342 lines
12 KiB
C++
342 lines
12 KiB
C++
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// 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) 2010-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
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// Copyright (C) 2016 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 MatrixType>
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bool equalsIdentity(const MatrixType& A)
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{
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typedef typename MatrixType::Scalar Scalar;
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Scalar zero = static_cast<Scalar>(0);
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bool offDiagOK = true;
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for (Index i = 0; i < A.rows(); ++i) {
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for (Index j = i+1; j < A.cols(); ++j) {
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offDiagOK = offDiagOK && (A(i,j) == zero);
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}
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}
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for (Index i = 0; i < A.rows(); ++i) {
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for (Index j = 0; j < (std::min)(i, A.cols()); ++j) {
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offDiagOK = offDiagOK && (A(i,j) == zero);
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}
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}
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bool diagOK = (A.diagonal().array() == 1).all();
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return offDiagOK && diagOK;
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}
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template<typename VectorType>
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void check_extremity_accuracy(const VectorType &v, const typename VectorType::Scalar &low, const typename VectorType::Scalar &high)
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{
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typedef typename VectorType::Scalar Scalar;
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typedef typename VectorType::RealScalar RealScalar;
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RealScalar prec = internal::is_same<RealScalar,float>::value ? NumTraits<RealScalar>::dummy_precision()*10 : NumTraits<RealScalar>::dummy_precision()/10;
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Index size = v.size();
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if(size<20)
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return;
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for (int i=0; i<size; ++i)
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{
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if(i<5 || i>size-6)
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{
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Scalar ref = (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1);
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if(std::abs(ref)>1)
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{
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if(!internal::isApprox(v(i), ref, prec))
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std::cout << v(i) << " != " << ref << " ; relative error: " << std::abs((v(i)-ref)/ref) << " ; required precision: " << prec << " ; range: " << low << "," << high << " ; i: " << i << "\n";
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VERIFY(internal::isApprox(v(i), (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1), prec));
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}
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}
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}
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}
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template<typename VectorType>
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void testVectorType(const VectorType& base)
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{
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typedef typename VectorType::Scalar Scalar;
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typedef typename VectorType::RealScalar RealScalar;
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const Index size = base.size();
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Scalar high = internal::random<Scalar>(-500,500);
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Scalar low = (size == 1 ? high : internal::random<Scalar>(-500,500));
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if (numext::real(low)>numext::real(high)) std::swap(low,high);
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// check low==high
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if(internal::random<float>(0.f,1.f)<0.05f)
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low = high;
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// check abs(low) >> abs(high)
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else if(size>2 && std::numeric_limits<RealScalar>::max_exponent10>0 && internal::random<float>(0.f,1.f)<0.1f)
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low = -internal::random<Scalar>(1,2) * RealScalar(std::pow(RealScalar(10),std::numeric_limits<RealScalar>::max_exponent10/2));
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const Scalar step = ((size == 1) ? 1 : (high-low)/RealScalar(size-1));
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// check whether the result yields what we expect it to do
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VectorType m(base);
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m.setLinSpaced(size,low,high);
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if(!NumTraits<Scalar>::IsInteger)
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{
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VectorType n(size);
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for (int i=0; i<size; ++i)
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n(i) = low+RealScalar(i)*step;
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VERIFY_IS_APPROX(m,n);
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CALL_SUBTEST( check_extremity_accuracy(m, low, high) );
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}
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RealScalar range_length = numext::real(high-low);
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if((!NumTraits<Scalar>::IsInteger) || (range_length>=size && (Index(range_length)%(size-1))==0) || (Index(range_length+1)<size && (size%Index(range_length+1))==0))
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{
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VectorType n(size);
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if((!NumTraits<Scalar>::IsInteger) || (range_length>=size))
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for (int i=0; i<size; ++i)
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n(i) = size==1 ? low : (low + ((high-low)*Scalar(i))/RealScalar(size-1));
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else
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for (int i=0; i<size; ++i)
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n(i) = size==1 ? low : low + Scalar((double(range_length+1)*double(i))/double(size));
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VERIFY_IS_APPROX(m,n);
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// random access version
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m = VectorType::LinSpaced(size,low,high);
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VERIFY_IS_APPROX(m,n);
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VERIFY( internal::isApprox(m(m.size()-1),high) );
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VERIFY( size==1 || internal::isApprox(m(0),low) );
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VERIFY_IS_EQUAL(m(m.size()-1) , high);
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if(!NumTraits<Scalar>::IsInteger)
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CALL_SUBTEST( check_extremity_accuracy(m, low, high) );
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}
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VERIFY( numext::real(m(m.size()-1)) <= numext::real(high) );
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VERIFY( (m.array().real() <= numext::real(high)).all() );
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VERIFY( (m.array().real() >= numext::real(low)).all() );
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VERIFY( numext::real(m(m.size()-1)) >= numext::real(low) );
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if(size>=1)
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{
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VERIFY( internal::isApprox(m(0),low) );
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VERIFY_IS_EQUAL(m(0) , low);
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}
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// check whether everything works with row and col major vectors
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Matrix<Scalar,Dynamic,1> row_vector(size);
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Matrix<Scalar,1,Dynamic> col_vector(size);
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row_vector.setLinSpaced(size,low,high);
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col_vector.setLinSpaced(size,low,high);
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// when using the extended precision (e.g., FPU) the relative error might exceed 1 bit
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// when computing the squared sum in isApprox, thus the 2x factor.
