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306 lines
12 KiB
306 lines
12 KiB
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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template<typename ArrayType> void array(const ArrayType& m)
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{
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType;
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typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols);
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ColVectorType cv1 = ColVectorType::Random(rows);
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RowVectorType rv1 = RowVectorType::Random(cols);
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Scalar s1 = internal::random<Scalar>(),
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s2 = internal::random<Scalar>();
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// scalar addition
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VERIFY_IS_APPROX(m1 + s1, s1 + m1);
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VERIFY_IS_APPROX(m1 + s1, ArrayType::Constant(rows,cols,s1) + m1);
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VERIFY_IS_APPROX(s1 - m1, (-m1)+s1 );
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VERIFY_IS_APPROX(m1 - s1, m1 - ArrayType::Constant(rows,cols,s1));
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VERIFY_IS_APPROX(s1 - m1, ArrayType::Constant(rows,cols,s1) - m1);
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VERIFY_IS_APPROX((m1*Scalar(2)) - s2, (m1+m1) - ArrayType::Constant(rows,cols,s2) );
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m3 = m1;
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m3 += s2;
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VERIFY_IS_APPROX(m3, m1 + s2);
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m3 = m1;
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m3 -= s1;
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VERIFY_IS_APPROX(m3, m1 - s1);
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// scalar operators via Maps
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) -= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 - m2);
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) += ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 + m2);
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m3 = m1;
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) *= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 * m2);
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m3 = m1;
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m2 = ArrayType::Random(rows,cols);
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m2 = (m2==0).select(1,m2);
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ArrayType::Map(m1.data(), m1.rows(), m1.cols()) /= ArrayType::Map(m2.data(), m2.rows(), m2.cols());
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VERIFY_IS_APPROX(m1, m3 / m2);
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// reductions
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VERIFY_IS_APPROX(m1.abs().colwise().sum().sum(), m1.abs().sum());
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VERIFY_IS_APPROX(m1.abs().rowwise().sum().sum(), m1.abs().sum());
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using std::abs;
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VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.colwise().sum().sum() - m1.sum()), m1.abs().sum());
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VERIFY_IS_MUCH_SMALLER_THAN(abs(m1.rowwise().sum().sum() - m1.sum()), m1.abs().sum());
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if (!internal::isMuchSmallerThan(abs(m1.sum() - (m1+m2).sum()), m1.abs().sum(), test_precision<Scalar>()))
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VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum());
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VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>()));
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// vector-wise ops
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m3 = m1;
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VERIFY_IS_APPROX(m3.colwise() += cv1, m1.colwise() + cv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.colwise() -= cv1, m1.colwise() - cv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.rowwise() += rv1, m1.rowwise() + rv1);
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m3 = m1;
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VERIFY_IS_APPROX(m3.rowwise() -= rv1, m1.rowwise() - rv1);
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}
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template<typename ArrayType> void comparisons(const ArrayType& m)
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{
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using std::abs;
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Index rows = m.rows();
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Index cols = m.cols();
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Index r = internal::random<Index>(0, rows-1),
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c = internal::random<Index>(0, cols-1);
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols);
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VERIFY(((m1 + Scalar(1)) > m1).all());
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VERIFY(((m1 - Scalar(1)) < m1).all());
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if (rows*cols>1)
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{
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m3 = m1;
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m3(r,c) += 1;
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VERIFY(! (m1 < m3).all() );
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VERIFY(! (m1 > m3).all() );
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}
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// comparisons to scalar
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VERIFY( (m1 != (m1(r,c)+1) ).any() );
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VERIFY( (m1 > (m1(r,c)-1) ).any() );
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VERIFY( (m1 < (m1(r,c)+1) ).any() );
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VERIFY( (m1 == m1(r,c) ).any() );
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// test Select
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VERIFY_IS_APPROX( (m1<m2).select(m1,m2), m1.cwiseMin(m2) );
