void test_commainitializer() { Matrix3d m3; Matrix4d m4; VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8) ); #ifndef _MSC_VER VERIFY_RAISES_ASSERT( (m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9, 10) ); #endif double data[] = {1, 2, 3, 4, 5, 6, 7, 8, 9}; Matrix3d ref = Map<Matrix<double,3,3,RowMajor> >(data); m3 = Matrix3d::Random(); m3 << 1, 2, 3, 4, 5, 6, 7, 8, 9; VERIFY_IS_APPROX(m3, ref ); Vector3d vec[3]; vec[0] << 1, 4, 7; vec[1] << 2, 5, 8; vec[2] << 3, 6, 9; m3 = Matrix3d::Random(); m3 << vec[0], vec[1], vec[2]; VERIFY_IS_APPROX(m3, ref); vec[0] << 1, 2, 3; vec[1] << 4, 5, 6; vec[2] << 7, 8, 9; m3 = Matrix3d::Random(); m3 << vec[0].transpose(), 4, 5, 6, vec[2].transpose(); VERIFY_IS_APPROX(m3, ref); }
template<typename MatrixType> void test_reference(const MatrixType& m) { typedef typename MatrixType::Scalar Scalar; enum { Flag = MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor}; enum { TransposeFlag = !MatrixType::IsRowMajor ? Eigen::RowMajor : Eigen::ColMajor}; typename MatrixType::Index rows = m.rows(), cols=m.cols(); typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, Flag > MatrixX; typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, TransposeFlag> MatrixXT; // Dynamic reference: typedef Eigen::Ref<const MatrixX > Ref; typedef Eigen::Ref<const MatrixXT > RefT; Ref r1(m); Ref r2(m.block(rows/3, cols/4, rows/2, cols/2)); RefT r3(m.transpose()); RefT r4(m.topLeftCorner(rows/2, cols/2).transpose()); VERIFY_RAISES_ASSERT(RefT r5(m)); VERIFY_RAISES_ASSERT(Ref r6(m.transpose())); VERIFY_RAISES_ASSERT(Ref r7(Scalar(2) * m)); // Copy constructors shall also never malloc Ref r8 = r1; RefT r9 = r3; // Initializing from a compatible Ref shall also never malloc Eigen::Ref<const MatrixX, Unaligned, Stride<Dynamic, Dynamic> > r10=r8, r11=m; // Initializing from an incompatible Ref will malloc: typedef Eigen::Ref<const MatrixX, Aligned> RefAligned; VERIFY_RAISES_ASSERT(RefAligned r12=r10); VERIFY_RAISES_ASSERT(Ref r13=r10); // r10 has more dynamic strides }
template<typename MatrixType> void swap(const MatrixType& m) { typedef typename other_matrix_type<MatrixType>::type OtherMatrixType; typedef typename MatrixType::Scalar Scalar; eigen_assert((!internal::is_same<MatrixType,OtherMatrixType>::value)); typename MatrixType::Index rows = m.rows(); typename MatrixType::Index cols = m.cols(); // construct 3 matrix guaranteed to be distinct MatrixType m1 = MatrixType::Random(rows,cols); MatrixType m2 = MatrixType::Random(rows,cols) + Scalar(100) * MatrixType::Identity(rows,cols); OtherMatrixType m3 = OtherMatrixType::Random(rows,cols) + Scalar(200) * OtherMatrixType::Identity(rows,cols); MatrixType m1_copy = m1; MatrixType m2_copy = m2; OtherMatrixType m3_copy = m3; // test swapping 2 matrices of same type Scalar *d1=m1.data(), *d2=m2.data(); m1.swap(m2); VERIFY_IS_APPROX(m1,m2_copy); VERIFY_IS_APPROX(m2,m1_copy); if(MatrixType::SizeAtCompileTime==Dynamic) { VERIFY(m1.data()==d2); VERIFY(m2.data()==d1); } m1 = m1_copy; m2 = m2_copy; // test swapping 2 matrices of different types m1.swap(m3); VERIFY_IS_APPROX(m1,m3_copy); VERIFY_IS_APPROX(m3,m1_copy); m1 = m1_copy; m3 = m3_copy; // test swapping matrix with expression m1.swap(m2.block(0,0,rows,cols)); VERIFY_IS_APPROX(m1,m2_copy); VERIFY_IS_APPROX(m2,m1_copy); m1 = m1_copy; m2 = m2_copy; // test swapping two expressions of different types m1.transpose().swap(m3.transpose()); VERIFY_IS_APPROX(m1,m3_copy); VERIFY_IS_APPROX(m3,m1_copy); m1 = m1_copy; m3 = m3_copy; // test assertion on mismatching size -- matrix case VERIFY_RAISES_ASSERT(m1.swap(m1.row(0))); // test assertion on mismatching size -- xpr case VERIFY_RAISES_ASSERT(m1.row(0).swap(m1)); }
template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m) { ComplexEigenSolver<MatrixType> eig; VERIFY_RAISES_ASSERT(eig.eigenvectors()); VERIFY_RAISES_ASSERT(eig.eigenvalues()); MatrixType a = MatrixType::Random(m.rows(),m.cols()); eig.compute(a, false); VERIFY_RAISES_ASSERT(eig.eigenvectors()); }
void bdcsvd_method() { enum { Size = MatrixType::RowsAtCompileTime }; typedef typename MatrixType::RealScalar RealScalar; typedef Matrix<RealScalar, Size, 1> RealVecType; MatrixType m = MatrixType::Identity(); VERIFY_IS_APPROX(m.bdcSvd().singularValues(), RealVecType::Ones()); VERIFY_RAISES_ASSERT(m.bdcSvd().matrixU()); VERIFY_RAISES_ASSERT(m.bdcSvd().matrixV()); VERIFY_IS_APPROX(m.bdcSvd(ComputeFullU|ComputeFullV).solve(m), m); }
template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime) { typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar; typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType; // Test basic functionality: T is triangular and A = U T U* for(int counter = 0; counter < g_repeat; ++counter) { MatrixType A = MatrixType::Random(size, size); ComplexSchur<MatrixType> schurOfA(A); VERIFY_IS_EQUAL(schurOfA.info(), Success); ComplexMatrixType U = schurOfA.matrixU(); ComplexMatrixType T = schurOfA.matrixT(); for(int row = 1; row < size; ++row) { for(int col = 0; col < row; ++col) { VERIFY(T(row,col) == (typename MatrixType::Scalar)0); } } VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint()); } // Test asserts when not initialized ComplexSchur<MatrixType> csUninitialized; VERIFY_RAISES_ASSERT(csUninitialized.matrixT()); VERIFY_RAISES_ASSERT(csUninitialized.matrixU()); VERIFY_RAISES_ASSERT(csUninitialized.info()); // Test whether compute() and constructor returns same result MatrixType A = MatrixType::Random(size, size); ComplexSchur<MatrixType> cs1; cs1.compute(A); ComplexSchur<MatrixType> cs2(A); VERIFY_IS_EQUAL(cs1.info(), Success); VERIFY_IS_EQUAL(cs2.info(), Success); VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT()); VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU()); // Test computation of only T, not U ComplexSchur<MatrixType> csOnlyT(A, false); VERIFY_IS_EQUAL(csOnlyT.info(), Success); VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT()); VERIFY_RAISES_ASSERT(csOnlyT.matrixU()); if (size > 1) { // Test matrix with NaN A(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); ComplexSchur<MatrixType> csNaN(A); VERIFY_IS_EQUAL(csNaN.info(), NoConvergence); } }
