[136] | 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) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 |
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| 12 | template<typename ArrayType> void array(const ArrayType& m)
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| 13 | {
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| 14 | typedef typename ArrayType::Index Index;
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| 15 | typedef typename ArrayType::Scalar Scalar;
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| 16 | typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
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| 17 | typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
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| 18 |
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| 19 | Index rows = m.rows();
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| 20 | Index cols = m.cols();
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| 21 |
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| 22 | ArrayType m1 = ArrayType::Random(rows, cols),
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| 23 | m2 = ArrayType::Random(rows, cols),
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| 24 | m3(rows, cols);
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| 25 |
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| 26 | ColVectorType cv1 = ColVectorType::Random(rows);
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| 27 | RowVectorType rv1 = RowVectorType::Random(cols);
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| 28 |
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| 29 | Scalar s1 = internal::random<Scalar>(),
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| 30 | s2 = internal::random<Scalar>();
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| 31 |
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| 32 | // scalar addition
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| 33 | VERIFY_IS_APPROX(m1 + s1, s1 + m1);
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| 34 | VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
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| 35 | VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
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| 36 | VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
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| 37 | VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
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| 38 | VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
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| 39 | m3 = m1;
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| 40 | m3 += s2;
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| 41 | VERIFY_IS_APPROX(m3, m1 + s2);
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| 42 | m3 = m1;
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| 43 | m3 -= s1;
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| 44 | VERIFY_IS_APPROX(m3, m1 - s1);
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| 45 |
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| 46 | // scalar operators via Maps
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| 47 | m3 = m1;
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| 48 | ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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| 49 | VERIFY_IS_APPROX(m1, m3 - m2);
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| 50 |
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| 51 | m3 = m1;
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| 52 | ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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| 53 | VERIFY_IS_APPROX(m1, m3 + m2);
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| 54 |
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| 55 | m3 = m1;
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| 56 | ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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| 57 | VERIFY_IS_APPROX(m1, m3 * m2);
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| 58 |
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| 59 | m3 = m1;
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| 60 | m2 = ArrayType::Random(rows,cols);
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| 61 | m2 = (m2==0).select(1,m2);
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| 62 | ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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| 63 | VERIFY_IS_APPROX(m1, m3 / m2);
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| 64 |
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| 65 | // reductions
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| 66 | VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
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| 67 | VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
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| 68 | using std::abs;
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| 69 | VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
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| 70 | VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
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| 71 | if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
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| 72 | VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
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| 73 | VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>()));
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| 74 |
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| 75 | // vector-wise ops
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| 76 | m3 = m1;
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| 77 | VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
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| 78 | m3 = m1;
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| 79 | VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
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| 80 | m3 = m1;
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| 81 | VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
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| 82 | m3 = m1;
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| 83 | VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
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| 84 | }
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| 85 |
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| 86 | template<typename ArrayType> void comparisons(const ArrayType& m)
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| 87 | {
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| 88 | using std::abs;
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| 89 | typedef typename ArrayType::Index Index;
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| 90 | typedef typename ArrayType::Scalar Scalar;
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| 91 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 92 |
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| 93 | Index rows = m.rows();
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| 94 | Index cols = m.cols();
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| 95 |
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| 96 | Index r = internal::random<Index>(0, rows-1),
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| 97 | c = internal::random<Index>(0, cols-1);
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| 98 |
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| 99 | ArrayType m1 = ArrayType::Random(rows, cols),
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| 100 | m2 = ArrayType::Random(rows, cols),
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| 101 | m3(rows, cols);
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| 102 |
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| 103 | VERIFY(((m1 + Scalar(1)) > m1).all());
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| 104 | VERIFY(((m1 - Scalar(1)) < m1).all());
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| 105 | if (rows*cols>1)
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| 106 | {
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| 107 | m3 = m1;
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| 108 | m3(r,c) += 1;
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| 109 | VERIFY(! (m1 < m3).all() );
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| 110 | VERIFY(! (m1 > m3).all() );
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| 111 | }
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| 112 | VERIFY(!(m1 > m2 && m1 < m2).any());
