template<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int size) { for (int i=0; i<size; ++i) { if (!ei_isApprox(a[i],b[i])) { std::cout << "a[" << i << "]: " << a[i] << " != b[" << i << "]: " << b[i] << std::endl; return false; } } return true; }
template<typename MatrixType> void array(const MatrixType& m) { /* this test covers the following files: Array.cpp */ typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; int rows = m.rows(); int cols = m.cols(); MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols); Scalar s1 = ei_random<Scalar>(), s2 = ei_random<Scalar>(); // scalar addition VERIFY_IS_APPROX(m1.cwise() + s1, s1 + m1.cwise()); VERIFY_IS_APPROX(m1.cwise() + s1, MatrixType::Constant(rows,cols,s1) + m1); VERIFY_IS_APPROX((m1*Scalar(2)).cwise() - s2, (m1+m1) - MatrixType::Constant(rows,cols,s2) ); m3 = m1; m3.cwise() += s2; VERIFY_IS_APPROX(m3, m1.cwise() + s2); m3 = m1; m3.cwise() -= s1; VERIFY_IS_APPROX(m3, m1.cwise() - s1); // reductions VERIFY_IS_APPROX(m1.colwise().sum().sum(), m1.sum()); VERIFY_IS_APPROX(m1.rowwise().sum().sum(), m1.sum()); if (!ei_isApprox(m1.sum(), (m1+m2).sum())) VERIFY_IS_NOT_APPROX(((m1+m2).rowwise().sum()).sum(), m1.sum()); VERIFY_IS_APPROX(m1.colwise().sum(), m1.colwise().redux(internal::scalar_sum_op<Scalar>())); }
template<typename MatrixType> void basicStuffComplex(const MatrixType& m) { typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, MatrixType::ColsAtCompileTime> RealMatrixType; Index rows = m.rows(); Index cols = m.cols(); Scalar s1 = ei_random<Scalar>(), s2 = ei_random<Scalar>(); VERIFY(ei_real(s1)==ei_real_ref(s1)); VERIFY(ei_imag(s1)==ei_imag_ref(s1)); ei_real_ref(s1) = ei_real(s2); ei_imag_ref(s1) = ei_imag(s2); VERIFY(ei_isApprox(s1, s2, NumTraits<RealScalar>::epsilon())); // extended precision in Intel FPUs means that s1 == s2 in the line above is not guaranteed. RealMatrixType rm1 = RealMatrixType::Random(rows,cols), rm2 = RealMatrixType::Random(rows,cols); MatrixType cm(rows,cols); cm.real() = rm1; cm.imag() = rm2; VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1); VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2); rm1.setZero(); rm2.setZero(); rm1 = cm.real(); rm2 = cm.imag(); VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).real(), rm1); VERIFY_IS_APPROX(static_cast<const MatrixType&>(cm).imag(), rm2); cm.real().setZero(); VERIFY(static_cast<const MatrixType&>(cm).real().isZero()); VERIFY(!static_cast<const MatrixType&>(cm).imag().isZero()); }
template<typename Scalar> void geometry(void) { /* this test covers the following files: Cross.h Quaternion.h, Transform.cpp */ typedef Matrix<Scalar,2,2> Matrix2; typedef Matrix<Scalar,3,3> Matrix3; typedef Matrix<Scalar,4,4> Matrix4; typedef Matrix<Scalar,2,1> Vector2; typedef Matrix<Scalar,3,1> Vector3; typedef Matrix<Scalar,4,1> Vector4; typedef Quaternion<Scalar> Quaternionx; typedef AngleAxis<Scalar> AngleAxisx; typedef Transform<Scalar,2> Transform2; typedef Transform<Scalar,3> Transform3; typedef Scaling<Scalar,2> Scaling2; typedef Scaling<Scalar,3> Scaling3; typedef Translation<Scalar,2> Translation2; typedef Translation<Scalar,3> Translation3; Scalar largeEps = test_precision<Scalar>(); if (ei_is_same_type<Scalar,float>::ret) largeEps = 1e-2f; Vector3 v0 = Vector3::Random(), v1 = Vector3::Random(), v2 = Vector3::Random(); Vector2 u0 = Vector2::Random(); Matrix3 matrot1; Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); // cross product