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Expose QR solvers from Eigen
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| /* | ||
| * Copyright 2024 INRIA | ||
| */ | ||
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| #ifndef __eigenpy_decompositions_col_piv_houselholder_qr_hpp__ | ||
| #define __eigenpy_decompositions_col_piv_houselholder_qr_hpp__ | ||
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| #include "eigenpy/eigenpy.hpp" | ||
| #include "eigenpy/utils/scalar-name.hpp" | ||
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| #include <Eigen/QR> | ||
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| namespace eigenpy { | ||
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| template <typename _MatrixType> | ||
| struct ColPivHouseholderQRSolverVisitor | ||
| : public boost::python::def_visitor< | ||
| ColPivHouseholderQRSolverVisitor<_MatrixType> > { | ||
| typedef _MatrixType MatrixType; | ||
| typedef typename MatrixType::Scalar Scalar; | ||
| typedef typename MatrixType::RealScalar RealScalar; | ||
| typedef Eigen::Matrix<Scalar, Eigen::Dynamic, 1, MatrixType::Options> | ||
| VectorXs; | ||
| typedef Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic, | ||
| MatrixType::Options> | ||
| MatrixXs; | ||
| typedef Eigen::ColPivHouseholderQR<MatrixType> Solver; | ||
| typedef Solver Self; | ||
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| template <class PyClass> | ||
| void visit(PyClass &cl) const { | ||
| cl.def(bp::init<>(bp::arg("self"), | ||
| "Default constructor.\n" | ||
| "The default constructor is useful in cases in which the " | ||
| "user intends to perform decompositions via " | ||
| "HouseholderQR.compute(matrix)")) | ||
| .def(bp::init<Eigen::DenseIndex, Eigen::DenseIndex>( | ||
| bp::args("self", "rows", "cols"), | ||
| "Default constructor with memory preallocation.\n" | ||
| "Like the default constructor but with preallocation of the " | ||
| "internal data according to the specified problem size. ")) | ||
| .def(bp::init<MatrixType>( | ||
| bp::args("self", "matrix"), | ||
| "Constructs a QR factorization from a given matrix.\n" | ||
| "This constructor computes the QR factorization of the matrix " | ||
| "matrix by calling the method compute().")) | ||
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| .def("absDeterminant", &Self::absDeterminant, bp::arg("self"), | ||
| "Returns the absolute value of the determinant of the matrix of " | ||
| "which *this is the QR decomposition.\n" | ||
| "It has only linear complexity (that is, O(n) where n is the " | ||
| "dimension of the square matrix) as the QR decomposition has " | ||
| "already been computed.\n" | ||
| "Note: This is only for square matrices.") | ||
| .def("logAbsDeterminant", &Self::logAbsDeterminant, bp::arg("self"), | ||
| "Returns the natural log of the absolute value of the determinant " | ||
| "of the matrix of which *this is the QR decomposition.\n" | ||
| "It has only linear complexity (that is, O(n) where n is the " | ||
| "dimension of the square matrix) as the QR decomposition has " | ||
| "already been computed.\n" | ||
| "Note: This is only for square matrices. This method is useful to " | ||
| "work around the risk of overflow/underflow that's inherent to " | ||
| "determinant computation.") | ||
| .def("dimensionOfKernel", &Self::dimensionOfKernel, bp::arg("self"), | ||
| "Returns the dimension of the kernel of the matrix of which *this " | ||
| "is the QR decomposition.") | ||
| .def("info", &Self::info, bp::arg("self"), | ||
| "Reports whether the QR factorization was successful.\n" | ||
| "Note: This function always returns Success. It is provided for " | ||
| "compatibility with other factorization routines.") | ||
| .def("isInjective", &Self::isInjective, bp::arg("self"), | ||
| "Returns true if the matrix associated with this QR decomposition " | ||
| "represents an injective linear map, i.e. has trivial kernel; " | ||
| "false otherwise.\n" | ||
| "\n" | ||
| "Note: This method has to determine which pivots should be " | ||
| "considered nonzero. For that, it uses the threshold value that " | ||
| "you can control by calling setThreshold(threshold).") | ||
| .def("isInvertible", &Self::isInvertible, bp::arg("self"), | ||
| "Returns true if the matrix associated with the QR decomposition " | ||
| "is invertible.\n" | ||
| "\n" | ||
| "Note: This method has to determine which pivots should be " | ||
| "considered nonzero. For that, it uses the threshold value that " | ||
| "you can control by calling setThreshold(threshold).") | ||
| .def("isSurjective", &Self::isSurjective, bp::arg("self"), | ||
| "Returns true if the matrix associated with this QR decomposition " | ||
| "represents a surjective linear map; false otherwise.\n" | ||
| "\n" | ||
| "Note: This method has to determine which pivots should be " | ||
