diff options
34 files changed, 108 insertions, 103 deletions
diff --git a/Eigen/src/Cholesky/LDLT.h b/Eigen/src/Cholesky/LDLT.h index 54bd2d58a..b794b0c43 100644 --- a/Eigen/src/Cholesky/LDLT.h +++ b/Eigen/src/Cholesky/LDLT.h @@ -206,7 +206,7 @@ LDLT<MatrixType>& LDLT<MatrixType>::compute(const MatrixType& a) // in "Analysis of the Cholesky Decomposition of a Semi-definite Matrix" by // Nicholas J. Higham. Also see "Accuracy and Stability of Numerical // Algorithms" page 217, also by Higham. - cutoff = ei_abs(epsilon<Scalar>() * RealScalar(size) * biggest_in_corner); + cutoff = ei_abs(NumTraits<Scalar>::epsilon() * RealScalar(size) * biggest_in_corner); m_sign = ei_real(m_matrix.diagonal().coeff(index_of_biggest_in_corner)) > 0 ? 1 : -1; } diff --git a/Eigen/src/Core/DenseBase.h b/Eigen/src/Core/DenseBase.h index 9ef9108e4..700c11929 100644 --- a/Eigen/src/Core/DenseBase.h +++ b/Eigen/src/Core/DenseBase.h @@ -381,17 +381,17 @@ template<typename Derived> class DenseBase template<typename OtherDerived> bool isApprox(const DenseBase<OtherDerived>& other, - RealScalar prec = dummy_precision<Scalar>()) const; + RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; bool isMuchSmallerThan(const RealScalar& other, - RealScalar prec = dummy_precision<Scalar>()) const; + RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; template<typename OtherDerived> bool isMuchSmallerThan(const DenseBase<OtherDerived>& other, - RealScalar prec = dummy_precision<Scalar>()) const; + RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; - bool isApproxToConstant(const Scalar& value, RealScalar prec = dummy_precision<Scalar>()) const; - bool isConstant(const Scalar& value, RealScalar prec = dummy_precision<Scalar>()) const; - bool isZero(RealScalar prec = dummy_precision<Scalar>()) const; - bool isOnes(RealScalar prec = dummy_precision<Scalar>()) const; + bool isApproxToConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; + bool isConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; + bool isZero(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; + bool isOnes(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; inline Derived& operator*=(const Scalar& other); inline Derived& operator/=(const Scalar& other); diff --git a/Eigen/src/Core/IO.h b/Eigen/src/Core/IO.h index 8f91e272e..3e8d2bc66 100644 --- a/Eigen/src/Core/IO.h +++ b/Eigen/src/Core/IO.h @@ -146,7 +146,7 @@ std::ostream & ei_print_matrix(std::ostream & s, const Derived& _m, const IOForm if (NumTraits<Scalar>::HasFloatingPoint) { typedef typename NumTraits<Scalar>::Real RealScalar; - RealScalar explicit_precision_fp = std::ceil(-ei_log(epsilon<Scalar>())/ei_log(10.0)); + RealScalar explicit_precision_fp = std::ceil(-ei_log(NumTraits<Scalar>::epsilon())/ei_log(10.0)); explicit_precision = static_cast<std::streamsize>(explicit_precision_fp); } else diff --git a/Eigen/src/Core/MathFunctions.h b/Eigen/src/Core/MathFunctions.h index 1ea0116b4..1a4561555 100644 --- a/Eigen/src/Core/MathFunctions.h +++ b/Eigen/src/Core/MathFunctions.h @@ -25,13 +25,6 @@ #ifndef EIGEN_MATHFUNCTIONS_H #define EIGEN_MATHFUNCTIONS_H -template<typename T> inline typename NumTraits<T>::Real epsilon() -{ - return std::numeric_limits<typename NumTraits<T>::Real>::epsilon(); -} - -template<typename T> inline typename NumTraits<T>::Real dummy_precision(); - template<typename T> inline T ei_random(T a, T b); template<typename T> inline T ei_random(); template<typename T> inline T ei_random_amplitude() @@ -55,7 +48,6 @@ template<typename T> inline typename NumTraits<T>::Real ei_hypot(T x, T y) *** int *** **************/ -template<> inline int dummy_precision<int>() { return 0; } inline int ei_real(int x) { return x; } inline int& ei_real_ref(int& x) { return x; } inline int ei_imag(int) { return 0; } @@ -92,15 +84,15 @@ template<> inline int ei_random() { return ei_random<int>(-ei_random_amplitude<int>(), ei_random_amplitude<int>()); } -inline bool ei_isMuchSmallerThan(int a, int, int = dummy_precision<int>()) +inline bool ei_isMuchSmallerThan(int a, int, int = NumTraits<int>::dummy_precision()) { return a == 0; } -inline bool ei_isApprox(int a, int b, int = dummy_precision<int>()) +inline bool ei_isApprox(int a, int b, int = NumTraits<int>::dummy_precision()) { return a == b; } -inline bool ei_isApproxOrLessThan(int a, int b, int = dummy_precision<int>()) +inline bool ei_isApproxOrLessThan(int a, int b, int = NumTraits<int>::dummy_precision()) { return a <= b; } @@ -109,7 +101,6 @@ inline bool ei_isApproxOrLessThan(int a, int b, int = dummy_precision<int>()) *** float *** **************/ -template<> inline float dummy_precision<float>() { return 1e-5f; } inline float ei_real(float x) { return x; } inline float& ei_real_ref(float& x) { return x; } inline float ei_imag(float) { return 0.f; } @@ -140,15 +131,15 @@ template<> inline float ei_random() { return ei_random<float>(-ei_random_amplitude<float>(), ei_random_amplitude<float>()); } -inline bool ei_isMuchSmallerThan(float a, float b, float prec = dummy_precision<float>()) +inline bool ei_isMuchSmallerThan(float a, float b, float prec = NumTraits<float>::dummy_precision()) { return ei_abs(a) <= ei_abs(b) * prec; } -inline bool ei_isApprox(float a, float b, float prec = dummy_precision<float>()) +inline bool ei_isApprox(float a, float b, float prec = NumTraits<float>::dummy_precision()) { return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec; } -inline bool ei_isApproxOrLessThan(float a, float b, float prec = dummy_precision<float>()) +inline bool ei_isApproxOrLessThan(float a, float b, float prec = NumTraits<float>::dummy_precision()) { return a <= b || ei_isApprox(a, b, prec); } @@ -157,8 +148,6 @@ inline bool ei_isApproxOrLessThan(float a, float b, float prec = dummy_precision *** double *** **************/ -template<> inline double dummy_precision<double>() { return 1e-12; } - inline double ei_real(double x) { return x; } inline double& ei_real_ref(double& x) { return x; } inline double ei_imag(double) { return 0.; } @@ -189,15 +178,15 @@ template<> inline double ei_random() { return ei_random<double>(-ei_random_amplitude<double>(), ei_random_amplitude<double>()); } -inline bool ei_isMuchSmallerThan(double a, double b, double prec = dummy_precision<double>()) +inline bool ei_isMuchSmallerThan(double a, double b, double prec = NumTraits<double>::dummy_precision()) { return ei_abs(a) <= ei_abs(b) * prec; } -inline bool ei_isApprox(double a, double b, double prec = dummy_precision<double>()) +inline bool ei_isApprox(double a, double b, double prec = NumTraits<double>::dummy_precision()) { return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec; } -inline bool ei_isApproxOrLessThan(double a, double b, double prec = dummy_precision<double>()) +inline bool ei_isApproxOrLessThan(double a, double b, double prec = NumTraits<double>::dummy_precision()) { return a <= b || ei_isApprox(a, b, prec); } @@ -206,7 +195,6 @@ inline bool ei_isApproxOrLessThan(double a, double b, double prec = dummy_precis *** complex<float> *** *********************/ -template<> inline float dummy_precision<std::complex<float> >() { return dummy_precision<float>(); } inline float ei_real(const std::complex<float>& x) { return std::real(x); } inline float ei_imag(const std::complex<float>& x) { return std::imag(x); } inline float& ei_real_ref(std::complex<float>& x) { return reinterpret_cast<float*>(&x)[0]; } @@ -225,15 +213,15 @@ template<> inline std::complex<float> ei_random() { return std::complex<float>(ei_random<float>(), ei_random<float>()); } -inline bool ei_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b, float prec = dummy_precision<float>()) +inline bool ei_isMuchSmallerThan(const std::complex<float>& a, const std::complex<float>& b, float prec = NumTraits<float>::dummy_precision()) { return ei_abs2(a) <= ei_abs2(b) * prec * prec; } -inline bool ei_isMuchSmallerThan(const std::complex<float>& a, float b, float prec = dummy_precision<float>()) +inline bool ei_isMuchSmallerThan(const std::complex<float>& a, float b, float prec = NumTraits<float>::dummy_precision()) { return ei_abs2(a) <= ei_abs2(b) * prec * prec; } -inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = dummy_precision<float>()) +inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>& b, float prec = NumTraits<float>::dummy_precision()) { return ei_isApprox(ei_real(a), ei_real(b), prec) && ei_isApprox(ei_imag(a), ei_imag(b), prec); @@ -244,7 +232,6 @@ inline bool ei_isApprox(const std::complex<float>& a, const std::complex<float>& *** complex<double> *** **********************/ -template<> inline double dummy_precision<std::complex<double> >() { return dummy_precision<double>(); } inline double ei_real(const std::complex<double>& x) { return std::real(x); } inline double ei_imag(const std::complex<double>& x) { return std::imag(x); } inline double& ei_real_ref(std::complex<double>& x) { return reinterpret_cast<double*>(&x)[0]; } @@ -263,15 +250,15 @@ template<> inline std::complex<double> ei_random() { return std::complex<double>(ei_random<double>(), ei_random<double>()); } -inline bool ei_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b, double