VERIFY_IS_MUCH_SMALLER_THAN(v1.cross(v2).eigen2_dot(v1), Scalar(1)); Matrix3 m; m << v0.normalized(), (v0.cross(v1)).normalized(), (v0.cross(v1).cross(v0)).normalized(); VERIFY(m.isUnitary()); // Quaternion: Identity(), setIdentity(); Quaternionx q1, q2; q2.setIdentity(); VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs()); q1.coeffs().setRandom(); VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs()); // unitOrthogonal VERIFY_IS_MUCH_SMALLER_THAN(u0.unitOrthogonal().eigen2_dot(u0), Scalar(1)); VERIFY_IS_MUCH_SMALLER_THAN(v0.unitOrthogonal().eigen2_dot(v0), Scalar(1)); VERIFY_IS_APPROX(u0.unitOrthogonal().norm(), Scalar(1)); VERIFY_IS_APPROX(v0.unitOrthogonal().norm(), Scalar(1)); VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0); VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0); VERIFY_IS_APPROX(ei_cos(a)*v0.squaredNorm(), v0.eigen2_dot(AngleAxisx(a, v0.unitOrthogonal()) * v0)); m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint(); VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized())); VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m); q1 = AngleAxisx(a, v0.normalized()); q2 = AngleAxisx(a, v1.normalized()); // angular distance Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle()); if (refangle>Scalar(M_PI)) refangle = Scalar(2)*Scalar(M_PI) - refangle; if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps) { VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps)); } // rotation matrix conversion VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2); VERIFY_IS_APPROX(q1 * q2 * v2, q1.toRotationMatrix() * q2.toRotationMatrix() * v2); VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox( q1.toRotationMatrix() * q2.toRotationMatrix() * v2)); q2 = q1.toRotationMatrix(); VERIFY_IS_APPROX(q1*v1,q2*v1); matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX()) * AngleAxisx(Scalar(0.2), Vector3::UnitY()) * AngleAxisx(Scalar(0.3), Vector3::UnitZ()); VERIFY_IS_APPROX(matrot1 * v1, AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix() * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix() * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1))); // angle-axis conversion AngleAxisx aa = q1; VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1); // from two vector creation VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized()); VERIFY_IS_APPROX(v2.normalized(),(q2.setFromTwoVectors(v1,v2)*v1).normalized()); // inverse and conjugate VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1); VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1); // AngleAxis VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(), Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix()); AngleAxisx aa1; m = q1.toRotationMatrix(); aa1 = m; VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(), Quaternionx(m).toRotationMatrix()); // Transform // TODO complete the tests ! a = 0; while (ei_abs(a)<Scalar(0.1)) a = ei_random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI)); q1 = AngleAxisx(a, v0.normalized()); Transform3 t0, t1, t2; // first test setIdentity() and Identity() t0.setIdentity(); VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); t0.matrix().setZero(); t0 = Transform3::Identity(); VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity()); t0.linear() = q1.toRotationMatrix(); t1.setIdentity(); t1.linear() = q1.toRotationMatrix(); v0 << 50, 2, 