Local variables */
Scalar h;
int nfev=0;
const typename InputType::Index n = _x.size();
const Scalar eps = internal::sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
const Scalar eps = sqrt(((std::max)(epsfcn,NumTraits<Scalar>::epsilon() )));
ValueType val1, val2;
InputType x = _x;
// TODO : we should do this only if the size is not already known
@ -89,7 +91,7 @@ public:
// Function Body
for (int j = 0; j < n; ++j) {
h = eps * internal::abs(x[j]);
h = eps * abs(x[j]);
if (h == 0.) {
h = eps;
}

1
unsupported/Eigen/src/Polynomials/Companion.h
View File

@ -210,6 +210,7 @@ bool companion<_Scalar,_Deg>::balancedR( Scalar colNorm, Scalar rowNorm,
template< typename _Scalar, int _Deg >
void companion<_Scalar,_Deg>::balance()
{
using std::abs;
EIGEN_STATIC_ASSERT( Deg == Dynamic || 1 < Deg, YOU_MADE_A_PROGRAMMING_MISTAKE );
const Index deg = m_monic.size();
const Index deg_1 = deg-1;

13
unsupported/Eigen/src/Polynomials/PolynomialSolver.h
View File

@ -69,10 +69,11 @@ class PolynomialSolverBase
inline void realRoots( Stl_back_insertion_sequence& bi_seq,
const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
{
using std::abs;
bi_seq.clear();
for(Index i=0; i<m_roots.size(); ++i )
{
if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold ){
if( abs( m_roots[i].imag() ) < absImaginaryThreshold ){
bi_seq.push_back( m_roots[i].real() ); }
}
}
@ -118,13 +119,14 @@ class PolynomialSolverBase
bool& hasArealRoot,
const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
{
using std::abs;
hasArealRoot = false;
Index res=0;
RealScalar abs2(0);
for( Index i=0; i<m_roots.size(); ++i )
{
if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold )
if( abs( m_roots[i].imag() ) < absImaginaryThreshold )
{
if( !hasArealRoot )
{
@ -144,7 +146,7 @@ class PolynomialSolverBase
}
else
{
if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){
if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
res = i; }
}
}
@ -158,13 +160,14 @@ class PolynomialSolverBase
bool& hasArealRoot,
const RealScalar& absImaginaryThreshold = NumTraits<Scalar>::dummy_precision() ) const
{
using std::abs;
hasArealRoot = false;
Index res=0;
RealScalar val(0);
for( Index i=0; i<m_roots.size(); ++i )
{
if( internal::abs( m_roots[i].imag() ) < absImaginaryThreshold )
if( abs( m_roots[i].imag() ) < absImaginaryThreshold )
{
if( !hasArealRoot )
{
@ -184,7 +187,7 @@ class PolynomialSolverBase
}
else
{
if( internal::abs( m_roots[i].imag() ) < internal::abs( m_roots[res].imag() ) ){
if( abs( m_roots[i].imag() ) < abs( m_roots[res].imag() ) ){
res = i; }
}
}

6
unsupported/Eigen/src/Polynomials/PolynomialUtils.h
View File

@ -74,6 +74,7 @@ template <typename Polynomial>
inline
typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Polynomial& poly )
{
using std::abs;
typedef typename Polynomial::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real Real;
@ -82,7 +83,7 @@ typename NumTraits<typename Polynomial::Scalar>::Real cauchy_max_bound( const Po
Real cb(0);
for( DenseIndex i=0; i<poly.size()-1; ++i ){
cb += internal::abs(poly[i]*inv_leading_coeff); }
cb += abs(poly[i]*inv_leading_coeff); }
return cb + Real(1);
}
@ -96,6 +97,7 @@ template <typename Polynomial>
inline
typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Polynomial& poly )
{
using std::abs;
typedef typename Polynomial::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real Real;
@ -107,7 +109,7 @@ typename NumTraits<typename Polynomial::Scalar>::Real cauchy_min_bound( const Po
const Scalar inv_min_coeff = Scalar(1)/poly[i];
Real cb(1);
for( DenseIndex j=i+1; j<poly.size(); ++j ){
cb += internal::abs(poly[j]*inv_min_coeff); }
cb += abs(poly[j]*inv_min_coeff); }
return Real(1)/cb;
}

