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;
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.
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]
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];
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]
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]

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.

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]

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]
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);
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));
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