prec = dummy_precision<double>()) +inline bool ei_isMuchSmallerThan(const std::complex<double>& a, const std::complex<double>& b, double prec = NumTraits<double>::dummy_precision()) { return ei_abs2(a) <= ei_abs2(b) * prec * prec; } -inline bool ei_isMuchSmallerThan(const std::complex<double>& a, double b, double prec = dummy_precision<double>()) +inline bool ei_isMuchSmallerThan(const std::complex<double>& a, double b, double prec = NumTraits<double>::dummy_precision()) { return ei_abs2(a) <= ei_abs2(b) * prec * prec; } -inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = dummy_precision<double>()) +inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double>& b, double prec = NumTraits<double>::dummy_precision()) { return ei_isApprox(ei_real(a), ei_real(b), prec) && ei_isApprox(ei_imag(a), ei_imag(b), prec); @@ -283,7 +270,6 @@ inline bool ei_isApprox(const std::complex<double>& a, const std::complex<double *** long double *** ******************/ -template<> inline long double dummy_precision<long double>() { return dummy_precision<double>(); } inline long double ei_real(long double x) { return x; } inline long double& ei_real_ref(long double& x) { return x; } inline long double ei_imag(long double) { return 0.; } @@ -306,15 +292,15 @@ template<> inline long double ei_random() { return ei_random<double>(-ei_random_amplitude<double>(), ei_random_amplitude<double>()); } -inline bool ei_isMuchSmallerThan(long double a, long double b, long double prec = dummy_precision<long double>()) +inline bool ei_isMuchSmallerThan(long double a, long double b, long double prec = NumTraits<long double>::dummy_precision()) { return ei_abs(a) <= ei_abs(b) * prec; } -inline bool ei_isApprox(long double a, long double b, long double prec = dummy_precision<long double>()) +inline bool ei_isApprox(long double a, long double b, long double prec = NumTraits<long double>::dummy_precision()) { return ei_abs(a - b) <= std::min(ei_abs(a), ei_abs(b)) * prec; } -inline bool ei_isApproxOrLessThan(long double a, long double b, long double prec = dummy_precision<long double>()) +inline bool ei_isApproxOrLessThan(long double a, long double b, long double prec = NumTraits<long double>::dummy_precision()) { return a <= b || ei_isApprox(a, b, prec); } @@ -323,7 +309,6 @@ inline bool ei_isApproxOrLessThan(long double a, long double b, long double prec *** bool *** **************/ -template<> inline bool dummy_precision<bool>() { return 0; } inline bool ei_real(bool x) { return x; } inline bool& ei_real_ref(bool& x) { return x; } inline bool ei_imag(bool) { return 0; } @@ -336,15 +321,15 @@ template<> inline bool ei_random() { return (ei_random<int>(0,1) == 1); } -inline bool ei_isMuchSmallerThan(bool a, bool, bool = dummy_precision<bool>()) +inline bool ei_isMuchSmallerThan(bool a, bool, bool = NumTraits<bool>::dummy_precision()) { return !a; } -inline bool ei_isApprox(bool a, bool b, bool = dummy_precision<bool>()) +inline bool ei_isApprox(bool a, bool b, bool = NumTraits<bool>::dummy_precision()) { return a == b; } -inline bool ei_isApproxOrLessThan(bool a, bool b, bool = dummy_precision<bool>()) +inline bool ei_isApproxOrLessThan(bool a, bool b, bool = NumTraits<bool>::dummy_precision()) { return int(a) <= int(b); } diff --git a/Eigen/src/Core/MatrixBase.h b/Eigen/src/Core/MatrixBase.h index 65b3bfb7c..229195046 100644 --- a/Eigen/src/Core/MatrixBase.h +++ b/Eigen/src/Core/MatrixBase.h @@ -253,16 +253,16 @@ template<typename Derived> class MatrixBase Derived& setIdentity(); Derived& setIdentity(int rows, int cols); - bool isIdentity(RealScalar prec = dummy_precision<Scalar>()) const; - bool isDiagonal(RealScalar prec = dummy_precision<Scalar>()) const; + bool isIdentity(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; + bool isDiagonal(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; - bool isUpperTriangular(RealScalar prec = dummy_precision<Scalar>()) const; - bool isLowerTriangular(RealScalar prec = dummy_precision<Scalar>()) const; + bool isUpperTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; + bool isLowerTriangular(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; template<typename OtherDerived> bool isOrthogonal(const MatrixBase<OtherDerived>& other, - RealScalar prec = dummy_precision<Scalar>()) const; - bool isUnitary(RealScalar prec = dummy_precision<Scalar>()) const; + RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; + bool isUnitary(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; /** \returns true if each coefficients of \c *this and \a other are all