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| Matrix [Linear Algebra] |

`#include <vigra/matrix.hxx>`

Inheritance diagram for Matrix:

List of all members.

## Public Types

typedef ALLOC | allocator_type
typedef BaseType::const_pointer | const_pointer
typedef BaseType::const_reference | const_reference
typedef BaseType::difference_type | difference_type
typedef BaseType::difference_type_1 | difference_type_1
typedef Matrix< T, ALLOC > | matrix_type
typedef BaseType::pointer | pointer
typedef BaseType::reference | reference
typedef BaseType::value_type | value_type
typedef MultiArrayView< 2, T, UnstridedArrayTag > | view_type

## Public Member Functions

difference_type_1 | columnCount () const
view_type | columnVector (difference_type_1 d) const
difference_type_1 | elementCount () const
template<class U>
Matrix & | init (const U &init)
bool | isSymmetric () const
template<class U, class C>
| Matrix (const MultiArrayView< 2, U, C > &rhs)
| Matrix (const TemporaryMatrix< T, ALLOC > &rhs)
| Matrix (const Matrix &rhs)
| Matrix (difference_type_1 rows, difference_type_1 columns, const_pointer init, RawArrayMemoryLayout layout=RowMajor, allocator_type const &alloc=allocator_type())
| Matrix (const difference_type &shape, const_pointer init, RawArrayMemoryLayout layout=RowMajor, allocator_type const &alloc=allocator_type())
| Matrix (difference_type_1 rows, difference_type_1 columns, const_reference init, allocator_type const &alloc=allocator_type())
| Matrix (const difference_type &shape, const_reference init, allocator_type const &alloc=allocator_type())
| Matrix (difference_type_1 rows, difference_type_1 columns, ALLOC const &alloc=allocator_type())
| Matrix (const difference_type &shape, ALLOC const &alloc=allocator_type())
| Matrix (ALLOC const &alloc)
| Matrix ()
NormTraits< Matrix >::NormType | norm () const
value_type | operator() (difference_type_1 row, difference_type_1 column) const
value_type & | operator() (difference_type_1 row, difference_type_1 column)
Matrix & | operator*= (T other)
template<class U, class C>
Matrix & | operator*= (MultiArrayView< 2, U, C > const &other)
Matrix & | operator+= (T other)
template<class U, class C>
Matrix & | operator+= (MultiArrayView< 2, U, C > const &other)
Matrix & | operator-= (T other)
template<class U, class C>
Matrix & | operator-= (MultiArrayView< 2, U, C > const &other)
Matrix & | operator/= (T other)
template<class U, class C>
Matrix & | operator/= (MultiArrayView< 2, U, C > const &other)
template<class U, class C>
Matrix & | operator= (const MultiArrayView< 2, U, C > &rhs)
Matrix & | operator= (const TemporaryMatrix< T, ALLOC > &rhs)
Matrix & | operator= (const Matrix &rhs)
void | reshape (difference_type const &shape, const_reference init)
void | reshape (difference_type const &shape)
void | reshape (difference_type_1 rows, difference_type_1 columns, const_reference init)
void | reshape (difference_type_1 rows, difference_type_1 columns)
difference_type_1 | rowCount () const
view_type | rowVector (difference_type_1 d) const
NormTraits< Matrix > ::SquaredNormType | squaredNorm () const
MultiArrayView< 2, vluae_type, StridedArrayTag > | transpose () const

## Detailed Description

### template<class T, class ALLOC = std::allocator<T>>
class vigra::linalg::Matrix< T, ALLOC >

Matrix class.

This is the basic class for all linear algebra computations. Matrices are strored in a column-major format, i.e. the row index is varying fastest. This is the same format as in the lapack and gmm++ libraries, so it will be easy to interface these libraries. In fact, if you need optimized high performance code, you should use them. The VIGRA linear algebra functionality is provided for smaller problems and rapid prototyping (no one wants to spend half the day installing a new library just to discover that the new algorithm idea didn't work anyway).

