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Reorganize test main file
This commit is contained in:
Kolja Brix
Rasmus Munk Larsen
parent
21640612be
commit
51a0b4e2d2
242
test/main.h
242
test/main.h
@ -1,4 +1,3 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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@ -385,34 +384,19 @@ inline void verify_impl(bool condition, const char *testname, const char *file,
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} while (0)
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namespace Eigen {
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// Forward declarations to avoid ICC warnings
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#if EIGEN_COMP_ICC
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template<typename T> std::string type_name();
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namespace Eigen {
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template<typename T, typename U>
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bool test_is_equal(const T& actual, const U& expected, bool expect_equal=true);
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template<typename MatrixType>
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void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
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template<typename PermutationVectorType>
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void randomPermutationVector(PermutationVectorType& v, Index size);
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template<typename MatrixType>
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MatrixType generateRandomUnitaryMatrix(const Index dim);
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template<typename MatrixType, typename RealScalarVectorType>
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void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M);
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template<typename VectorType, typename RealScalar>
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VectorType setupRandomSvs(const Index dim, const RealScalar max);
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template<typename VectorType, typename RealScalar>
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VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max);
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} // end namespace Eigen
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// Forward declaration to avoid ICC warnings
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template<typename T> std::string type_name();
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#endif // EIGEN_COMP_ICC
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namespace Eigen {
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@ -672,215 +656,7 @@ bool test_is_equal(const T& actual, const U& expected, bool expect_equal)
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return false;
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}
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// Forward declaration to avoid ICC warning
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template<typename MatrixType>
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void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
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/**
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* Creates a random partial isometry matrix of given rank.
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*
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* A partial isometry is a matrix all of whose singular values are either 0 or 1.
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* This is very useful to test rank-revealing algorithms.
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*
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* @tparam MatrixType type of random partial isometry matrix
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* @param desired_rank rank requested for the random partial isometry matrix
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* @param rows row dimension of requested random partial isometry matrix
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* @param cols column dimension of requested random partial isometry matrix
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* @param m random partial isometry matrix
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*/
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template<typename MatrixType>
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void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
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{
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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typedef Matrix<Scalar, Dynamic, 1> VectorType;
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typedef Matrix<Scalar, Rows, Rows> MatrixAType;
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typedef Matrix<Scalar, Cols, Cols> MatrixBType;
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if(desired_rank == 0)
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{
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m.setZero(rows,cols);
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return;
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}
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if(desired_rank == 1)
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{
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// here we normalize the vectors to get a partial isometry
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m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
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return;
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}
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MatrixAType a = MatrixAType::Random(rows,rows);
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MatrixType d = MatrixType::Identity(rows,cols);
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MatrixBType b = MatrixBType::Random(cols,cols);
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// set the diagonal such that only desired_rank non-zero entries remain
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const Index diag_size = (std::min)(d.rows(),d.cols());
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if(diag_size != desired_rank)
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d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
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HouseholderQR<MatrixAType> qra(a);
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HouseholderQR<MatrixBType> qrb(b);
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m = qra.householderQ() * d * qrb.householderQ();
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}
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// Forward declaration to avoid ICC warning
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template<typename PermutationVectorType>
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void randomPermutationVector(PermutationVectorType& v, Index size);
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/**
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* Generate random permutation vector.
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*
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* @tparam PermutationVectorType type of vector used to store permutation
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* @param v permutation vector
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* @param size length of permutation vector
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*/
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template<typename PermutationVectorType>
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void randomPermutationVector(PermutationVectorType& v, Index size)
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{
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typedef typename PermutationVectorType::Scalar Scalar;
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v.resize(size);
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for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
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if(size == 1) return;
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for(Index n = 0; n < 3 * size; ++n)
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{
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Index i = internal::random<Index>(0, size-1);
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Index j;
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do j = internal::random<Index>(0, size-1); while(j==i);
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std::swap(v(i), v(j));
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}
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}
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/**
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* Generate a random unitary matrix of prescribed dimension.