template<typename Scalar> void transform_alignment() { typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a; typedef Transform<Scalar,3,Projective,DontAlign> Projective3u; EIGEN_ALIGN16 Scalar array1[16]; EIGEN_ALIGN16 Scalar array2[16]; EIGEN_ALIGN16 Scalar array3[16+1]; Scalar* array3u = array3+1; Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a; Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u; Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u; p1->matrix().setRandom(); *p2 = *p1; *p3 = *p1; VERIFY_IS_APPROX(p1->matrix(), p2->matrix()); VERIFY_IS_APPROX(p1->matrix(), p3->matrix()); VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3)); #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY if(internal::packet_traits<Scalar>::Vectorizable) VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a)); #endif }
template<typename Scalar> void parametrizedline_alignment() { typedef ParametrizedLine<Scalar,4,AutoAlign> Line4a; typedef ParametrizedLine<Scalar,4,DontAlign> Line4u; EIGEN_ALIGN16 Scalar array1[8]; EIGEN_ALIGN16 Scalar array2[8]; EIGEN_ALIGN16 Scalar array3[8+1]; Scalar* array3u = array3+1; Line4a *p1 = ::new(reinterpret_cast<void*>(array1)) Line4a; Line4u *p2 = ::new(reinterpret_cast<void*>(array2)) Line4u; Line4u *p3 = ::new(reinterpret_cast<void*>(array3u)) Line4u; p1->origin().setRandom(); p1->direction().setRandom(); *p2 = *p1; *p3 = *p1; VERIFY_IS_APPROX(p1->origin(), p2->origin()); VERIFY_IS_APPROX(p1->origin(), p3->origin()); VERIFY_IS_APPROX(p1->direction(), p2->direction()); VERIFY_IS_APPROX(p1->direction(), p3->direction()); #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY if(internal::packet_traits<Scalar>::Vectorizable) VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Line4a)); #endif }
template<typename VectorType> void map_class_vector(const VectorType& m) { typedef typename VectorType::Index Index; typedef typename VectorType::Scalar Scalar; Index size = m.size(); Scalar* array1 = internal::aligned_new<Scalar>(size); Scalar* array2 = internal::aligned_new<Scalar>(size); Scalar* array3 = new Scalar[size+1]; Scalar* array3unaligned = (internal::UIntPtr(array3)%EIGEN_MAX_ALIGN_BYTES) == 0 ? array3+1 : array3; Scalar array4[EIGEN_TESTMAP_MAX_SIZE]; Map<VectorType, AlignedMax>(array1, size) = VectorType::Random(size); Map<VectorType, AlignedMax>(array2, size) = Map<VectorType,AlignedMax>(array1, size); Map<VectorType>(array3unaligned, size) = Map<VectorType>(array1, size); Map<VectorType>(array4, size) = Map<VectorType,AlignedMax>(array1, size); VectorType ma1 = Map<VectorType, AlignedMax>(array1, size); VectorType ma2 = Map<VectorType, AlignedMax>(array2, size); VectorType ma3 = Map<VectorType>(array3unaligned, size); VectorType ma4 = Map<VectorType>(array4, size); VERIFY_IS_EQUAL(ma1, ma2); VERIFY_IS_EQUAL(ma1, ma3); VERIFY_IS_EQUAL(ma1, ma4); #ifdef EIGEN_VECTORIZE if(internal::packet_traits<Scalar>::Vectorizable && size>=AlignedMax) VERIFY_RAISES_ASSERT((Map<VectorType,AlignedMax>(array3unaligned, size))) #endif internal::aligned_delete(array1, size); internal::aligned_delete(array2, size); delete[] array3; }
template<typename Scalar> void mapQuaternion(void){ typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA; typedef Map<Quaternion<Scalar> > MQuaternionUA; typedef Map<const Quaternion<Scalar> > MCQuaternionUA; typedef Quaternion<Scalar> Quaternionx; EIGEN_ALIGN16 Scalar array1[4]; EIGEN_ALIGN16 Scalar array2[4]; EIGEN_ALIGN16 Scalar array3[4+1]; Scalar* array3unaligned = array3+1; // std::cerr << array1 << " " << array2 << " " << array3 << "\n"; MQuaternionA(array1).coeffs().setRandom(); (MQuaternionA(array2)) = MQuaternionA(array1); (MQuaternionUA(array3unaligned)) = MQuaternionA(array1); Quaternionx q1 = MQuaternionA(array1); Quaternionx q2 = MQuaternionA(array2); Quaternionx q3 = MQuaternionUA(array3unaligned); Quaternionx q4 = MCQuaternionUA(array3unaligned); VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs()); VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs()); VERIFY_IS_APPROX(q4.coeffs(), q3.coeffs()); #ifdef EIGEN_VECTORIZE if(internal::packet_traits<Scalar>::Vectorizable) VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned))); #endif }
template<typename MatrixType> void vectorwiseop_matrix(const MatrixType& m) { typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType; typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType; Index rows = m.rows(); Index cols = m.cols(); Index r = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1); MatrixType m1 = MatrixType::Random(rows, cols), m2(rows, cols), m3(rows, cols); ColVectorType colvec = ColVectorType::Random(rows); RowVectorType rowvec = RowVectorType::Random(cols); // test addition m2 = m1; m2.colwise() += colvec; VERIFY_IS_APPROX(m2, m1.colwise() + colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec); VERIFY_RAISES_ASSERT(m2.colwise() += colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() + colvec.transpose()); m2 = m1; m2.rowwise() += rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() += rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() + rowvec.transpose()); // test substraction m2 = m1; m2.colwise() -= colvec; VERIFY_IS_APPROX(m2, m1.colwise() - colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec); VERIFY_RAISES_ASSERT(m2.colwise() -= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() - colvec.transpose()); m2 = m1; m2.rowwise() -= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() -= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() - rowvec.transpose()); }