See also:

- Matrix Functions

#include <vigra/matrix.hxx> or
#include <vigra/linear_algebra.hxx>
Namespaces: vigra and vigra::linalg

## Member Typedef Documentation

typedef ALLOC allocator_type

the allocator type used to allocate the memory

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::const_pointer const_pointer

const pointer type

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::const_reference const_reference

const reference type (result of operator[] const)

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::difference_type difference_type

difference type (used for multi-dimensional offsets and indices)

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::difference_type_1 difference_type_1

difference and index type for a single dimension

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef Matrix<T, ALLOC> matrix_type

the matrix type associated with this array.

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::pointer pointer

pointer type

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::reference reference

reference type (result of operator[])

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef BaseType::value_type value_type

the array's value type

Reimplemented from MultiArray< 2, T, ALLOC >.

typedef MultiArrayView<2, T, UnstridedArrayTag> view_type

the view type associated with this array.

Reimplemented from MultiArray< 2, T, ALLOC >.

## Constructor & Destructor Documentation

Matrix | ( |  | ) |

default constructor

Matrix | ( | ALLOC const & | alloc | ) | `[explicit]`

construct with given allocator

Matrix | ( | const difference_type & | shape,
|  | ALLOC const & | alloc = `allocator_type()` |
| ) |  |  | `[explicit]`

construct with given shape and init all elements with zero. Note that the order of the axes is `difference_type(rows, columns)` which is the opposite of the usual VIGRA convention.

Matrix | ( | difference_type_1 | rows,
|  | difference_type_1 | columns,
|  | ALLOC const & | alloc = `allocator_type()` |
| ) |  |  |

construct with given shape and init all elements with zero. Note that the order of the axes is `(rows, columns)` which is the opposite of the usual VIGRA convention.

Matrix | ( | const difference_type & | shape,
|  | const_reference | init,
|  | allocator_type const & | alloc = `allocator_type()` |
| ) |  |  |

construct with given shape and init all elements with the constant init. Note that the order of the axes is `difference_type(rows, columns)` which is the opposite of the usual VIGRA convention.

Matrix | ( | difference_type_1 | rows,
|  | difference_type_1 | columns,
|  | const_reference | init,
|  | allocator_type const & | alloc = `allocator_type()` |
| ) |  |  |

construct with given shape and init all elements with the constant init. Note that the order of the axes is `(rows, columns)` which is the opposite of the usual VIGRA convention.

Matrix | ( | const difference_type & | shape,
|  | const_pointer | init,
|  | RawArrayMemoryLayout | layout = `RowMajor`,
|  | allocator_type const & | alloc = `allocator_type()` |
| ) |  |  |

construct with given shape and copy data from C-style array init. Unless layout is `ColumnMajor`, the elements in this array are assumed to be given in row-major order (the C standard order) and will automatically be converted to the required column-major format. Note that the order of the axes is `difference_type(rows, columns)` which is the opposite of the usual VIGRA convention.

Matrix | ( | difference_type_1 | rows,
|  | difference_type_1 | columns,
|  | const_pointer | init,
|  | RawArrayMemoryLayout | layout = `RowMajor`,
|  | allocator_type const & | alloc = `allocator_type()` |
| ) |  |  |

construct with given shape and copy data from C-style array init. Unless layout is `ColumnMajor`, the elements in this array are assumed to be given in row-major order (the C standard order) and will automatically be converted to the required column-major format. Note that the order of the axes is `(rows, columns)` which is the opposite of the usual VIGRA convention.

Matrix | ( | const Matrix< T, ALLOC > & | rhs | ) |

copy constructor. Allocates new memory and copies tha data.

Matrix | ( | const TemporaryMatrix< T, ALLOC > & | rhs | ) |

construct from temporary matrix, which looses its data.

This operation is equivalent to

                    TemporaryMatrix<T> temp = ...;

                    Matrix<T> m;
                    m.swap(temp);

template<class U, class C>
Matrix | ( | const MultiArrayView< 2, U, C > & | rhs | ) |

construct from a MultiArrayView. Allocates new memory and copies tha data. rhs is assumed to be in column-major order already.

## Member Function Documentation

difference_type_1 columnCount | ( |  | ) | const

number of columns (width) of the matrix.

view_type columnVector | ( | difference_type_1 | d | ) | const

Create a matrix view that represents the column vector of column d.

difference_type_1 elementCount | ( |  | ) | const

number of elements (width*height) of the matrix.

