dune-common
2.6-git
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A dense n x m matrix. More...
#include <dune/common/densematrix.hh>
Public Types | |
enum | { blocklevel = 1 } |
We are at the leaf of the block recursion. More... | |
typedef Traits::derived_type | derived_type |
type of derived matrix class More... | |
typedef Traits::value_type | value_type |
export the type representing the field More... | |
typedef Traits::value_type | field_type |
export the type representing the field More... | |
typedef Traits::value_type | block_type |
export the type representing the components More... | |
typedef Traits::size_type | size_type |
The type used for the index access and size operation. More... | |
typedef Traits::row_type | row_type |
The type used to represent a row (must fulfill the Dune::DenseVector interface) More... | |
typedef Traits::row_reference | row_reference |
The type used to represent a reference to a row (usually row_type &) More... | |
typedef Traits::const_row_reference | const_row_reference |
The type used to represent a reference to a constant row (usually const row_type &) More... | |
typedef DenseIterator< DenseMatrix, row_type, row_reference > | Iterator |
Iterator class for sequential access. More... | |
typedef Iterator | iterator |
typedef for stl compliant access More... | |
typedef Iterator | RowIterator |
rename the iterators for easier access More... | |
typedef std::remove_reference< row_reference >::type::Iterator | ColIterator |
rename the iterators for easier access More... | |
typedef DenseIterator< const DenseMatrix, const row_type, const_row_reference > | ConstIterator |
Iterator class for sequential access. More... | |
typedef ConstIterator | const_iterator |
typedef for stl compliant access More... | |
typedef ConstIterator | ConstRowIterator |
rename the iterators for easier access More... | |
typedef std::remove_reference< const_row_reference >::type::ConstIterator | ConstColIterator |
rename the iterators for easier access More... | |
Public Member Functions | |
row_reference | operator[] (size_type i) |
random access More... | |
const_row_reference | operator[] (size_type i) const |
size_type | size () const |
size method (number of rows) More... | |
Iterator | begin () |
begin iterator More... | |
Iterator | end () |
end iterator More... | |
Iterator | beforeEnd () |
Iterator | beforeBegin () |
ConstIterator | begin () const |
begin iterator More... | |
ConstIterator | end () const |
end iterator More... | |
ConstIterator | beforeEnd () const |
ConstIterator | beforeBegin () const |
template<class RHS , class = std::enable_if_t< HasDenseMatrixAssigner< MAT, RHS >::value >> | |
derived_type & | operator= (const RHS &rhs) |
template<class Other > | |
derived_type & | operator+= (const DenseMatrix< Other > &y) |
vector space addition More... | |
template<class Other > | |
derived_type & | operator-= (const DenseMatrix< Other > &y) |
vector space subtraction More... | |
derived_type & | operator*= (const field_type &k) |
vector space multiplication with scalar More... | |
derived_type & | operator/= (const field_type &k) |
vector space division by scalar More... | |
template<class Other > | |
derived_type & | axpy (const field_type &k, const DenseMatrix< Other > &y) |
vector space axpy operation (*this += k y) More... | |
template<class Other > | |
bool | operator== (const DenseMatrix< Other > &y) const |
Binary matrix comparison. More... | |
template<class Other > | |
bool | operator!= (const DenseMatrix< Other > &y) const |
Binary matrix incomparison. More... | |
template<class X , class Y > | |
void | mv (const X &x, Y &y) const |
y = A x More... | |
template<class X , class Y > | |
void | mtv (const X &x, Y &y) const |
y = A^T x More... | |
template<class X , class Y > | |
void | umv (const X &x, Y &y) const |
y += A x More... | |
template<class X , class Y > | |
void | umtv (const X &x, Y &y) const |
y += A^T x More... | |
template<class X , class Y > | |
void | umhv (const X &x, Y &y) const |
y += A^H x More... | |
template<class X , class Y > | |
void | mmv (const X &x, Y &y) const |
y -= A x More... | |
template<class X , class Y > | |
void | mmtv (const X &x, Y &y) const |
y -= A^T x More... | |
template<class X , class Y > | |
void | mmhv (const X &x, Y &y) const |
y -= A^H x More... | |
template<class X , class Y > | |
void | usmv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const |
y += alpha A x More... | |
template<class X , class Y > | |
void | usmtv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const |
y += alpha A^T x More... | |
template<class X , class Y > | |
void | usmhv (const typename FieldTraits< Y >::field_type &alpha, const X &x, Y &y) const |
y += alpha A^H x More... | |
FieldTraits< value_type >::real_type | frobenius_norm () const |
frobenius norm: sqrt(sum over squared values of entries) More... | |
FieldTraits< value_type >::real_type | frobenius_norm2 () const |
square of frobenius norm, need for block recursion More... | |
template<typename vt = value_type, typename std::enable_if<!has_nan< vt >::value, int >::type = 0> | |
FieldTraits< vt >::real_type | infinity_norm () const |
infinity norm (row sum norm, how to generalize for blocks?) More... | |
template<typename vt = value_type, typename std::enable_if<!has_nan< vt >::value, int >::type = 0> | |
FieldTraits< vt >::real_type | infinity_norm_real () const |
simplified infinity norm (uses Manhattan norm for complex values) More... | |
template<typename vt = value_type, typename std::enable_if< has_nan< vt >::value, int >::type = 0> | |
FieldTraits< vt >::real_type | infinity_norm () const |
infinity norm (row sum norm, how to generalize for blocks?) More... | |
template<typename vt = value_type, typename std::enable_if< has_nan< vt >::value, int >::type = 0> | |
FieldTraits< vt >::real_type | infinity_norm_real () const |
simplified infinity norm (uses Manhattan norm for complex values) More... | |
template<class V > | |
void | solve (V &x, const V &b) const |
Solve system A x = b. More... | |
void | invert () |
Compute inverse. More... | |
field_type | determinant () const |
calculates the determinant of this matrix More... | |
template<typename M2 > | |
MAT & | leftmultiply (const DenseMatrix< M2 > &M) |
Multiplies M from the left to this matrix. More... | |
template<typename M2 > | |
MAT & | rightmultiply (const DenseMatrix< M2 > &M) |
Multiplies M from the right to this matrix. More... | |
size_type | N () const |
number of rows More... | |
size_type | M () const |
number of columns More... | |
size_type | rows () const |
number of rows More... | |
size_type | cols () const |
number of columns More... | |
bool | exists (size_type i, size_type j) const |
return true when (i,j) is in pattern More... | |
A dense n x m matrix.