1;//= ei_random_matrix<Vector3>().cwiseProduct(Vector3(10,2,0.5)); t0.scale(v0); t1.prescale(v0); VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).norm(), v0.x()); //VERIFY(!ei_isApprox((t1 * Vector3(1,0,0)).norm(), v0.x())); t0.setIdentity(); t1.setIdentity(); v1 << 1, 2, 3; t0.linear() = q1.toRotationMatrix(); t0.pretranslate(v0); t0.scale(v1); t1.linear() = q1.conjugate().toRotationMatrix(); t1.prescale(v1.cwise().inverse()); t1.translate(-v0); VERIFY((t0.matrix() * t1.matrix()).isIdentity(test_precision<Scalar>())); t1.fromPositionOrientationScale(v0, q1, v1); VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); VERIFY_IS_APPROX(t1*v1, t0*v1); t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix()); t1.setIdentity(); t1.scale(v0).rotate(q1); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix()); VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix()); // More transform constructors, operator=, operator*= Matrix3 mat3 = Matrix3::Random(); Matrix4 mat4; mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose(); Transform3 tmat3(mat3), tmat4(mat4); tmat4.matrix()(3,3) = Scalar(1); VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix()); Scalar a3 = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); Vector3 v3 = Vector3::Random().normalized(); AngleAxisx aa3(a3, v3); Transform3 t3(aa3); Transform3 t4; t4 = aa3; VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); t4.rotate(AngleAxisx(-a3,v3)); VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); t4 *= aa3; VERIFY_IS_APPROX(t3.matrix(), t4.matrix()); v3 = Vector3::Random(); Translation3 tv3(v3); Transform3 t5(tv3); t4 = tv3; VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); t4.translate(-v3); VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); t4 *= tv3; VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); Scaling3 sv3(v3); Transform3 t6(sv3); t4 = sv3; VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); t4.scale(v3.cwise().inverse()); VERIFY_IS_APPROX(t4.matrix(), Matrix4::Identity()); t4 *= sv3; VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); // matrix * transform VERIFY_IS_APPROX(Transform3(t3.matrix()*t4).matrix(), Transform3(t3*t4).matrix()); // chained Transform product VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix()); // check that Transform product doesn't have aliasing problems t5 = t4; t5 = t5*t5; VERIFY_IS_APPROX(t5, t4*t4); // 2D transformation Transform2 t20, t21; Vector2 v20 = Vector2::Random(); Vector2 v21 = Vector2::Random(); for (int k=0; k<2; ++k) if (ei_abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3); t21.setIdentity(); t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix(); VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(), t21.pretranslate(v20).scale(v21).matrix()); t21.setIdentity(); t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix(); VERIFY( (t20.fromPositionOrientationScale(v20,a,v21) * (t21.prescale(v21.cwise().inverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) ); // Transform - new API // 3D t0.setIdentity(); t0.rotate(q1).scale(v0).translate(v0); // mat * scaling and mat * translation t1 = (Matrix3(q1) * Scaling3(v0)) * Translation3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // mat * transformation and scaling * translation t1 = Matrix3(q1) * (Scaling3(v0) * Translation3(v0)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.setIdentity(); t0.prerotate(q1).prescale(v0).pretranslate(v0); // translation * scaling and transformation * mat t1 = (Translation3(v0) * Scaling3(v0)) * Matrix3(q1); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // scaling * mat and translation * mat t1 = Translation3(v0) * (Scaling3(v0) * Matrix3(q1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.setIdentity(); t0.scale(v0).translate(v0).rotate(q1); // translation * mat and scaling * transformation t1 = Scaling3(v0) * (Translation3(v0) * Matrix3(q1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // transformation * scaling t0.scale(v0); t1 = t1 * Scaling3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // transformation * translation t0.translate(v0); t1 = t1 * Translation3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // translation * transformation t0.pretranslate(v0); t1 = Translation3(v0) * t1; VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // transform * quaternion t0.rotate(q1); t1 = t1 * q1; VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // translation * quaternion t0.translate(v1).rotate(q1); t1 = t1 * (Translation3(v1) * q1); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // scaling * quaternion t0.scale(v1).rotate(q1); t1 = t1 * (Scaling3(v1) * q1); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // quaternion * transform t0.prerotate(q1); t1 = q1 * t1; VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // quaternion * translation t0.rotate(q1).translate(v1); t1 = t1 * (q1 * Translation3(v1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // quaternion * scaling t0.rotate(q1).scale(v1); t1 = t1 * (q1 * Scaling3(v1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // translation * vector t0.setIdentity(); t0.translate(v0); VERIFY_IS_APPROX(t0 * v1, Translation3(v0) * v1); // scaling * vector t0.setIdentity(); t0.scale(v0); VERIFY_IS_APPROX(t0 * v1, Scaling3(v0) * v1); // test transform inversion t0.setIdentity(); t0.translate(v0); t0.linear().setRandom(); VERIFY_IS_APPROX(t0.inverse(Affine), t0.matrix().inverse()); t0.setIdentity(); t0.translate(v0).rotate(q1); VERIFY_IS_APPROX(t0.inverse(Isometry), t0.matrix().inverse()); // test extract rotation and scaling t0.setIdentity(); t0.translate(v0).rotate(q1).scale(v1); VERIFY_IS_APPROX(t0.rotation() * v1, Matrix3(q1) * v1); Matrix3 mat_rotation, mat_scaling; t0.setIdentity(); t0.translate(v0).rotate(q1).scale(v1); t0.computeRotationScaling(&mat_rotation, &mat_scaling); VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling); VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); t0.computeScalingRotation(&mat_scaling, &mat_rotation); VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation); VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity()); VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1)); // test casting Transform<float,3> t1f = t1.template cast<float>(); VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1); Transform<double,3> t1d = t1.template cast<double>(); VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1); Translation3 tr1(v0); Translation<float,3> tr1f = tr1.template cast<float>(); VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1); Translation<double,3> tr1d = tr1.template cast<double>(); VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1); Scaling3 sc1(v0); Scaling<float,3> sc1f = sc1.template cast<float>(); VERIFY_IS_APPROX(sc1f.template cast<Scalar>(),sc1); Scaling<double,3> sc1d = sc1.template cast<double>(); VERIFY_IS_APPROX(sc1d.template cast<Scalar>(),sc1); Quaternion<float> q1f = q1.template