lsst::sphgeom::Matrix3d Class Reference

A 3x3 matrix with real entries stored in double precision. More...

#include <Matrix3d.h>

Public Member Functions
	Matrix3d ()
	This constructor creates a zero matrix. More...
	Matrix3d (double m00, double m01, double m02, double m10, double m11, double m12, double m20, double m21, double m22)
	This constructor creates a matrix from its components, where mij specifies the component for row i and column j. More...
	Matrix3d (Vector3d const &v)
	This constructor creates a diagonal matrix with diagonal components set to the components of v. More...
	Matrix3d (double s)
	This constructor returns the identity matrix scaled by s. More...
bool	operator== (Matrix3d const &m) const
bool	operator!= (Matrix3d const &m) const
Vector3d	getRow (int r) const
	getRow returns the r-th matrix row. Bounds are not checked. More...
Vector3d const &	getColumn (int c) const
	getColumn returns the c-th matrix column. Bounds are not checked. More...
double	operator() (int r, int c) const
	The function call operator returns the scalar at row r and column c. More...
double	inner (Matrix3d const &m) const
	inner returns the Frobenius inner product of this matrix with m. More...
double	getSquaredNorm () const
	getSquaredNorm returns the Frobenius inner product of this matrix with itself. More...
double	getNorm () const
	getNorm returns the L2 (Frobenius) norm of this matrix. More...
Vector3d	operator* (Vector3d const &v) const
	The multiplication operator returns the product of this matrix with vector v. More...
Matrix3d	operator* (Matrix3d const &m) const
	The multiplication operator returns the product of this matrix with matrix m. More...
Matrix3d	operator+ (Matrix3d const &m) const
	The addition operator returns the sum of this matrix and m. More...
Matrix3d	operator- (Matrix3d const &m) const
	The subtraction operator returns the difference between this matrix and m. More...
Matrix3d	cwiseProduct (Matrix3d const &m) const
	cwiseProduct returns the component-wise product of this matrix and m. More...
Matrix3d	transpose () const
	transpose returns the transpose of this matrix. More...
Matrix3d	inverse () const
	inverse returns the inverse of this matrix. More...

Detailed Description

A 3x3 matrix with real entries stored in double precision.

Definition at line 38 of file Matrix3d.h.

Constructor & Destructor Documentation

Matrix3d() [1/4]

lsst::sphgeom::Matrix3d::Matrix3d ( )

inline

This constructor creates a zero matrix.

Definition at line 41 of file Matrix3d.h.

{}

Matrix3d() [2/4]

lsst::sphgeom::Matrix3d::Matrix3d ( double  m00, double  m01, double  m02, double  m10, double  m11, double  m12, double  m20, double  m21, double  m22  )

inline

This constructor creates a matrix from its components, where mij specifies the component for row i and column j.

Definition at line 45 of file Matrix3d.h.

    {
        _c[0] = Vector3d(m00, m10, m20);
        _c[1] = Vector3d(m01, m11, m21);
        _c[2] = Vector3d(m02, m12, m22);
    }

Matrix3d() [3/4]

lsst::sphgeom::Matrix3d::Matrix3d ( Vector3d const &  v )

inlineexplicit

This constructor creates a diagonal matrix with diagonal components set to the components of v.

Definition at line 56 of file Matrix3d.h.

                                          {
        _c[0] = Vector3d(v.x(), 0.0, 0.0);
        _c[1] = Vector3d(0.0, v.y(), 0.0);
        _c[2] = Vector3d(0.0, 0.0, v.z());
    }

Matrix3d() [4/4]

lsst::sphgeom::Matrix3d::Matrix3d ( double  s )

inlineexplicit

This constructor returns the identity matrix scaled by s.

Definition at line 63 of file Matrix3d.h.

                                {
        _c[0] = Vector3d(s, 0.0, 0.0);
        _c[1] = Vector3d(0.0, s, 0.0);
        _c[2] = Vector3d(0.0, 0.0, s);
    }

Member Function Documentation

cwiseProduct()

Matrix3d lsst::sphgeom::Matrix3d::cwiseProduct ( Matrix3d const &  m ) const

inline

cwiseProduct returns the component-wise product of this matrix and m.

Definition at line 136 of file Matrix3d.h.

                                                    {
        Matrix3d r;
        for (int i = 0; i < 3; ++i) { r._c[i] = _c[i].cwiseProduct(m._c[i]); }
        return r;
    }

getColumn()

Vector3d const& lsst::sphgeom::Matrix3d::getColumn ( int  c ) const

inline

getColumn returns the c-th matrix column. Bounds are not checked.

Definition at line 87 of file Matrix3d.h.

{ return _c[c]; }

getNorm()

double lsst::sphgeom::Matrix3d::getNorm ( ) const

inline

getNorm returns the L2 (Frobenius) norm of this matrix.

Definition at line 105 of file Matrix3d.h.

{ return std::sqrt(getSquaredNorm()); }

getRow()

Vector3d lsst::sphgeom::Matrix3d::getRow ( int  r ) const

inline

getRow returns the r-th matrix row. Bounds are not checked.

Definition at line 82 of file Matrix3d.h.

                                 {
        return Vector3d(getColumn(0)(r), getColumn(1)(r), getColumn(2)(r));
    }

getSquaredNorm()

double lsst::sphgeom::Matrix3d::getSquaredNorm ( ) const

inline

getSquaredNorm returns the Frobenius inner product of this matrix with itself.