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*
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* The algorithm is using a random Householder sequence to produce
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* a random unitary matrix.
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*
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* @tparam MatrixType type of matrix to generate
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* @param dim row and column dimension of the requested square matrix
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* @return random unitary matrix
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*/
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template<typename MatrixType>
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MatrixType generateRandomUnitaryMatrix(const Index dim)
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{
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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typedef Matrix<Scalar, Dynamic, 1> VectorType;
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MatrixType v = MatrixType::Identity(dim, dim);
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VectorType h = VectorType::Zero(dim);
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for (Index i = 0; i < dim; ++i)
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{
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v.col(i).tail(dim - i - 1) = VectorType::Random(dim - i - 1);
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h(i) = 2 / v.col(i).tail(dim - i).squaredNorm();
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}
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const Eigen::HouseholderSequence<MatrixType, VectorType> HSeq(v, h);
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return MatrixType(HSeq);
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}
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/**
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* Generation of random matrix with prescribed singular values.
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*
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* We generate random matrices with given singular values by setting up
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* a singular value decomposition. By choosing the number of zeros as
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* singular values we can specify the rank of the matrix.
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* Moreover, we also control its spectral norm, which is the largest
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* singular value, as well as its condition number with respect to the
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* l2-norm, which is the quotient of the largest and smallest singular
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* value.
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*
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* Reference: For details on the method see e.g. Section 8.1 (pp. 62 f) in
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*
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* C. C. Paige, M. A. Saunders,
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* LSQR: An algorithm for sparse linear equations and sparse least squares.
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* ACM Transactions on Mathematical Software 8(1), pp. 43-71, 1982.
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* https://web.stanford.edu/group/SOL/software/lsqr/lsqr-toms82a.pdf
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*
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* and also the LSQR webpage https://web.stanford.edu/group/SOL/software/lsqr/.
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*
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* @tparam MatrixType matrix type to generate
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* @tparam RealScalarVectorType vector type with real entries used for singular values
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* @param svs vector of desired singular values
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* @param rows row dimension of requested random matrix
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* @param cols column dimension of requested random matrix
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* @param M generated matrix with prescribed singular values
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*/
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template<typename MatrixType, typename RealScalarVectorType>
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void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M)
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{
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enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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typedef Matrix<Scalar, Rows, Rows> MatrixAType;
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typedef Matrix<Scalar, Cols, Cols> MatrixBType;
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const Index min_dim = (std::min)(rows, cols);
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const MatrixAType U = generateRandomUnitaryMatrix<MatrixAType>(rows);
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const MatrixBType V = generateRandomUnitaryMatrix<MatrixBType>(cols);
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M = U.block(0, 0, rows, min_dim) * svs.asDiagonal() * V.block(0, 0, cols, min_dim).transpose();
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}
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/**
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* Setup a vector of random singular values with prescribed upper limit.
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* For use with generateRandomMatrixSvs().
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*
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* Singular values are non-negative real values. By convention (to be consistent with
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* singular value decomposition) we sort them in decreasing order.
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*
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* This strategy produces random singular values in the range [0, max], in particular
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* the singular values can be zero or arbitrarily close to zero.
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*
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* @tparam VectorType vector type with real entries used for singular values
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* @tparam RealScalar data type used for real entry
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* @param dim number of singular values to generate
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* @param max upper bound for singular values
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* @return vector of singular values
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*/
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template<typename VectorType, typename RealScalar>
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VectorType setupRandomSvs(const Index dim, const RealScalar max)
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{
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VectorType svs = max / RealScalar(2) * (VectorType::Random(dim) + VectorType::Ones(dim));
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std::sort(svs.begin(), svs.end(), std::greater<RealScalar>());
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return svs;
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}
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/**
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* Setup a vector of random singular values with prescribed range.
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* For use with generateRandomMatrixSvs().