cast<float>(); VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1); Quaternion<double> q1d = q1.template cast<double>(); VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1); AngleAxis<float> aa1f = aa1.template cast<float>(); VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1); AngleAxis<double> aa1d = aa1.template cast<double>(); VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1); Rotation2D<Scalar> r2d1(ei_random<Scalar>()); Rotation2D<float> r2d1f = r2d1.template cast<float>(); VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1); Rotation2D<double> r2d1d = r2d1.template cast<double>(); VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1); m = q1; // m.col(1) = Vector3(0,ei_random<Scalar>(),ei_random<Scalar>()).normalized(); // m.col(0) = Vector3(-1,0,0).normalized(); // m.col(2) = m.col(0).cross(m.col(1)); #define VERIFY_EULER(I,J,K, X,Y,Z) { \ Vector3 ea = m.eulerAngles(I,J,K); \ Matrix3 m1 = Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z())); \ VERIFY_IS_APPROX(m, m1); \ VERIFY_IS_APPROX(m, Matrix3(AngleAxisx(ea[0], Vector3::Unit##X()) * AngleAxisx(ea[1], Vector3::Unit##Y()) * AngleAxisx(ea[2], Vector3::Unit##Z()))); \ } VERIFY_EULER(0,1,2, X,Y,Z); VERIFY_EULER(0,1,0, X,Y,X); VERIFY_EULER(0,2,1, X,Z,Y); VERIFY_EULER(0,2,0, X,Z,X); VERIFY_EULER(1,2,0, Y,Z,X); VERIFY_EULER(1,2,1, Y,Z,Y); VERIFY_EULER(1,0,2, Y,X,Z); VERIFY_EULER(1,0,1, Y,X,Y); VERIFY_EULER(2,0,1, Z,X,Y); VERIFY_EULER(2,0,2, Z,X,Z); VERIFY_EULER(2,1,0, Z,Y,X); VERIFY_EULER(2,1,2, Z,Y,Z); // colwise/rowwise cross product mat3.setRandom(); Vector3 vec3 = Vector3::Random(); Matrix3 mcross; int i = ei_random<int>(0,2); mcross = mat3.colwise().cross(vec3); VERIFY_IS_APPROX(mcross.col(i), mat3.col(i).cross(vec3)); mcross = mat3.rowwise().cross(vec3); VERIFY_IS_APPROX(mcross.row(i), mat3.row(i).cross(vec3)); }
template<typename MatrixType> void adjoint(const MatrixType& m) { /* this test covers the following files: Transpose.h Conjugate.h Dot.h */ typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType; int rows = m.rows(); int cols = m.cols(); RealScalar largerEps = test_precision<RealScalar>(); if (ei_is_same_type<RealScalar,float>::ret) largerEps = RealScalar(1e-3f); MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), mzero = MatrixType::Zero(rows, cols), identity = SquareMatrixType::Identity(rows, rows), square = SquareMatrixType::Random(rows, rows); VectorType v1 = VectorType::Random(rows), v2 = VectorType::Random(rows), v3 = VectorType::Random(rows), vzero = VectorType::Zero(rows); Scalar s1 = ei_random<Scalar>(), s2 = ei_random<Scalar>(); // check basic compatibility of adjoint, transpose, conjugate VERIFY_IS_APPROX(m1.transpose().conjugate().adjoint(), m1); VERIFY_IS_APPROX(m1.adjoint().conjugate().transpose(), m1); // check multiplicative behavior VERIFY_IS_APPROX((m1.adjoint() * m2).adjoint(), m2.adjoint() * m1); VERIFY_IS_APPROX((s1 * m1).adjoint(), ei_conj(s1) * m1.adjoint()); // check basic properties of dot, norm, norm2 typedef typename NumTraits<Scalar>::Real RealScalar; VERIFY(ei_isApprox((s1 * v1 + s2 * v2).dot(v3), s1 * v1.dot(v3) + s2 * v2.dot(v3), largerEps)); VERIFY(ei_isApprox(v3.dot(s1 * v1 + s2 * v2), ei_conj(s1)*v3.dot(v1)+ei_conj(s2)*v3.dot(v2), largerEps)); VERIFY_IS_APPROX(ei_conj(v1.dot(v2)), v2.dot(v1)); VERIFY_IS_APPROX(ei_abs(v1.dot(v1)), v1.squaredNorm()); if(NumTraits<Scalar>::HasFloatingPoint) VERIFY_IS_APPROX(v1.squaredNorm(), v1.norm() * v1.norm()); VERIFY_IS_MUCH_SMALLER_THAN(ei_abs(vzero.dot(v1)), static_cast<RealScalar>(1)); if(NumTraits<Scalar>::HasFloatingPoint) VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1)); // check