void test_eigen2_nomalloc() { // check that our operator new is indeed called: VERIFY_RAISES_ASSERT(MatrixXd dummy = MatrixXd::Random(3,3)); CALL_SUBTEST_1( nomalloc(Matrix<float, 1, 1>()) ); CALL_SUBTEST_2( nomalloc(Matrix4d()) ); CALL_SUBTEST_3( nomalloc(Matrix<float,32,32>()) ); }
void test_adjoint() { for(int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1( adjoint(Matrix<float, 1, 1>()) ); CALL_SUBTEST_2( adjoint(Matrix3d()) ); CALL_SUBTEST_3( adjoint(Matrix4f()) ); CALL_SUBTEST_4( adjoint(MatrixXcf(internal::random<int>(1,50), internal::random<int>(1,50))) ); CALL_SUBTEST_5( adjoint(MatrixXi(internal::random<int>(1,50), internal::random<int>(1,50))) ); CALL_SUBTEST_6( adjoint(MatrixXf(internal::random<int>(1,50), internal::random<int>(1,50))) ); } // test a large matrix only once CALL_SUBTEST_7( adjoint(Matrix<float, 100, 100>()) ); #ifdef EIGEN_TEST_PART_4 { MatrixXcf a(10,10), b(10,10); VERIFY_RAISES_ASSERT(a = a.transpose()); VERIFY_RAISES_ASSERT(a = a.transpose() + b); VERIFY_RAISES_ASSERT(a = b + a.transpose()); VERIFY_RAISES_ASSERT(a = a.conjugate().transpose()); VERIFY_RAISES_ASSERT(a = a.adjoint()); VERIFY_RAISES_ASSERT(a = a.adjoint() + b); VERIFY_RAISES_ASSERT(a = b + a.adjoint()); // no assertion should be triggered for these cases: a.transpose() = a.transpose(); a.transpose() += a.transpose(); a.transpose() += a.transpose() + b; a.transpose() = a.adjoint(); a.transpose() += a.adjoint(); a.transpose() += a.adjoint() + b; } #endif }
template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime) { // Test basic functionality: T is quasi-triangular and A = U T U* for(int counter = 0; counter < g_repeat; ++counter) { MatrixType A = MatrixType::Random(size, size); RealSchur<MatrixType> schurOfA(A); VERIFY_IS_EQUAL(schurOfA.info(), Success); MatrixType U = schurOfA.matrixU(); MatrixType T = schurOfA.matrixT(); verifyIsQuasiTriangular(T); VERIFY_IS_APPROX(A, U * T * U.transpose()); } // Test asserts when not initialized RealSchur<MatrixType> rsUninitialized; VERIFY_RAISES_ASSERT(rsUninitialized.matrixT()); VERIFY_RAISES_ASSERT(rsUninitialized.matrixU()); VERIFY_RAISES_ASSERT(rsUninitialized.info()); // Test whether compute() and constructor returns same result MatrixType A = MatrixType::Random(size, size); RealSchur<MatrixType> rs1; rs1.compute(A); RealSchur<MatrixType> rs2(A); VERIFY_IS_EQUAL(rs1.info(), Success); VERIFY_IS_EQUAL(rs2.info(), Success); VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT()); VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU()); // Test computation of only T, not U RealSchur<MatrixType> rsOnlyT(A, false); VERIFY_IS_EQUAL(rsOnlyT.info(), Success); VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT()); VERIFY_RAISES_ASSERT(rsOnlyT.matrixU()); if (size > 2) { // Test matrix with NaN A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN(); RealSchur<MatrixType> rsNaN(A); VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence); } }
void unalignedassert() { check_unalignedassert_good<Good1>(); check_unalignedassert_good<Good2>(); check_unalignedassert_good<Good3>(); #if EIGEN_ARCH_WANTS_ALIGNMENT VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Bad4>()); VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Bad5>()); VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Bad6>()); #endif check_unalignedassert_good<Good7>(); check_unalignedassert_good<Good8>(); check_unalignedassert_good<Good9>(); check_unalignedassert_good<Depends<true> >(); #if EIGEN_ARCH_WANTS_ALIGNMENT VERIFY_RAISES_ASSERT(check_unalignedassert_bad<Depends<false> >()); #endif }
void test_nomalloc() { // check that our operator new is indeed called: VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3))); CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) ); CALL_SUBTEST_2(nomalloc(Matrix4d()) ); CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) ); // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms) CALL_SUBTEST_4(ctms_decompositions<float>()); }
template <typename MatrixType> void run_nesting_ops(const MatrixType& _m) { typename internal::nested_eval<MatrixType,2>::type m(_m); // Make really sure that we are in debug mode! VERIFY_RAISES_ASSERT(eigen_assert(false)); // The only intention of these tests is to ensure that this code does // not trigger any asserts or segmentation faults... more to come. VERIFY_IS_APPROX( (m.transpose() * m).diagonal().sum(), (m.transpose() * m).diagonal().sum() ); VERIFY_IS_APPROX( (m.transpose() * m).diagonal().array().abs().sum(), (m.transpose() * m).diagonal().array().abs().sum() ); VERIFY_IS_APPROX( (m.transpose() * m).array().abs().sum(), (m.transpose() * m).array().abs().sum() ); }
void test_blocks() { Matrix<int, M1+M2, N1+N2> m_fixed; MatrixXi m_dynamic(M1+M2, N1+N2); Matrix<int, M1, N1> mat11; mat11.setRandom(); Matrix<int, M1, N2> mat12; mat12.setRandom(); Matrix<int, M2, N1> mat21; mat21.setRandom(); Matrix<int, M2, N2> mat22; mat22.setRandom(); MatrixXi matx11 = mat11, matx12 = mat12, matx21 = mat21, matx22 = mat22; { VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat21, matx22).finished(), (m_dynamic << mat11, matx12, mat21, matx22).finished()); VERIFY_IS_EQUAL((m_fixed.template topLeftCorner<M1,N1>()), mat11); VERIFY_IS_EQUAL((m_fixed.template topRightCorner<M1,N2>()), mat12); VERIFY_IS_EQUAL((m_fixed.template bottomLeftCorner<M2,N1>()), mat21); VERIFY_IS_EQUAL((m_fixed.template bottomRightCorner<M2,N2>()), mat22); VERIFY_IS_EQUAL((m_fixed << mat12, mat11, matx21, mat22).finished(), (m_dynamic << mat12, matx11, matx21, mat22).finished()); } if(N1 > 0) { VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat11, mat21, mat22)); VERIFY_RAISES_ASSERT((m_fixed << mat11, mat12, mat21, mat21, mat22)); } else { // allow insertion of zero-column blocks: VERIFY_IS_EQUAL((m_fixed << mat11, mat12, mat11, mat11, mat21, mat21, mat22).finished(), (m_dynamic << mat12, mat22).finished()); } if(M1 != M2) { VERIFY_RAISES_ASSERT((m_fixed << mat11, mat21, mat12, mat22)); } }
