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lti::matrix

lti::matrix< T > Class Template Reference
[Linear Algebra, Aggregate Data Types]

Mathematical matrix container class. More...

#include <ltiMatrix.h>

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List of all members.

Public Types

typedef T value_type
typedef ipoint size_type

Public Member Functions

 matrix ()
 matrix (const int rows, const int cols, const T &iniValue=T())
 matrix (const int rows, const int cols, const T data[])
 matrix (const ipoint &size, const T &iniValue=T())
 matrix (const matrix< T > &other, const int fromRow=0, const int toRow=MaxInt32, const int fromCol=0, const int toCol=MaxInt32)
 matrix (const bool copyData, matrix< T > &other, const int fromRow=0, const int toRow=MaxInt32, const int fromCol=0, const int toCol=MaxInt32)
 matrix (const bool init, const int rows, const int cols)
 matrix (const bool init, const ipoint &size)
 matrix (const matrix< T > &other, const genericVector< int > &rows)
virtual ~matrix ()
virtual const char * getTypeName () const
vector< T > & getRow (const int row)
const vector< T > & getRow (const int row) const
vector< T > & operator[] (const int row)
const vector< T > & operator[] (const int row) const
vector< T > getRowCopy (const int row) const
void getRowCopy (const int row, vector< T > &theRow) const
vector< T > getColumnCopy (const int col) const
void getColumnCopy (const int col, vector< T > &theCol) const
vector< T > getDiagonal () const
void getDiagonal (vector< T > &diag) const
matrix< T > & copy (const matrix< T > &other)
matrix< T > & copy (const matrix< T > &other, const int fromRow, const int toRow=MaxInt32, const int fromCol=0, const int toCol=MaxInt32)
matrix< T > & copy (const matrix< T > &other, const irectangle &window)
matrix< T > & copy (const matrix< T > &other, const vector< int > &idx, bool rows=true)
template<class U>
matrix< T > & castFrom (const matrix< U > &other)
virtual mathObject * clone () const
bool prettyCloseTo (const matrix< T > &other, const T &tolerance) const
matrix< T > & operator= (const matrix< T > &other)
Apply Methods
Following methods are used to apply simple functions to each element of the vector.

matrix< T > & apply (T(*function)(T))
matrix< T > & apply (const matrix< T > &other, T(*function)(T))
matrix< T > & apply (T(*function)(const T &))
matrix< T > & apply (const matrix< T > &other, T(*function)(const T &))
matrix< T > & apply (const matrix< T > &other, T(*function)(const T &, const T &))
matrix< T > & apply (const matrix< T > &other, T(*function)(T, T))
matrix< T > & apply (const matrix< T > &a, const matrix< T > &b, T(*function)(const T &, const T &))
matrix< T > & apply (const matrix< T > &a, const matrix< T > &b, T(*function)(T, T))
Arithmetical Operations
matrix< T > & add (const matrix< T > &other)
matrix< T > & add (const matrix< T > &a, const matrix< T > &b)
matrix< T > & add (const T value)
matrix< T > & add (const matrix< T > &other, const T value)
matrix< T > & operator+= (const T value)
matrix< T > & operator+= (const matrix< T > &other)
matrix< T > operator+ (const matrix< T > &other) const
matrix< T > operator+ (const T value) const
matrix< T > & addScaled (const T b, const matrix< T > &other)
matrix< T > & addScaled (const matrix< T > &matA, const T b, const matrix< T > &matB)
matrix< T > & addScaled (const T a, const matrix< T > &first, const T b, const matrix< T > &second)
matrix< T > & subtract (const matrix< T > &other)
matrix< T > & subtract (const matrix< T > &a, const matrix< T > &b)
matrix< T > & subtract (const T value)
matrix< T > & subtract (const matrix< T > &other, const T value)
matrix< T > & operator-= (const T value)
matrix< T > & operator-= (const matrix< T > &other)
matrix< T > & multiply (const matrix< T > &other)
matrix< T > & multiply (const matrix< T > &first, const matrix< T > &second)
vector< T > & multiply (const vector< T > &other, vector< T > &result) const
vector< T > & multiply (vector< T > &srcdest) const
matrix< T > & multiply (const T value)
matrix< T > & multiply (const matrix< T > &other, const T value)
matrix< T > & operator *= (const matrix< T > &other)
matrix< T > & operator *= (const T value)
vector< T > & leftMultiply (const vector< T > &vct, vector< T > &result) const
vector< T > & leftMultiply (vector< T > &srcDest) const
matrix< T > & leftMultiply (const matrix< T > &mat)
matrix< T > & divide (const T value)
matrix< T > & divide (const matrix< T > &other, const T value)
matrix< T > & operator/= (const T value)
matrix< T > & emultiply (const matrix< T > &other)
matrix< T > & emultiply (const matrix< T > &a, const matrix< T > &b)
matrix< T > & edivide (const matrix< T > &other)
matrix< T > & edivide (const matrix< T > &a, const matrix< T > &b)
matrix< T > & outerProduct (const vector< T > &a, const vector< T > &b)
matrix< T > & transpose ()
matrix< T > & transpose (const matrix< T > &other)
T sumOfElements () const
T minimum () const
ipoint getIndexOfMinimum () const
T maximum () const
ipoint getIndexOfMaximum () const
void getExtremes (T &theMinimum, T &theMaximum) const
void getIndexOfExtremes (point &theIdxMinimum, ipoint &theIdxMaximum) const
void setIdentity (const T scale=T(1))
T trace () const

