template<typename MatrixType> void qr(const MatrixType& m) { /* this test covers the following files: QR.h */ int rows = m.rows(); int cols = m.cols(); typedef typename MatrixType::Scalar Scalar; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, MatrixType::ColsAtCompileTime> SquareMatrixType; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; MatrixType a = MatrixType::Random(rows,cols); QR<MatrixType> qrOfA(a); VERIFY_IS_APPROX(a, qrOfA.matrixQ() * qrOfA.matrixR()); VERIFY_IS_NOT_APPROX(a+MatrixType::Identity(rows, cols), qrOfA.matrixQ() * qrOfA.matrixR()); SquareMatrixType b = a.adjoint() * a; // check tridiagonalization Tridiagonalization<SquareMatrixType> tridiag(b); VERIFY_IS_APPROX(b, tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint()); // check hessenberg decomposition HessenbergDecomposition<SquareMatrixType> hess(b); VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint()); VERIFY_IS_APPROX(tridiag.matrixT(), hess.matrixH()); b = SquareMatrixType::Random(cols,cols); hess.compute(b); VERIFY_IS_APPROX(b, hess.matrixQ() * hess.matrixH() * hess.matrixQ().adjoint()); }
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 Scalar, int Options> 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,Options> Quaternionx; typedef AngleAxis<Scalar> AngleAxisx; Scalar largeEps = test_precision<Scalar>(); if (internal::is_same<Scalar,float>::value) largeEps = 1e-3f; Scalar eps = internal::random<Scalar>() * Scalar(1e-2); Vector3 v0 = Vector3::Random(), v1 = Vector3::Random(), v2 = Vector3::Random(), v3 = Vector3::Random(); Scalar a = internal::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 = internal::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_IS_MUCH_SMALLER_THAN(internal::abs(q1.angularDistance(q2) - refangle), Scalar(1)); } // 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); // Do not execute the test if the rotation angle is almost zero, or // the rotation axis and v1 are almost parallel. if (internal::abs(aa.angle()) > 5*test_precision<Scalar>() && (aa.axis() - v1.normalized()).norm() < 1.99 && (aa.axis() + v1.normalized()).norm() < 1.99) { 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 (internal::is_same<Scalar,double>::value) { 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); // test bug 369 - improper alignment. Quaternionx *q = new Quaternionx; delete q; }
template<typename MatrixType> void stable_norm(const MatrixType& m) { /* this test covers the following files: StableNorm.h */ typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; // Check the basic machine-dependent constants. { int ibeta, it, iemin, iemax; ibeta = std::numeric_limits<RealScalar>::radix; // base for floating-point numbers it = std::numeric_limits<RealScalar>::digits; // number of base-beta digits in mantissa iemin = std::numeric_limits<RealScalar>::min_exponent; // minimum exponent iemax = std::numeric_limits<RealScalar>::max_exponent; // maximum exponent VERIFY( (!(iemin > 1 - 2*it || 1+it>iemax || (it==2 && ibeta<5) || (it<=4 && ibeta <= 3 ) || it<2)) && "the stable norm algorithm cannot be guaranteed on this computer"); } Index rows = m.rows(); Index cols = m.cols(); Scalar big = internal::random<Scalar>() * (std::numeric_limits<RealScalar>::max() * RealScalar(1e-4)); Scalar small = internal::random<Scalar>() * (std::numeric_limits<RealScalar>::min() * RealScalar(1e4)); MatrixType vzero = MatrixType::Zero(rows, cols), vrand = MatrixType::Random(rows, cols), vbig(rows, cols), vsmall(rows,cols); vbig.fill(big); vsmall.fill(small); VERIFY_IS_MUCH_SMALLER_THAN(vzero.norm(), static_cast<RealScalar>(1)); VERIFY_IS_APPROX(vrand.stableNorm(), vrand.norm()); VERIFY_IS_APPROX(vrand.blueNorm(), vrand.norm()); VERIFY_IS_APPROX(vrand.hypotNorm(), vrand.norm()); RealScalar size = static_cast<RealScalar>(m.size()); // test isFinite