void unalignedassert() { #if EIGEN_ALIGN_STATICALLY construct_at_boundary<Vector2f>(4); construct_at_boundary<Vector3f>(4); construct_at_boundary<Vector4f>(16); construct_at_boundary<Matrix2f>(16); construct_at_boundary<Matrix3f>(4); construct_at_boundary<Matrix4f>(16); construct_at_boundary<Vector2d>(16); construct_at_boundary<Vector3d>(4); construct_at_boundary<Vector4d>(16); construct_at_boundary<Matrix2d>(16); construct_at_boundary<Matrix3d>(4); construct_at_boundary<Matrix4d>(16); construct_at_boundary<Vector2cf>(16); construct_at_boundary<Vector3cf>(4); construct_at_boundary<Vector2cd>(16); construct_at_boundary<Vector3cd>(16); #endif check_unalignedassert_good<TestNew1>(); check_unalignedassert_good<TestNew2>(); check_unalignedassert_good<TestNew3>(); check_unalignedassert_good<TestNew4>(); check_unalignedassert_good<TestNew5>(); check_unalignedassert_good<TestNew6>(); check_unalignedassert_good<Depends<true> >(); #if EIGEN_ALIGN_STATICALLY VERIFY_RAISES_ASSERT(construct_at_boundary<Vector4f>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Matrix4f>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Vector2d>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Vector4d>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Matrix2d>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Matrix4d>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Vector2cf>(8)); VERIFY_RAISES_ASSERT(construct_at_boundary<Vector2cd>(8)); #endif }
template<typename Scalar> void mapQuaternion(void){ typedef Map<Quaternion<Scalar>, Aligned> MQuaternionA; typedef Map<Quaternion<Scalar> > MQuaternionUA; typedef Quaternion<Scalar> Quaternionx; EIGEN_ALIGN16 Scalar array1[4]; EIGEN_ALIGN16 Scalar array2[4]; EIGEN_ALIGN16 Scalar array3[4+1]; Scalar* array3unaligned = array3+1; MQuaternionA(array1).coeffs().setRandom(); (MQuaternionA(array2)) = MQuaternionA(array1); (MQuaternionUA(array3unaligned)) = MQuaternionA(array1); Quaternionx q1 = MQuaternionA(array1); Quaternionx q2 = MQuaternionA(array2); Quaternionx q3 = MQuaternionUA(array3unaligned); VERIFY_IS_APPROX(q1.coeffs(), q2.coeffs()); VERIFY_IS_APPROX(q1.coeffs(), q3.coeffs()); VERIFY_RAISES_ASSERT((MQuaternionA(array3unaligned))); }
template<typename Scalar> void quaternionAlignment(void){ typedef Quaternion<Scalar,AutoAlign> QuaternionA; typedef Quaternion<Scalar,DontAlign> QuaternionUA; EIGEN_ALIGN16 Scalar array1[4]; EIGEN_ALIGN16 Scalar array2[4]; EIGEN_ALIGN16 Scalar array3[4+1]; Scalar* arrayunaligned = array3+1; QuaternionA *q1 = ::new(reinterpret_cast<void*>(array1)) QuaternionA; QuaternionUA *q2 = ::new(reinterpret_cast<void*>(array2)) QuaternionUA; QuaternionUA *q3 = ::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionUA; q1->coeffs().setRandom(); *q2 = *q1; *q3 = *q1; VERIFY_IS_APPROX(q1->coeffs(), q2->coeffs()); VERIFY_IS_APPROX(q1->coeffs(), q3->coeffs()); #ifdef EIGEN_VECTORIZE VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(arrayunaligned)) QuaternionA)); #endif }
void test_nomalloc() { // create some dynamic objects Eigen::MatrixXd M1 = MatrixXd::Random(3,3); Ref<const MatrixXd> R1 = 2.0*M1; // Ref requires temporary // from here on prohibit malloc: Eigen::internal::set_is_malloc_allowed(false); // check that our operator new is indeed called: VERIFY_RAISES_ASSERT(MatrixXd dummy(MatrixXd::Random(3,3))); CALL_SUBTEST_1(nomalloc(Matrix<float, 1, 1>()) ); CALL_SUBTEST_2(nomalloc(Matrix4d()) ); CALL_SUBTEST_3(nomalloc(Matrix<float,32,32>()) ); // Check decomposition modules with dynamic matrices that have a known compile-time max size (ctms) CALL_SUBTEST_4(ctms_decompositions<float>()); CALL_SUBTEST_5(test_zerosized()); CALL_SUBTEST_6(test_reference(Matrix<float,32,32>())); CALL_SUBTEST_7(test_reference(R1)); CALL_SUBTEST_8(Ref<MatrixXd> R2 = M1.topRows<2>(); test_reference(R2)); }
template<typename SparseMatrixType> void sparse_basic(const SparseMatrixType& ref) { const int rows = ref.rows(); const int cols = ref.cols(); typedef typename SparseMatrixType::Scalar Scalar; enum { Flags = SparseMatrixType::Flags }; double density = std::max(8./(rows*cols), 0.01); typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; typedef Matrix<Scalar,Dynamic,1> DenseVector; Scalar eps = 1e-6; SparseMatrixType m(rows, cols); DenseMatrix refMat = DenseMatrix::Zero(rows, cols); DenseVector vec1 = DenseVector::Random(rows); Scalar s1 = ei_random<Scalar>(); std::vector<Vector2i> zeroCoords; std::vector<Vector2i> nonzeroCoords; initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords); if (zeroCoords.size()==0 || nonzeroCoords.size()==0) return; // test coeff and coeffRef for (int i=0; i<(int)zeroCoords.size(); ++i) { VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps ); if(ei_is_same_type<SparseMatrixType,SparseMatrix<Scalar,Flags> >::ret) VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 ); } VERIFY_IS_APPROX(m, refMat); m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); VERIFY_IS_APPROX(m, refMat); /* // test InnerIterators and Block expressions for (int t=0; t<10; ++t) { int j = ei_random<int>(0,cols-1); int i = ei_random<int>(0,rows-1); int w = ei_random<int>(1,cols-j-1); int h = ei_random<int>(1,rows-i-1); // VERIFY_IS_APPROX(m.block(i,j,h,w), refMat.block(i,j,h,w)); for(int c=0; c<w; c++) { VERIFY_IS_APPROX(m.block(i,j,h,w).col(c), refMat.block(i,j,h,w).col(c)); for(int r=0; r<h; r++) { // VERIFY_IS_APPROX(m.block(i,j,h,w).col(c).coeff(r), refMat.block(i,j,h,w).col(c).coeff(r)); } } // for(int r=0; r<h; r++) // { // VERIFY_IS_APPROX(m.block(i,j,h,w).row(r), refMat.block(i,j,h,w).row(r)); // for(int c=0; c<w; c++) // { // VERIFY_IS_APPROX(m.block(i,j,h,w).row(r).coeff(c), refMat.block(i,j,h,w).row(r).coeff(c)); // } // } } for(int c=0; c<cols; c++) { VERIFY_IS_APPROX(m.col(c) + m.col(c), (m + m).col(c)); VERIFY_IS_APPROX(m.col(c) + m.col(c), refMat.col(c) + refMat.col(c)); } for(int r=0; r<rows; r++) { VERIFY_IS_APPROX(m.row(r) + m.row(r), (m + m).row(r)); VERIFY_IS_APPROX(m.row(r) + m.row(r), refMat.row(r) + refMat.row(r)); } */ // test SparseSetters // coherent setter // TODO extend the MatrixSetter // { // m.setZero(); // VERIFY_IS_NOT_APPROX(m, refMat); // SparseSetter<SparseMatrixType, FullyCoherentAccessPattern> w(m); // for (int i=0; i<nonzeroCoords.size(); ++i) // { // w->coeffRef(nonzeroCoords[i].x(),nonzeroCoords[i].y()) = refMat.coeff(nonzeroCoords[i].x(),nonzeroCoords[i].y()); // } // } // VERIFY_IS_APPROX(m, refMat); // random setter // { // m.setZero(); // VERIFY_IS_NOT_APPROX(m, refMat); // SparseSetter<SparseMatrixType, RandomAccessPattern> w(m); // std::vector<Vector2i> remaining = nonzeroCoords; // while(!remaining.empty()) // { // int i = ei_random<int>(0,remaining.size()-1); // w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y()); // remaining[i] = remaining.back(); // remaining.pop_back(); // } // } // VERIFY_IS_APPROX(m, refMat); VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdMapTraits> >(m,refMat,nonzeroCoords) )); #ifdef EIGEN_UNORDERED_MAP_SUPPORT VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdUnorderedMapTraits> >(m,refMat,nonzeroCoords) )); #endif #ifdef _DENSE_HASH_MAP_H_ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleDenseHashMapTraits> >(m,refMat,nonzeroCoords) )); #endif #ifdef _SPARSE_HASH_MAP_H_ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleSparseHashMapTraits> >(m,refMat,nonzeroCoords) )); #endif // test fillrand { DenseMatrix m1(rows,cols); m1.setZero(); SparseMatrixType m2(rows,cols); m2.startFill(); for (int j=0; j<cols; ++j) { for (int k=0; k<rows/2; ++k) { int i = ei_random<int>(0,rows-1); if (m1.coeff(i,j)==Scalar(0)) m2.fillrand(i,j) = m1(i,j) = ei_random<Scalar>(); } } m2.endFill(); VERIFY_IS_APPROX(m2,m1); } // test RandomSetter /*{ SparseMatrixType m1(rows,cols), m2(rows,cols); DenseMatrix refM1 = DenseMatrix::Zero(rows, rows); initSparse<Scalar>(density, refM1, m1); { Eigen::RandomSetter<SparseMatrixType > setter(m2); for (int j=0; j<m1.outerSize(); ++j) for (typename SparseMatrixType::InnerIterator i(m1,j); i; ++i) setter(i.index(), j) = i.value(); } VERIFY_IS_APPROX(m1, m2); }*/ // std::cerr << m.transpose() << "\n\n" << refMat.transpose() << "\n\n"; // VERIFY_IS_APPROX(m, refMat); // test basic computations { DenseMatrix refM1 = DenseMatrix::Zero(rows, rows); DenseMatrix refM2 = DenseMatrix::Zero(rows, rows); DenseMatrix refM3 = DenseMatrix::Zero(rows, rows); DenseMatrix refM4 = DenseMatrix::Zero(rows, rows); SparseMatrixType m1(rows, rows); SparseMatrixType m2(rows, rows); SparseMatrixType m3(rows, rows); SparseMatrixType m4(rows, rows); initSparse<Scalar>(density, refM1, m1); initSparse<Scalar>(density, refM2, m2); initSparse<Scalar>(density, refM3, m3); initSparse<Scalar>(density, refM4, m4); VERIFY_IS_APPROX(m1+m2, refM1+refM2); VERIFY_IS_APPROX(m1+m2+m3, refM1+refM2+refM3); VERIFY_IS_APPROX(m3.cwise()*(m1+m2), refM3.cwise()*(refM1+refM2)); VERIFY_IS_APPROX(m1*s1-m2, refM1*s1-refM2); VERIFY_IS_APPROX(m1*=s1, refM1*=s1); VERIFY_IS_APPROX(m1/=s1, refM1/=s1); VERIFY_IS_APPROX(m1+=m2, refM1+=refM2); VERIFY_IS_APPROX(m1-=m2, refM1-=refM2); VERIFY_IS_APPROX(m1.col(0).eigen2_dot(refM2.row(0)), refM1.col(0).eigen2_dot(refM2.row(0))); refM4.setRandom(); // sparse cwise* dense VERIFY_IS_APPROX(m3.cwise()*refM4, refM3.cwise()*refM4); // VERIFY_IS_APPROX(m3.cwise()/refM4, refM3.cwise()/refM4); } // test innerVector() { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); int j0 = ei_random(0,rows-1); int j1 = ei_random(0,rows-1); VERIFY_IS_APPROX(m2.innerVector(j0), refMat2.col(j0)); VERIFY_IS_APPROX(m2.innerVector(j0)+m2.innerVector(j1), refMat2.col(j0)+refMat2.col(j1)); //m2.innerVector(j0) = 2*m2.innerVector(j1); //refMat2.col(j0) = 2*refMat2.col(j1); //VERIFY_IS_APPROX(m2, refMat2); } // test innerVectors() { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); int j0 = ei_random(0,rows-2); int j1 = ei_random(0,rows-2); int n0 = ei_random<int>(1,rows-std::max(j0,j1)); VERIFY_IS_APPROX(m2.innerVectors(j0,n0), refMat2.block(0,j0,rows,n0)); VERIFY_IS_APPROX(m2.innerVectors(j0,n0)+m2.innerVectors(j1,n0), refMat2.block(0,j0,rows,n0)+refMat2.block(0,j1,rows,n0)); //m2.innerVectors(j0,n0) = m2.innerVectors(j0,n0) + m2.innerVectors(j1,n0); //refMat2.block(0,j0,rows,n0) = refMat2.block(0,j0,rows,n0) + refMat2.block(0,j1,rows,n0); } // test transpose { DenseMatrix refMat2 = DenseMatrix::Zero(rows, rows); SparseMatrixType m2(rows, rows); initSparse<Scalar>(density, refMat2, m2); VERIFY_IS_APPROX(m2.transpose().eval(), refMat2.transpose().eval()); VERIFY_IS_APPROX(m2.transpose(), refMat2.transpose()); } // test prune { SparseMatrixType m2(rows, rows); DenseMatrix refM2(rows, rows); refM2.setZero(); int countFalseNonZero = 0; int countTrueNonZero = 0; m2.startFill(); for (int j=0; j<m2.outerSize(); ++j) for (int i=0; i<m2.innerSize(); ++i) { float x = ei_random<float>(0,1); if (x<0.1) { // do nothing } else if (x<0.5) { countFalseNonZero++; m2.fill(i,j) = Scalar(0); } else { countTrueNonZero++; m2.fill(i,j) = refM2(i,j) = Scalar(1); } } m2.endFill(); VERIFY(countFalseNonZero+countTrueNonZero == m2.nonZeros()); VERIFY_IS_APPROX(m2, refM2); m2.prune(1); VERIFY(countTrueNonZero==m2.nonZeros()); VERIFY_IS_APPROX(m2, refM2); } }