Protected Member Functions

virtual genericVector< T > * allocRows (const int n)

Detailed Description

template<class T>
class lti::matrix< T >

Mathematical matrix container class.

The lti::matrix class allows the representation of n x m matrices. The rows will be indexed between 0 and n-1, and the columns between 0 and m-1.

All types defined in ltiTypes.h use static members and can be contained by the lti::vector and lti::matrix classes.

The matrix class is a container class implemented as template.

If you need to create a matrix of floats with 20 rows and 15 columns, all elements initialized with an initial value of 4.27 just create it:

 lti::matrix<float> myMat(20,15,4.27f) // creates matrix with 300 elements
                                       // all initialized with 4.27f

To access the matrix elements use the access operators. There are many possibilities. With at(const int row, const int col) is possible to access an element directly. With at(const int row) you can get the row vector. You cannot for instance resize nor change the memory referenced in this vector (see lti::vector::resize). For example:

 float accu = 0; // initialize accumulator
 lti::matrix<float> myMat(20,15,4.27f)
 lti::vector<float> myVct;

 for (int j = 0; j < myMat.rows(); j++) {
   for (int i = 0; i < myMat.columns(); i++) {
   tmp += myMat.at(j,i); // access each element of the matrix:
                         // j is the row and i the column
   }
 }

 myMat.getRowCopy(5,myVct); // copy the sixth row in myVct!
 myVct.resize(6);           // Valid, the vector has its own memory!
 myMat.at(5).resize(6)      // ERROR!! the vector is not resizable!

The image representation in the LTI-Lib is based on the lti::matrix class. It is quite confusing to use first the y-coordinate and then the x-coordinate to access the image elements. To avoid confusion use the lti::point class to access the elements of the matrix:

 lti::channel8 aChannel(20,15); // creates an 8bit image
 lti::channel8::value_type tmp; // tmp is of the element type of the
                                // channel8!
 lti::point p;


 for (p.y = 0; p.y < aChannel.rows(); p.y++) {
   for (p.x = 0; p.x < aChannel.columns(); p.x++) {
   tmp += aChannel.at(p); // access each element of the matrix:
                          // equivalent to: tmp += aChannel.at(p.y,p.x)!
   }
 }

See also:
lti::image, lti::channel, lti::channel8, lti::dmatrix, lti::fmatrix, lti::imatrix
The parent class is lti::genericMatrix and provides many memory management options.

The matrix has following methods:

Member Typedef Documentation

template<class T>
typedef ipoint lti::matrix< T >::size_type
 

return type of the size() member

Reimplemented from lti::genericMatrix< T >.

template<class T>
typedef T lti::matrix< T >::value_type
 

type of the contained data

Reimplemented from lti::genericMatrix< T >.

Constructor & Destructor Documentation

template<class T>
lti::matrix< T >::matrix (   ) 
 

default constructor creates an empty matrix

template<class T>
lti::matrix< T >::matrix (  const int  rows,
const int  cols,
const T &  iniValue = T()
) 
 

this constructor creates a connected rows x cols Matrix and initializes all elements with iniValue

Parameters:
rows number of rows of the matrix
cols number of columns of the matrix
iniValue all elements will be initialized with this value

template<class T>
lti::matrix< T >::matrix (  const int  rows,
const int  cols,
const T  data[]
) 
 

this constructor creates a connected rows x cols Matrix and initializes all elements with the data pointed by data.