2
unsupported/doc/examples/PolynomialSolver1.cpp
View File

@ -49,5 +49,5 @@ int main()
cout.precision(10);
cout << "The last root in float then in double: " << psolvef.roots()[5] << "\t" << psolve6d.roots()[5] << endl;
std::complex<float> castedRoot( psolve6d.roots()[5].real(), psolve6d.roots()[5].imag() );
cout << "Norm of the difference: " << internal::abs( psolvef.roots()[5] - castedRoot ) << endl;
cout << "Norm of the difference: " << std::abs( psolvef.roots()[5] - castedRoot ) << endl;
}

17
unsupported/test/NonLinearOptimization.cpp
View File

@ -12,6 +12,8 @@
// It is intended to be done for this test only.
#include <Eigen/src/Core/util/DisableStupidWarnings.h>
using std::sqrt;
int fcn_chkder(const VectorXd &x, VectorXd &fvec, MatrixXd &fjac, int iflag)
{
/* subroutine fcn for chkder example. */
@ -795,7 +797,9 @@ struct hahn1_functor : Functor<double>
static const double m_x[236];
int operator()(const VectorXd &b, VectorXd &fvec)
{
static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0 , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0 , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0 , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 , 16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0 , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0 , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , 12.596E0 , 13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0 , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0 , 20.935E0 , 21.035E0 , 20.93E0 , 21.074E0 , 21.085E0 , 20.935E0 };
static const double m_y[236] = { .591E0 , 1.547E0 , 2.902E0 , 2.894E0 , 4.703E0 , 6.307E0 , 7.03E0 , 7.898E0 , 9.470E0 , 9.484E0 , 10.072E0 , 10.163E0 , 11.615E0 , 12.005E0 , 12.478E0 , 12.982E0 , 12.970E0 , 13.926E0 , 14.452E0 , 14.404E0 , 15.190E0 , 15.550E0 , 15.528E0 , 15.499E0 , 16.131E0 , 16.438E0 , 16.387E0 , 16.549E0 , 16.872E0 , 16.830E0 , 16.926E0 , 16.907E0 , 16.966E0 , 17.060E0 , 17.122E0 , 17.311E0 , 17.355E0 , 17.668E0 , 17.767E0 , 17.803E0 , 17.765E0 , 17.768E0 , 17.736E0 , 17.858E0 , 17.877E0 , 17.912E0 , 18.046E0 , 18.085E0 , 18.291E0 , 18.357E0 , 18.426E0 , 18.584E0 , 18.610E0 , 18.870E0 , 18.795E0 , 19.111E0 , .367E0 , .796E0 , 0.892E0 , 1.903E0 , 2.150E0 , 3.697E0 , 5.870E0 , 6.421E0 , 7.422E0 , 9.944E0 , 11.023E0 , 11.87E0 , 12.786E0 , 14.067E0 , 13.974E0 , 14.462E0 , 14.464E0 , 15.381E0 , 15.483E0 , 15.59E0 , 16.075E0 , 16.347E0 , 16.181E0 , 16.915E0 , 17.003E0 , 16.978E0 , 17.756E0 , 17.808E0 , 17.868E0 , 18.481E0 , 18.486E0 , 19.090E0 , 16.062E0 , 16.337E0 , 16.345E0 ,
