TooN 2.1
Public Member Functions
Matrix< Rows, Cols, Precision, Layout > Struct Template Reference
Linear Algebra

A matrix. More...

#include <matrix.hh>

List of all members.

Public Member Functions

const double & operator() (int r, int c) const
const double & operator[] (const std::pair< int, int > &row_col) const
double & operator[] (const std::pair< int, int > &row_col)
double & operator() (int r, int c)
const Vector & operator[] (int r) const
Vector & operator[] (int r)
int num_rows () const
int num_cols () const
Construction and destruction
 Matrix ()
 Matrix (int rows, int cols)
 Matrix (Precision *p)
 Matrix (Precision *p, int r, int c)
 Matrix (Precision *data, int rows, int cols, int rowstride, int colstride, Internal::Slicing)
template<class Op >
 Matrix (const Operator< Op > &op)
template<int Rows2, int Cols2, typename Precision2 , typename Base2 >
 Matrix (const Matrix< Rows2, Cols2, Precision2, Base2 > &from)
Assignment

operator = from copy

Matrix & operator= (const Matrix &from)
template<class Op >
Matrix & operator= (const Operator< Op > &op)
template<int Rows2, int Cols2, typename Precision2 , typename Base2 >
Matrix & operator= (const Matrix< Rows2, Cols2, Precision2, Base2 > &from)
operations on the matrix
Matrix & operator*= (const Precision rhs)
Matrix & operator/= (const Precision rhs)
template<int Rows2, int Cols2, typename Precision2 , typename Base2 >
Matrix & operator+= (const Matrix< Rows2, Cols2, Precision2, Base2 > &from)
template<class Op >
Matrix & operator+= (const Operator< Op > &op)
template<class Op >
Matrix & operator-= (const Operator< Op > &op)
template<int Rows2, int Cols2, typename Precision2 , typename Base2 >
Matrix & operator-= (const Matrix< Rows2, Cols2, Precision2, Base2 > &from)
template<int Rows2, int Cols2, typename Precision2 , typename Base2 >
bool operator== (const Matrix< Rows2, Cols2, Precision2, Base2 > &rhs) const
template<int Rows2, int Cols2, typename Precision2 , typename Base2 >
bool operator!= (const Matrix< Rows2, Cols2, Precision2, Base2 > &rhs) const
template<class Op >
bool operator!= (const Operator< Op > &op)
Misc
Matrix & ref ()
Transpose and sub-matrices
const Matrix< Cols, Rows > & T () const
Matrix< Cols, Rows > & T ()
template<Rstart , Cstart , Rsize , Csize >
const Matrix< Rsize, Csize > & slice () const
template<Rstart , Cstart , Rsize , Csize >
Matrix< Rsize, Csize > & slice ()
const Matrix & slice (int rstart, int cstart, int rsize, int csize) const
Matrix & slice (int rstart, int cstart, int rsize, int csize)

Detailed Description

template<int Rows = Dynamic, int Cols = Rows, class Precision = DefaultPrecision, class Layout = RowMajor>
struct TooN::Matrix< Rows, Cols, Precision, Layout >

A matrix.

Support is provided for all the usual matrix operations:

See individual member function documentation for examples of usage.

Statically-sized matrices

The library provides classes for statically and dynamically sized matrices. As with Vectors, statically sized matrices are more efficient, since their size is determined at compile-time, not run-time. To create a $3\times4$ matrix, use: 

Matrix<3,4> M;

or replace 3 and 4 with the dimensions of your choice. If the matrix is square, it can be declared as: 

Matrix<3> M;

which just is a synonym for Matrix<3,3>. Matrices can also be constructed from pointers or static 1D or 2D arrays of doubles: 

  Matrix<2,3, Reference::RowMajor> M2 = Data(1,2,3,4,5,6);
Dynamically-sized matrices

To create a dynamically sized matrix, use: 

Matrix<> M(num_rows, num_cols);

where num_rows and num_cols are integers which will be evaluated at run time.

Half-dynamic matriced can be constructed in either dimension: 

    Matrix<Dynamic, 2> M(num_rows, 2);

note that the static dimension must be provided, but it is ignored.

Matrix<> is a synonym for Matrix<Dynamic, Dynamic> .