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VERIFY_IS_APPROX( (m1>m2).select(m1,m2), m1.cwiseMax(m2) );
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Scalar mid = (m1.cwiseAbs().minCoeff() + m1.cwiseAbs().maxCoeff())/Scalar(2);
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for (int j=0; j<cols; ++j)
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for (int i=0; i<rows; ++i)
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m3(i,j) = abs(m1(i,j))<mid ? 0 : m1(i,j);
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VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
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.select(ArrayType::Zero(rows,cols),m1), m3);
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// shorter versions:
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VERIFY_IS_APPROX( (m1.abs()<ArrayType::Constant(rows,cols,mid))
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.select(0,m1), m3);
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VERIFY_IS_APPROX( (m1.abs()>=ArrayType::Constant(rows,cols,mid))
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.select(m1,0), m3);
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// even shorter version:
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VERIFY_IS_APPROX( (m1.abs()<mid).select(0,m1), m3);
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// count
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VERIFY(((m1.abs()+1)>RealScalar(0.1)).count() == rows*cols);
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// and/or
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VERIFY( (m1<RealScalar(0) && m1>RealScalar(0)).count() == 0);
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VERIFY( (m1<RealScalar(0) || m1>=RealScalar(0)).count() == rows*cols);
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RealScalar a = m1.abs().mean();
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VERIFY( (m1<-a || m1>a).count() == (m1.abs()>a).count());
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typedef Array<typename ArrayType::Index, Dynamic, 1> ArrayOfIndices;
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// TODO allows colwise/rowwise for array
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VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).colwise().count(), ArrayOfIndices::Constant(cols,rows).transpose());
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VERIFY_IS_APPROX(((m1.abs()+1)>RealScalar(0.1)).rowwise().count(), ArrayOfIndices::Constant(rows, cols));
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}
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template<typename ArrayType> void array_real(const ArrayType& m)
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{
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using std::abs;
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using std::sqrt;
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2 = ArrayType::Random(rows, cols),
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m3(rows, cols);
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Scalar s1 = internal::random<Scalar>();
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// these tests are mostly to check possible compilation issues.
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VERIFY_IS_APPROX(m1.sin(), sin(m1));
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VERIFY_IS_APPROX(m1.cos(), cos(m1));
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VERIFY_IS_APPROX(m1.asin(), asin(m1));
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VERIFY_IS_APPROX(m1.acos(), acos(m1));
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VERIFY_IS_APPROX(m1.tan(), tan(m1));
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VERIFY_IS_APPROX(cos(m1+RealScalar(3)*m2), cos((m1+RealScalar(3)*m2).eval()));
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VERIFY_IS_APPROX(m1.abs().sqrt(), sqrt(abs(m1)));
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VERIFY_IS_APPROX(m1.abs(), sqrt(numext::abs2(m1)));
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VERIFY_IS_APPROX(numext::abs2(numext::real(m1)) + numext::abs2(numext::imag(m1)), numext::abs2(m1));
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VERIFY_IS_APPROX(numext::abs2(real(m1)) + numext::abs2(imag(m1)), numext::abs2(m1));
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if(!NumTraits<Scalar>::IsComplex)
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VERIFY_IS_APPROX(numext::real(m1), m1);
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// shift argument of logarithm so that it is not zero
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Scalar smallNumber = NumTraits<Scalar>::dummy_precision();
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VERIFY_IS_APPROX((m1.abs() + smallNumber).log() , log(abs(m1) + smallNumber));
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VERIFY_IS_APPROX(m1.exp() * m2.exp(), exp(m1+m2));
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VERIFY_IS_APPROX(m1.exp(), exp(m1));
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VERIFY_IS_APPROX(m1.exp() / m2.exp(),(m1-m2).exp());
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VERIFY_IS_APPROX(m1.pow(2), m1.square());
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VERIFY_IS_APPROX(pow(m1,2), m1.square());
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ArrayType exponents = ArrayType::Constant(rows, cols, RealScalar(2));
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VERIFY_IS_APPROX(Eigen::pow(m1,exponents), m1.square());
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m3 = m1.abs();
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VERIFY_IS_APPROX(m3.pow(RealScalar(0.5)), m3.sqrt());
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VERIFY_IS_APPROX(pow(m3,RealScalar(0.5)), m3.sqrt());
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// scalar by array division
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const RealScalar tiny = sqrt(std::numeric_limits<RealScalar>::epsilon());
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s1 += Scalar(tiny);
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m1 += ArrayType::Constant(rows,cols,Scalar(tiny));
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VERIFY_IS_APPROX(s1/m1, s1 * m1.inverse());
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// check inplace transpose
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m3 = m1;
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m3.transposeInPlace();
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VERIFY_IS_APPROX(m3,m1.transpose());