The first cols-elements of the data will be copied on the first row, the next ones on the second row and so on.

Parameters:
rows number of rows of the matrix
cols number of columns of the matrix
data pointer to the memory block with the data to be initialized with.

template<class T>
lti::matrix< T >::matrix (  const ipoint &  size,
const T &  iniValue = T()
) 
 

this constructor creates a connected size.y x size.x Matrix and initializes all elements with iniValue

Parameters:
size lti::point with the size of the matrix (size.x is the number of columns and size.y the number of rows)
iniValue all elements will be initialized with this value

template<class T>
lti::matrix< T >::matrix (  const matrix< T > &  other,
const int  fromRow = 0,
const int  toRow = MaxInt32,
const int  fromCol = 0,
const int  toCol = MaxInt32
) 
 

copy constructor.

create this matrix as a connected copy of another matrix for this const version, the data will be always copied! It is also possible to create a copy of a submatrix of another matrix.

Parameters:
other the matrix to be copied.
fromRow initial row of the other matrix to be copied
toRow last row to be copied of the other matrix
fromCol initial column of the other matrix to be copied
toCol last column to be copied of the other matrix
Example: 
 lti::matrix<int> m(4,6,0); // integer matrix with 25 elements
 // ...
 // initialize Matrix with:
 //        0  1  2  3  4  5
 //        2  1  5  4  0  3
 //        1  2  1  2  3  2
 //        3  3  2  1  2  3

 lti::matrix<int> sm(m,0,2,1,3)  // last line will lead to
 //                                 following contents in sm:
 //        1  2  3
 //        1  5  4
 //        2  1  2

template<class T>
lti::matrix< T >::matrix (  const bool  copyData,
matrix< T > &  other,
const int  fromRow = 0,
const int  toRow = MaxInt32,
const int  fromCol = 0,
const int  toCol = MaxInt32
) 
 

copy constructor (reference to a submatrix).

creates submatrix of another matrix.

if copyData == true, the new object has its own data (equivalent to previous copy constructor).

if copyData == false, the new object has references to the other matrix, which means that the data is not necessarily consecutive. (This will not be a connected but a lined matrix)

Those algorithms which use direct access to the matrix memory block should check first if the memory lies in a consecutive block! (see getMode())

Parameters:
copyData should the data of the other matrix be copied or not
other the matrix with the data to be copied or to be shared
fromRow initial row of the other matrix to be copied
toRow last row to be copied of the other matrix
fromCol initial column of the other matrix to be copied
toCol last column to be copied of the other matrix

template<class T>
lti::matrix< T >::matrix (  const bool  init,
const int  rows,
const int  cols
) 
 

If init is true this constructor is equivalent to calling matrix(const int rows, const int cols), and thus initializing all elements with T().

However, in some cases the elements need not be initialized during construction, since complex initializion is required. Especially for large matrices, the unnecessary constructor initialization is very time consuming.

If init is false, memory is allocated but no initialization takes place. Thus the following is equivalent: 

 matrix<int> a(false,100,100);

 matrix<int> a;
 a.resize(100,100,0,false,false);

Parameters:
init initialize matrix or not
rows number of rows of the matrix
cols number of columns of the matrix

template<class T>
lti::matrix< T >::matrix (  const bool  init,
const ipoint &  size
) 
 

If init is true this constructor is equivalent to calling matrix(const int rows, const int cols), and thus initializing all elements with T().

However, in some cases the elements need not be initialized during construction, since complex initializion is required. Especially for large matrices, the unnecessary constructor initialization is very time consuming.

If init is false, memory is allocated but no initialization takes place. Thus the following is equivalent: 

 matrix<int> a(false,100,100);

 matrix<int> a;
 a.resize(100,100,0,false,false);

Parameters:
init initialize matrix or not
size desired size for the matrix

template<class T>
lti::matrix< T >::matrix (  const matrix< T > &  other,
const genericVector< int > &  rows
) 
 

copy constructor.

create this matrix as a connected copy of another matrix taking only the rows indicated by the vector. for this const version, the data will be always copied! Multiple occurence of one row index in rows is allowed.

