qr_decomposition.h

// Description: QR decomposition

#ifndef PASTELMATH_QR_DECOMPOSITION_H
#define PASTELMATH_QR_DECOMPOSITION_H

#include "pastel/math/matrix/matrix.h"

namespace Pastel
{

    template <typename Real>
    class QrDecomposition
    {
    public:
        // Using default copy constructor.
        // Using default assignment.
        // Using default destructor.

        //! A qr decomposition of the identity.
        /*!
       Preconditions:
       m >= 0
       n >= 0

       Both q and r are set to identity matrices.

       Exception safety:
       basic

       Time complexity:
       O(n^2)
       */
        explicit QrDecomposition(integer m, integer n);

        //! Decomposes the given matrix.
        /*!
       Exception safety:
       basic

       Time complexity:
       O(n^3)
       */
        QrDecomposition(Matrix<Real> that);

        //! Copy-constructs from another decomposition.
        QrDecomposition(const QrDecomposition& that);

        //! Move-constructs from another decomposition.
        QrDecomposition(QrDecomposition&& that);

        //! Returns the width of the decomposed matrix.
        integer n() const;

        //! Returns the height of the decomposed matrix.
        integer m() const;

        //! Swaps two decompositions.
        /*!
       Exception safety:
       nothrow

       Time complexity:
       constant (dynamic matrices)
       n^2 (static matrices)       
       */
        void swap(
            QrDecomposition& that);

        //! Assigns from another decomposition.
        QrDecomposition& operator=(QrDecomposition that);

        //! Decomposes the given matrix.
        /*!
       Exception safety:
       basic

       Time complexity:
       O(n^3)
       */
        void decompose(Matrix<Real> that);

        //! Returns the orthogonal matrix Q^T.
        /*!
       Exception safety:
       nothrow

       Time complexity:
       constant
       */
        const Matrix<Real>& qTransposed() const;

        //! Returns the upper triangular matrix R.
        /*!
       Exception safety:
       nothrow

       Time complexity:
       constant
       */
        const Matrix<Real>& r() const;

    private:
        QrDecomposition() = delete;
        void decompose();

        Matrix<Real> q_;
        Matrix<Real> r_;
    };

}

namespace Pastel
{

    //! Computes the absolute determinant from a qr decomposition.
    /*!
   The determinant of the orthogonal matrix is either -1 or 1.
   It would be costly to find out which. However, the
   absolute value of the determinant can be found quickly
   from the upper triangular matrix.
   */
    template <typename Real>
    Real absDeterminant(
        const QrDecomposition<Real>& qr);

    //! Solves the linear system QRx = b.
    template <typename Real, integer N, typename Expression>
    Vector<Real> solveLinear(
        const QrDecomposition<Real>& qr,
        const VectorExpression<Real, N, Expression>& b);

}

#include "pastel/math/matrix/qr_decomposition/qr_decomposition.hpp"

#endif