16.388E0 , 17.159E0 , 17.116E0 , 17.164E0 , 17.123E0 , 17.979E0 , 17.974E0 , 18.007E0 , 17.993E0 , 18.523E0 , 18.669E0 , 18.617E0 , 19.371E0 , 19.330E0 , 0.080E0 , 0.248E0 , 1.089E0 , 1.418E0 , 2.278E0 , 3.624E0 , 4.574E0 , 5.556E0 , 7.267E0 , 7.695E0 , 9.136E0 , 9.959E0 , 9.957E0 , 11.600E0 , 13.138E0 , 13.564E0 , 13.871E0 , 13.994E0 , 14.947E0 , 15.473E0 , 15.379E0 , 15.455E0 , 15.908E0 , 16.114E0 , 17.071E0 , 17.135E0 , 17.282E0 , 17.368E0 , 17.483E0 , 17.764E0 , 18.185E0 , 18.271E0 , 18.236E0 , 18.237E0 , 18.523E0 , 18.627E0 , 18.665E0 , 19.086E0 , 0.214E0 , 0.943E0 , 1.429E0 , 2.241E0 , 2.951E0 , 3.782E0 , 4.757E0 , 5.602E0 , 7.169E0 , 8.920E0 , 10.055E0 , 12.035E0 , 12.861E0 , 13.436E0 , 14.167E0 , 14.755E0 , 15.168E0 , 15.651E0 , 15.746E0 , 16.216E0 , 16.445E0 , 16.965E0 , 17.121E0 , 17.206E0 , 17.250E0 , 17.339E0 , 17.793E0 , 18.123E0 , 18.49E0 , 18.566E0 , 18.645E0 , 18.706E0 , 18.924E0 , 19.1E0 , 0.375E0 , 0.471E0 , 1.504E0 , 2.204E0 , 2.813E0 , 4.765E0 , 9.835E0 , 10.040E0 , 11.946E0 , 12.596E0 ,
13.303E0 , 13.922E0 , 14.440E0 , 14.951E0 , 15.627E0 , 15.639E0 , 15.814E0 , 16.315E0 , 16.334E0 , 16.430E0 , 16.423E0 , 17.024E0 , 17.009E0 , 17.165E0 , 17.134E0 , 17.349E0 , 17.576E0 , 17.848E0 , 18.090E0 , 18.276E0 , 18.404E0 , 18.519E0 , 19.133E0 , 19.074E0 , 19.239E0 , 19.280E0 , 19.101E0 , 19.398E0 , 19.252E0 , 19.89E0 , 20.007E0 , 19.929E0 , 19.268E0 , 19.324E0 , 20.049E0 , 20.107E0 , 20.062E0 , 20.065E0 , 19.286E0 , 19.972E0 , 20.088E0 , 20.743E0 , 20.83E0 , 20.935E0 , 21.035E0 , 20.93E0 , 21.074E0 , 21.085E0 , 20.935E0 };
// int called=0; printf("call hahn1_functor with iflag=%d, called=%d\n", iflag, called); if (iflag==1) called++;
@ -828,7 +832,9 @@ struct hahn1_functor : Functor<double>
return 0;
}
};
const double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0 , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 , 282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 , 141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0 , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0 , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};
const double hahn1_functor::m_x[236] = { 24.41E0 , 34.82E0 , 44.09E0 , 45.07E0 , 54.98E0 , 65.51E0 , 70.53E0 , 75.70E0 , 89.57E0 , 91.14E0 , 96.40E0 , 97.19E0 , 114.26E0 , 120.25E0 , 127.08E0 , 133.55E0 , 133.61E0 , 158.67E0 , 172.74E0 , 171.31E0 , 202.14E0 , 220.55E0 , 221.05E0 , 221.39E0 , 250.99E0 , 268.99E0 , 271.80E0 , 271.97E0 , 321.31E0 , 321.69E0 , 330.14E0 , 333.03E0 , 333.47E0 , 340.77E0 , 345.65E0 , 373.11E0 , 373.79E0 , 411.82E0 , 419.51E0 , 421.59E0 , 422.02E0 , 422.47E0 , 422.61E0 , 441.75E0 , 447.41E0 , 448.7E0 , 472.89E0 , 476.69E0 , 522.47E0 , 522.62E0 , 524.43E0 , 546.75E0 , 549.53E0 , 575.29E0 , 576.00E0 , 625.55E0 , 20.15E0 , 28.78E0 , 29.57E0 , 37.41E0 , 39.12E0 , 50.24E0 , 61.38E0 , 66.25E0 , 73.42E0 , 95.52E0 , 107.32E0 , 122.04E0 , 134.03E0 , 163.19E0 , 163.48E0 , 175.70E0 , 179.86E0 , 211.27E0 , 217.78E0 , 219.14E0 , 262.52E0 , 268.01E0 , 268.62E0 , 336.25E0 , 337.23E0 , 339.33E0 , 427.38E0 , 428.58E0 , 432.68E0 , 528.99E0 , 531.08E0 , 628.34E0 , 253.24E0 , 273.13E0 , 273.66E0 ,