Row-major and column-major

The library supports both row major (the default - but you can change this if you prefer) and column major layout ordering. Row major implies that the matrix is laid out in memory in raster scan order:

\[\begin{matrix}\text{Row major} & \text {Column major}\\ \begin{bmatrix}1&2&3\\4&5&6\\7&8&9\end{bmatrix} & \begin{bmatrix}1&4&7\\2&5&8\\3&6&9\end{bmatrix} \end{matrix}\]

You can override the default for a specific matrix by specifying the layout when you construct it: 

Matrix<3,3,double,ColMajor> M1;
Matrix<Dynamic,Dynamic,double,RowMajor> M2(nrows, ncols);

In this case the precision template argument must be given as it precedes the layout argument

Constructor & Destructor Documentation

Matrix ( Precision *  data,
int  rows,
int  cols,
int  rowstride,
int  colstride,
Internal::Slicing   
)

Advanced construction of dynamically sized slice matrices.

Internal constructor used by GenericMBase::slice(...).

Member Function Documentation

const double& operator() ( int  r,
int  c 
) const

Access an element from the matrix.

The index starts at zero, i.e. the top-left element is m(0, 0). 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        double e = m(1,2);     // now e = 6.0;

This method is not defined by Matrix: it is inherited.

const double& operator[] ( const std::pair< int, int > &  row_col) const

Access an element from the matrix.

Parameters:
row_colrow_col.first holds the row, row_col.second holds the column.

This method is not defined by Matrix: it is inherited.

double& operator() ( int  r,
int  c 
)

Access an element from the matrix.

This can be used as either an r-value or an l-value. The index starts at zero, i.e. the top-left element is m(0, 0). 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        Matrix<2,3> m(d);
        m(1,2) = 8;     // now d = [1 2 3]
                      //         [4 5 8]

This method is not defined by Matrix: it is inherited.

const Vector& operator[] ( int  r) const

Access a row from the matrix.

This can be used either as an r-value or an l-value. The index starts at zero, i.e. the first row is m[0]. To extract a column from a matrix, apply [] to the transpose of the matrix (see example). This can be used either as an r-value or an l-value. The index starts at zero, i.e. the first row (or column) is m[0]. 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        Matrix<2,3> m(d);
        Vector<3> v = m[1];       // now v = [4 5 6];
        Vector<2> v2 = m.T()[0];  // now v2 = [1 4];

This method is not defined by Matrix: it is inherited.

Vector& operator[] ( int  r)

Access a row from the matrix.

This can be used either as an r-value or an l-value. The index starts at zero, i.e. the first row is m[0]. To extract a column from a matrix, apply [] to the transpose of the matrix (see example). This can be used either as an r-value or an l-value. The index starts at zero, i.e. the first row (or column) is m[0]. 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        Matrix<2,3> m(d);
        Zero(m[0]);   // set the first row to zero
        Vector<2> v = 8,9;
        m.T()[1] = v; // now m = [0 8 0]
                    //         [4 9 6]

This method is not defined by Matrix: it is inherited.

int num_rows ( ) const

How many rows does this matrix have?

This method is not defined by Matrix: it is inherited.

Referenced by WLS< Size, Precision >::add_mJ(), WLS< Size, Precision >::add_prior(), SIM3< Precision >::adjoint(), SE3< Precision >::adjoint(), LU< Size, Precision >::backsub(), Cholesky< Size, Precision >::backsub(), Cholesky< Size, Precision >::Cholesky(), WLS< Size, Precision >::compute(), SymEigen< Size, Precision >::compute(), ComputeSymEigen< Size >::compute(), LU< Size, Precision >::compute(), Cholesky< Size, Precision >::compute(), LU< Size, Precision >::determinant(), TooN::determinant(), Cholesky< Size, Precision >::determinant(), TooN::determinant_gaussian_elimination(), TooN::exp(), TooN::Internal::exp_taylor(), TooN::Fill(), DownhillSimplex< N, Precision >::find_next_point(), TooN::gauss_jordan(), TooN::gaussian_elimination(), LU< Size, Precision >::get_inverse(), Cholesky< Size, Precision >::get_inverse(), SVD< Size, Size, Precision >::get_U(), SVD< Size, Size, Precision >::get_VT(), TooN::Internal::log_taylor(), TooN::norm_1(), TooN::norm_fro(), TooN::norm_inf(), DownhillSimplex< N, Precision >::restart(), TooN::sqrt(), TooN::Symmetrize(), TooN::trace(), SIM3< Precision >::trinvadjoint(), and SE3< Precision >::trinvadjoint().

int num_cols ( ) const

How many columns does this matrix have?

This method is not defined by Matrix: it is inherited.