template<typename ArrayType> void vectorwiseop_array(const ArrayType& m) { typedef typename ArrayType::Index Index; typedef typename ArrayType::Scalar Scalar; typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType; typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType; Index rows = m.rows(); Index cols = m.cols(); Index r = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1); ArrayType m1 = ArrayType::Random(rows, cols), m2(rows, cols), m3(rows, cols); ColVectorType colvec = ColVectorType::Random(rows); RowVectorType rowvec = RowVectorType::Random(cols); // test addition m2 = m1; m2.colwise() += colvec; VERIFY_IS_APPROX(m2, m1.colwise() + colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec); VERIFY_RAISES_ASSERT(m2.colwise() += colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() + colvec.transpose()); m2 = m1; m2.rowwise() += rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() += rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() + rowvec.transpose()); // test substraction m2 = m1; m2.colwise() -= colvec; VERIFY_IS_APPROX(m2, m1.colwise() - colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec); VERIFY_RAISES_ASSERT(m2.colwise() -= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() - colvec.transpose()); m2 = m1; m2.rowwise() -= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() -= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() - rowvec.transpose()); // test multiplication m2 = m1; m2.colwise() *= colvec; VERIFY_IS_APPROX(m2, m1.colwise() * colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) * colvec); VERIFY_RAISES_ASSERT(m2.colwise() *= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() * colvec.transpose()); m2 = m1; m2.rowwise() *= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() * rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) * rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() *= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() * rowvec.transpose()); // test quotient m2 = m1; m2.colwise() /= colvec; VERIFY_IS_APPROX(m2, m1.colwise() / colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) / colvec); VERIFY_RAISES_ASSERT(m2.colwise() /= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() / colvec.transpose()); m2 = m1; m2.rowwise() /= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() / rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) / rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() /= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() / rowvec.transpose()); }
template<typename MatrixType> void inverse(const MatrixType& m) { typedef typename MatrixType::Index Index; /* this test covers the following files: Inverse.h */ Index rows = m.rows(); Index cols = m.cols(); typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::ColsAtCompileTime, 1> VectorType; MatrixType m1(rows, cols), m2(rows, cols), mzero = MatrixType::Zero(rows, cols), identity = MatrixType::Identity(rows, rows); createRandomPIMatrixOfRank(rows,rows,rows,m1); m2 = m1.inverse(); VERIFY_IS_APPROX(m1, m2.inverse() ); VERIFY_IS_APPROX((Scalar(2)*m2).inverse(), m2.inverse()*Scalar(0.5)); VERIFY_IS_APPROX(identity, m1.inverse() * m1 ); VERIFY_IS_APPROX(identity, m1 * m1.inverse() ); VERIFY_IS_APPROX(m1, m1.inverse().inverse() ); // since for the general case we implement separately row-major and col-major, test that VERIFY_IS_APPROX(MatrixType(m1.transpose().inverse()), MatrixType(m1.inverse().transpose())); #if !defined(EIGEN_TEST_PART_5) && !defined(EIGEN_TEST_PART_6) //computeInverseAndDetWithCheck tests //First: an invertible matrix bool invertible; RealScalar det; m2.setZero(); m1.computeInverseAndDetWithCheck(m2, det, invertible); VERIFY(invertible); VERIFY_IS_APPROX(identity, m1*m2); VERIFY_IS_APPROX(det, m1.determinant()); m2.setZero(); m1.computeInverseWithCheck(m2, invertible); VERIFY(invertible); VERIFY_IS_APPROX(identity, m1*m2); //Second: a rank one matrix (not invertible, except for 1x1 matrices) VectorType v3 = VectorType::Random(rows); MatrixType m3 = v3*v3.transpose(), m4(rows,cols); m3.computeInverseAndDetWithCheck(m4, det, invertible); VERIFY( rows==1 ? invertible : !invertible ); VERIFY_IS_MUCH_SMALLER_THAN(internal::abs(det-m3.determinant()), RealScalar(1)); m3.computeInverseWithCheck(m4, invertible); VERIFY( rows==1 ? invertible : !invertible ); #endif // check in-place inversion if(MatrixType::RowsAtCompileTime>=2 && MatrixType::RowsAtCompileTime<=4) { // in-place is forbidden VERIFY_RAISES_ASSERT(m1 = m1.inverse()); } else { m2 = m1.inverse(); m1 = m1.inverse(); VERIFY_IS_APPROX(m1,m2); } }
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 SparseMatrixType> void sparse_extra(const SparseMatrixType& ref) { typedef typename SparseMatrixType::Index Index; const Index rows = ref.rows(); const Index cols = ref.cols(); typedef typename SparseMatrixType::Scalar Scalar; enum { Flags = SparseMatrixType::Flags }; double density = (std::max)(8./(rows*cols), 0.01); typedef Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; typedef Matrix<Scalar,Dynamic,1> DenseVector; Scalar eps = 1e-6; SparseMatrixType m(rows, cols); DenseMatrix refMat = DenseMatrix::Zero(rows, cols); DenseVector vec1 = DenseVector::Random(rows); std::vector<Vector2i> zeroCoords; std::vector<Vector2i> nonzeroCoords; initSparse<Scalar>(density, refMat, m, 0, &zeroCoords, &nonzeroCoords); if (zeroCoords.size()==0 || nonzeroCoords.size()==0) return; // test coeff and coeffRef for (int i=0; i<(int)zeroCoords.size(); ++i) { VERIFY_IS_MUCH_SMALLER_THAN( m.coeff(zeroCoords[i].x(),zeroCoords[i].y()), eps ); if(internal::is_same<SparseMatrixType,SparseMatrix<Scalar,Flags> >::value) VERIFY_RAISES_ASSERT( m.coeffRef(zeroCoords[0].x(),zeroCoords[0].y()) = 5 ); } VERIFY_IS_APPROX(m, refMat); m.