Reference documentation for deal.II version Git d132f0c 2017-03-23 19:35:29 -0400
Classes | Public Types | Static Public Member Functions | List of all members
FullMatrix< number > Class Template Reference

#include <deal.II/lac/full_matrix.h>

Inheritance diagram for FullMatrix< number >:
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Classes

class  Accessor
 
class  const_iterator
 

Public Types

typedef unsigned int size_type
 
typedef number value_type
 
typedef numbers::NumberTraits< number >::real_type real_type
 
- Public Types inherited from TableBase< N, T >
typedef AlignedVector< T >::size_type size_type
 

Public Member Functions

Constructors and initalization. See also the base class Table.
 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)
 
Copying into and out of other matrices
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)
 
Non-modifying operators
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
 
Iterator functions
const_iterator begin () const
 
const_iterator end () const
 
const_iterator begin (const size_type r) const
 
const_iterator end (const size_type r) const
 
Modifying operators
FullMatrixoperator*= (const number factor)
 
FullMatrixoperator/= (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)
 
Multiplications
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
 
- Public 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)
 
- Public Member Functions inherited from Subscriptor
 Subscriptor ()
 
 Subscriptor (const Subscriptor &)
 
 Subscriptor (Subscriptor &&)
 
virtual ~Subscriptor ()
 
Subscriptoroperator= (const Subscriptor &)
 
Subscriptoroperator= (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 Public Member Functions

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 Public Member Functions inherited from Subscriptor
static::ExceptionBase & ExcInUse (int arg1, char *arg2, std::string &arg3)
 
static::ExceptionBase & ExcNoSubscriber (char *arg1, char *arg2)
 

Additional Inherited Members

- Protected Member Functions inherited from TableBase< N, T >
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
 
- Protected Attributes inherited from TableBase< N, T >
AlignedVector< T > values
 
TableIndices< N > table_size
 

Detailed Description

template<typename number>
class FullMatrix< number >

Implementation of a classical rectangular scheme of numbers. The data type of the entries is provided in the template argument number. The interface is quite fat and in fact has grown every time a new feature was needed. So, a lot of functions are provided.

Internal calculations are usually done with the accuracy of the vector argument to functions. If there is no argument with a number type, the matrix number type is used.

Note
Instantiations for this template are provided for <float>, <double>, <std::complex<float>>, <std::complex<double>>. Others can be generated in application programs, see Template instantiations for details.
Author
Guido Kanschat, Franz-Theo Suttmeier, Wolfgang Bangerth, 1993-2004

Definition at line 29 of file dof_accessor.h.

Member Typedef Documentation

template<typename number>
typedef unsigned int FullMatrix< number >::size_type

A type of used to index into this container. Because we can not expect to store matrices bigger than what can be indexed by a regular unsigned integer, unsigned int is completely sufficient as an index type.

Definition at line 73 of file full_matrix.h.

template<typename number>
typedef number FullMatrix< number >::value_type

Type of matrix entries. This typedef is analogous to value_type in the standard library containers.

Definition at line 79 of file full_matrix.h.

template<typename number>
typedef numbers::NumberTraits<number>::real_type FullMatrix< number >::real_type

Declare a type that has holds real-valued numbers with the same precision as the template argument to this class. If the template argument of this class is a real data type, then real_type equals the template argument. If the template argument is a std::complex type then real_type equals the type underlying the complex numbers.

This typedef is used to represent the return type of norms.

Definition at line 91 of file full_matrix.h.

Constructor & Destructor Documentation

template<typename number>
FullMatrix< number >::FullMatrix ( const size_type  n = 0)
explicit

Constructor. Initialize the matrix as a square matrix with dimension n.

In order to avoid the implicit conversion of integers and other types to a matrix, this constructor is declared explicit.

By default, no memory is allocated.

template<typename number>
FullMatrix< number >::FullMatrix ( const size_type  rows,
const size_type  cols 
)

Constructor. Initialize the matrix as a rectangular matrix.

template<typename number>
FullMatrix< number >::FullMatrix ( const size_type  rows,
const size_type  cols,
const number *  entries 
)

Constructor initializing from an array of numbers. The array is arranged line by line. No range checking is performed.

template<typename number>
FullMatrix< number >::FullMatrix ( const IdentityMatrix id)

Construct a full matrix that equals the identity matrix of the size of the argument. Using this constructor, one can easily create an identity matrix of size n by saying

Member Function Documentation

template<typename number>
template<typename number2 >
FullMatrix<number>& FullMatrix< number >::operator= ( const FullMatrix< number2 > &  )

Variable assignment operator.

template<typename number>
FullMatrix<number>& FullMatrix< number >::operator= ( const number  d)

This operator assigns a scalar to a matrix. To avoid confusion with the semantics of this function, zero is the only value allowed for d, allowing you to clear a matrix in an intuitive way.

