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));
}
