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Reference documentation for deal.II version 8.5.1
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Reference documentation for deal.II version 8.5.1
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#include <deal.II/lac/householder.h>
Public Types | |
| typedef types::global_dof_index | size_type |
Public Member Functions | |
| Householder () | |
| template<typename number2 > | |
| Householder (const FullMatrix< number2 > &) | |
| template<typename number2 > | |
| void | initialize (const FullMatrix< number2 > &) |
| template<typename number2 > | |
| double | least_squares (Vector< number2 > &dst, const Vector< number2 > &src) const |
| template<typename number2 > | |
| double | least_squares (BlockVector< number2 > &dst, const BlockVector< number2 > &src) const |
| template<class VectorType > | |
| void | vmult (VectorType &dst, const VectorType &src) const |
Private Attributes | |
| std::vector< number > | diagonal |
 Private Attributes inherited from TableBase< N, T > | |
| AlignedVector< T > | values |
| TableIndices< N > | table_size |
Additional Inherited Members | |
| Private Types inherited from FullMatrix< number > | |
| typedef unsigned int | size_type |
| typedef number | value_type |
| typedef numbers::NumberTraits< number >::real_type | real_type |
| Private Types inherited from TableBase< N, T > | |
| typedef AlignedVector< T >::size_type | size_type |
| Private Member Functions inherited from FullMatrix< number > | |
| FullMatrix (const size_type n=0) | |
| FullMatrix (const size_type rows, const size_type cols) | |
| FullMatrix (const size_type rows, const size_type cols, const number *entries) | |
| FullMatrix (const IdentityMatrix &id) | |
| template<typename number2 > | |
| FullMatrix< number > & | operator= (const FullMatrix< number2 > &) |
| FullMatrix< number > & | operator= (const number d) |
| FullMatrix< number > & | operator= (const IdentityMatrix &id) |
| template<typename number2 > | |
| FullMatrix< number > & | operator= (const LAPACKFullMatrix< number2 > &) |
| template<typename MatrixType > | |
| void | copy_from (const MatrixType &) |
| template<typename MatrixType > | |
| void | copy_transposed (const MatrixType &) |
| template<int dim> | |
| void | copy_from (const Tensor< 2, dim > &T, const size_type src_r_i=0, const size_type src_r_j=dim-1, const size_type src_c_i=0, const size_type src_c_j=dim-1, const size_type dst_r=0, const size_type dst_c=0) |
| template<int dim> | |
| void | copy_to (Tensor< 2, dim > &T, const size_type src_r_i=0, const size_type src_r_j=dim-1, const size_type src_c_i=0, const size_type src_c_j=dim-1, const size_type dst_r=0, const size_type dst_c=0) const |
| template<typename MatrixType , typename index_type > | |
| void | extract_submatrix_from (const MatrixType &matrix, const std::vector< index_type > &row_index_set, const std::vector< index_type > &column_index_set) |
| template<typename MatrixType , typename index_type > | |
| void | scatter_matrix_to (const std::vector< index_type > &row_index_set, const std::vector< index_type > &column_index_set, MatrixType &matrix) const |
| template<typename number2 > | |
| void | fill (const FullMatrix< number2 > &src, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0) |
| template<typename number2 > | |
| void | fill (const number2 *) |
| template<typename number2 > | |
| void | fill_permutation (const FullMatrix< number2 > &src, const std::vector< size_type > &p_rows, const std::vector< size_type > &p_cols) |
| void | set (const size_type i, const size_type j, const number value) |
| bool | operator== (const FullMatrix< number > &) const |
| size_type | m () const |
| size_type | n () const |
| bool | all_zero () const |
| template<typename number2 > | |
| number2 | matrix_norm_square (const Vector< number2 > &v) const |
| template<typename number2 > | |
| number2 | matrix_scalar_product (const Vector< number2 > &u, const Vector< number2 > &v) const |
| real_type | l1_norm () const |
| real_type | linfty_norm () const |
| real_type | frobenius_norm () const |
| real_type | relative_symmetry_norm2 () const |
| number | determinant () const |
| number | trace () const |
| template<class StreamType > | |
| void | print (StreamType &s, const unsigned int width=5, const unsigned int precision=2) const |
| void | print_formatted (std::ostream &out, const unsigned int precision=3, const bool scientific=true, const unsigned int width=0, const char *zero_string=" ", const double denominator=1., const double threshold=0.) const |
| std::size_t | memory_consumption () const |
| const_iterator | begin () const |
| const_iterator | end () const |