Note
If deal.II is configured with threads, this operation will run multi-threaded by splitting the work into smaller chunks (assuming there is enough work to make this worthwhile).
template<typename number>
FullMatrix<number>& FullMatrix< number >::operator= ( const IdentityMatrix id)

Copy operator to create a full matrix that equals the identity matrix of the size of the argument. This way, one can easily create an identity matrix of size n by saying

template<typename number>
template<typename number2 >
FullMatrix<number>& FullMatrix< number >::operator= ( const LAPACKFullMatrix< number2 > &  )

Assignment operator for a LapackFullMatrix. The calling matrix must be of the same size as the LAPACK matrix.

template<typename number>
template<typename MatrixType >
void FullMatrix< number >::copy_from ( const MatrixType &  )

Assignment from different matrix classes. This assignment operator uses iterators of the typename MatrixType. Therefore, sparse matrices are possible sources.

template<typename number>
template<typename MatrixType >
void FullMatrix< number >::copy_transposed ( const MatrixType &  )

Transposing assignment from different matrix classes. This assignment operator uses iterators of the typename MatrixType. Therefore, sparse matrices are possible sources.

template<typename number>
template<int dim>
void FullMatrix< number >::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 
)

Fill matrix with elements extracted from a tensor, taking rows included between r_i and r_j and columns between c_i and c_j. The resulting matrix is then inserted in the destination matrix at position (dst_r, dst_c) Checks on the indices are made.

template<typename number>
template<int dim>
void FullMatrix< number >::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

Insert a submatrix (also rectangular) into a tensor, putting its upper left element at the specified position (dst_r, dst_c) and the other elements consequently. Default values are chosen so that no parameter needs to be specified if the size of the tensor and that of the matrix coincide.

template<typename number>
template<typename MatrixType , typename index_type >
void FullMatrix< number >::extract_submatrix_from ( const MatrixType &  matrix,
const std::vector< index_type > &  row_index_set,
const std::vector< index_type > &  column_index_set 
)

Copy a subset of the rows and columns of another matrix into the current object.

Parameters
matrixThe matrix from which a subset is to be taken from.
row_index_setThe set of rows of matrix from which to extract.
column_index_setThe set of columns of matrix from which to extract.
Precondition
The number of elements in row_index_set and column_index_set shall be equal to the number of rows and columns in the current object. In other words, the current object is not resized for this operation.
template<typename number>
template<typename MatrixType , typename index_type >
void FullMatrix< number >::scatter_matrix_to ( const std::vector< index_type > &  row_index_set,
const std::vector< index_type > &  column_index_set,
MatrixType &  matrix 
) const

Copy the elements of the current matrix object into a specified set of rows and columns of another matrix. Thus, this is a scatter operation.

Parameters
row_index_setThe rows of matrix into which to write.
column_index_setThe columns of matrix into which to write.
matrixThe matrix within which certain elements are to be replaced.
Precondition
The number of elements in row_index_set and column_index_set shall be equal to the number of rows and columns in the current object. In other words, the current object is not resized for this operation.
template<typename number>
template<typename number2 >
void FullMatrix< number >::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 
)

Fill rectangular block.

A rectangular block of the matrix src is copied into this. The upper left corner of the block being copied is (src_offset_i,src_offset_j). The upper left corner of the copied block is (dst_offset_i,dst_offset_j). The size of the rectangular block being copied is the maximum size possible, determined either by the size of this or src.

template<typename number>
template<typename number2 >
void FullMatrix< number >::fill ( const number2 *  )

Make function of base class available.

template<typename number>
template<typename number2 >
void FullMatrix< number >::fill_permutation ( const FullMatrix< number2 > &  src,
const std::vector< size_type > &  p_rows,
const std::vector< size_type > &  p_cols 
)

Fill with permutation of another matrix.

The matrix src is copied into the target. The two permutation p_r and p_c operate in a way, such that result(i,j) = src(p_r[i], p_c[j]).

