Dune Core Modules (unstable)
Matrix and Vector classes that support a block recursive structure capable of representing the natural structure from Finite Element discretisations. More...
Modules | |
Block Recursive Iterative Kernels | |
IO for matrices and vectors. | |
Provides methods for reading and writing matrices and vectors in various formats. | |
Dense Matrix and Vector Template Library | |
Type traits to retrieve the field and the real type of classes. | |
Files | |
file | matrixmatrix.hh |
provides functions for sparse matrix matrix multiplication. | |
file | matrixutils.hh |
Some handy generic functions for ISTL matrices. | |
Classes | |
struct | Dune::CompressionStatistics< size_type > |
Statistics about compression achieved in implicit mode. More... | |
class | Dune::ImplicitMatrixBuilder< M_ > |
A wrapper for uniform access to the BCRSMatrix during and after the build stage in implicit build mode. More... | |
class | Dune::BCRSMatrix< B, A > |
A sparse block matrix with compressed row storage. More... | |
class | Dune::BDMatrix< B, A > |
A block-diagonal matrix. More... | |
class | Dune::BTDMatrix< B, A > |
A block-tridiagonal matrix. More... | |
class | Dune::BlockVector< B, A > |
A vector of blocks with memory management. More... | |
class | Dune::Matrix< T, A > |
A generic dynamic dense matrix. More... | |
struct | Dune::MatMultMatResult< M1, M2 > |
Helper TMP to get the result type of a sparse matrix matrix multiplication ( \(C=A*B\)) More... | |
struct | Dune::TransposedMatMultMatResult< M1, M2 > |
Helper TMP to get the result type of a sparse matrix matrix multiplication ( \(C=A*B\)) More... | |
struct | Dune::CheckIfDiagonalPresent< Matrix, blocklevel, l > |
Check whether the a matrix has diagonal values on blocklevel recursion levels. More... | |
class | Dune::MultiTypeBlockMatrix< FirstRow, Args > |
A Matrix class to support different block types. More... | |
class | Dune::MultiTypeBlockVector< Args > |
A Vector class to support different block types. More... | |
struct | std::tuple_element< i, Dune::MultiTypeBlockVector< Args... > > |
Make std::tuple_element work for MultiTypeBlockVector. More... | |
struct | std::tuple_size< Dune::MultiTypeBlockVector< Args... > > |
Make std::tuple_size work for MultiTypeBlockVector. More... | |
class | Dune::VariableBlockVector< B, A > |
A Vector of blocks with different blocksizes. More... | |
Typedefs | |
using | Dune::MultiTypeBlockVector< Args >::size_type = std::size_t |
Type used for vector sizes. | |
typedef MultiTypeBlockVector< Args... > | Dune::MultiTypeBlockVector< Args >::type |
using | Dune::MultiTypeBlockVector< Args >::field_type = Std::detected_t< std::common_type_t, typename FieldTraits< std::decay_t< Args > >::field_type... > |
The type used for scalars. More... | |
using | Dune::MultiTypeBlockVector< Args >::real_type = Std::detected_t< std::common_type_t, typename FieldTraits< std::decay_t< Args > >::real_type... > |
The type used for real values. More... | |
Functions | |
template<class T , class A , class A1 , class A2 , int n, int m, int k> | |
void | Dune::matMultTransposeMat (BCRSMatrix< FieldMatrix< T, n, k >, A > &res, const BCRSMatrix< FieldMatrix< T, n, m >, A1 > &mat, const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &matt, bool tryHard=false) |
Calculate product of a sparse matrix with a transposed sparse matrices ( \(C=A*B^T\)). More... | |
template<class T , class A , class A1 , class A2 , int n, int m, int k> | |
void | Dune::matMultMat (BCRSMatrix< FieldMatrix< T, n, m >, A > &res, const BCRSMatrix< FieldMatrix< T, n, k >, A1 > &mat, const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &matt, bool tryHard=false) |
Calculate product of two sparse matrices ( \(C=A*B\)). More... | |
template<class T , class A , class A1 , class A2 , int n, int m, int k> | |
void | Dune::transposeMatMultMat (BCRSMatrix< FieldMatrix< T, n, m >, A > &res, const BCRSMatrix< FieldMatrix< T, k, n >, A1 > &mat, const BCRSMatrix< FieldMatrix< T, k, m >, A2 > &matt, bool tryHard=false) |
Calculate product of a transposed sparse matrix with another sparse matrices ( \(C=A^T*B\)). More... | |