| const_iterator | begin (const size_type r) const |
| const_iterator | end (const size_type r) const |
| FullMatrix & | operator*= (const number factor) |
| FullMatrix & | operator/= (const number factor) |
| template<typename number2 > | |
| void | add (const number a, const FullMatrix< number2 > &A) |
| template<typename number2 > | |
| void | add (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B) |
| template<typename number2 > | |
| void | add (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B, const number c, const FullMatrix< number2 > &C) |
| template<typename number2 > | |
| void | add (const FullMatrix< number2 > &src, const number factor, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0) |
| template<typename number2 > | |
| void | Tadd (const number s, const FullMatrix< number2 > &B) |
| template<typename number2 > | |
| void | Tadd (const FullMatrix< number2 > &src, const number factor, const size_type dst_offset_i=0, const size_type dst_offset_j=0, const size_type src_offset_i=0, const size_type src_offset_j=0) |
| void | add (const size_type row, const size_type column, const number value) |
| template<typename number2 , typename index_type > | |
| void | add (const size_type row, const unsigned int n_cols, const index_type *col_indices, const number2 *values, const bool elide_zero_values=true, const bool col_indices_are_sorted=false) |
| void | add_row (const size_type i, const number s, const size_type j) |
| void | add_row (const size_type i, const number s, const size_type j, const number t, const size_type k) |
| void | add_col (const size_type i, const number s, const size_type j) |
| void | add_col (const size_type i, const number s, const size_type j, const number t, const size_type k) |
| void | swap_row (const size_type i, const size_type j) |
| void | swap_col (const size_type i, const size_type j) |
| void | diagadd (const number s) |
| template<typename number2 > | |
| void | equ (const number a, const FullMatrix< number2 > &A) |
| template<typename number2 > | |
| void | equ (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B) |
| template<typename number2 > | |
| void | equ (const number a, const FullMatrix< number2 > &A, const number b, const FullMatrix< number2 > &B, const number c, const FullMatrix< number2 > &C) |
| void | symmetrize () |
| void | gauss_jordan () |
| template<typename number2 > | |
| void | invert (const FullMatrix< number2 > &M) |
| template<typename number2 > | |
| void | cholesky (const FullMatrix< number2 > &A) |
| template<typename number2 > | |
| void | outer_product (const Vector< number2 > &V, const Vector< number2 > &W) |
| template<typename number2 > | |
| void | left_invert (const FullMatrix< number2 > &M) |
| template<typename number2 > | |
| void | right_invert (const FullMatrix< number2 > &M) |
| template<typename number2 > | |
| void | mmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const |
| template<typename number2 > | |
| void | Tmmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const |
| template<typename number2 > | |
| void | mTmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const |
| template<typename number2 > | |
| void | TmTmult (FullMatrix< number2 > &C, const FullMatrix< number2 > &B, const bool adding=false) const |
| void | triple_product (const FullMatrix< number > &A, const FullMatrix< number > &B, const FullMatrix< number > &D, const bool transpose_B=false, const bool transpose_D=false, const number scaling=number(1.)) |
| template<typename number2 > | |
| void | vmult (Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const |
| template<typename number2 > | |
| void | vmult_add (Vector< number2 > &w, const Vector< number2 > &v) const |
| template<typename number2 > | |
| void | Tvmult (Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const |
| template<typename number2 > | |
| void | Tvmult_add (Vector< number2 > &w, const Vector< number2 > &v) const |
| template<typename somenumber > | |
| void | precondition_Jacobi (Vector< somenumber > &dst, const Vector< somenumber > &src, const number omega=1.) const |
| template<typename number2 , typename number3 > | |
| number | residual (Vector< number2 > &dst, const Vector< number2 > &x, const Vector< number3 > &b) const |
| template<typename number2 > | |
| void | forward (Vector< number2 > &dst, const Vector< number2 > &src) const |
| template<typename number2 > | |
| void | backward (Vector< number2 > &dst, const Vector< number2 > &src) const |
| Private Member Functions inherited from TableBase< N, T > | |
| TableBase () | |
| TableBase (const TableIndices< N > &sizes) | |
| template<typename InputIterator > | |
