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eigen/test/nullary.cpp

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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2010-2011 Jitse Niesen <jitse@maths.leeds.ac.uk>
// Copyright (C) 2016 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
template<typename MatrixType>
bool equalsIdentity(const MatrixType& A)
{
typedef typename MatrixType::Scalar Scalar;
Scalar zero = static_cast<Scalar>(0);
bool offDiagOK = true;
for (Index i = 0; i < A.rows(); ++i) {
for (Index j = i+1; j < A.cols(); ++j) {
offDiagOK = offDiagOK && (A(i,j) == zero);
}
}
for (Index i = 0; i < A.rows(); ++i) {
for (Index j = 0; j < (std::min)(i, A.cols()); ++j) {
offDiagOK = offDiagOK && (A(i,j) == zero);
}
}
bool diagOK = (A.diagonal().array() == 1).all();
return offDiagOK && diagOK;
}
template<typename VectorType>
void check_extremity_accuracy(const VectorType &v, const typename VectorType::Scalar &low, const typename VectorType::Scalar &high)
{
typedef typename VectorType::Scalar Scalar;
typedef typename VectorType::RealScalar RealScalar;
RealScalar prec = internal::is_same<RealScalar,float>::value ? NumTraits<RealScalar>::dummy_precision()*10 : NumTraits<RealScalar>::dummy_precision()/10;
Index size = v.size();
if(size<20)
return;
for (int i=0; i<size; ++i)
{
if(i<5 || i>size-6)
{
Scalar ref = (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1);
if(std::abs(ref)>1)
{
if(!internal::isApprox(v(i), ref, prec))
std::cout << v(i) << " != " << ref << " ; relative error: " << std::abs((v(i)-ref)/ref) << " ; required precision: " << prec << " ; range: " << low << "," << high << " ; i: " << i << "\n";
VERIFY(internal::isApprox(v(i), (low*RealScalar(size-i-1))/RealScalar(size-1) + (high*RealScalar(i))/RealScalar(size-1), prec));
}
}
}
}
template<typename VectorType>
void testVectorType(const VectorType& base)
{
typedef typename VectorType::Scalar Scalar;
typedef typename VectorType::RealScalar RealScalar;
const Index size = base.size();
Scalar high = internal::random<Scalar>(-500,500);
Scalar low = (size == 1 ? high : internal::random<Scalar>(-500,500));
if (low>high) std::swap(low,high);
// check low==high
if(internal::random<float>(0.f,1.f)<0.05f)
low = high;
// check abs(low) >> abs(high)
else if(size>2 && std::numeric_limits<RealScalar>::max_exponent10>0 && internal::random<float>(0.f,1.f)<0.1f)
low = -internal::random<Scalar>(1,2) * RealScalar(std::pow(RealScalar(10),std::numeric_limits<RealScalar>::max_exponent10/2));
const Scalar step = ((size == 1) ? 1 : (high-low)/(size-1));
// check whether the result yields what we expect it to do
VectorType m(base);
m.setLinSpaced(size,low,high);
if(!NumTraits<Scalar>::IsInteger)
{
VectorType n(size);
for (int i=0; i<size; ++i)
n(i) = low+i*step;
VERIFY_IS_APPROX(m,n);
CALL_SUBTEST( check_extremity_accuracy(m, low, high) );
}
if((!NumTraits<Scalar>::IsInteger) || ((high-low)>=size && (Index(high-low)%(size-1))==0) || (Index(high-low+1)<size && (size%Index(high-low+1))==0))
{
VectorType n(size);
if((!NumTraits<Scalar>::IsInteger) || (high-low>=size))
for (int i=0; i<size; ++i)
n(i) = size==1 ? low : (low + ((high-low)*Scalar(i))/(size-1));
else
for (int i=0; i<size; ++i)
n(i) = size==1 ? low : low + Scalar((double(high-low+1)*double(i))/double(size));
VERIFY_IS_APPROX(m,n);
// random access version
m = VectorType::LinSpaced(size,low,high);
VERIFY_IS_APPROX(m,n);
VERIFY( internal::isApprox(m(m.size()-1),high) );
VERIFY( size==1 || internal::isApprox(m(0),low) );
VERIFY_IS_EQUAL(m(m.size()-1) , high);
if(!NumTraits<Scalar>::IsInteger)
CALL_SUBTEST( check_extremity_accuracy(m, low, high) );
}
VERIFY( m(m.size()-1) <= high );
VERIFY( (m.array() <= high).all() );
VERIFY( (m.array() >= low).all() );
VERIFY( m(m.size()-1) >= low );
if(size>=1)
{
VERIFY( internal::isApprox(m(0),low) );
VERIFY_IS_EQUAL(m(0) , low);
}
// check whether everything works with row and col major vectors
Matrix<Scalar,Dynamic,1> row_vector(size);
Matrix<Scalar,1,Dynamic> col_vector(size);
row_vector.setLinSpaced(size,low,high);
col_vector.setLinSpaced(size,low,high);
// when using the extended precision (e.g., FPU) the relative error might exceed 1 bit
// when computing the squared sum in isApprox, thus the 2x factor.
