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() );
}