| TableBase (const TableIndices< N > &sizes, InputIterator entries, const bool C_style_indexing=true) | |
| TableBase (const TableBase< N, T > &src) | |
| template<typename T2 > | |
| TableBase (const TableBase< N, T2 > &src) | |
| TableBase (TableBase< N, T > &&src) | |
| ~TableBase () | |
| TableBase< N, T > & | operator= (const TableBase< N, T > &src) |
| template<typename T2 > | |
| TableBase< N, T > & | operator= (const TableBase< N, T2 > &src) |
| TableBase< N, T > & | operator= (TableBase< N, T > &&src) |
| bool | operator== (const TableBase< N, T > &T2) const |
| void | reset_values () |
| void | reinit (const TableIndices< N > &new_size, const bool omit_default_initialization=false) |
| unsigned int | size (const unsigned int i) const |
| const TableIndices< N > & | size () const |
| size_type | n_elements () const |
| bool | empty () const |
| template<typename InputIterator > | |
| void | fill (InputIterator entries, const bool C_style_indexing=true) |
| void | fill (const T &value) |
| AlignedVector< T >::reference | operator() (const TableIndices< N > &indices) |
| AlignedVector< T >::const_reference | operator() (const TableIndices< N > &indices) const |
| void | swap (TableBase< N, T > &v) |
| std::size_t | memory_consumption () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
| size_type | position (const TableIndices< N > &indices) const |
| AlignedVector< T >::reference | el (const TableIndices< N > &indices) |
| AlignedVector< T >::const_reference | el (const TableIndices< N > &indices) const |
| Private Member Functions inherited from Subscriptor | |
| Subscriptor () | |
| Subscriptor (const Subscriptor &) | |
| Subscriptor (Subscriptor &&) | |
| virtual | ~Subscriptor () |
| Subscriptor & | operator= (const Subscriptor &) |
| Subscriptor & | operator= (Subscriptor &&) |
| void | subscribe (const char *identifier=0) const |
| void | unsubscribe (const char *identifier=0) const |
| unsigned int | n_subscriptions () const |
| void | list_subscribers () const |
| template<class Archive > | |
| void | serialize (Archive &ar, const unsigned int version) |
| Static Private Member Functions inherited from FullMatrix< number > | |
| static ::ExceptionBase & | ExcEmptyMatrix () |
| static ::ExceptionBase & | ExcNotRegular (number arg1) |
| static ::ExceptionBase & | ExcInvalidDestination (size_type arg1, size_type arg2, size_type arg3) |
| static ::ExceptionBase & | ExcSourceEqualsDestination () |
| static ::ExceptionBase & | ExcMatrixNotPositiveDefinite () |
| Static Private Member Functions inherited from Subscriptor | |
| static ::ExceptionBase & | ExcInUse (int arg1, char *arg2, std::string &arg3) |
| static ::ExceptionBase & | ExcNoSubscriber (char *arg1, char *arg2) |
QR-decomposition of a full matrix.
Whenever an object of this class is created, it copies the matrix given and computes its QR-decomposition by Householder algorithm. Then, the function least_squares() can be used to compute the vector x minimizing ||Ax-b|| for a given vector b.
<float> and <double>; others can be generated in application programs (see the section on Template instantiations in the manual).Definition at line 56 of file householder.h.
| typedef types::global_dof_index Householder< number >::size_type |
Declare type of container size.
Definition at line 62 of file householder.h.
| Householder< number >::Householder | ( | ) |
Create an empty object.
| Householder< number >::Householder | ( | const FullMatrix< number2 > & | ) |
Create an object holding the QR-decomposition of a matrix.
| void Householder< number >::initialize | ( | const FullMatrix< number2 > & | ) |
Compute the QR-decomposition of another matrix.
| double Householder< number >::least_squares | ( | Vector< number2 > & | dst, |
| const Vector< number2 > & | src | ||
| ) | const |
Solve the least-squares problem for the right hand side src. The return value is the Euclidean norm of the approximation error.
dst contains the solution of the least squares problem on return.src contains the right hand side b of the least squares problem. It will be changed during the algorithm and is unusable on return. | double Householder< number >::least_squares | ( | BlockVector< number2 > & | dst, |
| const BlockVector< number2 > & | src | ||
| ) | const |
This function does the same as the one for BlockVectors.
| void Householder< number >::vmult | ( | VectorType & | dst, |
| const VectorType & | src | ||
| ) | const |
A wrapper to least_squares(), implementing the standard MatrixType interface.
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private |
Storage for the diagonal elements of the orthogonal transformation.
Definition at line 118 of file householder.h.
1.8.13