Program Listing for File FullPivHouseholderQR.hpp
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/*
* Copyright 2024 INRIA
*/
#ifndef __eigenpy_decompositions_full_piv_houselholder_qr_hpp__
#define __eigenpy_decompositions_full_piv_houselholder_qr_hpp__
#include "eigenpy/eigenpy.hpp"
#include "eigenpy/utils/scalar-name.hpp"
#include <Eigen/QR>
namespace eigenpy {
template <typename _MatrixType>
struct FullPivHouseholderQRSolverVisitor
: public boost::python::def_visitor<
FullPivHouseholderQRSolverVisitor<_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::FullPivHouseholderQR<MatrixType> Solver;
typedef Solver Self;
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()."))
.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("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).")
.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().")
.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(
"compute",
(Solver & (Solver::*)(const Eigen::EigenBase<MatrixType> &matrix)) &
Solver::compute,
bp::args("self", "matrix"),
"Computes the QR factorization of given matrix.",
bp::return_self<>())
.def("inverse", inverse, bp::arg("self"),
"Returns the inverse of the matrix associated with the QR "
"decomposition..")
.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.");
}
static void expose() {
static const std::string classname =
"FullPivHouseholderQR" + scalar_name<Scalar>::shortname();
expose(classname);
}
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, P', Q and R such that:\n"
"PAP′=QR\n"
"by using Householder transformations. Here, P and P' are permutation "
"matrices, Q a unitary matrix and R an upper triangular matrix.\n"
"\n"
"This decomposition performs a very prudent full pivoting in order to "
"be rank-revealing and achieve optimal numerical stability. The "
"trade-off is that it is slower than HouseholderQR and "
"ColPivHouseholderQR.",
bp::no_init)
.def(FullPivHouseholderQRSolverVisitor())
.def(IdVisitor<Solver>());
}
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(); }
};
} // namespace eigenpy
#endif // ifndef __eigenpy_decompositions_full_piv_houselholder_qr_hpp__