FullPivLU.hpp

/*
 * Copyright 2025 INRIA
 */

#ifndef __eigenpy_decompositions_fullpivlu_hpp__
#define __eigenpy_decompositions_fullpivlu_hpp__

#include <Eigen/LU>
#include <Eigen/Core>

#include "eigenpy/eigenpy.hpp"
#include "eigenpy/utils/scalar-name.hpp"
#include "eigenpy/eigen/EigenBase.hpp"

namespace eigenpy {

template <typename _MatrixType>
struct FullPivLUSolverVisitor
 : public boost::python::def_visitor<FullPivLUSolverVisitor<_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::FullPivLU<MatrixType> Solver;

 template <class PyClass>
 void visit(PyClass &cl) const {
 cl.def(bp::init<>(bp::arg("self"), "Default constructor"))
 .def(bp::init<Eigen::DenseIndex, Eigen::DenseIndex>(
 bp::args("self", "rows", "cols"),
 "Default constructor with memory preallocation"))
 .def(bp::init<MatrixType>(
 bp::args("self", "matrix"),
 "Constructs a LU factorization from a given matrix."))

 .def(EigenBaseVisitor<Solver>())

 .def(
 "compute",
 (Solver & (Solver::*)(const Eigen::EigenBase<MatrixType> &matrix)) &
 Solver::compute,
 bp::args("self", "matrix"),
 "Computes the LU decomposition of the given matrix.",
 bp::return_self<>())

 .def("determinant", &Solver::determinant, bp::arg("self"),
 "Returns the determinant of the matrix of which *this is the LU "
 "decomposition.")
 .def("dimensionOfKernel", &Solver::dimensionOfKernel, bp::arg("self"),
 "Returns the dimension of the kernel of the matrix of which *this "
 "is the LU decomposition.")
 .def(
 "image",
 +[](Solver &self, const MatrixType &mat) -> MatrixType {
 return self.image(mat);
 },
 bp::args("self", "originalMatrix"),
 "Returns the image of the matrix, also called its column-space. "
 "The columns of the returned matrix will form a basis of the "
 "image (column-space).")
 .def(
 "inverse",
 +[](Solver &self) -> MatrixType { return self.inverse(); },
 bp::arg("self"),
 "Returns the inverse of the matrix of which *this is the LU "
 "decomposition.")

 .def("isInjective", &Solver::isInjective, bp::arg("self"))
 .def("isInvertible", &Solver::isInvertible, bp::arg("self"))
 .def("isSurjective", &Solver::isSurjective, bp::arg("self"))

 .def(
 "kernel", +[](Solver &self) -> MatrixType { return self.kernel(); },
 bp::arg("self"),
 "Returns the kernel of the matrix, also called its null-space. "
 "The columns of the returned matrix will form a basis of the "
 "kernel.")

 .def("matrixLU", &Solver::matrixLU, bp::arg("self"),
 "Returns the LU decomposition matrix.",
 bp::return_internal_reference<>())

 .def("maxPivot", &Solver::maxPivot, bp::arg("self"))
 .def("nonzeroPivots", &Solver::nonzeroPivots, bp::arg("self"))

 .def("permutationP", &Solver::permutationP, bp::arg("self"),
 "Returns the permutation P.",
 bp::return_value_policy<bp::copy_const_reference>())
 .def("permutationQ", &Solver::permutationQ, bp::arg("self"),
 "Returns the permutation Q.",
 bp::return_value_policy<bp::copy_const_reference>())

 .def("rank", &Solver::rank, bp::arg("self"))

 .def("rcond", &Solver::rcond, bp::arg("self"),
 "Returns an estimate of the reciprocal condition number of the "
 "matrix.")
 .def("reconstructedMatrix", &Solver::reconstructedMatrix,
 bp::arg("self"),
 "Returns the matrix represented by the decomposition, i.e., it "
 "returns the product: P-1LUQ-1. This function is provided for "
 "debug "
 "purpose.")

 .def("setThreshold",
 (Solver & (Solver::*)(const RealScalar &)) & Solver::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 LU 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(
 "setThreshold",
 +[](Solver &self) -> Solver & {
 return self.setThreshold(Eigen::Default);
 },
 bp::arg("self"),
 "Allows to come back to the default behavior, letting Eigen use "
 "its default formula for determining the threshold.",
 bp::return_self<>())

 .def("solve", &solve<VectorXs>, bp::args("self", "b"),
 "Returns the solution x of A x = b using the current "
 "decomposition of A.")
 .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.")

 .def("threshold", &Solver::threshold, bp::arg("self"),
 "Returns the threshold that will be used by certain methods such "
 "as rank().");
 }

 static void expose() {
 static const std::string classname =
 "FullPivLU" + scalar_name<Scalar>::shortname();
 expose(classname);
 }

 static void expose(const std::string &name) {
 bp::class_<Solver>(
 name.c_str(),
 "LU decomposition of a matrix with complete pivoting, and related "
 "features.\n\n"
 "This class represents a LU decomposition of any matrix, with complete "
 "pivoting: the matrix A is decomposed as A=P−1LUQ−1 where L is "
 "unit-lower-triangular, U is upper-triangular, and P and Q are "
 "permutation matrices. This is a rank-revealing LU decomposition. "
 "The eigenvalues (diagonal coefficients) of U are sorted in such a "
 "way that any zeros are at the end.\n\n"
 "This decomposition provides the generic approach to solving systems "
 "of "
 "linear equations, computing the rank, invertibility, inverse, kernel, "
 "and determinant. \n\n"
 "This LU decomposition is very stable and well tested with large "
 "matrices. "
 "However there are use cases where the SVD decomposition is inherently "
 "more "
 "stable and/or flexible. For example, when computing the kernel of a "
 "matrix, "
 "working with the SVD allows to select the smallest singular values of "
 "the matrix, something that the LU decomposition doesn't see.",
 bp::no_init)
 .def(IdVisitor<Solver>())
 .def(FullPivLUSolverVisitor());
 }

 private:
 template <typename MatrixOrVector>
 static MatrixOrVector solve(const Solver &self, const MatrixOrVector &vec) {
 return self.solve(vec);
 }
};

} // namespace eigenpy

#endif // ifndef __eigenpy_decompositions_fullpivlu_hpp__