VERIFY( row_vector.isApprox(col_vector.transpose(), Scalar(2)*NumTraits<Scalar>::epsilon()));
Matrix<Scalar,Dynamic,1> size_changer(size+50);
size_changer.setLinSpaced(size,low,high);
VERIFY( size_changer.size() == size );
typedef Matrix<Scalar,1,1> ScalarMatrix;
ScalarMatrix scalar;
scalar.setLinSpaced(1,low,high);
VERIFY_IS_APPROX( scalar, ScalarMatrix::Constant(high) );
VERIFY_IS_APPROX( ScalarMatrix::LinSpaced(1,low,high), ScalarMatrix::Constant(high) );
// regression test for bug 526 (linear vectorized transversal)
if (size > 1 && (!NumTraits<Scalar>::IsInteger)) {
m.tail(size-1).setLinSpaced(low, high);
VERIFY_IS_APPROX(m(size-1), high);
}
// regression test for bug 1383 (LinSpaced with empty size/range)
{
Index n0 = VectorType::SizeAtCompileTime==Dynamic ? 0 : VectorType::SizeAtCompileTime;
low = internal::random<Scalar>();
m = VectorType::LinSpaced(n0,low,low-1);
VERIFY(m.size()==n0);
if(VectorType::SizeAtCompileTime==Dynamic)
{
VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,0,Scalar(n0-1)).sum(),Scalar(0));
VERIFY_IS_EQUAL(VectorType::LinSpaced(n0,low,low-1).sum(),Scalar(0));
}
m.setLinSpaced(n0,0,Scalar(n0-1));
VERIFY(m.size()==n0);
m.setLinSpaced(n0,low,low-1);
VERIFY(m.size()==n0);
// empty range only:
VERIFY_IS_APPROX(VectorType::LinSpaced(size,low,low),VectorType::Constant(size,low));
m.setLinSpaced(size,low,low);
VERIFY_IS_APPROX(m,VectorType::Constant(size,low));
if(NumTraits<Scalar>::IsInteger)
{
VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,Scalar(low+size-1)), VectorType::LinSpaced(size,Scalar(low+size-1),low).reverse() );
if(VectorType::SizeAtCompileTime==Dynamic)
{
// Check negative multiplicator path:
for(Index k=1; k<5; ++k)
VERIFY_IS_APPROX( VectorType::LinSpaced(size,low,Scalar(low+(size-1)*k)), VectorType::LinSpaced(size,Scalar(low+(size-1)*k),low).reverse() );
// Check negative divisor path:
for(Index k=1; k<5; ++k)
VERIFY_IS_APPROX( VectorType::LinSpaced(size*k,low,Scalar(low+size-1)), VectorType::LinSpaced(size*k,Scalar(low+size-1),low).reverse() );
}
}
}
}
template<typename MatrixType>
void testMatrixType(const MatrixType& m)
{
using std::abs;
const Index rows = m.rows();
const Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename MatrixType::RealScalar RealScalar;
Scalar s1;
do {
s1 = internal::random<Scalar>();
} while(abs(s1)<RealScalar(1e-5) && (!NumTraits<Scalar>::IsInteger));
MatrixType A;
A.setIdentity(rows, cols);
VERIFY(equalsIdentity(A));
VERIFY(equalsIdentity(MatrixType::Identity(rows, cols)));
A = MatrixType::Constant(rows,cols,s1);
Index i = internal::random<Index>(0,rows-1);
Index j = internal::random<Index>(0,cols-1);
VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1)(i,j), s1 );
VERIFY_IS_APPROX( MatrixType::Constant(rows,cols,s1).coeff(i,j), s1 );
VERIFY_IS_APPROX( A(i,j), s1 );
}
void test_nullary()
{
CALL_SUBTEST_1( testMatrixType(Matrix2d()) );
CALL_SUBTEST_2( testMatrixType(MatrixXcf(internal::random<int>(1,300),internal::random<int>(1,300))) );
CALL_SUBTEST_3( testMatrixType(MatrixXf(internal::random<int>(1,300),internal::random<int>(1,300))) );
for(int i = 0; i < g_repeat*10; i++) {
CALL_SUBTEST_4( testVectorType(VectorXd(internal::random<int>(1,30000))) );
CALL_SUBTEST_5( testVectorType(Vector4d()) ); // regression test for bug 232
CALL_SUBTEST_6( testVectorType(Vector3d()) );
CALL_SUBTEST_7( testVectorType(VectorXf(internal::random<int>(1,30000))) );
CALL_SUBTEST_8( testVectorType(Vector3f()) );
CALL_SUBTEST_8( testVectorType(Vector4f()) );
CALL_SUBTEST_8( testVectorType(Matrix<float,8,1>()) );
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>()) );
}
#ifdef EIGEN_TEST_PART_6
// Assignment of a RowVectorXd to a MatrixXd (regression test for bug #79).