| "considered nonzero. For that, it uses the threshold value that " | ||
| "you can control by calling setThreshold(threshold).") | ||
| .def("maxPivot", &Self::maxPivot, bp::arg("self"), | ||
| "Returns the absolute value of the biggest pivot, i.e. the " | ||
| "biggest diagonal coefficient of U.") | ||
| .def("nonzeroPivots", &Self::nonzeroPivots, bp::arg("self"), | ||
| "Returns the number of nonzero pivots in the QR decomposition. " | ||
| "Here nonzero is meant in the exact sense, not in a fuzzy sense. " | ||
| "So that notion isn't really intrinsically interesting, but it is " | ||
| "still useful when implementing algorithms.") | ||
| .def("rank", &Self::rank, bp::arg("self"), | ||
| "Returns the rank of the matrix associated with the QR " | ||
| "decomposition.\n" | ||
| "\n" | ||
| "Note: This method has to determine which pivots should be " | ||
| "considered nonzero. For that, it uses the threshold value that " | ||
| "you can control by calling setThreshold(threshold).") | ||
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| .def("setThreshold", | ||
| (Self & (Self::*)(const RealScalar &)) & Self::setThreshold, | ||
| bp::args("self", "threshold"), | ||
| "Allows to prescribe a threshold to be used by certain methods, " | ||
| "such as rank(), who need to determine when pivots are to be " | ||
| "considered nonzero. This is not used for the QR decomposition " | ||
| "itself.\n" | ||
| "\n" | ||
| "When it needs to get the threshold value, Eigen calls " | ||
| "threshold(). By default, this uses a formula to automatically " | ||
| "determine a reasonable threshold. Once you have called the " | ||
| "present method setThreshold(const RealScalar&), your value is " | ||
| "used instead.\n" | ||
| "\n" | ||
| "Note: A pivot will be considered nonzero if its absolute value " | ||
| "is strictly greater than |pivot| ⩽ threshold×|maxpivot| where " | ||
| "maxpivot is the biggest pivot.", | ||
| bp::return_self<>()) | ||
| .def("threshold", &Self::threshold, bp::arg("self"), | ||
| "Returns the threshold that will be used by certain methods such " | ||
| "as rank().") | ||
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| .def("matrixQR", &Self::matrixQR, bp::arg("self"), | ||
| "Returns the matrix where the Householder QR decomposition is " | ||
| "stored in a LAPACK-compatible way.", | ||
| bp::return_value_policy<bp::copy_const_reference>()) | ||
| .def("matrixR", &Self::matrixR, bp::arg("self"), | ||
| "Returns the matrix where the result Householder QR is stored.", | ||
| bp::return_value_policy<bp::copy_const_reference>()) | ||
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| .def( | ||
| "compute", | ||
| (Solver & (Solver::*)(const Eigen::EigenBase<MatrixType> &matrix)) & | ||
| Solver::compute, | ||
| bp::args("self", "matrix"), | ||
| "Computes the QR factorization of given matrix.", | ||
| bp::return_self<>()) | ||
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| .def("inverse", inverse, bp::arg("self"), | ||
| "Returns the inverse of the matrix associated with the QR " | ||
| "decomposition..") | ||
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| .def("solve", &solve<MatrixXs>, bp::args("self", "B"), | ||
| "Returns the solution X of A X = B using the current " | ||
| "decomposition of A where B is a right hand side matrix."); | ||
| } | ||
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| static void expose() { | ||
| static const std::string classname = | ||
| "ColPivHouseholderQR" + scalar_name<Scalar>::shortname(); | ||
| expose(classname); | ||
| } | ||
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| static void expose(const std::string &name) { | ||
| bp::class_<Solver>( | ||
| name.c_str(), | ||
| "This class performs a rank-revealing QR decomposition of a matrix A " | ||
| "into matrices P, Q and R such that:\n" | ||
| "AP=QR\n" | ||
| "by using Householder transformations. Here, P is a permutation " | ||
| "matrix, Q a unitary matrix and R an upper triangular matrix.\n" | ||
| "\n" | ||
| "This decomposition performs column pivoting in order to be " | ||
| "rank-revealing and improve numerical stability. It is slower than " | ||
| "HouseholderQR, and faster than FullPivHouseholderQR.", | ||
| bp::no_init) | ||
| .def(ColPivHouseholderQRSolverVisitor()) | ||
| .def(IdVisitor<Solver>()); | ||
| } | ||
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| private: | ||
| template <typename MatrixOrVector> | ||
| static MatrixOrVector solve(const Solver &self, const MatrixOrVector &vec) { | ||
| return self.solve(vec); | ||
| } | ||
| static MatrixXs inverse(const Self &self) { return self.inverse(); } | ||
| }; | ||
|
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| } // namespace eigenpy | ||
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| #endif // ifndef __eigenpy_decompositions_col_piv_houselholder_qr_hpp__ |
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