Parameters:
other the matrix to be copied.
rows inidices of the rows to be copied
Example: 
 lti::vector<int> rows(2);
 // initialize with
 // 1 3
 lti::matrix<int> m(4,6,0); // integer matrix with 25 elements
 // ...
 // initialize Matrix with:
 //        0  1  2  3  4  5
 //        2  1  5  4  0  3
 //        1  2  1  2  3  2
 //        3  3  2  1  2  3

 lti::matrix<int> sm(m,rows)     // last line will lead to
 //                                 following contents in sm:
 //        2  1  5  4  0  3
 //        3  3  2  1  2  3

template<class T>
virtual lti::matrix< T >::~matrix (   )  [virtual]
 

destructor

Member Function Documentation

template<class T>
matrix<T>& lti::matrix< T >::add (  const matrix< T > &  other,
const T  value
) 
 

add constant value to the other matrix and leave result here.

Parameters:
other the other matrix
value a constant value to be added to all matrix elements
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::add (  const T  value  ) 
 

add constant value to this matrix, and leave result here

Parameters:
value a constant value to be added to all matrix elements
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::add (  const matrix< T > &  a,
const matrix< T > &  b
) 
 

add matrices a and b and write the result in this matrix

Parameters:
a the first matrix
b the second matrix
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::add (  const matrix< T > &  other  ) 
 

add other matrix to this matrix, and leave result here

Parameters:
other the matrix to be added with
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::addScaled (  const T  a,
const matrix< T > &  first,
const T  b,
const matrix< T > &  second
) 
 

Leave the scaled sum of two matrices in this matrix.

The matrices must be of the same types and dimensions. Let $A$ be the first matrix and $B$ the second matrix with corresponding scaling factors $a$ and $b$ , further $C$ this matrix, then this method performs:

$C=a\cdot A+b\cdot B$

Parameters:
a scaling factor for first
first the first matrix to be added after scaling
b scaling factor for second
second the second matrix to be added after scaling
Returns:
a reference to this matrix

template<class T>
matrix<T>& lti::matrix< T >::addScaled (  const matrix< T > &  matA,
const T  b,
const matrix< T > &  matB
) 
 

Add a matrix A with a matrix B scaled by $b$ , and leave the result in this matrix.

The matrices must be of the same types and dimensions. This method performs:

$A+b\cdot B$

Parameters:
matA the first matrix
b scaling factor for matB
matB the matrix to be added after scaling
Returns:
a reference to this matrix

template<class T>
matrix<T>& lti::matrix< T >::addScaled (  const T  b,
const matrix< T > &  other
) 
 

Add another matrix scaled by $b$ to this matrix.

The matrices must be of the same types and dimensions. Let $A$ be this matrix and $B$ the other matrix, then this method performs:

$A=A+b\cdot B$

Parameters:
b scaling factor for other
other the matrix to be added after scaling
Returns:
a reference to this matrix

template<class T>
virtual genericVector<T>* lti::matrix< T >::allocRows (  const int  n  )  [inline, protected, virtual]
 

Allocate n number of rows or the appropriate type.

Reimplemented from lti::genericMatrix< T >.

template<class T>
matrix<T>& lti::matrix< T >::apply (  const matrix< T > &  a,
const matrix< T > &  b,
T(*)(T, T)  function
) 
 

a two-parameter C-function receives the i-th elements of both given matrices and leaves the result here.

Note that both matrices must have the same size!

Parameters:
a the first matrix
b the second matrix
function a pointer to C-function with two parameters
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::apply (  const matrix< T > &  a,
const matrix< T > &  b,
T(*)(const T &, const T &)  function
) 
 

a two-parameter C-function receives the i-th elements of both given matrices and leaves the result here.

Note that both matrices must have the same size!

Parameters:
a the first matrix
b the second matrix
function a pointer to C-function with two parameters
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::apply (  const matrix< T > &  other,
T(*)(T, T)  function
) 
 

a two-parameter C-function receives the i-th elements of this and the given matrix and the result will be left in this matrix.

Note that both matrices must have the same size!

Parameters:
other the second matrix to be considered (the first matrix will be this object!)
function a pointer to C-function with two parameters
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::apply (  const matrix< T > &  other,
T(*)(const T &, const T &)  function
) 
 

a two-parameter C-function receives the i-th elements of this and the given matrix and the result will be left in this matrix.

Note that both matrices must have the same size!