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VERIFY( row_vector.isApprox(col_vector.transpose(), RealScalar(2)*NumTraits<Scalar>::epsilon()));
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Matrix<Scalar,Dynamic,1> size_changer(size+50);
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size_changer.setLinSpaced(size,low,high);
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VERIFY( size_changer.size() == size );
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typedef Matrix<Scalar,1,1> ScalarMatrix;
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ScalarMatrix scalar;
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scalar.setLinSpaced(1,low,high);
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VERIFY_IS_APPROX( scalar, ScalarMatrix::Constant(high) );
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VERIFY_IS_APPROX( ScalarMatrix::LinSpaced(1,low,high), ScalarMatrix::Constant(high) );
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// regression test for bug 526 (linear vectorized transversal)
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if (size > 1 && (!NumTraits<Scalar>::IsInteger)) {
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m.tail(size-1).setLinSpaced(low, high);
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VERIFY_IS_APPROX(m(size-1), high);
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}
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// regression test for bug 1383 (LinSpaced with empty size/range)
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{
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Index n0 = VectorType::SizeAtCompileTime==Dynamic ? 0 : VectorType::SizeAtCompileTime;
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low = internal::random<Scalar>();
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m = VectorType::LinSpaced(n0,low,low-RealScalar(1));
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VERIFY(m.size()==n0);
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if(VectorType::SizeAtCompileTime==Dynamic)
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{
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VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,0,Scalar(n0-1)).sum(),Scalar(0));
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VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,low,low-RealScalar(1)).sum(),Scalar(0));
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}
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m.setLinSpaced(n0,0,Scalar(n0-1));
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VERIFY(m.size()==n0);
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m.setLinSpaced(n0,low,low-RealScalar(1));
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VERIFY(m.size()==n0);
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// empty range only:
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VERIFY_IS_APPROX(VectorType::LinSpaced(size,low,low),VectorType::Constant(size,low));
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m.setLinSpaced(size,low,low);
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VERIFY_IS_APPROX(m,VectorType::Constant(size,low));
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if(NumTraits<Scalar>::IsInteger)
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{
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VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,low+Scalar(size-1)), VectorType::LinSpaced(size,low+Scalar(size-1),low).reverse() );
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if(VectorType::SizeAtCompileTime==Dynamic)
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{
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// Check negative multiplicator path:
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for(Index k=1; k<5; ++k)
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VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,low+Scalar((size-1)*k)), VectorType::LinSpaced(size,low+Scalar((size-1)*k),low).reverse() );
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// Check negative divisor path:
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for(Index k=1; k<5; ++k)
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VERIFY_IS_APPROX( VectorType::LinSpaced(size*k,low,low+Scalar(size-1)), VectorType::LinSpaced(size*k,low+Scalar(size-1),low).reverse() );
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}
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}
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}
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// test setUnit()
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if(m.size()>0)
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{
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for(Index k=0; k<10; ++k)
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{
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Index i = internal::random<Index>(0,m.size()-1);
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m.setUnit(i);
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VERIFY_IS_APPROX( m, VectorType::Unit(m.size(), i) );
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}
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if(VectorType::SizeAtCompileTime==Dynamic)
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{
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Index i = internal::random<Index>(0,2*m.size()-1);
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m.setUnit(2*m.size(),i);
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VERIFY_IS_APPROX( m, VectorType::Unit(m.size(),i) );
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}
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}
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}
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template<typename MatrixType>
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void testMatrixType(const MatrixType& m)
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{
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using std::abs;
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const Index rows = m.rows();
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const Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename MatrixType::RealScalar RealScalar;
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Scalar s1;
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do {
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s1 = internal::random<Scalar>();
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} while(abs(s1)<RealScalar(1e-5) && (!NumTraits<Scalar>::IsInteger));
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MatrixType A;
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A.setIdentity(rows, cols);
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VERIFY(equalsIdentity(A));
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VERIFY(equalsIdentity(MatrixType::Identity(rows, cols)));
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A = MatrixType::Constant(rows,cols,s1);
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Index i = internal::random<Index>(0,rows-1);
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Index j = internal::random<Index>(0,cols-1);
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VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1)(i,j), s1 );
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VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1).coeff(i,j), s1 );
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VERIFY_IS_APPROX( A(i,j), s1 );
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}
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template<int>
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void bug79()
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{
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// Assignment of a RowVectorXd to a MatrixXd (regression test for bug #79).