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); refMat.coeffRef(nonzeroCoords[0].x(), nonzeroCoords[0].y()) = Scalar(5); VERIFY_IS_APPROX(m, refMat); // random setter // { // m.setZero(); // VERIFY_IS_NOT_APPROX(m, refMat); // SparseSetter<SparseMatrixType, RandomAccessPattern> w(m); // std::vector<Vector2i> remaining = nonzeroCoords; // while(!remaining.empty()) // { // int i = internal::random<int>(0,remaining.size()-1); // w->coeffRef(remaining[i].x(),remaining[i].y()) = refMat.coeff(remaining[i].x(),remaining[i].y()); // remaining[i] = remaining.back(); // remaining.pop_back(); // } // } // VERIFY_IS_APPROX(m, refMat); VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdMapTraits> >(m,refMat,nonzeroCoords) )); #ifdef EIGEN_UNORDERED_MAP_SUPPORT VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, StdUnorderedMapTraits> >(m,refMat,nonzeroCoords) )); #endif #ifdef _DENSE_HASH_MAP_H_ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleDenseHashMapTraits> >(m,refMat,nonzeroCoords) )); #endif #ifdef _SPARSE_HASH_MAP_H_ VERIFY(( test_random_setter<RandomSetter<SparseMatrixType, GoogleSparseHashMapTraits> >(m,refMat,nonzeroCoords) )); #endif // test RandomSetter /*{ SparseMatrixType m1(rows,cols), m2(rows,cols); DenseMatrix refM1 = DenseMatrix::Zero(rows, rows); initSparse<Scalar>(density, refM1, m1); { Eigen::RandomSetter<SparseMatrixType > setter(m2); for (int j=0; j<m1.outerSize(); ++j) for (typename SparseMatrixType::InnerIterator i(m1,j); i; ++i) setter(i.index(), j) = i.value(); } VERIFY_IS_APPROX(m1, m2); }*/ }
template<typename MatrixType> void vectorwiseop_matrix(const MatrixType& m) { typedef typename MatrixType::Index Index; typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> ColVectorType; typedef Matrix<Scalar, 1, MatrixType::ColsAtCompileTime> RowVectorType; typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealColVectorType; typedef Matrix<RealScalar, 1, MatrixType::ColsAtCompileTime> RealRowVectorType; Index rows = m.rows(); Index cols = m.cols(); Index r = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1); MatrixType m1 = MatrixType::Random(rows, cols), m2(rows, cols), m3(rows, cols); ColVectorType colvec = ColVectorType::Random(rows); RowVectorType rowvec = RowVectorType::Random(cols); RealColVectorType rcres; RealRowVectorType rrres; // test addition m2 = m1; m2.colwise() += colvec; VERIFY_IS_APPROX(m2, m1.colwise() + colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec); if(rows>1) { VERIFY_RAISES_ASSERT(m2.colwise() += colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() + colvec.transpose()); } m2 = m1; m2.rowwise() += rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec); if(cols>1) { VERIFY_RAISES_ASSERT(m2.rowwise() += rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() + rowvec.transpose()); } // test substraction m2 = m1; m2.colwise() -= colvec; VERIFY_IS_APPROX(m2, m1.colwise() - colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec); if(rows>1) { VERIFY_RAISES_ASSERT(m2.colwise() -= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() - colvec.transpose()); } m2 = m1; m2.rowwise() -= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec); if(cols>1) { VERIFY_RAISES_ASSERT(m2.rowwise() -= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() - rowvec.transpose()); } // test norm rrres = m1.colwise().norm(); VERIFY_IS_APPROX(rrres(c), m1.col(c).norm()); rcres = m1.rowwise().norm(); VERIFY_IS_APPROX(rcres(r), m1.row(r).norm()); VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum(), m1.colwise().template lpNorm<1>()); VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().sum(), m1.rowwise().template lpNorm<1>()); VERIFY_IS_APPROX(m1.cwiseAbs().colwise().maxCoeff(), m1.colwise().template lpNorm<Infinity>()); VERIFY_IS_APPROX(m1.cwiseAbs().rowwise().maxCoeff(), m1.rowwise().template lpNorm<Infinity>()); // regression for bug 1158 VERIFY_IS_APPROX(m1.cwiseAbs().colwise().sum().x(), m1.col(0).cwiseAbs().sum()); // test normalized m2 = m1.colwise().normalized(); VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized()); m2 = m1.rowwise().normalized(); VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized()); // test normalize m2 = m1; m2.colwise().normalize(); VERIFY_IS_APPROX(m2.col(c), m1.col(c).normalized()); m2 = m1; m2.rowwise().normalize(); VERIFY_IS_APPROX(m2.row(r), m1.row(r).normalized()); // test with partial reduction of products Matrix<Scalar,MatrixType::RowsAtCompileTime,MatrixType::RowsAtCompileTime> m1m1 = m1 * m1.transpose(); VERIFY_IS_APPROX( (m1 * m1.transpose()).colwise().sum(), m1m1.colwise().sum()); Matrix<Scalar,1,MatrixType::RowsAtCompileTime> tmp(rows); VERIFY_EVALUATION_COUNT( tmp = (m1 * m1.transpose()).colwise().sum(), (MatrixType::RowsAtCompileTime==Dynamic ? 1 : 0)); m2 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows())).eval(); m1 = m1.rowwise() - (m1.colwise().sum()/RealScalar(m1.rows())); VERIFY_IS_APPROX( m1, m2 ); VERIFY_EVALUATION_COUNT( m2 = (m1.rowwise() - m1.colwise().sum()/RealScalar(m1.rows())), (MatrixType::RowsAtCompileTime==Dynamic && MatrixType::ColsAtCompileTime!=1 ? 1 : 0) ); }
template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) { typedef typename MatrixType::Index Index; /* this test covers the following files: EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h) */ Index rows = m.rows(); Index cols = m.cols(); typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; RealScalar largerEps = 10*test_precision<RealScalar>(); MatrixType a = MatrixType::Random(rows,cols); MatrixType a1 = MatrixType::Random(rows,cols); MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; MatrixType symmC = symmA; svd_fill_random(symmA,Symmetric); symmA.template triangularView<StrictlyUpper>().setZero(); symmC.template triangularView<StrictlyUpper>().setZero(); MatrixType b = MatrixType::Random(rows,cols); MatrixType b1 = MatrixType::Random(rows,cols); MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; symmB.template triangularView<StrictlyUpper>().setZero(); CALL_SUBTEST( selfadjointeigensolver_essential_check(symmA) ); SelfAdjointEigenSolver<MatrixType> eiSymm(symmA); // generalized eigen pb GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB); SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false); VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success); VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues()); // generalized eigen problem Ax = lBx