Parameters:
other the second matrix to be considered (the first matrix will be this object!)
function a pointer to C-function with two parameters
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::apply (  const matrix< T > &  other,
T(*)(const T &)  function
) 
 

applies a C-function to each element of the other matrix

Parameters:
other the matrix which elements will go through the given function.
function a pointer to a C-function
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::apply (  T(*)(const T &)  function  ) 
 

applies a C-function to each element of the matrix.

Parameters:
function a pointer to a C-function
Returns:
a reference to the actual matrix

Reimplemented from lti::genericMatrix< T >.

template<class T>
matrix<T>& lti::matrix< T >::apply (  const matrix< T > &  other,
T(*)(T)  function
) 
 

applies a C-function to each element of the other matrix

Parameters:
other the matrix which elements will go through the given function.
function a pointer to a C-function
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::apply (  T(*)(T)  function  ) 
 

applies a C-function to each element of the matrix.

Parameters:
function a pointer to a C-function
Returns:
a reference to the actual matrix

Reimplemented from lti::genericMatrix< T >.

template<class T>
template<class U>
matrix<T>& lti::matrix< T >::castFrom (  const matrix< U > &  other  )  [inline]
 

copy the other matrix by casting each of its elements

Parameters:
other The matrix to be casted Example: 
   lti::matrix<int> matA(10,10,1);// a matrix of integers
   lti::matrix<double> matB;      // a matrix of doubles

   matB.castFrom(matA);          // this will copy matA in matB!!

Reimplemented in lti::channel, lti::channel8, and lti::channel32.

template<class T>
virtual mathObject* lti::matrix< T >::clone (   )  const [virtual]
 

create a clone of this matrix

Returns:
a pointer to a copy of this matrix

Reimplemented from lti::genericMatrix< T >.

Reimplemented in lti::image, lti::channel, lti::channel8, lti::channel32, lti::kernel2D< T >, lti::kernel2D< float >, and lti::kernel2D< ubyte >.

template<class T>
matrix<T>& lti::matrix< T >::copy (  const matrix< T > &  other,
const vector< int > &  idx,
bool  rows = true
)  [inline]
 

assigment operator.

copy the contents of the specified rows/columns of other into this object. Multiple occurence of one row/column index in idx is allowed. If the argument rows is true, idx specifies rows, if false idx specifies columns.

The result of the copy is always a connected matrix. I.e. you cannot copy the sub-matrix property of another matrix.

Parameters:
other the other matrix to be copied
idx indices of the rows to be copied.
rows if true works on rows, else on columns

template<class T>
matrix<T>& lti::matrix< T >::copy (  const matrix< T > &  other,
const irectangle &  window
)  [inline]
 

assigment operator.

copy the contents of other in this object.

The result of the copy is always a connected matrix. I.e. you cannot copy the sub-matrix property of another matrix.

Parameters:
other the other matrix to be copied
window rectangle define the copy area

template<class T>
matrix<T>& lti::matrix< T >::copy (  const matrix< T > &  other,
const int  fromRow,
const int  toRow = MaxInt32,
const int  fromCol = 0,
const int  toCol = MaxInt32
)  [inline]
 

assigment operator.

copy the contents of other in this object.

The result of the copy is always a connected matrix. I.e. you cannot copy the sub-matrix property of another matrix.

Parameters:
other the other matrix to be copied
fromRow initial row of the other matrix to be copied
toRow last row to be copied of the other matrix
fromCol initial column of the other matrix to be copied
toCol last column to be copied of the other matrix

template<class T>
matrix<T>& lti::matrix< T >::copy (  const matrix< T > &  other  )  [inline]
 

assigment operator.

copy the contents of other in this object.

The result of the copy is always a connected matrix. I.e. you cannot copy the sub-matrix property of another matrix.

Parameters:
other the other matrix to be copied

template<class T>
matrix<T>& lti::matrix< T >::divide (  const matrix< T > &  other,
const T  value
) 
 

divide the elements of the other matrix by a constant value and leave the result here.

Parameters:
other the other matrix
value the constant value (divisor)
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::divide (  const T  value  ) 
 

divide the elements of the matrix by a constant value, and leave the result here

Parameters:
value the constant value (divisor)
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::edivide (  const matrix< T > &  a,
const matrix< T > &  b
) 
 

element-wise division of a and b.