VERIFY(!isFinite( std::numeric_limits<RealScalar>::infinity())); VERIFY(!isFinite(internal::sqrt(-internal::abs(big)))); // test overflow VERIFY(isFinite(internal::sqrt(size)*internal::abs(big))); VERIFY_IS_NOT_APPROX(internal::sqrt(copy(vbig.squaredNorm())), internal::abs(internal::sqrt(size)*big)); // here the default norm must fail VERIFY_IS_APPROX(vbig.stableNorm(), internal::sqrt(size)*internal::abs(big)); VERIFY_IS_APPROX(vbig.blueNorm(), internal::sqrt(size)*internal::abs(big)); VERIFY_IS_APPROX(vbig.hypotNorm(), internal::sqrt(size)*internal::abs(big)); // test underflow VERIFY(isFinite(internal::sqrt(size)*internal::abs(small))); VERIFY_IS_NOT_APPROX(internal::sqrt(copy(vsmall.squaredNorm())), internal::abs(internal::sqrt(size)*small)); // here the default norm must fail VERIFY_IS_APPROX(vsmall.stableNorm(), internal::sqrt(size)*internal::abs(small)); VERIFY_IS_APPROX(vsmall.blueNorm(), internal::sqrt(size)*internal::abs(small)); VERIFY_IS_APPROX(vsmall.hypotNorm(), internal::sqrt(size)*internal::abs(small)); // Test compilation of cwise() version VERIFY_IS_APPROX(vrand.colwise().stableNorm(), vrand.colwise().norm()); VERIFY_IS_APPROX(vrand.colwise().blueNorm(), vrand.colwise().norm()); VERIFY_IS_APPROX(vrand.colwise().hypotNorm(), vrand.colwise().norm()); VERIFY_IS_APPROX(vrand.rowwise().stableNorm(), vrand.rowwise().norm()); VERIFY_IS_APPROX(vrand.rowwise().blueNorm(), vrand.rowwise().norm()); VERIFY_IS_APPROX(vrand.rowwise().hypotNorm(), vrand.rowwise().norm()); }
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 basicStuff(const MatrixType& m) { typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType; Index rows = m.rows(); Index cols = m.cols(); // this test relies a lot on Random.h, and there's not much more that we can do // to test it, hence I consider that we will have tested Random.h MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), mzero = MatrixType::Zero(rows, cols), square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows); VectorType v1 = VectorType::Random(rows), vzero = VectorType::Zero(rows); SquareMatrixType sm1 = SquareMatrixType::Random(rows,rows), sm2(rows,rows); Scalar x = 0; while(x == Scalar(0)) x = internal::random<Scalar>(); Index r = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1); m1.coeffRef(r,c) = x; VERIFY_IS_APPROX(x, m1.coeff(r,c)); m1(r,c) = x; VERIFY_IS_APPROX(x, m1(r,c)); v1.coeffRef(r) = x; VERIFY_IS_APPROX(x, v1.coeff(r)); v1(r) = x; VERIFY_IS_APPROX(x, v1(r)); v1[r] = x; VERIFY_IS_APPROX(x, v1[r]); VERIFY_IS_APPROX( v1, v1); VERIFY_IS_NOT_APPROX( v1, 2*v1); VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1); VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1.squaredNorm()); VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1, v1); VERIFY_IS_APPROX( vzero, v1-v1); VERIFY_IS_APPROX( m1, m1); VERIFY_IS_NOT_APPROX( m1, 2*m1); VERIFY_IS_MUCH_SMALLER_THAN( mzero, m1); VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1, m1); VERIFY_IS_APPROX( mzero, m1-m1); // always test operator() on each read-only expression class, // in order to check const-qualifiers. // indeed, if an expression class (here Zero) is meant to be read-only, // hence has no _write() method, the corresponding MatrixBase method (here zero()) // should return a const-qualified object so that it is the const-qualified // operator() that gets called, which in turn calls _read(). VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast<Scalar>(1)); // now test copying a row-vector into a (column-)vector and conversely. square.col(r) = square.row(r).eval(); Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows); Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows); rv = square.row(r); cv = square.col(r); VERIFY_IS_APPROX(rv, cv.transpose()); if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic) { VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1))); } if(cols!=1 && rows!