template<class M > | |
auto | Dune::countNonZeros (const M &, typename std::enable_if_t< Dune::IsNumber< M >::value > *sfinae=nullptr) |
Get the number of nonzero fields in the matrix. More... | |
static constexpr size_type | Dune::MultiTypeBlockVector< Args >::size () |
Return the number of non-zero vector entries. More... | |
static constexpr size_type | Dune::MultiTypeBlockVector< Args >::N () |
Number of elements. | |
size_type | Dune::MultiTypeBlockVector< Args >::dim () const |
Number of scalar elements. | |
template<size_type index> | |
std::tuple_element< index, TupleType >::type & | Dune::MultiTypeBlockVector< Args >::operator[] (const std::integral_constant< size_type, index > indexVariable) |
Random-access operator. More... | |
template<size_type index> | |
const std::tuple_element< index, TupleType >::type & | Dune::MultiTypeBlockVector< Args >::operator[] (const std::integral_constant< size_type, index > indexVariable) const |
Const random-access operator. More... | |
template<typename T > | |
void | Dune::MultiTypeBlockVector< Args >::operator= (const T &newval) |
Assignment operator. | |
void | Dune::MultiTypeBlockVector< Args >::operator+= (const type &newv) |
void | Dune::MultiTypeBlockVector< Args >::operator-= (const type &newv) |
template<class T , std::enable_if_t< IsNumber< T >::value, int > = 0> | |
void | Dune::MultiTypeBlockVector< Args >::operator*= (const T &w) |
Multiplication with a scalar. | |
template<class T , std::enable_if_t< IsNumber< T >::value, int > = 0> | |
void | Dune::MultiTypeBlockVector< Args >::operator/= (const T &w) |
Division by a scalar. | |
auto | Dune::MultiTypeBlockVector< Args >::one_norm () const |
Compute the 1-norm. | |
auto | Dune::MultiTypeBlockVector< Args >::one_norm_real () const |
Compute the simplified 1-norm (uses 1-norm also for complex values) | |
real_type | Dune::MultiTypeBlockVector< Args >::two_norm2 () const |
Compute the squared Euclidean norm. | |
real_type | Dune::MultiTypeBlockVector< Args >::two_norm () const |
Compute the Euclidean norm. | |
real_type | Dune::MultiTypeBlockVector< Args >::infinity_norm () const |
Compute the maximum norm. | |
real_type | Dune::MultiTypeBlockVector< Args >::infinity_norm_real () const |
Compute the simplified maximum norm (uses 1-norm for complex values) | |
template<typename Ta > | |
void | Dune::MultiTypeBlockVector< Args >::axpy (const Ta &a, const type &y) |
Axpy operation on this vector (*this += a * y) More... | |
template<typename... Args> | |
std::ostream & | Dune::operator<< (std::ostream &s, const MultiTypeBlockVector< Args... > &v) |
Send MultiTypeBlockVector to an outstream. | |
Detailed Description
Matrix and Vector classes that support a block recursive structure capable of representing the natural structure from Finite Element discretisations.
The interface of our matrices is designed according to what they represent from a mathematical point of view. The vector classes are representations of vector spaces:
- FieldVector represents a vector space \(V=K^n\) where the field \(K\) is represented by a numeric type (e.g. double, float, complex). \(n\) is known at compile time.
- BlockVector represents a vector space \(V=W\times W \times W \times\cdots\times W\) where W is itself a vector space.
- VariableBlockVector represents a vector space having a two-level block structure of the form \(V=B^{n_1}\times B^{n_2}\times\ldots \times B^{n_m}\), i.e. it is constructed from \(m\) vector spaces, \(i=1,\ldots,m\).
The matrix classes represent linear maps \(A: V \mapsto W\) from vector space \(V\) to vector space \(W\) the recursive block structure of the matrix rows and columns immediately follows from the recursive block structure of the vectors representing the domain and range of the mapping, respectively:
- FieldMatrix represents a linear map \(M: V_1 \to V_2\) where \(V_1=K^n\) and \(V_2=K^m\) are vector spaces over the same field represented by a numerix type.
- BCRSMatrix represents a linear map \(M: V_1 \to V_2\) where \(V_1=W\times W \times W \times\cdots\times W\) and \(V_2=W\times W \times W \times\cdots\times W\) where W is itself a vector space.