Reimplemented from MultiArrayView< N, T >.

Matrix& init | ( | const U & | init | ) |

init elements with a constant

Reimplemented from MultiArray< 2, T, ALLOC >.

bool isSymmetric | ( |  | ) | const

check whether the matrix is symmetric.

NormTraits<Matrix>::NormType norm | ( |  | ) | const

Frobenius norm. Root of sum of squares of the matrix elements.

value_type operator() | ( | difference_type_1 | row,
|  | difference_type_1 | column |
| ) |  |  | const

read access to matrix element `(row, column)`. Note that the order of the argument is the opposite of the usual VIGRA convention due to column-major matrix order.

value_type& operator() | ( | difference_type_1 | row,
|  | difference_type_1 | column |
| ) |  |  |

read/write access to matrix element `(row, column)`. Note that the order of the argument is the opposite of the usual VIGRA convention due to column-major matrix order.

Matrix& operator*= | ( | T | other | ) |

scalar multiply this with other

Matrix& operator*= | ( | MultiArrayView< 2, U, C > const & | other | ) |

multiply other element-wise with this matrix (sizes must match).

Matrix& operator+= | ( | T | other | ) |

add other to each element of this matrix

Matrix& operator+= | ( | MultiArrayView< 2, U, C > const & | other | ) |

add other to this (sizes must match).

Matrix& operator-= | ( | T | other | ) |

subtraxt other from each element of this matrix

Matrix& operator-= | ( | MultiArrayView< 2, U, C > const & | other | ) |

subtract other from this (sizes must match).

Matrix& operator/= | ( | T | other | ) |

scalar devide this by other

Matrix& operator/= | ( | MultiArrayView< 2, U, C > const & | other | ) |

divide this matrix element-wise by other (sizes must match).

Matrix& operator= | ( | const MultiArrayView< 2, U, C > & | rhs | ) |

assignment from arbitrary 2-dimensional MultiArrayView.
If the size of rhs is the same as the matrix's old size, only the data are copied. Otherwise, new storage is allocated, which invalidates all objects (array views, iterators) depending on the matrix. rhs is assumed to be in column-major order already.

Matrix& operator= | ( | const TemporaryMatrix< T, ALLOC > & | rhs | ) |

assign a temporary matrix. If the shapes of the two matrices match, only the data are copied (in order to not invalidate views and iterators depending on this matrix). Otherwise, the memory is swapped between the two matrices, so that all depending objects (array views, iterators) ar invalidated.

Matrix& operator= | ( | const Matrix< T, ALLOC > & | rhs | ) |

assignment. If the size of rhs is the same as the matrix's old size, only the data are copied. Otherwise, new storage is allocated, which invalidates all objects (array views, iterators) depending on the matrix.

void reshape | ( | difference_type const & | shape,
|  | const_reference | init |
| ) |  |  |

reshape to the given shape and initialize with init.

void reshape | ( | difference_type const & | shape | ) |

reshape to the given shape and initialize with zero.

void reshape | ( | difference_type_1 | rows,
|  | difference_type_1 | columns,
|  | const_reference | init |
| ) |  |  |

reshape to the given shape and initialize with init.

void reshape | ( | difference_type_1 | rows,
|  | difference_type_1 | columns |
| ) |  |  |

reshape to the given shape and initialize with zero.

difference_type_1 rowCount | ( |  | ) | const

number of rows (height) of the matrix.

view_type rowVector | ( | difference_type_1 | d | ) | const

Create a matrix view that represents the row vector of row d.

NormTraits<Matrix>::SquaredNormType squaredNorm | ( |  | ) | const

squared Frobenius norm. Sum of squares of the matrix elements.

Reimplemented from MultiArrayView< N, T >.

MultiArrayView<2, vluae_type, StridedArrayTag> transpose | ( |  | ) | const

create a transposed view of this matrix. No data are copied. If you want to transpose this matrix permanently, you have to assign the transposed view:

                a = a.transpose();

Reimplemented from MultiArrayView< N, T >.

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

- vigra/matrix.hxx

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python VIGRA 1.6.0 (13 Aug 2008)