=1) { VERIFY_RAISES_ASSERT(m1[0]); VERIFY_RAISES_ASSERT((m1+m1)[0]); } VERIFY_IS_APPROX(m3 = m1,m1); MatrixType m4; VERIFY_IS_APPROX(m4 = m1,m1); m3.real() = m1.real(); VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real()); VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real()); // check == / != operators VERIFY(m1==m1); VERIFY(m1!=m2); VERIFY(!(m1==m2)); VERIFY(!(m1!=m1)); m1 = m2; VERIFY(m1==m2); VERIFY(!(m1!=m2)); // check automatic transposition sm2.setZero(); for(typename MatrixType::Index i=0;i<rows;++i) sm2.col(i) = sm1.row(i); VERIFY_IS_APPROX(sm2,sm1.transpose()); sm2.setZero(); for(typename MatrixType::Index i=0;i<rows;++i) sm2.col(i).noalias() = sm1.row(i); VERIFY_IS_APPROX(sm2,sm1.transpose()); sm2.setZero(); for(typename MatrixType::Index i=0;i<rows;++i) sm2.col(i).noalias() += sm1.row(i); VERIFY_IS_APPROX(sm2,sm1.transpose()); sm2.setZero(); for(typename MatrixType::Index i=0;i<rows;++i) sm2.col(i).noalias() -= sm1.row(i); VERIFY_IS_APPROX(sm2,-sm1.transpose()); // check ternary usage { bool b = internal::random<int>(0,10)>5; m3 = b ? m1 : m2; if(b) VERIFY_IS_APPROX(m3,m1); else VERIFY_IS_APPROX(m3,m2); m3 = b ? -m1 : m2; if(b) VERIFY_IS_APPROX(m3,-m1); else VERIFY_IS_APPROX(m3,m2); m3 = b ? m1 : -m2; if(b) VERIFY_IS_APPROX(m3,m1); else VERIFY_IS_APPROX(m3,-m2); } }
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 MatrixType> void basicStuff(const MatrixType& m) { typedef typename MatrixType::Scalar Scalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; int rows = m.rows(); int cols = m.cols(); // this test relies a lot on Random.h, and there's not much more that we can do // to test it, hence I consider that we will have tested Random.h MatrixType m1 = MatrixType::Random(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), mzero = MatrixType::Zero(rows, cols), identity = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> ::Identity(rows, rows), square = Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime>::Random(rows, rows); VectorType v1 = VectorType::Random(rows), v2 = VectorType::Random(rows), vzero = VectorType::Zero(rows); Scalar x = ei_random<Scalar>(); int r = ei_random<int>(0, rows-1), c = ei_random<int>(0, cols-1); m1.coeffRef(r,c) = x; VERIFY_IS_APPROX(x, m1.coeff(r,c)); m1(r,c) = x; VERIFY_IS_APPROX(x, m1(r,c)); v1.coeffRef(r) = x; VERIFY_IS_APPROX(x, v1.coeff(r)); v1(r) = x; VERIFY_IS_APPROX(x, v1(r)); v1[r] = x; VERIFY_IS_APPROX(x, v1[r]); VERIFY_IS_APPROX( v1, v1); VERIFY_IS_NOT_APPROX( v1, 2*v1); VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1); if(NumTraits<Scalar>::HasFloatingPoint) VERIFY_IS_MUCH_SMALLER_THAN( vzero, v1.norm()); VERIFY_IS_NOT_MUCH_SMALLER_THAN(v1, v1); VERIFY_IS_APPROX( vzero, v1-v1); VERIFY_IS_APPROX( m1, m1); VERIFY_IS_NOT_APPROX( m1, 2*m1); VERIFY_IS_MUCH_SMALLER_THAN( mzero, m1); VERIFY_IS_NOT_MUCH_SMALLER_THAN(m1, m1); VERIFY_IS_APPROX( mzero, m1-m1); // always test operator() on each read-only expression class, // in order to check const-qualifiers. // indeed, if an expression class (here Zero) is meant to be read-only, // hence has no _write() method, the corresponding MatrixBase method (here zero()) // should return a const-qualified object so that it is the const-qualified // operator() that gets called, which in turn calls _read(). VERIFY_IS_MUCH_SMALLER_THAN(MatrixType::Zero(rows,cols)(r,c), static_cast<Scalar>(1)); // now test copying a row-vector into a (column-)vector and conversely. square.col(r) = square.row(r).eval(); Matrix<Scalar, 1, MatrixType::RowsAtCompileTime> rv(rows); Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> cv(rows); rv = square.row(r); cv = square.col(r); VERIFY_IS_APPROX(rv, cv.transpose()); if(cols!=1 && rows!=1 && MatrixType::SizeAtCompileTime!=Dynamic) { VERIFY_RAISES_ASSERT(m1 = (m2.block(0,0, rows-1, cols-1))); } VERIFY_IS_APPROX(m3 = m1,m1); MatrixType m4; VERIFY_IS_APPROX(m4 = m1,m1); // test swap m3 = m1; m1.swap(m2); VERIFY_IS_APPROX(m3, m2); if(rows*cols>=3) { VERIFY_IS_NOT_APPROX(m3, m1); } }