Parameters:
a the first matrix
b the second matrix (with same dimensions of a)
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::edivide (  const matrix< T > &  other  ) 
 

element-wise division with other matrix

Parameters:
other the other matrix. It should have the same dimensions of this matrix.
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::emultiply (  const matrix< T > &  a,
const matrix< T > &  b
) 
 

element-wise multiplication of a and b.

Parameters:
a the first matrix
b the second matrix (with same dimensions of a)
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::emultiply (  const matrix< T > &  other  ) 
 

element-wise multiplication with other matrix

Parameters:
other the other matrix. It should have the same dimensions of this matrix.
Returns:
a reference to the actual matrix

template<class T>
void lti::matrix< T >::getColumnCopy (  const int  col,
vector< T > &  theCol
)  const [inline]
 

return genericMatrix-column as a vector.

This method copies the data of the genericMatrix, therefore is not as fast as getRow()

Parameters:
col the number of the column to be copied
theCol a vector, where the column vector of the genericMatrix should be copied.

template<class T>
vector<T> lti::matrix< T >::getColumnCopy (  const int  col  )  const [inline]
 

return matrix-column as a vector.

This method copies the data of the matrix, therefore is not as fast as getRow()

Parameters:
col the number of the column to be copied
Returns:
a vector with the contents of the column of the matrix

Reimplemented from lti::genericMatrix< T >.

template<class T>
void lti::matrix< T >::getDiagonal (  vector< T > &  diag  )  const [inline]
 

Return the diagonal elements of the genericMatrix as vector.

This method copies the diagonal elements of the genericMatrix into the vector. If the genericMatrix is non-symmetrical, the vector will be of dimension min(rows(),columns()).

Parameters:
diag a vector, where the diagonal of the genericMatrix should be copied.

template<class T>
vector<T> lti::matrix< T >::getDiagonal (   )  const [inline]
 

Return the diagonal elements of the matrix as vector.

This method copies the diagonal elements of the matrix into the vector. If the matrix is non-symmetrical, the vector will be of dimension min(rows(),columns()).

Returns:
a vector with the diagonal elements of the matrix.

Reimplemented from lti::genericMatrix< T >.

template<class T>
void lti::matrix< T >::getExtremes (  T &  theMinimum,
T &  theMaximum
)  const
 

get the extremes of the matrix (smallest and biggest elements)

template<class T>
void lti::matrix< T >::getIndexOfExtremes (  point &  theIdxMinimum,
ipoint &  theIdxMaximum
)  const
 

get the indices of the extremes of the matrix (smallest and biggest elements)

template<class T>
ipoint lti::matrix< T >::getIndexOfMaximum (   )  const
 

get the index of the biggest element of the matrix

template<class T>
ipoint lti::matrix< T >::getIndexOfMinimum (   )  const
 

get the index of the smallest element of the matrix

template<class T>
const vector<T>& lti::matrix< T >::getRow (  const int  row  )  const [inline]
 

return matrix-row as a const vector.

This method works fast, since it returns a reference to the row vector. The data will NOT be copied.

Parameters:
row the row to be accessed
Returns:
a const reference to the vector row

Reimplemented from lti::genericMatrix< T >.

template<class T>
vector<T>& lti::matrix< T >::getRow (  const int  row  )  [inline]
 

return matrix-row as a vector.

This method works fast, since it returns a reference to the row vector. The data will NOT be copied.

Parameters:
row the row to be accessed
Returns:
a reference to the vector row

Reimplemented from lti::genericMatrix< T >.

template<class T>
void lti::matrix< T >::getRowCopy (  const int  row,
vector< T > &  theRow
)  const [inline]
 

Copy a row vector in the given parameter.

This method copies the data of a given row of the genericMatrix in the given vector.

Parameters:
row the number of the row to be copied
theRow the vector, where the data will be copied
See also:
getRow()

template<class T>
vector<T> lti::matrix< T >::getRowCopy (  const int  row  )  const [inline]
 

return matrix-row as a vector.

This method copies the data of the matrix, therefore is not as fast as getRow()

Parameters:
row the number of tthe row to be copied
Returns:
a vector with the contents of the row of the matrix

Reimplemented from lti::genericMatrix< T >.

template<class T>
virtual const char* lti::matrix< T >::getTypeName (   )  const [virtual]
 

returns the name of this class: "matrix"

Reimplemented from lti::genericMatrix< T >.