eiSymmGen.compute(symmC, symmB,Ax_lBx); VERIFY_IS_EQUAL(eiSymmGen.info(), Success); VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox( symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); // generalized eigen problem BAx = lx eiSymmGen.compute(symmC, symmB,BAx_lx); VERIFY_IS_EQUAL(eiSymmGen.info(), Success); VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); // generalized eigen problem ABx = lx eiSymmGen.compute(symmC, symmB,ABx_lx); VERIFY_IS_EQUAL(eiSymmGen.info(), Success); VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); eiSymm.compute(symmC); MatrixType sqrtSymmA = eiSymm.operatorSqrt(); VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA); VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt()); MatrixType id = MatrixType::Identity(rows, cols); VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1)); SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized; VERIFY_RAISES_ASSERT(eiSymmUninitialized.info()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); eiSymmUninitialized.compute(symmA, false); VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); // test Tridiagonalization's methods Tridiagonalization<MatrixType> tridiag(symmC); VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal()); VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>()); Matrix<RealScalar,Dynamic,Dynamic> T = tridiag.matrixT(); if(rows>1 && cols>1) { // FIXME check that upper and lower part are 0: //VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView<Upper>().isZero()); } VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal()); VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>()); VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint()); VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint()); // Test computation of eigenvalues from tridiagonal matrix if(rows > 1) { SelfAdjointEigenSolver<MatrixType> eiSymmTridiag; eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors); VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues()); VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() * eiSymmTridiag.eigenvectors().real().transpose()); } if (rows > 1) { // Test matrix with NaN symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC); VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence); } }
template<typename ArrayType> void vectorwiseop_array(const ArrayType& m) { typedef typename ArrayType::Index Index; typedef typename ArrayType::Scalar Scalar; typedef Array<Scalar, ArrayType::RowsAtCompileTime, 1> ColVectorType; typedef Array<Scalar, 1, ArrayType::ColsAtCompileTime> RowVectorType; Index rows = m.rows(); Index cols = m.cols(); Index r = internal::random<Index>(0, rows-1), c = internal::random<Index>(0, cols-1); ArrayType m1 = ArrayType::Random(rows, cols), m2(rows, cols), m3(rows, cols); ColVectorType colvec = ColVectorType::Random(rows); RowVectorType rowvec = RowVectorType::Random(cols); // test addition m2 = m1; m2.colwise() += colvec; VERIFY_IS_APPROX(m2, m1.colwise() + colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) + colvec); VERIFY_RAISES_ASSERT(m2.colwise() += colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() + colvec.transpose()); m2 = m1; m2.rowwise() += rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() + rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) + rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() += rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() + rowvec.transpose()); // test substraction m2 = m1; m2.colwise() -= colvec; VERIFY_IS_APPROX(m2, m1.colwise() - colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) - colvec); VERIFY_RAISES_ASSERT(m2.colwise() -= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() - colvec.transpose()); m2 = m1; m2.rowwise() -= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() - rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) - rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() -= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() - rowvec.transpose()); // test multiplication m2 = m1; m2.colwise() *= colvec; VERIFY_IS_APPROX(m2, m1.colwise() * colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) * colvec); VERIFY_RAISES_ASSERT(m2.colwise() *= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() * colvec.transpose()); m2 = m1; m2.rowwise() *= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() * rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) * rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() *= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() * rowvec.transpose()); // test quotient m2 = m1; m2.colwise() /= colvec; VERIFY_IS_APPROX(m2, m1.colwise() / colvec); VERIFY_IS_APPROX(m2.col(c), m1.col(c) / colvec); VERIFY_RAISES_ASSERT(m2.colwise() /= colvec.transpose()); VERIFY_RAISES_ASSERT(m1.colwise() / colvec.transpose()); m2 = m1; m2.rowwise() /= rowvec; VERIFY_IS_APPROX(m2, m1.rowwise() / rowvec); VERIFY_IS_APPROX(m2.row(r), m1.row(r) / rowvec); VERIFY_RAISES_ASSERT(m2.rowwise() /= rowvec.transpose()); VERIFY_RAISES_ASSERT(m1.rowwise() / rowvec.transpose()); m2 = m1; // yes, there might be an aliasing issue there but ".rowwise() /=" // is supposed to evaluate " m2.colwise().sum()" into a temporary to avoid // evaluating the reduction multiple times if(ArrayType::RowsAtCompileTime>2 || ArrayType::RowsAtCompileTime==Dynamic) { m2.rowwise() /= m2.colwise().sum(); VERIFY_IS_APPROX(m2, m1.rowwise() / m1.colwise().sum()); } // all/any Array<bool,Dynamic,Dynamic> mb(rows,cols); mb = (m1.real()<=0.7).colwise().all(); VERIFY( (mb.col(c) == (m1.real().col(c)<=0.7).all()).all() ); mb = (m1.real()<=0.7).rowwise().all(); VERIFY( (mb.row(r) == (m1.real().row(r)<=0.7).all()).all() ); mb = (m1.real()>=0.7).colwise().any(); VERIFY( (mb.col(c) == (m1.real().col(c)>=0.7).any()).all() ); mb = (m1.real()>=0.7).rowwise().any(); VERIFY( (mb.row(r) == (m1.real().row(r)>=0.7).any()).all() ); }