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*
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* Singular values are non-negative real values. By convention (to be consistent with
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* singular value decomposition) we sort them in decreasing order.
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*
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* For dim > 1 this strategy generates a vector with largest entry max, smallest entry
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* min, and remaining entries in the range [min, max]. For dim == 1 the only entry is
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* min.
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*
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* @tparam VectorType vector type with real entries used for singular values
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* @tparam RealScalar data type used for real entry
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* @param dim number of singular values to generate
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* @param min smallest singular value to use
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* @param max largest singular value to use
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* @return vector of singular values
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*/
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template<typename VectorType, typename RealScalar>
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VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max)
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{
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VectorType svs = VectorType::Random(dim);
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if(dim == 0)
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return svs;
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if(dim == 1)
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{
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svs(0) = min;
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return svs;
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}
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std::sort(svs.begin(), svs.end(), std::greater<RealScalar>());
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// scale to range [min, max]
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const RealScalar c_min = svs(dim - 1), c_max = svs(0);
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svs = (svs - VectorType::Constant(dim, c_min)) / (c_max - c_min);
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return min * (VectorType::Ones(dim) - svs) + max * svs;
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}
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/**
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* Check if number is "not a number" (NaN).
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@ -920,6 +696,10 @@ template<typename T> bool isMinusInf(const T& x)
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} // end namespace Eigen
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#include "random_matrix_helper.h"
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template<typename T> struct GetDifferentType;
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template<> struct GetDifferentType<float> { typedef double type; };
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256
test/random_matrix_helper.h
Normal file
256
test/random_matrix_helper.h
Normal file
@ -0,0 +1,256 @@
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// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2021 Kolja Brix <kolja.brix@rwth-aachen.de>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#ifndef EIGEN_RANDOM_MATRIX_HELPER
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#define EIGEN_RANDOM_MATRIX_HELPER
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#include <typeinfo>
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#include <Eigen/QR> // required for createRandomPIMatrixOfRank and generateRandomMatrixSvs
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// Forward declarations to avoid ICC warnings
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#if EIGEN_COMP_ICC
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namespace Eigen {
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template<typename MatrixType>
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void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m);
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template<typename PermutationVectorType>
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void randomPermutationVector(PermutationVectorType& v, Index size);
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template<typename MatrixType>
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MatrixType generateRandomUnitaryMatrix(const Index dim);
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template<typename MatrixType, typename RealScalarVectorType>
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void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M);
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template<typename VectorType, typename RealScalar>
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VectorType setupRandomSvs(const Index dim, const RealScalar max);
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template<typename VectorType, typename RealScalar>
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VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max);
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} // end namespace Eigen
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#endif // EIGEN_COMP_ICC
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namespace Eigen {
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/**
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* Creates a random partial isometry matrix of given rank.
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*
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* A partial isometry is a matrix all of whose singular values are either 0 or 1.
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* This is very useful to test rank-revealing algorithms.
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*
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* @tparam MatrixType type of random partial isometry matrix
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* @param desired_rank rank requested for the random partial isometry matrix
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* @param rows row dimension of requested random partial isometry matrix
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* @param cols column dimension of requested random partial isometry matrix
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* @param m random partial isometry matrix
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*/
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template<typename MatrixType>
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void createRandomPIMatrixOfRank(Index desired_rank, Index rows, Index cols, MatrixType& m)
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{
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
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typedef Matrix<Scalar, Dynamic, 1> VectorType;
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typedef Matrix<Scalar, Rows, Rows> MatrixAType;
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typedef Matrix<Scalar, Cols, Cols> MatrixBType;
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if(desired_rank == 0)
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{
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m.setZero(rows,cols);
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return;
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}
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if(desired_rank == 1)
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{
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// here we normalize the vectors to get a partial isometry
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m = VectorType::Random(rows).normalized() * VectorType::Random(cols).normalized().transpose();
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return;
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}
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MatrixAType a = MatrixAType::Random(rows,rows);
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MatrixType d = MatrixType::Identity(rows,cols);
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MatrixBType b = MatrixBType::Random(cols,cols);
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// set the diagonal such that only desired_rank non-zero entries remain
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const Index diag_size = (std::min)(d.rows(),d.cols());
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if(diag_size != desired_rank)
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d.diagonal().segment(desired_rank, diag_size-desired_rank) = VectorType::Zero(diag_size-desired_rank);
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HouseholderQR<MatrixAType> qra(a);
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HouseholderQR<MatrixBType> qrb(b);
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m = qra.householderQ() * d * qrb.householderQ();
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}
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/**
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* Generate random permutation vector.