282.10E0 , 346.62E0 , 347.19E0 , 348.78E0 , 351.18E0 , 450.10E0 , 450.35E0 , 451.92E0 , 455.56E0 , 552.22E0 , 553.56E0 , 555.74E0 , 652.59E0 , 656.20E0 , 14.13E0 , 20.41E0 , 31.30E0 , 33.84E0 , 39.70E0 , 48.83E0 , 54.50E0 , 60.41E0 , 72.77E0 , 75.25E0 , 86.84E0 , 94.88E0 , 96.40E0 , 117.37E0 , 139.08E0 , 147.73E0 , 158.63E0 , 161.84E0 , 192.11E0 , 206.76E0 , 209.07E0 , 213.32E0 , 226.44E0 , 237.12E0 , 330.90E0 , 358.72E0 , 370.77E0 , 372.72E0 , 396.24E0 , 416.59E0 , 484.02E0 , 495.47E0 , 514.78E0 , 515.65E0 , 519.47E0 , 544.47E0 , 560.11E0 , 620.77E0 , 18.97E0 , 28.93E0 , 33.91E0 , 40.03E0 , 44.66E0 , 49.87E0 , 55.16E0 , 60.90E0 , 72.08E0 , 85.15E0 , 97.06E0 , 119.63E0 , 133.27E0 , 143.84E0 , 161.91E0 , 180.67E0 , 198.44E0 , 226.86E0 , 229.65E0 , 258.27E0 , 273.77E0 , 339.15E0 , 350.13E0 , 362.75E0 , 371.03E0 , 393.32E0 , 448.53E0 , 473.78E0 , 511.12E0 , 524.70E0 , 548.75E0 , 551.64E0 , 574.02E0 , 623.86E0 , 21.46E0 , 24.33E0 , 33.43E0 , 39.22E0 , 44.18E0 , 55.02E0 , 94.33E0 , 96.44E0 , 118.82E0 , 128.48E0 ,
141.94E0 , 156.92E0 , 171.65E0 , 190.00E0 , 223.26E0 , 223.88E0 , 231.50E0 , 265.05E0 , 269.44E0 , 271.78E0 , 273.46E0 , 334.61E0 , 339.79E0 , 349.52E0 , 358.18E0 , 377.98E0 , 394.77E0 , 429.66E0 , 468.22E0 , 487.27E0 , 519.54E0 , 523.03E0 , 612.99E0 , 638.59E0 , 641.36E0 , 622.05E0 , 631.50E0 , 663.97E0 , 646.9E0 , 748.29E0 , 749.21E0 , 750.14E0 , 647.04E0 , 646.89E0 , 746.9E0 , 748.43E0 , 747.35E0 , 749.27E0 , 647.61E0 , 747.78E0 , 750.51E0 , 851.37E0 , 845.97E0 , 847.54E0 , 849.93E0 , 851.61E0 , 849.75E0 , 850.98E0 , 848.23E0};
// http://www.itl.nist.gov/div898/strd/nls/data/hahn1.shtml
void testNistHahn1(void)
@ -1485,8 +1491,11 @@ struct Bennett5_functor : Functor<double>
return 0;
}
};
const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0, 11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };
const double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0 ,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };
const double Bennett5_functor::x[154] = { 7.447168E0, 8.102586E0, 8.452547E0, 8.711278E0, 8.916774E0, 9.087155E0, 9.232590E0, 9.359535E0, 9.472166E0, 9.573384E0, 9.665293E0, 9.749461E0, 9.827092E0, 9.899128E0, 9.966321E0, 10.029280E0, 10.088510E0, 10.144430E0, 10.197380E0, 10.247670E0, 10.295560E0, 10.341250E0, 10.384950E0, 10.426820E0, 10.467000E0, 10.505640E0, 10.542830E0, 10.578690E0, 10.613310E0, 10.646780E0, 10.679150E0, 10.710520E0, 10.740920E0, 10.770440E0, 10.799100E0, 10.826970E0, 10.854080E0, 10.880470E0, 10.906190E0, 10.931260E0, 10.955720E0, 10.979590E0, 11.002910E0, 11.025700E0, 11.047980E0, 11.069770E0, 11.091100E0, 11.111980E0, 11.132440E0, 11.152480E0, 11.172130E0, 11.191410E0, 11.210310E0, 11.228870E0, 11.247090E0, 11.264980E0, 11.282560E0, 11.299840E0, 11.316820E0, 11.333520E0, 11.349940E0, 11.366100E0, 11.382000E0, 11.397660E0, 11.413070E0, 11.428240E0, 11.443200E0, 11.457930E0, 11.472440E0, 11.486750E0, 11.500860E0, 11.514770E0, 11.528490E0, 11.542020E0, 11.555380E0, 11.568550E0,