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VERIFY( (MatrixXd(RowVectorXd::LinSpaced(3, 0, 1)) - RowVector3d(0, 0.5, 1)).norm() < std::numeric_limits<double>::epsilon() );
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}
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template<int>
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void bug1630()
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{
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Array4d x4 = Array4d::LinSpaced(0.0, 1.0);
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Array3d x3(Array4d::LinSpaced(0.0, 1.0).head(3));
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VERIFY_IS_APPROX(x4.head(3), x3);
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}
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template<int>
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void nullary_overflow()
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{
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// Check possible overflow issue
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int n = 60000;
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ArrayXi a1(n), a2(n);
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a1.setLinSpaced(n, 0, n-1);
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for(int i=0; i<n; ++i)
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a2(i) = i;
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VERIFY_IS_APPROX(a1,a2);
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}
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template<int>
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void nullary_internal_logic()
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{
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// check some internal logic
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VERIFY(( internal::has_nullary_operator<internal::scalar_constant_op<double> >::value ));
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VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<double> >::value ));
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VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<double> >::value ));
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VERIFY(( internal::functor_has_linear_access<internal::scalar_constant_op<double> >::ret ));
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VERIFY(( !internal::has_nullary_operator<internal::scalar_identity_op<double> >::value ));
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VERIFY(( !internal::has_unary_operator<internal::scalar_identity_op<double> >::value ));
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VERIFY(( internal::has_binary_operator<internal::scalar_identity_op<double> >::value ));
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VERIFY(( !internal::functor_has_linear_access<internal::scalar_identity_op<double> >::ret ));
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VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<float> >::value ));
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VERIFY(( internal::has_unary_operator<internal::linspaced_op<float> >::value ));
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VERIFY(( !internal::has_binary_operator<internal::linspaced_op<float> >::value ));
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VERIFY(( internal::functor_has_linear_access<internal::linspaced_op<float> >::ret ));
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// Regression unit test for a weird MSVC bug.
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// Search "nullary_wrapper_workaround_msvc" in CoreEvaluators.h for the details.
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// See also traits<Ref>::match.
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{
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MatrixXf A = MatrixXf::Random(3,3);
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Ref<const MatrixXf> R = 2.0*A;
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VERIFY_IS_APPROX(R, A+A);
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Ref<const MatrixXf> R1 = MatrixXf::Random(3,3)+A;
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VectorXi V = VectorXi::Random(3);
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Ref<const VectorXi> R2 = VectorXi::LinSpaced(3,1,3)+V;
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VERIFY_IS_APPROX(R2, V+Vector3i(1,2,3));
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VERIFY(( internal::has_nullary_operator<internal::scalar_constant_op<float> >::value ));
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VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<float> >::value ));
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VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<float> >::value ));
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VERIFY(( internal::functor_has_linear_access<internal::scalar_constant_op<float> >::ret ));
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VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<int> >::value ));
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VERIFY(( internal::has_unary_operator<internal::linspaced_op<int> >::value ));
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VERIFY(( !internal::has_binary_operator<internal::linspaced_op<int> >::value ));
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VERIFY(( internal::functor_has_linear_access<internal::linspaced_op<int> >::ret ));
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}
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}
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EIGEN_DECLARE_TEST(nullary)
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{
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CALL_SUBTEST_1( testMatrixType(Matrix2d()) );
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CALL_SUBTEST_2( testMatrixType(MatrixXcf(internal::random<int>(1,300),internal::random<int>(1,300))) );
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CALL_SUBTEST_3( testMatrixType(MatrixXf(internal::random<int>(1,300),internal::random<int>(1,300))) );
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||
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||
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for(int i = 0; i < g_repeat*10; i++) {
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CALL_SUBTEST_3( testVectorType(VectorXcd(internal::random<int>(1,30000))) );
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||
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CALL_SUBTEST_4( testVectorType(VectorXd(internal::random<int>(1,30000))) );
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||
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CALL_SUBTEST_5( testVectorType(Vector4d()) ); // regression test for bug 232
|
||
|
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CALL_SUBTEST_6( testVectorType(Vector3d()) );
|
||
|
|
CALL_SUBTEST_7( testVectorType(VectorXf(internal::random<int>(1,30000))) );
|
||
|
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CALL_SUBTEST_8( testVectorType(Vector3f()) );
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||
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CALL_SUBTEST_8( testVectorType(Vector4f()) );
|
||
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CALL_SUBTEST_8( testVectorType(Matrix<float,8,1>()) );
|
||
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CALL_SUBTEST_8( testVectorType(Matrix<float,1,1>()) );
|
||
|
|
|
||
|
|
CALL_SUBTEST_9( testVectorType(VectorXi(internal::random<int>(1,10))) );
|
||
|
|
CALL_SUBTEST_9( testVectorType(VectorXi(internal::random<int>(9,300))) );
|
||
|
|
CALL_SUBTEST_9( testVectorType(Matrix<int,1,1>()) );
|
||
|
|
}
|
||
|
|
|
||
|
|
CALL_SUBTEST_6( bug79<0>() );
|
||
|
|
CALL_SUBTEST_6( bug1630<0>() );
|
||
|
|
CALL_SUBTEST_9( nullary_overflow<0>() );
|
||
|
|
CALL_SUBTEST_10( nullary_internal_logic<0>() );
|
||
|
|
}
|