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*
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* @tparam PermutationVectorType type of vector used to store permutation
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* @param v permutation vector
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* @param size length of permutation vector
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*/
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template<typename PermutationVectorType>
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void randomPermutationVector(PermutationVectorType& v, Index size)
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{
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typedef typename PermutationVectorType::Scalar Scalar;
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v.resize(size);
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for(Index i = 0; i < size; ++i) v(i) = Scalar(i);
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if(size == 1) return;
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for(Index n = 0; n < 3 * size; ++n)
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{
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Index i = internal::random<Index>(0, size-1);
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Index j;
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do j = internal::random<Index>(0, size-1); while(j==i);
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std::swap(v(i), v(j));
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}
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}
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/**
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* Generate a random unitary matrix of prescribed dimension.
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*
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* The algorithm is using a random Householder sequence to produce
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* a random unitary matrix.
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*
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* @tparam MatrixType type of matrix to generate
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* @param dim row and column dimension of the requested square matrix
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* @return random unitary matrix
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*/
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template<typename MatrixType>
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MatrixType generateRandomUnitaryMatrix(const Index dim)
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{
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typedef typename internal::traits<MatrixType>::Scalar Scalar;
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typedef Matrix<Scalar, Dynamic, 1> VectorType;
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MatrixType v = MatrixType::Identity(dim, dim);
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VectorType h = VectorType::Zero(dim);
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for (Index i = 0; i < dim; ++i)
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{
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v.col(i).tail(dim - i - 1) = VectorType::Random(dim - i - 1);
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h(i) = 2 / v.col(i).tail(dim - i).squaredNorm();
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}
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const Eigen::HouseholderSequence<MatrixType, VectorType> HSeq(v, h);
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return MatrixType(HSeq);
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}
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/**
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* Generation of random matrix with prescribed singular values.
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*
|
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* We generate random matrices with given singular values by setting up
|
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* a singular value decomposition. By choosing the number of zeros as
|
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* singular values we can specify the rank of the matrix.
|
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* Moreover, we also control its spectral norm, which is the largest
|
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* singular value, as well as its condition number with respect to the
|
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* l2-norm, which is the quotient of the largest and smallest singular
|
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* value.
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*
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* Reference: For details on the method see e.g. Section 8.1 (pp. 62 f) in
|
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*
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* C. C. Paige, M. A. Saunders,
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* LSQR: An algorithm for sparse linear equations and sparse least squares.
|
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* ACM Transactions on Mathematical Software 8(1), pp. 43-71, 1982.
|
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* https://web.stanford.edu/group/SOL/software/lsqr/lsqr-toms82a.pdf
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*
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* and also the LSQR webpage https://web.stanford.edu/group/SOL/software/lsqr/.