Definition at line 102 of file Matrix3d.h.

{ return inner(*this); }

inner()

double lsst::sphgeom::Matrix3d::inner ( Matrix3d const &  m ) const

inline

inner returns the Frobenius inner product of this matrix with m.

Definition at line 94 of file Matrix3d.h.

                                           {
        Matrix3d p = cwiseProduct(m);
        Vector3d sum = p._c[0] + p._c[1] + p._c[2];
        return sum(0) + sum(1) + sum(2);
    }

inverse()

Matrix3d lsst::sphgeom::Matrix3d::inverse ( ) const

inline

inverse returns the inverse of this matrix.

Definition at line 152 of file Matrix3d.h.

                             {
        Matrix3d inv;
        Matrix3d const & m = *this;
        // Find the first column of Adj(m), the adjugate matrix of m.
        Vector3d a0(m(1, 1) * m(2, 2) - m(2, 1) * m(1, 2),
                    m(1, 2) * m(2, 0) - m(2, 2) * m(1, 0),
                    m(1, 0) * m(2, 1) - m(2, 0) * m(1, 1));
        // Find 1.0/det(m), where the determinant of m is the dot product of
        // the first row of m with the first column of Adj(m).
        double rdet = 1.0 / (a0(0) * m(0,0) + a0(1) * m(0,1) + a0(2) * m(0,2));
        // The inverse of m is Adj(m)/det(m); compute it column by column.
        inv._c[0] = a0 * rdet;
        inv._c[1] = Vector3d((m(0, 2) * m(2, 1) - m(2, 2) * m(0, 1)) * rdet,
                             (m(0, 0) * m(2, 2) - m(2, 0) * m(0, 2)) * rdet,
                             (m(0, 1) * m(2, 0) - m(2, 1) * m(0, 0)) * rdet);
        inv._c[2] = Vector3d((m(0, 1) * m(1, 2) - m(1, 1) * m(0, 2)) * rdet,
                             (m(0, 2) * m(1, 0) - m(1, 2) * m(0, 0)) * rdet,
                             (m(0, 0) * m(1, 1) - m(1, 0) * m(0, 1)) * rdet);
        return inv;
    }

operator!=()

bool lsst::sphgeom::Matrix3d::operator!= ( Matrix3d const &  m ) const

inline

Definition at line 75 of file Matrix3d.h.

                                              {
        return _c[0] != m._c[0] ||
               _c[1] != m._c[1] ||
               _c[2] != m._c[2];
    }

operator()()

double lsst::sphgeom::Matrix3d::operator() ( int  r, int  c  ) const

inline

The function call operator returns the scalar at row r and column c.

Bounds are not checked.

Definition at line 91 of file Matrix3d.h.

{ return getColumn(c)(r); }

operator*() [1/2]

Vector3d lsst::sphgeom::Matrix3d::operator* ( Vector3d const &  v ) const

inline

The multiplication operator returns the product of this matrix with vector v.

Definition at line 109 of file Matrix3d.h.

                                                 {
        return Vector3d(_c[0] * v(0) + _c[1] * v(1) + _c[2] * v(2));
    }

operator*() [2/2]

Matrix3d lsst::sphgeom::Matrix3d::operator* ( Matrix3d const &  m ) const

inline

The multiplication operator returns the product of this matrix with matrix m.

Definition at line 115 of file Matrix3d.h.

                                                 {
        Matrix3d r;
        for (int i = 0; i < 3; ++i) { r._c[i] = this->operator*(m._c[i]); }
        return r;
    }

operator+()

Matrix3d lsst::sphgeom::Matrix3d::operator+ ( Matrix3d const &  m ) const

inline

The addition operator returns the sum of this matrix and m.

Definition at line 122 of file Matrix3d.h.

                                                 {
        Matrix3d r;
        for (int i = 0; i < 3; ++i) { r._c[i] = _c[i] + m._c[i]; }
        return r;
    }

operator-()

Matrix3d lsst::sphgeom::Matrix3d::operator- ( Matrix3d const &  m ) const

inline

The subtraction operator returns the difference between this matrix and m.

Definition at line 129 of file Matrix3d.h.

                                                 {
        Matrix3d r;
        for (int i = 0; i < 3; ++i) { r._c[i] = _c[i] - m._c[i]; }
        return r;
    }

operator==()

bool lsst::sphgeom::Matrix3d::operator== ( Matrix3d const &  m ) const

inline

Definition at line 69 of file Matrix3d.h.

                                              {
        return _c[0] == m._c[0] &&
               _c[1] == m._c[1] &&
               _c[2] == m._c[2];
    }

transpose()

Matrix3d lsst::sphgeom::Matrix3d::transpose ( ) const

inline

transpose returns the transpose of this matrix.

Definition at line 143 of file Matrix3d.h.

                               {
        Matrix3d t;
        t._c[0] = Vector3d(_c[0].x(), _c[1].x(), _c[2].x());
        t._c[1] = Vector3d(_c[0].y(), _c[1].y(), _c[2].y());
        t._c[2] = Vector3d(_c[0].z(), _c[1].z(), _c[2].z());
        return t;
    }

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The documentation for this class was generated from the following file:

• /j/snowflake/release/lsstsw/stack/Linux64/sphgeom/17.0+14/include/lsst/sphgeom/Matrix3d.h