Matrices represent linear maps from a vector space V to a vector space W. This class represents such a linear map by storing a two-dimensional array of numbers of a given field type K. The number of rows and columns is given at compile time.
MAT | type of the matrix implementation |
typedef Traits::value_type Dune::DenseMatrix< MAT >::block_type |
export the type representing the components
typedef std::remove_reference<row_reference>::type::Iterator Dune::DenseMatrix< MAT >::ColIterator |
rename the iterators for easier access
typedef ConstIterator Dune::DenseMatrix< MAT >::const_iterator |
typedef for stl compliant access
typedef Traits::const_row_reference Dune::DenseMatrix< MAT >::const_row_reference |
The type used to represent a reference to a constant row (usually const row_type &)
typedef std::remove_reference<const_row_reference>::type::ConstIterator Dune::DenseMatrix< MAT >::ConstColIterator |
rename the iterators for easier access
typedef DenseIterator<const DenseMatrix,const row_type,const_row_reference> Dune::DenseMatrix< MAT >::ConstIterator |
Iterator class for sequential access.
typedef ConstIterator Dune::DenseMatrix< MAT >::ConstRowIterator |
rename the iterators for easier access
typedef Traits::derived_type Dune::DenseMatrix< MAT >::derived_type |
type of derived matrix class
typedef Traits::value_type Dune::DenseMatrix< MAT >::field_type |
export the type representing the field
typedef DenseIterator<DenseMatrix,row_type,row_reference> Dune::DenseMatrix< MAT >::Iterator |
Iterator class for sequential access.
typedef Iterator Dune::DenseMatrix< MAT >::iterator |
typedef for stl compliant access
typedef Traits::row_reference Dune::DenseMatrix< MAT >::row_reference |
The type used to represent a reference to a row (usually row_type &)
typedef Traits::row_type Dune::DenseMatrix< MAT >::row_type |
The type used to represent a row (must fulfill the Dune::DenseVector interface)
typedef Iterator Dune::DenseMatrix< MAT >::RowIterator |
rename the iterators for easier access
typedef Traits::size_type Dune::DenseMatrix< MAT >::size_type |
The type used for the index access and size operation.
typedef Traits::value_type Dune::DenseMatrix< MAT >::value_type |
export the type representing the field
anonymous enum |
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vector space axpy operation (*this += k y)
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begin iterator
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begin iterator
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number of columns
field_type Dune::DenseMatrix< MAT >::determinant | ( | ) | const |
calculates the determinant of this matrix
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end iterator
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end iterator
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return true when (i,j) is in pattern
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frobenius norm: sqrt(sum over squared values of entries)
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square of frobenius norm, need for block recursion
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infinity norm (row sum norm, how to generalize for blocks?)
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inline |
infinity norm (row sum norm, how to generalize for blocks?)
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simplified infinity norm (uses Manhattan norm for complex values)
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simplified infinity norm (uses Manhattan norm for complex values)
void Dune::DenseMatrix< MAT >::invert | ( | ) |
Compute inverse.
FMatrixError | if the matrix is singular |
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Multiplies M from the left to this matrix.
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number of columns
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y -= A^H x
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y -= A^T x
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y -= A x
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y = A^T x
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y = A x
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number of rows
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Binary matrix incomparison.
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vector space multiplication with scalar
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vector space addition
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vector space subtraction
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vector space division by scalar
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Binary matrix comparison.
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random access
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Multiplies M from the right to this matrix.
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number of rows
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size method (number of rows)
void Dune::DenseMatrix< MAT >::solve | ( | V & | x, |
const V & | b | ||
) | const |
Solve system A x = b.
FMatrixError | if the matrix is singular |
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y += A^H x
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y += A^T x
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y += A x
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y += alpha A^H x
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y += alpha A^T x
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y += alpha A x