template<typename Scalar, int Mode, int Options> void transformations() { /* 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,Mode,Options> Transform2; typedef Transform<Scalar,3,Mode,Options> Transform3; typedef Transform<Scalar,2,Isometry,Options> Isometry2; typedef Transform<Scalar,3,Isometry,Options> Isometry3; typedef typename Transform3::MatrixType MatrixType; typedef DiagonalMatrix<Scalar,2> AlignedScaling2; typedef DiagonalMatrix<Scalar,3> AlignedScaling3; typedef Translation<Scalar,2> Translation2; typedef Translation<Scalar,3> Translation3; Vector3 v0 = Vector3::Random(), v1 = Vector3::Random(); Matrix3 matrot1, m; Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI)); Scalar s0 = internal::random<Scalar>(); VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0); VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0); VERIFY_IS_APPROX(internal::cos(a)*v0.squaredNorm(), v0.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); Quaternionx q1, q2; q1 = AngleAxisx(a, v0.normalized()); q2 = AngleAxisx(a, v1.normalized()); // rotation matrix conversion 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 = AngleAxisx(q1); VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1); aa.fromRotationMatrix(aa.toRotationMatrix()); VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1); VERIFY_IS_NOT_APPROX(q1 * v1, Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * 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 (internal::abs(a)<Scalar(0.1)) a = internal::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.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.cwiseInverse()); t1.translate(-v0); VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>())); t1.fromPositionOrientationScale(v0, q1, v1); VERIFY_IS_APPROX(t1.matrix(), t0.matrix()); 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); if(Mode!=int(AffineCompact)) tmat4.matrix()(3,3) = Scalar(1); VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix()); Scalar a3 = internal::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(), MatrixType::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(), MatrixType::Identity()); t4 *= tv3; VERIFY_IS_APPROX(t5.matrix(), t4.matrix()); AlignedScaling3 sv3(v3); Transform3 t6(sv3); t4 = sv3; VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); t4.scale(v3.cwiseInverse()); VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity()); t4 *= sv3; VERIFY_IS_APPROX(t6.matrix(), t4.matrix()); // matrix * transform VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (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 (internal::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.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) ); // Transform - new API // 3D t0.setIdentity(); t0.rotate(q1).scale(v0).translate(v0); // mat * aligned scaling and mat * translation t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // mat * transformation and aligned scaling * translation t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.setIdentity(); t0.scale(s0).translate(v0); t1 = Eigen::Scaling(s0) * Translation3(v0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.prescale(s0); t1 = Eigen::Scaling(s0) * t1; VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0 = t3; t0.scale(s0); t1 = t3 * Eigen::Scaling(s0,s0,s0); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.prescale(s0); t1 = Eigen::Scaling(s0,s0,s0) * t1; VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.setIdentity(); t0.prerotate(q1).prescale(v0).pretranslate(v0); // translation * aligned scaling and transformation * mat t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // scaling * mat and translation * mat t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); t0.setIdentity(); t0.scale(v0).translate(v0).rotate(q1); // translation * mat and aligned scaling * transformation t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // transformation * aligned scaling t0.scale(v0); t1 *= AlignedScaling3(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()); // aligned scaling * quaternion t0.scale(v1).rotate(q1); t1 = t1 * (AlignedScaling3(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 * aligned scaling t0.rotate(q1).scale(v1); t1 = t1 * (q1 * AlignedScaling3(v1)); VERIFY_IS_APPROX(t0.matrix(), t1.matrix()); // test transform inversion t0.setIdentity(); t0.translate(v0); t0.linear().setRandom(); Matrix4 t044 = Matrix4::Zero(); t044(3,3) = 1; t044.block(0,0,t0.matrix().rows(),4) = t0.matrix(); VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4)); t0.setIdentity(); t0.translate(v0).rotate(q1); t044 = Matrix4::Zero(); t044(3,3) = 1; t044.block(0,0,t0.matrix().rows(),4) = t0.matrix(); VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4)); 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,Mode> t1f = t1.template cast<float>(); VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1); Transform<double,3,Mode> 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); 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(internal::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); t20 = Translation2(v20) * (Rotation2D<Scalar>(s0) * Scaling(s0)); t21 = Translation2(v20) * Rotation2D<Scalar>(s0) * Scaling(s0); VERIFY_IS_APPROX(t20,t21); }
template<typename MatrixType> void integer_type_tests(const MatrixType& m) { typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; VERIFY(NumTraits<Scalar>::IsInteger); enum { is_signed = (Scalar(-1) > Scalar(0)) ? 0 : 1 }; VERIFY(int(NumTraits<Scalar>::IsSigned) == is_signed); typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; Index rows = m.rows(); Index cols = m.cols(); // this test relies a lot on Random.h, and there's not much more that we can do // to test it, hence I consider that we will have tested Random.h MatrixType m1(rows, cols), m2 = MatrixType::Random(rows, cols), m3(rows, cols), mzero = MatrixType::Zero(rows, cols); typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, MatrixType::RowsAtCompileTime> SquareMatrixType; SquareMatrixType identity = SquareMatrixType::Identity(rows, rows), square = SquareMatrixType::Random(rows, rows); VectorType v1(rows), v2 = VectorType::Random(rows), vzero = VectorType::Zero(rows); do { m1 = MatrixType::Random(rows, cols); } while(m1 == mzero || m1 == m2); do { v1 = VectorType::Random(rows); } while(v1 == vzero || v1 == v2); VERIFY_IS_APPROX( v1, v1); VERIFY_IS_NOT_APPROX( v1, 2*v1); VERIFY_IS_APPROX( vzero, v1-v1); VERIFY_IS_APPROX( m1, m1); VERIFY_IS_NOT_APPROX( m1, 2*m1); VERIFY_IS_APPROX( mzero, m1-m1); VERIFY_IS_APPROX(m3 = m1,m1); MatrixType m4; VERIFY_IS_APPROX(m4 = m1,m1); m3.real() = m1.real(); VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), static_cast<const MatrixType&>(m1).real()); VERIFY_IS_APPROX(static_cast<const MatrixType&>(m3).real(), m1.real()); // check == / != operators VERIFY(m1==m1); VERIFY(m1!=m2); VERIFY(!(m1==m2)); VERIFY(!(m1!=m1)); m1 = m2; VERIFY(m1==m2); VERIFY(!(m1!=m2)); // check linear structure Scalar s1; do { s1 = ei_random<Scalar>(); } while(s1 == 0); VERIFY_IS_EQUAL(m1+m1, 2*m1); VERIFY_IS_EQUAL(m1+m2-m1, m2); VERIFY_IS_EQUAL(m1*s1, s1*m1); VERIFY_IS_EQUAL((m1+m2)*s1, s1*m1+s1*m2); m3 = m2; m3 += m1; VERIFY_IS_EQUAL(m3, m1+m2); m3 = m2; m3 -= m1; VERIFY_IS_EQUAL(m3, m2-m1); m3 = m2; m3 *= s1; VERIFY_IS_EQUAL(m3, s1*m2); // check matrix product. VERIFY_IS_APPROX(identity * m1, m1); VERIFY_IS_APPROX(square * (m1 + m2), square * m1 + square * m2); VERIFY_IS_APPROX((m1 + m2).transpose() * square, m1.transpose() * square + m2.transpose() * square); VERIFY_IS_APPROX((m1 * m2.transpose()) * m1, m1 * (m2.transpose() * m1)); }