11.581560E0, 11.594420E0, 11.607121E0, 11.619640E0, 11.632000E0, 11.644210E0, 11.656280E0, 11.668200E0, 11.679980E0, 11.691620E0, 11.703130E0, 11.714510E0, 11.725760E0, 11.736880E0, 11.747890E0, 11.758780E0, 11.769550E0, 11.780200E0, 11.790730E0, 11.801160E0, 11.811480E0, 11.821700E0, 11.831810E0, 11.841820E0, 11.851730E0, 11.861550E0, 11.871270E0, 11.880890E0, 11.890420E0, 11.899870E0, 11.909220E0, 11.918490E0, 11.927680E0, 11.936780E0, 11.945790E0, 11.954730E0, 11.963590E0, 11.972370E0, 11.981070E0, 11.989700E0, 11.998260E0, 12.006740E0, 12.015150E0, 12.023490E0, 12.031760E0, 12.039970E0, 12.048100E0, 12.056170E0, 12.064180E0, 12.072120E0, 12.080010E0, 12.087820E0, 12.095580E0, 12.103280E0, 12.110920E0, 12.118500E0, 12.126030E0, 12.133500E0, 12.140910E0, 12.148270E0, 12.155570E0, 12.162830E0, 12.170030E0, 12.177170E0, 12.184270E0, 12.191320E0, 12.198320E0, 12.205270E0, 12.212170E0, 12.219030E0, 12.225840E0, 12.232600E0, 12.239320E0, 12.245990E0, 12.252620E0, 12.259200E0, 12.265750E0, 12.272240E0 };
const double Bennett5_functor::y[154] = { -34.834702E0 ,-34.393200E0 ,-34.152901E0 ,-33.979099E0 ,-33.845901E0 ,-33.732899E0 ,-33.640301E0 ,-33.559200E0 ,-33.486801E0 ,-33.423100E0 ,-33.365101E0 ,-33.313000E0 ,-33.260899E0 ,-33.217400E0 ,-33.176899E0 ,-33.139198E0 ,-33.101601E0 ,-33.066799E0 ,-33.035000E0 ,-33.003101E0 ,-32.971298E0 ,-32.942299E0 ,-32.916302E0 ,-32.890202E0 ,-32.864101E0 ,-32.841000E0 ,-32.817799E0 ,-32.797501E0 ,-32.774300E0 ,-32.757000E0 ,-32.733799E0 ,-32.716400E0 ,-32.699100E0 ,-32.678799E0 ,-32.661400E0 ,-32.644001E0 ,-32.626701E0 ,-32.612202E0 ,-32.597698E0 ,-32.583199E0 ,-32.568699E0 ,-32.554298E0 ,-32.539799E0 ,-32.525299E0 ,-32.510799E0 ,-32.499199E0 ,-32.487598E0 ,-32.473202E0 ,-32.461601E0 ,-32.435501E0 ,-32.435501E0 ,-32.426800E0 ,-32.412300E0 ,-32.400799E0 ,-32.392101E0 ,-32.380501E0 ,-32.366001E0 ,-32.357300E0 ,-32.348598E0 ,-32.339901E0 ,-32.328400E0 ,-32.319698E0 ,-32.311001E0 ,-32.299400E0 ,-32.290699E0 ,-32.282001E0 ,-32.273300E0 ,-32.264599E0 ,-32.256001E0 ,-32.247299E0
,-32.238602E0 ,-32.229900E0 ,-32.224098E0 ,-32.215401E0 ,-32.203800E0 ,-32.198002E0 ,-32.189400E0 ,-32.183601E0 ,-32.174900E0 ,-32.169102E0 ,-32.163300E0 ,-32.154598E0 ,-32.145901E0 ,-32.140099E0 ,-32.131401E0 ,-32.125599E0 ,-32.119801E0 ,-32.111198E0 ,-32.105400E0 ,-32.096699E0 ,-32.090900E0 ,-32.088001E0 ,-32.079300E0 ,-32.073502E0 ,-32.067699E0 ,-32.061901E0 ,-32.056099E0 ,-32.050301E0 ,-32.044498E0 ,-32.038799E0 ,-32.033001E0 ,-32.027199E0 ,-32.024300E0 ,-32.018501E0 ,-32.012699E0 ,-32.004002E0 ,-32.001099E0 ,-31.995300E0 ,-31.989500E0 ,-31.983700E0 ,-31.977900E0 ,-31.972099E0 ,-31.969299E0 ,-31.963501E0 ,-31.957701E0 ,-31.951900E0 ,-31.946100E0 ,-31.940300E0 ,-31.937401E0 ,-31.931601E0 ,-31.925800E0 ,-31.922899E0 ,-31.917101E0 ,-31.911301E0 ,-31.908400E0 ,-31.902599E0 ,-31.896900E0 ,-31.893999E0 ,-31.888201E0 ,-31.885300E0 ,-31.882401E0 ,-31.876600E0 ,-31.873699E0 ,-31.867901E0 ,-31.862101E0 ,-31.859200E0 ,-31.856300E0 ,-31.850500E0 ,-31.844700E0 ,-31.841801E0 ,-31.838900E0 ,-31.833099E0 ,-31.830200E0 ,
-31.827299E0 ,-31.821600E0 ,-31.818701E0 ,-31.812901E0 ,-31.809999E0 ,-31.807100E0 ,-31.801300E0 ,-31.798401E0 ,-31.795500E0 ,-31.789700E0 ,-31.786800E0 };
// http://www.itl.nist.gov/div898/strd/nls/data/bennett5.shtml
void testNistBennett5(void)