VERIFY( (MatrixXd(RowVectorXd::LinSpaced(3, 0, 1)) - RowVector3d(0, 0.5, 1)).norm() < std::numeric_limits<double>::epsilon() );
#endif
#ifdef EIGEN_TEST_PART_9
// Check possible overflow issue
{
int n = 60000;
ArrayXi a1(n), a2(n);
a1.setLinSpaced(n, 0, n-1);
for(int i=0; i<n; ++i)
a2(i) = i;
VERIFY_IS_APPROX(a1,a2);
}
#endif
#ifdef EIGEN_TEST_PART_10
// check some internal logic
VERIFY(( internal::has_nullary_operator<internal::scalar_constant_op<double> >::value ));
VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<double> >::value ));
VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<double> >::value ));
VERIFY(( internal::functor_has_linear_access<internal::scalar_constant_op<double> >::ret ));
VERIFY(( !internal::has_nullary_operator<internal::scalar_identity_op<double> >::value ));
VERIFY(( !internal::has_unary_operator<internal::scalar_identity_op<double> >::value ));
VERIFY(( internal::has_binary_operator<internal::scalar_identity_op<double> >::value ));
VERIFY(( !internal::functor_has_linear_access<internal::scalar_identity_op<double> >::ret ));
VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<float,float> >::value ));
VERIFY(( internal::has_unary_operator<internal::linspaced_op<float,float> >::value ));
VERIFY(( !internal::has_binary_operator<internal::linspaced_op<float,float> >::value ));
VERIFY(( internal::functor_has_linear_access<internal::linspaced_op<float,float> >::ret ));
// Regression unit test for a weird MSVC bug.
// Search "nullary_wrapper_workaround_msvc" in CoreEvaluators.h for the details.
// See also traits<Ref>::match.
{
MatrixXf A = MatrixXf::Random(3,3);
Ref<const MatrixXf> R = 2.0*A;
VERIFY_IS_APPROX(R, A+A);
Ref<const MatrixXf> R1 = MatrixXf::Random(3,3)+A;
VectorXi V = VectorXi::Random(3);
Ref<const VectorXi> R2 = VectorXi::LinSpaced(3,1,3)+V;
VERIFY_IS_APPROX(R2, V+Vector3i(1,2,3));
VERIFY(( internal::has_nullary_operator<internal::scalar_constant_op<float> >::value ));
VERIFY(( !internal::has_unary_operator<internal::scalar_constant_op<float> >::value ));
VERIFY(( !internal::has_binary_operator<internal::scalar_constant_op<float> >::value ));
VERIFY(( internal::functor_has_linear_access<internal::scalar_constant_op<float> >::ret ));
VERIFY(( !internal::has_nullary_operator<internal::linspaced_op<int,int> >::value ));
VERIFY(( internal::has_unary_operator<internal::linspaced_op<int,int> >::value ));
VERIFY(( !internal::has_binary_operator<internal::linspaced_op<int,int> >::value ));
VERIFY(( internal::functor_has_linear_access<internal::linspaced_op<int,int> >::ret ));
}
#endif
}
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