- VariableBCRSMatrix is not yet implemented.
Typedef Documentation
◆ field_type
using Dune::MultiTypeBlockVector< Args >::field_type = Std::detected_t<std::common_type_t, typename FieldTraits< std::decay_t<Args> >::field_type...> |
The type used for scalars.
Use the std::common_type_t
of the Args
' field_type and use nonesuch
if no implementation of std::common_type
is provided for the given field_type
arguments.
◆ real_type
using Dune::MultiTypeBlockVector< Args >::real_type = Std::detected_t<std::common_type_t, typename FieldTraits< std::decay_t<Args> >::real_type...> |
The type used for real values.
Use the std::common_type_t
of the Args
' real_type and use nonesuch
if no implementation of std::common_type
is provided for the given real_type
arguments.
◆ type
typedef MultiTypeBlockVector<Args...> Dune::MultiTypeBlockVector< Args >::type |
own class' type
Function Documentation
◆ axpy()
|
inline |
Axpy operation on this vector (*this += a * y)
- Template Parameters
-
Ta Type of the scalar 'a'
References Dune::Hybrid::forEach(), and Dune::Hybrid::integralRange().
◆ countNonZeros()
|
inline |
Get the number of nonzero fields in the matrix.
This is not the number of nonzero blocks, but the number of non zero scalar entries (on blocklevel 1) if the matrix is viewed as a flat matrix.
For FieldMatrix this is simply the number of columns times the number of rows, for a BCRSMatrix<FieldMatrix<K,n,m>> this is the number of nonzero blocks time n*m.
Referenced by Dune::Amg::MatrixHierarchy< M, PI, A >::build().
◆ matMultMat()
void Dune::matMultMat | ( | BCRSMatrix< FieldMatrix< T, n, m >, A > & | res, |
const BCRSMatrix< FieldMatrix< T, n, k >, A1 > & | mat, | ||
const BCRSMatrix< FieldMatrix< T, k, m >, A2 > & | matt, | ||
bool | tryHard = false |
||
) |
◆ matMultTransposeMat()
void Dune::matMultTransposeMat | ( | BCRSMatrix< FieldMatrix< T, n, k >, A > & | res, |
const BCRSMatrix< FieldMatrix< T, n, m >, A1 > & | mat, | ||
const BCRSMatrix< FieldMatrix< T, k, m >, A2 > & | matt, | ||
bool | tryHard = false |
||
) |
◆ operator+=()
|
inline |
operator for MultiTypeBlockVector += MultiTypeBlockVector operations
References Dune::Hybrid::forEach(), and Dune::Hybrid::integralRange().
◆ operator-=()
|
inline |
operator for MultiTypeBlockVector -= MultiTypeBlockVector operations
References Dune::Hybrid::forEach(), and Dune::Hybrid::integralRange().
◆ operator[]() [1/2]
|
inline |
Random-access operator.
This method mimics the behavior of normal vector access with square brackets like, e.g., v[5] = 1. The problem is that the return type is different for each value of the argument in the brackets. Therefore we implement a trick using std::integral_constant. To access the first entry of a MultiTypeBlockVector named v write
The name '_0' used here as a static replacement of the integer number zero is arbitrary. Any other variable name can be used. If you don't like the separate variable, you can writee
◆ operator[]() [2/2]
|
inline |
Const random-access operator.
This is the const version of the random-access operator. See the non-const version for a full explanation of how to use it.
◆ size()
|
inlinestaticconstexpr |
Return the number of non-zero vector entries.
As this is a dense vector data structure, all entries are non-zero, and hence 'size' returns the same number as 'N'.
◆ transposeMatMultMat()
void Dune::transposeMatMultMat | ( | BCRSMatrix< FieldMatrix< T, n, m >, A > & | res, |
const BCRSMatrix< FieldMatrix< T, k, n >, A1 > & | mat, | ||
const BCRSMatrix< FieldMatrix< T, k, m >, A2 > & | matt, | ||
bool | tryHard = false |
||
) |
Calculate product of a transposed sparse matrix with another sparse matrices ( \(C=A^T*B\)).
- Parameters
-
res Matrix for the result of the computation. mat Matrix A, which will be transposed before the multiplication. matt Matrix B. tryHard ignored
Referenced by MatrixInfo< BCRSMatrix >::computeNonSymCond2().