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| 113 | VERIFY((m1 <= m2 || m1 >= m2).all());
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| 114 |
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| 115 | // comparisons to scalar
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| 116 | VERIFY( (m1 != (m1(r,c)+1) ).any() );
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| 117 | VERIFY( (m1 > (m1(r,c)-1) ).any() );
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| 118 | VERIFY( (m1 < (m1(r,c)+1) ).any() );
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| 119 | VERIFY( (m1 == m1(r,c) ).any() );
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| 120 |
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| 121 | // test Select
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| 122 | VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
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| 123 | VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
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| 124 | Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
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| 125 | for (int j=0; j<cols; ++j)
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| 126 | for (int i=0; i<rows; ++i)
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| 127 | m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
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| 128 | VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
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| 129 | .select(ArrayType::Zero(rows,cols),m1), m3);
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| 130 | // shorter versions:
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| 131 | VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
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| 132 | .select(0,m1), m3);
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| 133 | VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
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| 134 | .select(m1,0), m3);
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| 135 | // even shorter version:
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| 136 | VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
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| 137 |
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| 138 | // count
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| 139 | VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
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| 140 |
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| 141 | // and/or
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| 142 | VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
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| 143 | VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
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| 144 | RealScalar a = m1.abs().mean();
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| 145 | VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
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| 146 |
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| 147 | typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
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| 148 |
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| 149 | // TODO allows colwise/rowwise for array
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| 150 | VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
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| 151 | VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
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| 152 | }
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| 153 |
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| 154 | template<typename ArrayType> void array_real(const ArrayType& m)
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| 155 | {
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| 156 | using std::abs;
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| 157 | using std::sqrt;
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| 158 | typedef typename ArrayType::Index Index;
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| 159 | typedef typename ArrayType::Scalar Scalar;
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| 160 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 161 |
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| 162 | Index rows = m.rows();
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| 163 | Index cols = m.cols();
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| 164 |
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| 165 | ArrayType m1 = ArrayType::Random(rows, cols),
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| 166 | m2 = ArrayType::Random(rows, cols),
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| 167 | m3(rows, cols);
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| 168 |
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| 169 | Scalar s1 = internal::random<Scalar>();
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| 170 |
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| 171 | // these tests are mostly to check possible compilation issues.
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| 172 | VERIFY_IS_APPROX(m1.sin(), sin(m1));
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| 173 | VERIFY_IS_APPROX(m1.cos(), cos(m1));
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| 174 | VERIFY_IS_APPROX(m1.asin(), asin(m1));
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| 175 | VERIFY_IS_APPROX(m1.acos(), acos(m1));
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| 176 | VERIFY_IS_APPROX(m1.tan(), tan(m1));
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| 177 |
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| 178 | VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
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| 179 |
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| 180 | VERIFY_IS_APPROX(m1.abs().sqrt(), sqrt(abs(m1)));
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| 181 | VERIFY_IS_APPROX(m1.abs(), sqrt(numext::abs2(m1)));
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| 182 |
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| 183 | VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
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| 184 | VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));
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| 185 | if(!NumTraits<Scalar>::IsComplex)
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| 186 | VERIFY_IS_APPROX(numext::real(m1), m1);
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| 187 |
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| 188 | // shift argument of logarithm so that it is not zero
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| 189 | Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
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| 190 | VERIFY_IS_APPROX((m1.abs() + smallNumber).log() , log(abs(m1) + smallNumber));
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| 191 |
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| 192 | VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
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| 193 | VERIFY_IS_APPROX(m1.exp(), exp(m1));
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| 194 | VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
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| 195 |
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| 196 | VERIFY_IS_APPROX(m1.pow(2), m1.square());
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| 197 | VERIFY_IS_APPROX(pow(m1,2), m1.square());
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| 198 |
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| 199 | ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
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| 200 | VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
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| 201 |
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| 202 | m3 = m1.abs();
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| 203 | VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
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| 204 | VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
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| 205 |
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| 206 | // scalar by array division
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| 207 | const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
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| 208 | s1 += Scalar(tiny);