Reimplemented in lti::image, lti::channel, lti::channel8, lti::channel32, lti::kernel2D< T >, lti::kernel2D< float >, and lti::kernel2D< ubyte >.

template<class T>
matrix<T>& lti::matrix< T >::leftMultiply (  const matrix< T > &  mat  ) 
 

multiply the matrix mat with this matrix, and leave the result in this matrix.

Parameters:
mat the matrix to be multiplied with.
Returns:
a reference to this matrix

template<class T>
vector<T>& lti::matrix< T >::leftMultiply (  vector< T > &  srcDest  )  const
 

multiply the given vector srcdest with this matrix, and save the result in the same vector.

The given vector will be interpreted as a row-vector (or a transposed column vector).

Parameters:
srcDest the vector to be multiplied with, and where the result must be written.
Returns:
a reference to the result vector

template<class T>
vector<T>& lti::matrix< T >::leftMultiply (  const vector< T > &  vct,
vector< T > &  result
)  const
 

multiply the vector vct with this matrix, and save the result in the vector result.

The given vector will be interpreted as a row-vector (or a transposed column vector).

Parameters:
vct the vector to be multiplied with.
result the resulting vector.
Returns:
a reference to the result vector

template<class T>
T lti::matrix< T >::maximum (   )  const
 

get the biggest element of the matrix

template<class T>
T lti::matrix< T >::minimum (   )  const
 

get the smallest element of the matrix

template<class T>
matrix<T>& lti::matrix< T >::multiply (  const matrix< T > &  other,
const T  value
) 
 

multiply constant value with the other matrix and leave result here.

Parameters:
other the other matrix
value the constant value to be multiplied with
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::multiply (  const T  value  ) 
 

multiply constant value with this matrix, and leave result here

Parameters:
value the constant value to be multiplied with
Returns:
a reference to the actual matrix

template<class T>
vector<T>& lti::matrix< T >::multiply (  vector< T > &  srcdest  )  const
 

multiply this matrix with a vector and leave the result in same vector (In-Place Method) A reference to the vector is returned.

Parameters:
srcdest the vector to be multiplied with. Its dimension must be equal to the number of columns of the matrix. The result vector will be left here too, and the resulting size will be the number of rows of the matrix.
Returns:
a reference to the result

template<class T>
vector<T>& lti::matrix< T >::multiply (  const vector< T > &  other,
vector< T > &  result
)  const
 

multiply this matrix with a vector and leave the result in result.

A reference to result is returned.

Parameters:
other the vector to be multiplied with. Its dimension must be equal to the number of columns of the matrix.
result the resulting vector. It will have a number of dimensions equal to the number of rows of the matrix.
Returns:
a reference to the result

template<class T>
matrix<T>& lti::matrix< T >::multiply (  const matrix< T > &  first,
const matrix< T > &  second
) 
 

multiply first with second and leave the result in this object.

Parameters:
first the first matrix
second this second matrix will be multiplied with the first one.
Returns:
a reference to this matrix, which has now the multiplication result.

template<class T>
matrix<T>& lti::matrix< T >::multiply (  const matrix< T > &  other  ) 
 

multiply this matrix with other matrix, and leave result here.

The dimensions of this matrix will change if needed!

Parameters:
other the other matrix to be multiplied with.
Returns:
a reference to this matrix.

template<class T>
matrix<T>& lti::matrix< T >::operator *= (  const T  value  )  [inline]
 

alias for multiply(const T& value)

Parameters:
value the constant value to be multiplied with
Returns:
a reference to this matrix.

template<class T>
matrix<T>& lti::matrix< T >::operator *= (  const matrix< T > &  other  )  [inline]
 

alias for multiply(const matrix)

Parameters:
other the other matrix to be multiplied with.
Returns:
a reference to this matrix.

template<class T>
matrix<T> lti::matrix< T >::operator+ (  const T  value  )  const
 

add constant value to this matrix, and leave result in a new matrix.

This object is not changed.

Parameters:
value a constant value to be added to all matrix elements
Returns:
a new matrix with the result

template<class T>
matrix<T> lti::matrix< T >::operator+ (  const matrix< T > &  other  )  const
 

add other matrix to this matrix and leave the result in a new matrix.

This object is not changed.