exactly equal. * \warning When using floating point scalar values you probably should rather use a @@ -310,13 +310,13 @@ template<typename Derived> class MatrixBase ResultType& inverse, typename ResultType::Scalar& determinant, bool& invertible, - const RealScalar& absDeterminantThreshold = dummy_precision<Scalar>() + const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() ) const; template<typename ResultType> void computeInverseWithCheck( ResultType& inverse, bool& invertible, - const RealScalar& absDeterminantThreshold = dummy_precision<Scalar>() + const RealScalar& absDeterminantThreshold = NumTraits<Scalar>::dummy_precision() ) const; Scalar determinant() const; diff --git a/Eigen/src/Core/NumTraits.h b/Eigen/src/Core/NumTraits.h index 304e2c1d6..7279e156d 100644 --- a/Eigen/src/Core/NumTraits.h +++ b/Eigen/src/Core/NumTraits.h @@ -49,6 +49,7 @@ template<typename T> struct NumTraits; template<> struct NumTraits<int> + : std::numeric_limits<int> { typedef int Real; typedef double FloatingPoint; @@ -60,9 +61,12 @@ template<> struct NumTraits<int> AddCost = 1, MulCost = 1 }; + + inline static int dummy_precision() { return 0; } }; template<> struct NumTraits<float> + : std::numeric_limits<float> { typedef float Real; typedef float FloatingPoint; @@ -74,9 +78,12 @@ template<> struct NumTraits<float> AddCost = 1, MulCost = 1 }; + + inline static float dummy_precision() { return 1e-5f; } }; template<> struct NumTraits<double> + : std::numeric_limits<double> { typedef double Real; typedef double FloatingPoint; @@ -88,9 +95,12 @@ template<> struct NumTraits<double> AddCost = 1, MulCost = 1 }; + + inline static double dummy_precision() { return 1e-12; } }; template<typename _Real> struct NumTraits<std::complex<_Real> > + : std::numeric_limits<std::complex<_Real> > { typedef _Real Real; typedef std::complex<_Real> FloatingPoint; @@ -102,9 +112,13 @@ template<typename _Real> struct NumTraits<std::complex<_Real> > AddCost = 2 * NumTraits<Real>::AddCost, MulCost = 4 * NumTraits<Real>::MulCost + 2 * NumTraits<Real>::AddCost }; + + inline static Real epsilon() { return std::numeric_limits<Real>::epsilon(); } + inline static Real dummy_precision() { return NumTraits<Real>::dummy_precision(); } }; template<> struct NumTraits<long long int> + : std::numeric_limits<long long int> { typedef long long int Real; typedef long double FloatingPoint; @@ -119,6 +133,7 @@ template<> struct NumTraits<long long int> }; template<> struct NumTraits<long double> + : std::numeric_limits<long double> { typedef long double Real; typedef long double FloatingPoint; @@ -130,9 +145,12 @@ template<> struct NumTraits<long double> AddCost = 1, MulCost = 1 }; + + static inline long double dummy_precision() { return NumTraits<double>::dummy_precision(); } }; template<> struct NumTraits<bool> + : std::numeric_limits<bool> { typedef bool Real; typedef float FloatingPoint; @@ -144,6 +162,8 @@ template<> struct NumTraits<bool> AddCost = 1, MulCost = 1 }; + + inline static bool dummy_precision() { return 0; } }; #endif // EIGEN_NUMTRAITS_H diff --git a/Eigen/src/Eigenvalues/ComplexEigenSolver.h b/Eigen/src/Eigenvalues/ComplexEigenSolver.h index d55dc2a96..27c52b4dc 100644 --- a/Eigen/src/Eigenvalues/ComplexEigenSolver.h +++ b/Eigen/src/Eigenvalues/ComplexEigenSolver.h @@ -94,7 +94,7 @@ void ComplexEigenSolver<MatrixType>::compute(const MatrixType& matrix) m_eivalues.resize(n,1); m_eivec.resize(n,n); - RealScalar eps = epsilon<RealScalar>(); + RealScalar eps = NumTraits<RealScalar>::epsilon(); // Reduce to complex Schur form ComplexSchur<MatrixType> schur(matrix); diff --git a/Eigen/src/Eigenvalues/ComplexSchur.h b/Eigen/src/Eigenvalues/ComplexSchur.h index 38a1f56dc..5deac3247 100644 --- a/Eigen/src/Eigenvalues/ComplexSchur.h +++ b/Eigen/src/Eigenvalues/ComplexSchur.h @@ -159,7 +159,7 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU) RealScalar d,sd,sf; Complex c,b,disc,r1,r2,kappa; - RealScalar eps = epsilon<RealScalar>(); + RealScalar eps = NumTraits<RealScalar>::epsilon(); int iter = 0; while(true) diff --git a/Eigen/src/Geometry/AlignedBox.h b/Eigen/src/Geometry/AlignedBox.h index 1865b179b..5c1f992c6 100644 --- a/Eigen/src/Geometry/AlignedBox.h +++ b/Eigen/src/Geometry/AlignedBox.h @@ -171,7 +171,7 @@ EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const AlignedBox& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); } protected: diff --git a/Eigen/src/Geometry/AngleAxis.h b/Eigen/src/Geometry/AngleAxis.h index 284c60a74..d02ecf4c5 100644 --- a/Eigen/src/Geometry/AngleAxis.h +++ b/Eigen/src/Geometry/AngleAxis.h @@ -146,7 +146,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const AngleAxis& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return m_axis.isApprox(other.m_axis, prec) && ei_isApprox(m_angle,other.m_angle, prec); } }; @@ -165,7 +165,7 @@ template<typename QuatDerived> AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q) { Scalar n2 = q.vec().squaredNorm(); - if (n2 < dummy_precision<Scalar>()*dummy_precision<Scalar>()) + if (n2 < NumTraits<Scalar>::dummy_precision()*NumTraits<Scalar>::dummy_precision()) { m_angle = 0; m_axis << 1, 0, 0; diff --git a/Eigen/src/Geometry/EulerAngles.h b/Eigen/src/Geometry/EulerAngles.h index b6dbf8ae9..13d23761a 100644 --- a/Eigen/src/Geometry/EulerAngles.h +++ b/Eigen/src/Geometry/EulerAngles.h @@ -50,7 +50,7 @@ MatrixBase<Derived>::eulerAngles(int a0, int a1, int a2) const Matrix<Scalar,3,1> res; typedef Matrix<typename Derived::Scalar,2,1> Vector2; - const Scalar epsilon = dummy_precision<Scalar>(); + const Scalar epsilon = NumTraits<Scalar>::dummy_precision(); const int odd = ((a0+1)%3 == a1) ? 0 : 1; const int i = a0; diff --git a/Eigen/src/Geometry/Hyperplane.h b/Eigen/src/Geometry/Hyperplane.h index aab3d5b35..1d0b299ba 100644 --- a/Eigen/src/Geometry/Hyperplane.h +++ b/Eigen/src/Geometry/Hyperplane.h @@ -257,7 +257,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const Hyperplane& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return m_coeffs.isApprox(other.m_coeffs, prec); } protected: diff --git a/Eigen/src/Geometry/ParametrizedLine.h b/Eigen/src/Geometry/ParametrizedLine.h index 21a5595b9..1846a440a 100644 --- a/Eigen/src/Geometry/ParametrizedLine.h +++ b/Eigen/src/Geometry/ParametrizedLine.h @@ -123,7 +123,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); } protected: diff --git a/Eigen/src/Geometry/Quaternion.h b/Eigen/src/Geometry/Quaternion.h index 98b91e2de..67319d15b 100644 --- a/Eigen/src/Geometry/Quaternion.h +++ b/Eigen/src/Geometry/Quaternion.h @@ -163,7 +163,7 @@ public: * * \sa MatrixBase::isApprox() */ template<class OtherDerived> - bool isApprox(const QuaternionBase<OtherDerived>& other, RealScalar prec = dummy_precision<Scalar>()) const + bool isApprox(const QuaternionBase<OtherDerived>& other, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const { return coeffs().isApprox(other.coeffs(), prec); } /** return the result vector of \a v through the rotation*/ @@ -508,7 +508,7 @@ inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Deri // under the constraint: // ||x|| = 1 // which yields a singular value problem - if (c < Scalar(-1)+dummy_precision<Scalar>()) + if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision()) { c = std::max<Scalar>(c,-1); Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose(); @@ -584,7 +584,7 @@ template <class OtherDerived> Quaternion<typename ei_traits<Derived>::Scalar> QuaternionBase<Derived>::slerp(Scalar t, const QuaternionBase<OtherDerived>& other) const { - static const Scalar one = Scalar(1) - epsilon<Scalar>(); + static const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon(); Scalar d = this->dot(other); Scalar absD = ei_abs(d); diff --git a/Eigen/src/Geometry/Rotation2D.h b/Eigen/src/Geometry/Rotation2D.h index 7f24a3eae..73f731f76 100644 --- a/Eigen/src/Geometry/Rotation2D.h +++ b/Eigen/src/Geometry/Rotation2D.h @@ -121,7 +121,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const Rotation2D& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return ei_isApprox(m_angle,other.m_angle, prec); } }; diff --git a/Eigen/src/Geometry/Scaling.h b/Eigen/src/Geometry/Scaling.h index 4695914fd..2ff8eaba3 100644 --- a/Eigen/src/Geometry/Scaling.h +++ b/Eigen/src/Geometry/Scaling.h @@ -107,7 +107,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const UniformScaling& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const UniformScaling& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return ei_isApprox(m_factor, other.factor(), prec); } }; diff --git a/Eigen/src/Geometry/Transform.h b/Eigen/src/Geometry/Transform.h index 309c1e1fd..40bc7033a 100644 --- a/Eigen/src/Geometry/Transform.h +++ b/Eigen/src/Geometry/Transform.h @@ -429,7 +429,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return m_matrix.isApprox(other.m_matrix, prec); } /** Sets the last row to [0 ... 