1
unsupported/test/minres.cpp
View File

@ -7,6 +7,7 @@
// 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/.
#include <cmath>
#include "../../test/sparse_solver.h"
#include <Eigen/IterativeSolvers>

4
unsupported/test/mpreal/mpreal.h
View File

@ -3194,7 +3194,7 @@ namespace std
}
}
inline static mpfr::mpreal min(mp_prec_t precision = mpfr::mpreal::get_default_prec())
inline static mpfr::mpreal (min)(mp_prec_t precision = mpfr::mpreal::get_default_prec())
{
// min = 1/2*2^emin = 2^(emin-1)
return mpfr::mpreal(1, precision) << mpfr::mpreal::get_emin()-1;
@ -3205,7 +3205,7 @@ namespace std
return (-(max)(precision));
}
inline static mpfr::mpreal max(mp_prec_t precision = mpfr::mpreal::get_default_prec())
inline static mpfr::mpreal (max)(mp_prec_t precision = mpfr::mpreal::get_default_prec())
{
// max = (1-eps)*2^emax, eps is machine epsilon
return (mpfr::mpreal(1, precision) - epsilon(precision)) << mpfr::mpreal::get_emax();

1
unsupported/test/mpreal_support.cpp
View File

@ -5,7 +5,6 @@
#include <sstream>
using namespace mpfr;
using namespace std;
using namespace Eigen;
void test_mpreal_support()

11
unsupported/test/polynomialsolver.cpp
View File

@ -92,6 +92,7 @@ void evalSolver( const POLYNOMIAL& pols )
template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS >
void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots )
{
using std::sqrt;
typedef typename POLYNOMIAL::Scalar Scalar;
typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
@ -115,7 +116,7 @@ void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const
psolve.realRoots( calc_realRoots );
VERIFY( calc_realRoots.size() == (size_t)real_roots.size() );
const Scalar psPrec = internal::sqrt( test_precision<Scalar>() );
const Scalar psPrec = sqrt( test_precision<Scalar>() );
for( size_t i=0; i<calc_realRoots.size(); ++i )
{
@ -130,24 +131,24 @@ void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const
//Test greatestRoot
VERIFY( internal::isApprox( roots.array().abs().maxCoeff(),
internal::abs( psolve.greatestRoot() ), psPrec ) );
abs( psolve.greatestRoot() ), psPrec ) );
//Test smallestRoot
VERIFY( internal::isApprox( roots.array().abs().minCoeff(),
internal::abs( psolve.smallestRoot() ), psPrec ) );
abs( psolve.smallestRoot() ), psPrec ) );
bool hasRealRoot;
//Test absGreatestRealRoot
Real r = psolve.absGreatestRealRoot( hasRealRoot );
VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
if( hasRealRoot ){
VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), internal::abs(r), psPrec ) ); }
VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), abs(r), psPrec ) ); }
//Test absSmallestRealRoot
r = psolve.absSmallestRealRoot( hasRealRoot );
VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
if( hasRealRoot ){
VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), internal::abs( r ), psPrec ) ); }
VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), abs( r ), psPrec ) ); }
//Test greatestRealRoot
r = psolve.greatestRealRoot( hasRealRoot );