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bug #1004: improve accuracy of LinSpaced for abs(low) >> abs(high).

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This commit is contained in:
Gael Guennebaud 2016-11-02 11:34:38 +01:00
parent 598de8b193
commit a07bb428df
2 changed files with 61 additions and 9 deletions
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31
Eigen/src/Core/functors/NullaryFunctors.h
View File

@ -43,12 +43,17 @@ template <typename Scalar, typename Packet>
struct linspaced_op_impl<Scalar,Packet,/*IsInteger*/false>
{
linspaced_op_impl(const Scalar& low, const Scalar& high, Index num_steps) :
m_low(low), m_high(high), m_size1(num_steps==1 ? 1 : num_steps-1), m_step(num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1)), m_interPacket(plset<Packet>(0))
m_low(low), m_high(high), m_size1(num_steps==1 ? 1 : num_steps-1), m_step(num_steps==1 ? Scalar() : (high-low)/Scalar(num_steps-1)),
m_interPacket(plset<Packet>(0)),
m_flip(std::abs(high)<std::abs(low))
{}
template<typename IndexType>
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const Scalar operator() (IndexType i) const {
return (i==m_size1)? m_high : (m_low + i*m_step);
if(m_flip)
return (i==0)? m_low : (m_high - (m_size1-i)*m_step);
else
return (i==m_size1)? m_high : (m_low + i*m_step);
}
template<typename IndexType>
@ -56,11 +61,22 @@ struct linspaced_op_impl<Scalar,Packet,/*IsInteger*/false>
{
// Principle:
// [low, ..., low] + ( [step, ..., step] * ( [i, ..., i] + [0, ..., size] ) )
Packet pi = padd(pset1<Packet>(Scalar(i)),m_interPacket);
Packet res = padd(pset1<Packet>(m_low), pmul(pset1<Packet>(m_step), pi));
if(i==m_size1-unpacket_traits<Packet>::size+1)
res = pinsertlast(res, m_high);
return res;
if(m_flip)
{
Packet pi = padd(pset1<Packet>(Scalar(i-m_size1)),m_interPacket);
Packet res = padd(pset1<Packet>(m_high), pmul(pset1<Packet>(m_step), pi));
if(i==0)
res = pinsertfirst(res, m_low);
return res;
}
else
{
Packet pi = padd(pset1<Packet>(Scalar(i)),m_interPacket);
Packet res = padd(pset1<Packet>(m_low), pmul(pset1<Packet>(m_step), pi));
if(i==m_size1-unpacket_traits<Packet>::size+1)
res = pinsertlast(res, m_high);
return res;
}
}
const Scalar m_low;
@ -68,6 +84,7 @@ struct linspaced_op_impl<Scalar,Packet,/*IsInteger*/false>
const Index m_size1;
const Scalar m_step;
const Packet m_interPacket;
const bool m_flip;
};
template <typename Scalar, typename Packet>

39
test/nullary.cpp
View File

@ -33,10 +33,38 @@ bool equalsIdentity(const MatrixType& A)
}
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();
@ -47,6 +75,9 @@ void testVectorType(const VectorType& base)
// 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));
@ -60,6 +91,8 @@ void testVectorType(const VectorType& base)
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))
@ -79,6 +112,8 @@ void testVectorType(const VectorType& base)
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 );
@ -154,10 +189,10 @@ void test_nullary()
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>(1,300))) );
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>(1,300))) );
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>()) );