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| 209 | m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
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| 210 | VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
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| 211 |
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| 212 | // check inplace transpose
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| 213 | m3 = m1;
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| 214 | m3.transposeInPlace();
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| 215 | VERIFY_IS_APPROX(m3,m1.transpose());
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| 216 | m3.transposeInPlace();
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| 217 | VERIFY_IS_APPROX(m3,m1);
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| 218 | }
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| 219 |
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| 220 | template<typename ArrayType> void array_complex(const ArrayType& m)
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| 221 | {
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| 222 | typedef typename ArrayType::Index Index;
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| 223 |
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| 224 | Index rows = m.rows();
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| 225 | Index cols = m.cols();
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| 226 |
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| 227 | ArrayType m1 = ArrayType::Random(rows, cols),
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| 228 | m2(rows, cols);
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| 229 |
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| 230 | for (Index i = 0; i < m.rows(); ++i)
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| 231 | for (Index j = 0; j < m.cols(); ++j)
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| 232 | m2(i,j) = sqrt(m1(i,j));
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| 233 |
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| 234 | VERIFY_IS_APPROX(m1.sqrt(), m2);
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| 235 | VERIFY_IS_APPROX(m1.sqrt(), Eigen::sqrt(m1));
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| 236 | }
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| 237 |
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| 238 | template<typename ArrayType> void min_max(const ArrayType& m)
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| 239 | {
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| 240 | typedef typename ArrayType::Index Index;
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| 241 | typedef typename ArrayType::Scalar Scalar;
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| 242 |
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| 243 | Index rows = m.rows();
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| 244 | Index cols = m.cols();
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| 245 |
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| 246 | ArrayType m1 = ArrayType::Random(rows, cols);
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| 247 |
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| 248 | // min/max with array
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| 249 | Scalar maxM1 = m1.maxCoeff();
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| 250 | Scalar minM1 = m1.minCoeff();
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| 251 |
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| 252 | VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
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| 253 | VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
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| 254 |
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| 255 | VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
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| 256 | VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
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| 257 |
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| 258 | // min/max with scalar input
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| 259 | VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
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| 260 | VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
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| 261 |
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| 262 | VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
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| 263 | VERIFY_IS_APPROX(m1, (m1.max)( minM1));
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| 264 |
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| 265 | }
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| 266 |
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| 267 | void test_array()
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| 268 | {
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| 269 | for(int i = 0; i < g_repeat; i++) {
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| 270 | CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
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| 271 | CALL_SUBTEST_2( array(Array22f()) );
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| 272 | CALL_SUBTEST_3( array(Array44d()) );
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| 273 | CALL_SUBTEST_4( array(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 274 | CALL_SUBTEST_5( array(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 275 | CALL_SUBTEST_6( array(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 276 | }
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| 277 | for(int i = 0; i < g_repeat; i++) {
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| 278 | CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
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| 279 | CALL_SUBTEST_2( comparisons(Array22f()) );
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| 280 | CALL_SUBTEST_3( comparisons(Array44d()) );
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| 281 | CALL_SUBTEST_5( comparisons(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 282 | CALL_SUBTEST_6( comparisons(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 283 | }
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| 284 | for(int i = 0; i < g_repeat; i++) {
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| 285 | CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
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| 286 | CALL_SUBTEST_2( min_max(Array22f()) );
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| 287 | CALL_SUBTEST_3( min_max(Array44d()) );
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| 288 | CALL_SUBTEST_5( min_max(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 289 | CALL_SUBTEST_6( min_max(ArrayXXi(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 290 | }
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| 291 | for(int i = 0; i < g_repeat; i++) {
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| 292 | CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
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| 293 | CALL_SUBTEST_2( array_real(Array22f()) );
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| 294 | CALL_SUBTEST_3( array_real(Array44d()) );
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| 295 | CALL_SUBTEST_5( array_real(ArrayXXf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 296 | }
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| 297 | for(int i = 0; i < g_repeat; i++) {
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| 298 | CALL_SUBTEST_4( array_complex(ArrayXXcf(internal::random<int>(1,EIGEN_TEST_MAX_SIZE), internal::random<int>(1,EIGEN_TEST_MAX_SIZE))) );
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| 299 | }
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| 300 |
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| 301 | VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
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| 302 | VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
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| 303 | VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
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| 304 | typedef CwiseUnaryOp<internal::scalar_sum_op<double>, ArrayXd > Xpr;
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| 305 | VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
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| 306 | ArrayBase<Xpr>
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| 307 | >::value));
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| 308 | }
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