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Improve numerical robustness of some unit tests

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This commit is contained in:
Gael Guennebaud 2015-11-23 10:53:55 +01:00
parent 82bd4e546a
commit 8a2659f0cb
1 changed files with 22 additions and 13 deletions
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33
test/geo_transformations.cpp
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@ -12,6 +12,12 @@
#include <Eigen/LU> #include <Eigen/LU>
#include <Eigen/SVD> #include <Eigen/SVD>
template<typename T>
Matrix<T,2,1> angleToVec(T a)
{
return Matrix<T,2,1>(std::cos(a), std::sin(a));
}
template<typename Scalar, int Mode, int Options> void non_projective_only() template<typename Scalar, int Mode, int Options> void non_projective_only()
{ {
/* this test covers the following files: /* this test covers the following files:
@ -130,14 +136,16 @@ template<typename Scalar, int Mode, int Options> void transformations()
AngleAxisx aa = AngleAxisx(q1); AngleAxisx aa = AngleAxisx(q1);
VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
if(abs(aa.angle()) > NumTraits<Scalar>::dummy_precision()) // The following test is stable only if 2*angle != angle and v1 is not colinear with axis
if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )
{ {
VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) ); VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
} }
aa.fromRotationMatrix(aa.toRotationMatrix()); aa.fromRotationMatrix(aa.toRotationMatrix());
VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
if(abs(aa.angle()) > NumTraits<Scalar>::dummy_precision()) // The following test is stable only if 2*angle != angle and v1 is not colinear with axis
if( (abs(aa.angle()) > test_precision<Scalar>()) && (abs(aa.axis().dot(v1.normalized()))<(Scalar(1)-Scalar(4)*test_precision<Scalar>())) )
{ {
VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) ); VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
} }
@ -214,7 +222,9 @@ template<typename Scalar, int Mode, int Options> void transformations()
t4 *= aa3; t4 *= aa3;
VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
do {
v3 = Vector3::Random(); v3 = Vector3::Random();
} while (v3.cwiseAbs().minCoeff()<NumTraits<Scalar>::epsilon());
Translation3 tv3(v3); Translation3 tv3(v3);
Transform3 t5(tv3); Transform3 t5(tv3);
t4 = tv3; t4 = tv3;
@ -414,14 +424,12 @@ template<typename Scalar, int Mode, int Options> void transformations()
Scalar angle = internal::random<Scalar>(-100,100); Scalar angle = internal::random<Scalar>(-100,100);
Rotation2D<Scalar> rot2(angle); Rotation2D<Scalar> rot2(angle);
VERIFY( rot2.smallestPositiveAngle() >= 0 ); VERIFY( rot2.smallestPositiveAngle() >= 0 );
VERIFY( rot2.smallestPositiveAngle() < Scalar(2)*Scalar(EIGEN_PI) ); VERIFY( rot2.smallestPositiveAngle() <= Scalar(2)*Scalar(EIGEN_PI) );
VERIFY_IS_APPROX( std::cos(rot2.smallestPositiveAngle()), std::cos(rot2.angle()) ); VERIFY_IS_APPROX( angleToVec(rot2.smallestPositiveAngle()), angleToVec(rot2.angle()) );
VERIFY_IS_APPROX( std::sin(rot2.smallestPositiveAngle()), std::sin(rot2.angle()) );
VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) ); VERIFY( rot2.smallestAngle() >= -Scalar(EIGEN_PI) );
VERIFY( rot2.smallestAngle() <= Scalar(EIGEN_PI) ); VERIFY( rot2.smallestAngle() <= Scalar(EIGEN_PI) );
VERIFY_IS_APPROX( std::cos(rot2.smallestAngle()), std::cos(rot2.angle()) ); VERIFY_IS_APPROX( angleToVec(rot2.smallestAngle()), angleToVec(rot2.angle()) );
VERIFY_IS_APPROX( std::sin(rot2.smallestAngle()), std::sin(rot2.angle()) );
} }
s0 = internal::random<Scalar>(-100,100); s0 = internal::random<Scalar>(-100,100);
@ -437,7 +445,7 @@ template<typename Scalar, int Mode, int Options> void transformations()
VERIFY_IS_APPROX(t20,t21); VERIFY_IS_APPROX(t20,t21);
VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle()); VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle());
VERIFY_IS_APPROX(R1.smallestPositiveAngle(), (R0.slerp(1, R1)).smallestPositiveAngle()); VERIFY_IS_APPROX( angleToVec(R1.smallestPositiveAngle()), angleToVec((R0.slerp(1, R1)).smallestPositiveAngle()) );
VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle()); VERIFY_IS_APPROX(R0.smallestPositiveAngle(), (R0.slerp(0.5, R0)).smallestPositiveAngle());
if(std::cos(s0)>0) if(std::cos(s0)>0)
@ -447,13 +455,14 @@ template<typename Scalar, int Mode, int Options> void transformations()
// Check path length // Check path length
Scalar l = 0; Scalar l = 0;
for(int k=0; k<100; ++k) int path_steps = 100;
for(int k=0; k<path_steps; ++k)
{ {
Scalar a1 = R0.slerp(Scalar(k)/Scalar(100), R1).angle(); Scalar a1 = R0.slerp(Scalar(k)/Scalar(path_steps), R1).angle();
Scalar a2 = R0.slerp(Scalar(k+1)/Scalar(100), R1).angle(); Scalar a2 = R0.slerp(Scalar(k+1)/Scalar(path_steps), R1).angle();
l += std::abs(a2-a1); l += std::abs(a2-a1);
} }
VERIFY(l<=EIGEN_PI); VERIFY(l<=EIGEN_PI*(Scalar(1)+NumTraits<Scalar>::epsilon()*Scalar(path_steps/2)));
// check basic features // check basic features
{ {