1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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6 | //
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7 | // This Source Code Form is subject to the terms of the Mozilla
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8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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10 |
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11 | #ifndef EIGEN_FUZZY_H
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12 | #define EIGEN_FUZZY_H
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13 |
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14 | namespace Eigen {
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15 |
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16 | namespace internal
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17 | {
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18 |
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19 | template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
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20 | struct isApprox_selector
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21 | {
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22 | static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
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23 | {
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24 | using std::min;
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25 | typename internal::nested<Derived,2>::type nested(x);
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26 | typename internal::nested<OtherDerived,2>::type otherNested(y);
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27 | return (nested - otherNested).cwiseAbs2().sum() <= prec * prec * (min)(nested.cwiseAbs2().sum(), otherNested.cwiseAbs2().sum());
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28 | }
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29 | };
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30 |
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31 | template<typename Derived, typename OtherDerived>
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32 | struct isApprox_selector<Derived, OtherDerived, true>
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33 | {
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34 | static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar&)
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35 | {
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36 | return x.matrix() == y.matrix();
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37 | }
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38 | };
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39 |
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40 | template<typename Derived, typename OtherDerived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
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41 | struct isMuchSmallerThan_object_selector
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42 | {
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43 | static bool run(const Derived& x, const OtherDerived& y, const typename Derived::RealScalar& prec)
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44 | {
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45 | return x.cwiseAbs2().sum() <= numext::abs2(prec) * y.cwiseAbs2().sum();
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46 | }
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47 | };
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48 |
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49 | template<typename Derived, typename OtherDerived>
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50 | struct isMuchSmallerThan_object_selector<Derived, OtherDerived, true>
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51 | {
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52 | static bool run(const Derived& x, const OtherDerived&, const typename Derived::RealScalar&)
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53 | {
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54 | return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
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55 | }
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56 | };
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57 |
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58 | template<typename Derived, bool is_integer = NumTraits<typename Derived::Scalar>::IsInteger>
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59 | struct isMuchSmallerThan_scalar_selector
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60 | {
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61 | static bool run(const Derived& x, const typename Derived::RealScalar& y, const typename Derived::RealScalar& prec)
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62 | {
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63 | return x.cwiseAbs2().sum() <= numext::abs2(prec * y);
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64 | }
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65 | };
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66 |
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67 | template<typename Derived>
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68 | struct isMuchSmallerThan_scalar_selector<Derived, true>
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69 | {
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70 | static bool run(const Derived& x, const typename Derived::RealScalar&, const typename Derived::RealScalar&)
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71 | {
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72 | return x.matrix() == Derived::Zero(x.rows(), x.cols()).matrix();
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73 | }
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74 | };
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75 |
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76 | } // end namespace internal
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77 |
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78 |
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79 | /** \returns \c true if \c *this is approximately equal to \a other, within the precision
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80 | * determined by \a prec.
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81 | *
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82 | * \note The fuzzy compares are done multiplicatively. Two vectors \f$ v \f$ and \f$ w \f$
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83 | * are considered to be approximately equal within precision \f$ p \f$ if
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84 | * \f[ \Vert v - w \Vert \leqslant p\,\min(\Vert v\Vert, \Vert w\Vert). \f]
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85 | * For matrices, the comparison is done using the Hilbert-Schmidt norm (aka Frobenius norm
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86 | * L2 norm).
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87 | *
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88 | * \note Because of the multiplicativeness of this comparison, one can't use this function
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89 | * to check whether \c *this is approximately equal to the zero matrix or vector.
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90 | * Indeed, \c isApprox(zero) returns false unless \c *this itself is exactly the zero matrix
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91 | * or vector. If you want to test whether \c *this is zero, use internal::isMuchSmallerThan(const
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92 | * RealScalar&, RealScalar) instead.
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93 | *
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94 | * \sa internal::isMuchSmallerThan(const RealScalar&, RealScalar) const
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95 | */
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96 | template<typename Derived>
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97 | template<typename OtherDerived>
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98 | bool DenseBase<Derived>::isApprox(
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99 | const DenseBase<OtherDerived>& other,
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100 | const RealScalar& prec
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101 | ) const
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102 | {
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103 | return internal::isApprox_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
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104 | }
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105 |
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106 | /** \returns \c true if the norm of \c *this is much smaller than \a other,
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107 | * within the precision determined by \a prec.
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108 | *
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109 | * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
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110 | * considered to be much smaller than \f$ x \f$ within precision \f$ p \f$ if
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111 | * \f[ \Vert v \Vert \leqslant p\,\vert x\vert. \f]
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112 | *
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113 | * For matrices, the comparison is done using the Hilbert-Schmidt norm. For this reason,
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114 | * the value of the reference scalar \a other should come from the Hilbert-Schmidt norm
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115 | * of a reference matrix of same dimensions.
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116 | *
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117 | * \sa isApprox(), isMuchSmallerThan(const DenseBase<OtherDerived>&, RealScalar) const
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118 | */
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119 | template<typename Derived>
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120 | bool DenseBase<Derived>::isMuchSmallerThan(
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121 | const typename NumTraits<Scalar>::Real& other,
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122 | const RealScalar& prec
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123 | ) const
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124 | {
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125 | return internal::isMuchSmallerThan_scalar_selector<Derived>::run(derived(), other, prec);
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126 | }
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127 |
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128 | /** \returns \c true if the norm of \c *this is much smaller than the norm of \a other,
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129 | * within the precision determined by \a prec.
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130 | *
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131 | * \note The fuzzy compares are done multiplicatively. A vector \f$ v \f$ is
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132 | * considered to be much smaller than a vector \f$ w \f$ within precision \f$ p \f$ if
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133 | * \f[ \Vert v \Vert \leqslant p\,\Vert w\Vert. \f]
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134 | * For matrices, the comparison is done using the Hilbert-Schmidt norm.
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135 | *
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136 | * \sa isApprox(), isMuchSmallerThan(const RealScalar&, RealScalar) const
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137 | */
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138 | template<typename Derived>
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139 | template<typename OtherDerived>
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140 | bool DenseBase<Derived>::isMuchSmallerThan(
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141 | const DenseBase<OtherDerived>& other,
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142 | const RealScalar& prec
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143 | ) const
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144 | {
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145 | return internal::isMuchSmallerThan_object_selector<Derived, OtherDerived>::run(derived(), other.derived(), prec);
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146 | }
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147 |
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148 | } // end namespace Eigen
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149 |
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150 | #endif // EIGEN_FUZZY_H
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