Parameters:
other the other matrix to be added with.
Returns:
a matrix with the sum of this matrix and other
Note that the use of this operator is not as efficient as the use of the add() methods, in which the programmer can decide when to use temporal and when not...

template<class T>
matrix<T>& lti::matrix< T >::operator+= (  const matrix< T > &  other  )  [inline]
 

alias for add(const matrix)

Parameters:
other the matrix to be added with
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::operator+= (  const T  value  )  [inline]
 

alias for add(const T value)

Parameters:
value a constant value to be added to all matrix elements
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::operator-= (  const matrix< T > &  other  )  [inline]
 

alias for subtract(const matrix)

Parameters:
other the matrix to be subtracted
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::operator-= (  const T  value  )  [inline]
 

alias for subtract(const T value)

Parameters:
value a constant value to be subtracted from all matrix elements
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::operator/= (  const T  value  )  [inline]
 

alias for divide(const T& value)

Parameters:
value the constant value to be divided by
Returns:
a reference to this matrix.

template<class T>
matrix<T>& lti::matrix< T >::operator= (  const matrix< T > &  other  )  [inline]
 

assigment operator (alias for copy(other)).

Parameters:
other the matrix to be copied
Returns:
a reference to the actual matrix

template<class T>
const vector<T>& lti::matrix< T >::operator[] (  const int  row  )  const [inline]
 

alias for getRow()

Reimplemented from lti::genericMatrix< T >.

template<class T>
vector<T>& lti::matrix< T >::operator[] (  const int  row  )  [inline]
 

alias for getRow()

Reimplemented from lti::genericMatrix< T >.

template<class T>
matrix<T>& lti::matrix< T >::outerProduct (  const vector< T > &  a,
const vector< T > &  b
) 
 

outer-product of two vectors.

The result will be left in this matrix. The dimensions of this matrix will change if needed. The outer product of two column vectors is defined as $a \cdot b^T$

Parameters:
a first vector (will determine the number of rows)
b second vector (will determine the number of columns)
Returns:
a reference to the actual matrix

template<class T>
bool lti::matrix< T >::prettyCloseTo (  const matrix< T > &  other,
const T &  tolerance
)  const
 

compare this matrix with other, and use the given tolerance to determine if the value of each element of the other matrix approximately equals the values of the actual matrix elements.

An element x is approximately equal to another element y with a tolerance t, if following equation holds: x-t < y < x+t

Parameters:
other the other matrix to be compared with
tolerance the tolerance to be used
Returns:
true if both matrices are approximatly equal

template<class T>
void lti::matrix< T >::setIdentity (  const T  scale = T(1)  ) 
 

Set the diagonal of this matrix to scale (default: 1), and all other elements to 0.

If the matrix is square (which it need not be), this results in a scaled identity matrix.

template<class T>
matrix<T>& lti::matrix< T >::subtract (  const matrix< T > &  other,
const T  value
) 
 

subtract constant value from the other matrix and leave result here.

Parameters:
other the other matrix
value a constant value to be subtracted from all matrix elements
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::subtract (  const T  value  ) 
 

subtract constant value from this matrix, and leave result here

Parameters:
value a constant value to be subtracted from all matrix elements
Returns:
a reference to the actual matrix

template<class T>
matrix<T>& lti::matrix< T >::subtract (  const matrix< T > &  a,
const matrix< T > &  b
) 
 

subtract matrices b from a and write result in this matrix.

Parameters:
a the first matrix
b the second matrix
Returns:
a reference to this matrix, which is now a-b.

template<class T>
matrix<T>& lti::matrix< T >::subtract (  const matrix< T > &  other  ) 
 

subtract other matrix from this matrix, and leave result here.

Parameters:
other the matrix to be subtracted
Returns:
a reference to this matrix.

template<class T>
T lti::matrix< T >::sumOfElements (   )  const
 

calculate the sum of all elements of the matrix.

This member can be used with classes which define the operator '+='

Reimplemented in lti::channel8.

template<class T>
T lti::matrix< T >::trace (   )  const
 

returns the trace (i.e.

the sum of the diagonal elements) of this matrix. If the matrix is not symmetrical, it will return the sum of all elements (i,i) with i from 0 to n-1; n being min(rows(),columns())

template<class T>
matrix<T>& lti::matrix< T >::transpose (  const matrix< T > &  other  ) 
 

transpose the other matrix and leave the result here.

Returns:
a reference to the actual (now transposed) matrix

template<class T>
matrix<T>& lti::matrix< T >::transpose (   ) 
 

transpose matrix and leave the result here.

Returns:
a reference to the actual (now transposed) matrix

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