0 1] diff --git a/Eigen/src/Geometry/Translation.h b/Eigen/src/Geometry/Translation.h index b7477df9f..1e3906bde 100644 --- a/Eigen/src/Geometry/Translation.h +++ b/Eigen/src/Geometry/Translation.h @@ -154,7 +154,7 @@ public: * determined by \a prec. * * \sa MatrixBase::isApprox() */ - bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = dummy_precision<Scalar>()) const + bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const { return m_coeffs.isApprox(other.m_coeffs, prec); } }; diff --git a/Eigen/src/LU/FullPivLU.h b/Eigen/src/LU/FullPivLU.h index 657cbbf1c..72e878223 100644 --- a/Eigen/src/LU/FullPivLU.h +++ b/Eigen/src/LU/FullPivLU.h @@ -276,7 +276,7 @@ template<typename _MatrixType> class FullPivLU return m_usePrescribedThreshold ? m_prescribedThreshold // this formula comes from experimenting (see "LU precision tuning" thread on the list) // and turns out to be identical to Higham's formula used already in LDLt. - : epsilon<Scalar>() * m_lu.diagonalSize(); + : NumTraits<Scalar>::epsilon() * m_lu.diagonalSize(); } /** \returns the rank of the matrix of which *this is the LU decomposition. diff --git a/Eigen/src/QR/ColPivHouseholderQR.h b/Eigen/src/QR/ColPivHouseholderQR.h index 63d069081..bf28605dd 100644 --- a/Eigen/src/QR/ColPivHouseholderQR.h +++ b/Eigen/src/QR/ColPivHouseholderQR.h @@ -282,7 +282,7 @@ template<typename _MatrixType> class ColPivHouseholderQR return m_usePrescribedThreshold ? m_prescribedThreshold // this formula comes from experimenting (see "LU precision tuning" thread on the list) // and turns out to be identical to Higham's formula used already in LDLt. - : epsilon<Scalar>() * m_qr.diagonalSize(); + : NumTraits<Scalar>::epsilon() * m_qr.diagonalSize(); } /** \returns the number of nonzero pivots in the QR decomposition. @@ -350,7 +350,7 @@ ColPivHouseholderQR<MatrixType>& ColPivHouseholderQR<MatrixType>::compute(const for(int k = 0; k < cols; ++k) colSqNorms.coeffRef(k) = m_qr.col(k).squaredNorm(); - RealScalar threshold_helper = colSqNorms.maxCoeff() * ei_abs2(epsilon<Scalar>()) / rows; + RealScalar threshold_helper = colSqNorms.maxCoeff() * ei_abs2(NumTraits<Scalar>::epsilon()) / rows; m_nonzero_pivots = size; // the generic case is that in which all pivots are nonzero (invertible case) m_maxpivot = RealScalar(0); diff --git a/Eigen/src/QR/FullPivHouseholderQR.h b/Eigen/src/QR/FullPivHouseholderQR.h index 8e8dbbbf8..1ec60aeaf 100644 --- a/Eigen/src/QR/FullPivHouseholderQR.h +++ b/Eigen/src/QR/FullPivHouseholderQR.h @@ -270,7 +270,7 @@ FullPivHouseholderQR<MatrixType>& FullPivHouseholderQR<MatrixType>::compute(cons RowVectorType temp(cols); - m_precision = epsilon<Scalar>() * size; + m_precision = NumTraits<Scalar>::epsilon() * size; m_rows_transpositions.resize(matrix.rows()); IntRowVectorType cols_transpositions(matrix.cols()); @@ -370,7 +370,7 @@ struct ei_solve_retval<FullPivHouseholderQR<_MatrixType>, Rhs> RealScalar biggest_in_upper_part_of_c = c.corner(TopLeft, dec().rank(), c.cols()).cwiseAbs().maxCoeff(); RealScalar biggest_in_lower_part_of_c = c.corner(BottomLeft, rows-dec().rank(), c.cols()).cwiseAbs().maxCoeff(); // FIXME brain dead - const RealScalar m_precision = epsilon<Scalar>() * std::min(rows,cols); + const RealScalar m_precision = NumTraits<Scalar>::epsilon() * std::min(rows,cols); if(!ei_isMuchSmallerThan(biggest_in_lower_part_of_c, biggest_in_upper_part_of_c, m_precision)) return; } diff --git a/Eigen/src/SVD/JacobiSVD.h b/Eigen/src/SVD/JacobiSVD.h index 55fac3d12..94375725f 100644 --- a/Eigen/src/SVD/JacobiSVD.h +++ b/Eigen/src/SVD/JacobiSVD.h @@ -295,7 +295,7 @@ JacobiSVD<MatrixType, Options>& JacobiSVD<MatrixType, Options>::compute(const Ma int cols = matrix.cols(); int diagSize = std::min(rows, cols); m_singularValues.resize(diagSize); - const RealScalar precision = 2 * epsilon<Scalar>(); + const RealScalar precision = 2 * NumTraits<Scalar>::epsilon(); if(!ei_svd_precondition_if_more_rows_than_cols<MatrixType, Options>::run(matrix, work_matrix, *this) && !ei_svd_precondition_if_more_cols_than_rows<MatrixType, Options>::run(matrix, work_matrix, *this)) diff --git a/Eigen/src/SVD/SVD.h b/Eigen/src/SVD/SVD.h index 1d4bbe417..c308ff3ee 100644 --- a/Eigen/src/SVD/SVD.h +++ b/Eigen/src/SVD/SVD.h @@ -193,7 +193,7 @@ SVD<MatrixType>& SVD<MatrixType>::compute(const MatrixType& matrix) int i=0,its=0,j=0,k=0,l=0,nm=0; Scalar anorm, c, f, g, h, s, scale, x, y, z; bool convergence = true; - Scalar eps = dummy_precision<Scalar>(); + Scalar eps = NumTraits<Scalar>::dummy_precision(); Matrix<Scalar,Dynamic,1> rv1(n); g = scale = anorm = 0; diff --git a/Eigen/src/Sparse/AmbiVector.h b/Eigen/src/Sparse/AmbiVector.h index 6bb6ee3e4..1ac28272b 100644 --- a/Eigen/src/Sparse/AmbiVector.h +++ b/Eigen/src/Sparse/AmbiVector.h @@ -296,7 +296,7 @@ class AmbiVector<_Scalar>::Iterator * In practice, all coefficients having a magnitude