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*
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* @tparam MatrixType matrix type to generate
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* @tparam RealScalarVectorType vector type with real entries used for singular values
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* @param svs vector of desired singular values
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* @param rows row dimension of requested random matrix
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* @param cols column dimension of requested random matrix
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* @param M generated matrix with prescribed singular values
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*/
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template<typename MatrixType, typename RealScalarVectorType>
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void generateRandomMatrixSvs(const RealScalarVectorType &svs, const Index rows, const Index cols, MatrixType& M)
|
||||
{
|
||||
enum { Rows = MatrixType::RowsAtCompileTime, Cols = MatrixType::ColsAtCompileTime };
|
||||
typedef typename internal::traits<MatrixType>::Scalar Scalar;
|
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typedef Matrix<Scalar, Rows, Rows> MatrixAType;
|
||||
typedef Matrix<Scalar, Cols, Cols> MatrixBType;
|
||||
|
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const Index min_dim = (std::min)(rows, cols);
|
||||
|
||||
const MatrixAType U = generateRandomUnitaryMatrix<MatrixAType>(rows);
|
||||
const MatrixBType V = generateRandomUnitaryMatrix<MatrixBType>(cols);
|
||||
|
||||
M = U.block(0, 0, rows, min_dim) * svs.asDiagonal() * V.block(0, 0, cols, min_dim).transpose();
|
||||
}
|
||||
|
||||
/**
|
||||
* Setup a vector of random singular values with prescribed upper limit.
|
||||
* For use with generateRandomMatrixSvs().
|
||||
*
|
||||
* Singular values are non-negative real values. By convention (to be consistent with
|
||||
* singular value decomposition) we sort them in decreasing order.
|
||||
*
|
||||
* This strategy produces random singular values in the range [0, max], in particular
|
||||
* the singular values can be zero or arbitrarily close to zero.
|
||||
*
|
||||
* @tparam VectorType vector type with real entries used for singular values
|
||||
* @tparam RealScalar data type used for real entry
|
||||
* @param dim number of singular values to generate
|
||||
* @param max upper bound for singular values
|
||||
* @return vector of singular values
|
||||
*/
|
||||
template<typename VectorType, typename RealScalar>
|
||||
VectorType setupRandomSvs(const Index dim, const RealScalar max)
|
||||
{
|
||||
VectorType svs = max / RealScalar(2) * (VectorType::Random(dim) + VectorType::Ones(dim));
|
||||
std::sort(svs.begin(), svs.end(), std::greater<RealScalar>());
|
||||
return svs;
|
||||
}
|
||||
|
||||
/**
|
||||
* Setup a vector of random singular values with prescribed range.
|
||||
* For use with generateRandomMatrixSvs().
|
||||
*
|
||||
* Singular values are non-negative real values. By convention (to be consistent with
|
||||
* singular value decomposition) we sort them in decreasing order.
|
||||
*
|
||||
* For dim > 1 this strategy generates a vector with largest entry max, smallest entry
|
||||
* min, and remaining entries in the range [min, max]. For dim == 1 the only entry is
|
||||
* min.
|
||||
*
|
||||
* @tparam VectorType vector type with real entries used for singular values
|
||||
* @tparam RealScalar data type used for real entry
|
||||
* @param dim number of singular values to generate
|
||||
* @param min smallest singular value to use
|
||||
* @param max largest singular value to use
|
||||
* @return vector of singular values
|
||||
*/
|
||||
template<typename VectorType, typename RealScalar>
|
||||
VectorType setupRangeSvs(const Index dim, const RealScalar min, const RealScalar max)
|
||||
{
|
||||
VectorType svs = VectorType::Random(dim);
|
||||
if(dim == 0)
|
||||
return svs;
|
||||
if(dim == 1)
|
||||
{
|
||||
svs(0) = min;
|
||||
return svs;
|
||||
}
|
||||
std::sort(svs.begin(), svs.end(), std::greater<RealScalar>());
|
||||
|
||||
// scale to range [min, max]
|
||||
const RealScalar c_min = svs(dim - 1), c_max = svs(0);
|
||||
svs = (svs - VectorType::Constant(dim, c_min)) / (c_max - c_min);
|
||||
return min * (VectorType::Ones(dim) - svs) + max * svs;
|
||||
}
|
||||
|
||||
} // end namespace Eigen
|
||||
|
||||
#endif // EIGEN_RANDOM_MATRIX_HELPER
|
||||
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Reference in New Issue
Block a user