compatibility of dot and adjoint VERIFY(ei_isApprox(v1.dot(square * v2), (square.adjoint() * v1).dot(v2), largerEps)); // like in testBasicStuff, test operator() to check const-qualification int r = ei_random<int>(0, rows-1), c = ei_random<int>(0, cols-1); VERIFY_IS_APPROX(m1.conjugate()(r,c), ei_conj(m1(r,c))); VERIFY_IS_APPROX(m1.adjoint()(c,r), ei_conj(m1(r,c))); if(NumTraits<Scalar>::HasFloatingPoint) { // check that Random().normalized() works: tricky as the random xpr must be evaluated by // normalized() in order to produce a consistent result. VERIFY_IS_APPROX(VectorType::Random(rows).normalized().norm(), RealScalar(1)); } // check inplace transpose m3 = m1; m3.transposeInPlace(); VERIFY_IS_APPROX(m3,m1.transpose()); m3.transposeInPlace(); VERIFY_IS_APPROX(m3,m1); }
template<typename Scalar> void packetmath() { typedef typename ei_packet_traits<Scalar>::type Packet; const int PacketSize = ei_packet_traits<Scalar>::size; typedef typename NumTraits<Scalar>::Real RealScalar; const int size = PacketSize*4; EIGEN_ALIGN16 Scalar data1[ei_packet_traits<Scalar>::size*4]; EIGEN_ALIGN16 Scalar data2[ei_packet_traits<Scalar>::size*4]; EIGEN_ALIGN16 Packet packets[PacketSize*2]; EIGEN_ALIGN16 Scalar ref[ei_packet_traits<Scalar>::size*4]; RealScalar refvalue = 0; for (int i=0; i<size; ++i) { data1[i] = ei_random<Scalar>(); data2[i] = ei_random<Scalar>(); refvalue = std::max(refvalue,ei_abs(data1[i])); } ei_pstore(data2, ei_pload(data1)); VERIFY(areApprox(data1, data2, PacketSize) && "aligned load/store"); for (int offset=0; offset<PacketSize; ++offset) { ei_pstore(data2, ei_ploadu(data1+offset)); VERIFY(areApprox(data1+offset, data2, PacketSize) && "ei_ploadu"); } for (int offset=0; offset<PacketSize; ++offset) { ei_pstoreu(data2+offset, ei_pload(data1)); VERIFY(areApprox(data1, data2+offset, PacketSize) && "ei_pstoreu"); } for (int offset=0; offset<PacketSize; ++offset) { packets[0] = ei_pload(data1); packets[1] = ei_pload(data1+PacketSize); if (offset==0) ei_palign<0>(packets[0], packets[1]); else if (offset==1) ei_palign<1>(packets[0], packets[1]); else if (offset==2) ei_palign<2>(packets[0], packets[1]); else if (offset==3) ei_palign<3>(packets[0], packets[1]); ei_pstore(data2, packets[0]); for (int i=0; i<PacketSize; ++i) ref[i] = data1[i+offset]; typedef Matrix<Scalar, PacketSize, 1> Vector; VERIFY(areApprox(ref, data2, PacketSize) && "ei_palign"); } CHECK_CWISE2(REF_ADD, ei_padd); CHECK_CWISE2(REF_SUB, ei_psub); CHECK_CWISE2(REF_MUL, ei_pmul); #ifndef EIGEN_VECTORIZE_ALTIVEC if (!ei_is_same_type<Scalar,int>::ret) CHECK_CWISE2(REF_DIV, ei_pdiv); #endif CHECK_CWISE2(std::min, ei_pmin); CHECK_CWISE2(std::max, ei_pmax); CHECK_CWISE1(ei_abs, ei_pabs); CHECK_CWISE1(ei_negate, ei_pnegate); for (int i=0; i<PacketSize; ++i) ref[i] = data1[0]; ei_pstore(data2, ei_pset1(data1[0])); VERIFY(areApprox(ref, data2, PacketSize) && "ei_pset1"); VERIFY(ei_isApprox(data1[0], ei_pfirst(ei_pload(data1))) && "ei_pfirst"); ref[0] = 0; for (int i=0; i<PacketSize; ++i) ref[0] += data1[i]; VERIFY(isApproxAbs(ref[0], ei_predux(ei_pload(data1)), refvalue) && "ei_predux"); ref[0] = 1; for (int i=0; i<PacketSize; ++i) ref[0] *= data1[i]; VERIFY(ei_isApprox(ref[0], ei_predux_mul(ei_pload(data1))) && "ei_predux_mul"); ref[0] = data1[0]; for (int i=0; i<PacketSize; ++i) ref[0] = std::min(ref[0],data1[i]); VERIFY(ei_isApprox(ref[0], ei_predux_min(ei_pload(data1))) && "ei_predux_min"); ref[0] = data1[0]; for (int i=0; i<PacketSize; ++i) ref[0] = std::max(ref[0],data1[i]); VERIFY(ei_isApprox(ref[0], ei_predux_max(ei_pload(data1))) && "ei_predux_max"); for (int j=0; j<PacketSize; ++j) { ref[j] = 0; for (int i=0; i<PacketSize; ++i) ref[j] += data1[i+j*PacketSize]; packets[j] = ei_pload(data1+j*PacketSize); } ei_pstore(data2, ei_preduxp(packets)); VERIFY(areApproxAbs(ref, data2, PacketSize, refvalue) && "ei_preduxp"); for (int i=0; i<PacketSize; ++i) ref[i] = data1[PacketSize-i-1]; ei_pstore(data2, ei_preverse(ei_pload(data1))); VERIFY(areApprox(ref, data2, PacketSize) && "ei_preverse"); }
template<typename Scalar> void quaternion(void) { /* this test covers the following files: Quaternion.h */ typedef Matrix<Scalar,3,3> Matrix3; typedef Matrix<Scalar,3,1> Vector3; typedef Quaternion<Scalar> Quaternionx; typedef AngleAxis<Scalar> AngleAxisx; Scalar largeEps = test_precision<Scalar>(); if (ei_is_same_type<Scalar,float>::ret) largeEps = 1e-3f; Scalar eps = ei_random<Scalar>() * Scalar(1e-2); Vector3 v0 = Vector3::Random(), v1 = Vector3::Random(), v2 = Vector3::Random(), v3 = Vector3::Random(); Scalar a = ei_random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); // Quaternion: Identity(), setIdentity(); Quaternionx q1, q2; q2.setIdentity(); VERIFY_IS_APPROX(Quaternionx(Quaternionx::Identity()).coeffs(), q2.coeffs()); q1.coeffs().setRandom(); VERIFY_IS_APPROX(q1.coeffs(), (q1*q2).coeffs()); // concatenation q1 *= q2; q1 = AngleAxisx(a, v0.normalized()); q2 = AngleAxisx(a, v1.normalized()); // angular distance Scalar refangle = ei_abs(AngleAxisx(q1.inverse()*q2).angle()); if (refangle>Scalar(M_PI)) refangle = Scalar(2)*Scalar(M_PI) - refangle; if((q1.coeffs()-q2.coeffs()).norm() > 10*largeEps) { VERIFY(ei_isApprox(q1.angularDistance(q2), refangle, largeEps)); } // rotation matrix conversion VERIFY_IS_APPROX(q1 * v2, q1.toRotationMatrix() * v2); VERIFY_IS_APPROX(q1 * q2 * v2, q1.toRotationMatrix() * q2.toRotationMatrix() * v2); VERIFY( (q2*q1).isApprox(q1*q2, largeEps) || !(q2 * q1 * v2).isApprox(q1.toRotationMatrix() * q2.toRotationMatrix() * v2)); q2 = q1.toRotationMatrix(); VERIFY_IS_APPROX(q1*v1,q2*v1); // angle-axis conversion AngleAxisx aa = AngleAxisx(q1); VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1); // from two vector creation VERIFY_IS_APPROX( v2.normalized(),(q2.setFromTwoVectors(v1, v2)*v1).normalized()); VERIFY_IS_APPROX( v1.normalized(),(q2.setFromTwoVectors(v1, v1)*v1).normalized()); VERIFY_IS_APPROX(-v1.normalized(),(q2.setFromTwoVectors(v1,-v1)*v1).normalized()); if (ei_is_same_type<Scalar,double>::ret) { v3 = (v1.array()+eps).matrix(); VERIFY_IS_APPROX( v3.normalized(),(q2.setFromTwoVectors(v1, v3)*v1).normalized()); VERIFY_IS_APPROX(-v3.normalized(),(q2.setFromTwoVectors(v1,-v3)*v1).normalized()); } // inverse and conjugate VERIFY_IS_APPROX(q1 * (q1.inverse() * v1), v1); VERIFY_IS_APPROX(q1 * (q1.conjugate() * v1), v1); // test casting Quaternion<float> q1f = q1.template cast<float>(); VERIFY_IS_APPROX(q1f.template cast<Scalar>(),q1); Quaternion<double> q1d = q1.template cast<double>(); VERIFY_IS_APPROX(q1d.template cast<Scalar>(),q1); }
template<typename Scalar> bool areApprox(const Scalar* a, const Scalar* b, int size) { for (int i=0; i<size; ++i) if (!ei_isApprox(a[i],b[i])) return false; return true; }