smaller than \a epsilon * are skipped. */ - Iterator(const AmbiVector& vec, RealScalar epsilon = RealScalar(0.1)*dummy_precision<RealScalar>()) + Iterator(const AmbiVector& vec, RealScalar epsilon = RealScalar(0.1)*NumTraits<RealScalar>::dummy_precision()) : m_vector(vec) { m_epsilon = epsilon; diff --git a/Eigen/src/Sparse/CompressedStorage.h b/Eigen/src/Sparse/CompressedStorage.h index b25b05e91..4fc1797d1 100644 --- a/Eigen/src/Sparse/CompressedStorage.h +++ b/Eigen/src/Sparse/CompressedStorage.h @@ -185,7 +185,7 @@ class CompressedStorage return m_values[id]; } - void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) + void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision()) { size_t k = 0; size_t n = size(); diff --git a/Eigen/src/Sparse/DynamicSparseMatrix.h b/Eigen/src/Sparse/DynamicSparseMatrix.h index 96385df50..2594ffebc 100644 --- a/Eigen/src/Sparse/DynamicSparseMatrix.h +++ b/Eigen/src/Sparse/DynamicSparseMatrix.h @@ -209,7 +209,7 @@ class DynamicSparseMatrix inline void finalize() {} - void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) + void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision()) { for (int j=0; j<outerSize(); ++j) m_data[j].prune(reference,epsilon); diff --git a/Eigen/src/Sparse/SparseLDLT.h b/Eigen/src/Sparse/SparseLDLT.h index 7dfcf329c..28797a6c4 100644 --- a/Eigen/src/Sparse/SparseLDLT.h +++ b/Eigen/src/Sparse/SparseLDLT.h @@ -94,7 +94,7 @@ class SparseLDLT : m_flags(flags), m_status(0) { ei_assert((MatrixType::Flags&RowMajorBit)==0); - m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar>(); + m_precision = RealScalar(0.1) * Eigen::NumTraits<RealScalar>::dummy_precision(); } /** Creates a LDLT object and compute the respective factorization of \a matrix using @@ -103,7 +103,7 @@ class SparseLDLT : m_matrix(matrix.rows(), matrix.cols()), m_flags(flags), m_status(0) { ei_assert((MatrixType::Flags&RowMajorBit)==0); - m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar>(); + m_precision = RealScalar(0.1) * Eigen::NumTraits<RealScalar>::dummy_precision(); compute(matrix); } diff --git a/Eigen/src/Sparse/SparseLLT.h b/Eigen/src/Sparse/SparseLLT.h index 9018fe0df..a1c10ba13 100644 --- a/Eigen/src/Sparse/SparseLLT.h +++ b/Eigen/src/Sparse/SparseLLT.h @@ -54,7 +54,7 @@ class SparseLLT SparseLLT(int flags = 0) : m_flags(flags), m_status(0) { - m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar>(); + m_precision = RealScalar(0.1) * Eigen::NumTraits<RealScalar>::dummy_precision(); } /** Creates a LLT object and compute the respective factorization of \a matrix using @@ -62,7 +62,7 @@ class SparseLLT SparseLLT(const MatrixType& matrix, int flags = 0) : m_matrix(matrix.rows(), matrix.cols()), m_flags(flags), m_status(0) { - m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar>(); + m_precision = RealScalar(0.1) * Eigen::NumTraits<RealScalar>::dummy_precision(); compute(matrix); } diff --git a/Eigen/src/Sparse/SparseLU.h b/Eigen/src/Sparse/SparseLU.h index 0802b0807..3fe9df1ef 100644 --- a/Eigen/src/Sparse/SparseLU.h +++ b/Eigen/src/Sparse/SparseLU.h @@ -59,7 +59,7 @@ class SparseLU SparseLU(int flags = 0) : m_flags(flags), m_status(0) { - m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar>(); + m_precision = RealScalar(0.1) * Eigen::NumTraits<RealScalar>::dummy_precision(); } /** Creates a LU object and compute the respective factorization of \a matrix using @@ -67,7 +67,7 @@ class SparseLU SparseLU(const MatrixType& matrix, int flags = 0) : /*m_matrix(matrix.rows(), matrix.cols()),*/ m_flags(flags), m_status(0) { - m_precision = RealScalar(0.1) * Eigen::dummy_precision<RealScalar>(); + m_precision = RealScalar(0.1) * Eigen::NumTraits<RealScalar>::dummy_precision(); compute(matrix); } diff --git a/Eigen/src/Sparse/SparseMatrix.h b/Eigen/src/Sparse/SparseMatrix.h index bba0404c3..68385f564 100644 --- a/Eigen/src/Sparse/SparseMatrix.h +++ b/Eigen/src/Sparse/SparseMatrix.h @@ -350,7 +350,7 @@ class SparseMatrix } } - void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) + void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision()) { int k = 0; for (int j=0; j<m_outerSize; ++j) diff --git a/Eigen/src/Sparse/SparseMatrixBase.h b/Eigen/src/Sparse/SparseMatrixBase.h index 9e426c2b9..205325939 100644 --- a/Eigen/src/Sparse/SparseMatrixBase.h +++ b/Eigen/src/Sparse/SparseMatrixBase.h @@ -513,32 +513,32 @@ template<typename Derived> class SparseMatrixBase : public AnyMatrixBase<Derived template<typename OtherDerived> bool isApprox(const SparseMatrixBase<OtherDerived>& other, - RealScalar prec = dummy_precision<Scalar>()) const + RealScalar prec = NumTraits<Scalar>::dummy_precision()) const { return toDense().isApprox(other.toDense(),prec); } template<typename OtherDerived> bool isApprox(const MatrixBase<OtherDerived>& other, - RealScalar prec = dummy_precision<Scalar>()) const + RealScalar prec = NumTraits<Scalar>::dummy_precision()) const { return toDense().isApprox(other,prec); } // bool isMuchSmallerThan(const RealScalar& other, -// RealScalar prec = dummy_precision<Scalar>()) const; +// RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; // template<typename OtherDerived> // bool isMuchSmallerThan(const MatrixBase<OtherDerived>& other, -// RealScalar prec = dummy_precision<Scalar>()) const; +// RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; -// bool isApproxToConstant(const Scalar& value, RealScalar prec = dummy_precision<Scalar>()) const; -// bool isZero(RealScalar prec = dummy_precision<Scalar>()) const; -// bool isOnes(RealScalar prec = dummy_precision<Scalar>()) const; -// bool isIdentity(RealScalar prec = dummy_precision<Scalar>()) const; -// bool isDiagonal(RealScalar prec = dummy_precision<Scalar>()) const; +// bool isApproxToConstant(const Scalar& value, RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; +// bool isZero(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; +// bool isOnes(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; +// bool isIdentity(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; +// bool isDiagonal(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; -// bool isUpper(RealScalar prec = dummy_precision<Scalar>()) const; -// bool isLower(RealScalar prec = dummy_precision<Scalar>()) const; +// bool isUpper(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; +// bool isLower(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; // template<typename OtherDerived> // bool isOrthogonal(const MatrixBase<OtherDerived>& other, -// RealScalar prec = dummy_precision<Scalar>()) const; -// bool isUnitary(RealScalar prec = dummy_precision<Scalar>()) const; +// RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; +// bool isUnitary(RealScalar prec = NumTraits<Scalar>::dummy_precision()) const; // template<typename OtherDerived> // inline bool operator==(const MatrixBase<OtherDerived>& other) const diff --git a/Eigen/src/Sparse/SparseVector.h b/Eigen/src/Sparse/SparseVector.h index 13b4f75a6..58f3ec342 100644 --- a/Eigen/src/Sparse/SparseVector.h +++ b/Eigen/src/Sparse/SparseVector.h @@ -202,7 +202,7 @@ class SparseVector EIGEN_DEPRECATED void endFill() {} inline void finalize() {} - void prune(Scalar reference, RealScalar epsilon = dummy_precision<RealScalar>()) + void prune(Scalar reference, RealScalar epsilon = NumTraits<RealScalar>::dummy_precision()) { m_data.prune(reference,epsilon); } diff --git a/test/prec_inverse_4x4.cpp b/test/prec_inverse_4x4.cpp index e1b05aa0d..59ccbbcaf 100644 --- a/test/prec_inverse_4x4.cpp +++ b/test/prec_inverse_4x4.cpp @@ -35,7 +35,7 @@ template<typename MatrixType> void inverse_permutation_4x4() { MatrixType m = PermutationMatrix<4>(indices); MatrixType inv = m.inverse(); - double error = double( (m*inv-MatrixType::Identity()).norm() / epsilon<Scalar>() ); + double error = double( (m*inv-MatrixType::Identity()).norm() / NumTraits<Scalar>::epsilon() ); VERIFY(error == 0.0); std::next_permutation(indices.data(),indices.data()+4); } @@ -53,9 +53,9 @@ template<typename MatrixType> void inverse_general_4x4(int repeat) do { m = MatrixType::Random(); absdet = ei_abs(m.determinant()); - } while(absdet < epsilon<Scalar>()); + } while(absdet < NumTraits<Scalar>::epsilon()); MatrixType inv = m.inverse(); - double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / epsilon<Scalar>() ); + double error = double( (m*inv-MatrixType::Identity()).norm() * absdet / NumTraits<Scalar>::epsilon() ); error_sum += error; error_max = std::max(error_max, error); } diff --git a/test/product.h b/test/product.h index 85afbe1e4..f6109fae4 100644 --- a/test/product.h +++ b/test/product.h @@ -26,7 +26,7 @@ #include <Eigen/QR> template<typename Derived1, typename Derived2> -bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = dummy_precision<typename Derived1::RealScalar>()) +bool areNotApprox(const MatrixBase<Derived1>& m1, const MatrixBase<Derived2>& m2, typename Derived1::RealScalar epsilon = NumTraits<typename Derived1::RealScalar>::dummy_precision()) { return !((m1-m2).cwiseAbs2().maxCoeff() < epsilon * epsilon * std::max(m1.cwiseAbs2().maxCoeff(), m2.cwiseAbs2().maxCoeff())); 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