Referenced by WLS< Size, Precision >::add_sparse_mJ_rows(), SIM3< Precision >::adjoint(), SE3< Precision >::adjoint(), LU< Size, Precision >::backsub(), Cholesky< Size, Precision >::backsub(), Cholesky< Size, Precision >::Cholesky(), SymEigen< Size, Precision >::compute(), ComputeSymEigen< Size >::compute(), LU< Size, Precision >::compute(), Cholesky< Size, Precision >::compute(), TooN::determinant(), TooN::determinant_gaussian_elimination(), TooN::exp(), TooN::Internal::exp_taylor(), TooN::Fill(), DownhillSimplex< N, Precision >::find_next_point(), TooN::gauss_jordan(), TooN::gaussian_elimination(), SVD< Size, Size, Precision >::get_U(), SVD< Size, Size, Precision >::get_VT(), TooN::Internal::log_taylor(), TooN::norm_1(), TooN::norm_fro(), TooN::norm_inf(), TooN::project(), DownhillSimplex< N, Precision >::restart(), TooN::sqrt(), TooN::Symmetrize(), TooN::trace(), SIM3< Precision >::trinvadjoint(), and SE3< Precision >::trinvadjoint().

const Matrix<Cols, Rows>& T ( ) const

The transpose of the matrix.

This is a very fast operation--it simply reinterprets a row-major matrix as column-major or vice-versa. This can be used as an l-value. 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        Matrix<2,3> m(d);
        Zero(m[0]);   // set the first row to zero
        Vector<2> v = 8,9;
        m.T()[1] = v; // now m = [0 8 0]
                    //         [4 9 6]

This method is not defined by Matrix: it is inherited.

Referenced by WLS< Size, Precision >::add_mJ(), WLS< Size, Precision >::add_mJ_rows(), WLS< Size, Precision >::add_sparse_mJ_rows(), SIM3< Precision >::adjoint(), SE3< Precision >::adjoint(), SymEigen< Size, Precision >::backsub(), SymEigen< Size, Precision >::get_isqrtm(), SymEigen< Size, Precision >::get_pinv(), GR_SVD< M, N, Precision, WANT_U, WANT_V >::get_pinv(), SymEigen< Size, Precision >::get_sqrtm(), GR_SVD< M, N, Precision, WANT_U, WANT_V >::reorder(), SO3< P >::SO3(), SIM3< Precision >::trinvadjoint(), and SE3< Precision >::trinvadjoint().

Matrix<Cols, Rows>& T ( )

The transpose of the matrix.

This is a very fast operation--it simply reinterprets a row-major matrix as column-major or vice-versa. The result can be used as an l-value. 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        Matrix<2,3> m(d);
        Vector<2> v = 8,9;
        // Set the first column to v
        m.T()[0] = v; // now m = [8 2 3]
                    //         [9 5 6]

This means that the semantics of M=M.T() are broken. In general, it is not necessary to say M=M.T(), since you can use M.T() for free whenever you need the transpose, but if you do need to, you have to use the Tranpose() function defined in helpers.h.

This method is not defined by Matrix: it is inherited.

const Matrix<Rsize, Csize>& slice ( ) const

Extract a sub-matrix.

The matrix extracted will be begin at element (Rstart, Cstart) and will contain the next Rsize by Csize elements. 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6
            7,8,9));
        Matrix<3> m(d);
        Extract the top-left 2x2 matrix
        Matrix<2> b = m.slice<0,0,2,2>();  // b = [1 2]
                                          //     [4 5]

This method is not defined by Matrix: it is inherited.

Referenced by WLS< Size, Precision >::add_sparse_mJ_rows(), and TooN::project().

Matrix<Rsize, Csize>& slice ( )

Extract a sub-matrix.

The matrix extracted will be begin at element (Rstart, Cstart) and will contain the next Rsize by Csize elements. This can be used as either an r-value or an l-value. 

        Matrix<2,3> m(Data(
            1,2,3
            4,5,6));
        Matrix<2,3> m(d);
        Zero(m.slice<0,2,2,1>());  // b = [1 2 0]
                                  //     [4 5 0]

This method is not defined by Matrix: it is inherited.

const Matrix& slice ( int  rstart,
int  cstart,
int  rsize,
int  csize 
) const

Extract a sub-matrix with runtime location and size.

The matrix extracted will begin at element (rstart, cstart) and will contain the next rsize by csize elements. 

        Matrix<> m(3,3);
        Extract the top-left 2x2 matrix
        Matrix<2> b = m.slice(0,0,2,2);

This method is not defined by Matrix: it is inherited.

Matrix& slice ( int  rstart,
int  cstart,
int  rsize,
int  csize 
)

Extract a sub-matrix with runtime location and size, which can be used as an l-value.

The matrix extracted will be begin at element (rstart, cstart) and will contain the next rsize by csize elements. 

        Matrix<> m(3,3);
        Zero(m.slice(0,0,2,2));

This method is not defined by Matrix: it is inherited.

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