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m3.transposeInPlace();
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VERIFY_IS_APPROX(m3,m1);
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}
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template<typename ArrayType> void array_complex(const ArrayType& m)
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{
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typedef typename ArrayType::Index Index;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols),
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m2(rows, cols);
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for (Index i = 0; i < m.rows(); ++i)
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for (Index j = 0; j < m.cols(); ++j)
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m2(i,j) = sqrt(m1(i,j));
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VERIFY_IS_APPROX(m1.sqrt(), m2);
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VERIFY_IS_APPROX(m1.sqrt(), Eigen::sqrt(m1));
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}
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template<typename ArrayType> void min_max(const ArrayType& m)
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{
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typedef typename ArrayType::Index Index;
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typedef typename ArrayType::Scalar Scalar;
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Index rows = m.rows();
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Index cols = m.cols();
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ArrayType m1 = ArrayType::Random(rows, cols);
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// min/max with array
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Scalar maxM1 = m1.maxCoeff();
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Scalar minM1 = m1.minCoeff();
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VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)(ArrayType::Constant(rows,cols, minM1)));
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VERIFY_IS_APPROX(m1, (m1.min)(ArrayType::Constant(rows,cols, maxM1)));
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VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)(ArrayType::Constant(rows,cols, maxM1)));
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VERIFY_IS_APPROX(m1, (m1.max)(ArrayType::Constant(rows,cols, minM1)));
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// min/max with scalar input
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VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, minM1), (m1.min)( minM1));
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VERIFY_IS_APPROX(m1, (m1.min)( maxM1));
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VERIFY_IS_APPROX(ArrayType::Constant(rows,cols, maxM1), (m1.max)( maxM1));
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VERIFY_IS_APPROX(m1, (m1.max)( minM1));
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}
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void test_array()
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{
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( array(Array<float, 1, 1>()) );
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CALL_SUBTEST_2( array(Array22f()) );
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CALL_SUBTEST_3( array(Array44d()) );
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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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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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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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}
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( comparisons(Array<float, 1, 1>()) );
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CALL_SUBTEST_2( comparisons(Array22f()) );
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CALL_SUBTEST_3( comparisons(Array44d()) );
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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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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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}
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( min_max(Array<float, 1, 1>()) );
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CALL_SUBTEST_2( min_max(Array22f()) );
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CALL_SUBTEST_3( min_max(Array44d()) );
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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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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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}
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for(int i = 0; i < g_repeat; i++) {
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CALL_SUBTEST_1( array_real(Array<float, 1, 1>()) );
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CALL_SUBTEST_2( array_real(Array22f()) );
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CALL_SUBTEST_3( array_real(Array44d()) );
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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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}
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for(int i = 0; i < g_repeat; i++) {
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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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}
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VERIFY((internal::is_same< internal::global_math_functions_filtering_base<int>::type, int >::value));
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VERIFY((internal::is_same< internal::global_math_functions_filtering_base<float>::type, float >::value));
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VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Array2i>::type, ArrayBase<Array2i> >::value));
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typedef CwiseUnaryOp<internal::scalar_sum_op<double>, ArrayXd > Xpr;
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VERIFY((internal::is_same< internal::global_math_functions_filtering_base<Xpr>::type,
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ArrayBase<Xpr>
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>::value));
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}
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