The vectors may also be a selection from a larger set of integers, if the matrix src is bigger. It is also possible to duplicate rows or columns by this method.

template<typename number>
void FullMatrix< number >::set ( const size_type  i,
const size_type  j,
const number  value 
)

Set a particular entry of the matrix to a value. Thus, calling A.set(1,2,3.141); is entirely equivalent to the operation A(1,2) = 3.141;. This function exists for compatibility with the various sparse matrix objects.

Parameters
iThe row index of the element to be set.
jThe columns index of the element to be set.
valueThe value to be written into the element.
template<typename number>
bool FullMatrix< number >::operator== ( const FullMatrix< number > &  ) const

Comparison operator. Be careful with this thing, it may eat up huge amounts of computing time! It is most commonly used for internal consistency checks of programs.

template<typename number>
size_type FullMatrix< number >::m ( ) const

Number of rows of this matrix. Note that the matrix is of dimension m x n.

template<typename number>
size_type FullMatrix< number >::n ( ) const

Number of columns of this matrix. Note that the matrix is of dimension m x n.

template<typename number>
bool FullMatrix< number >::all_zero ( ) const

Return whether the matrix contains only elements with value zero. This function is mainly for internal consistency checks and should seldom be used when not in debug mode since it uses quite some time.

template<typename number>
template<typename number2 >
number2 FullMatrix< number >::matrix_norm_square ( const Vector< number2 > &  v) const

Return the square of the norm of the vector v induced by this matrix, i.e. (v,Mv). This is useful, e.g. in the finite element context, where the L2 norm of a function equals the matrix norm with respect to the mass matrix of the vector representing the nodal values of the finite element function.

Obviously, the matrix needs to be quadratic for this operation, and for the result to actually be a norm it also needs to be either real symmetric or complex hermitian.

The underlying template types of both this matrix and the given vector should either both be real or complex-valued, but not mixed, for this function to make sense.

template<typename number>
template<typename number2 >
number2 FullMatrix< number >::matrix_scalar_product ( const Vector< number2 > &  u,
const Vector< number2 > &  v 
) const

Build the matrix scalar product uT M v. This function is mostly useful when building the cellwise scalar product of two functions in the finite element context.

The underlying template types of both this matrix and the given vector should either both be real or complex-valued, but not mixed, for this function to make sense.

template<typename number>
real_type FullMatrix< number >::l1_norm ( ) const

Return the l1-norm of the matrix, where \(||M||_1 = \max_j \sum_i |M_{ij}|\) (maximum of the sums over columns).

template<typename number>
real_type FullMatrix< number >::linfty_norm ( ) const

Return the \(l_\infty\)-norm of the matrix, where \(||M||_\infty = \max_i \sum_j |M_{ij}|\) (maximum of the sums over rows).

template<typename number>
real_type FullMatrix< number >::frobenius_norm ( ) const

Compute the Frobenius norm of the matrix. Return value is the root of the square sum of all matrix entries.

Note
For the timid among us: this norm is not the norm compatible with the l2-norm of the vector space.
template<typename number>
real_type FullMatrix< number >::relative_symmetry_norm2 ( ) const

Compute the relative norm of the skew-symmetric part. The return value is the Frobenius norm of the skew-symmetric part of the matrix divided by that of the matrix.

Main purpose of this function is to check, if a matrix is symmetric within a certain accuracy, or not.

template<typename number>
number FullMatrix< number >::determinant ( ) const

Compute the determinant of a matrix. This is only implemented for one, two, and three dimensions, since for higher dimensions the numerical work explodes. Obviously, the matrix needs to be quadratic for this function.

template<typename number>
number FullMatrix< number >::trace ( ) const

Return the trace of the matrix, i.e. the sum of the diagonal values (which happens to also equal the sum of the eigenvalues of a matrix). Obviously, the matrix needs to be quadratic for this function.

template<typename number>
template<class StreamType >
void FullMatrix< number >::print ( StreamType &  s,
const unsigned int  width = 5,
const unsigned int  precision = 2 
) const

Output of the matrix in user-defined format given by the specified precision and width. This function saves width and precision of the stream before setting these given values for output, and restores the previous values after output.

template<typename number>
void FullMatrix< number >::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

Print the matrix and allow formatting of entries.

The parameters allow for a flexible setting of the output format:

  • precision denotes the number of trailing digits.
  • scientific is used to determine the number format, where scientific = false means fixed point notation.
  • width denotes the with of each column. A zero entry for width makes the function compute a width, but it may be changed to a positive value, if output is crude.
  • zero_string specifies a string printed for zero entries.
  • denominator Multiply the whole matrix by this common denominator to get nicer numbers.
  • threshold: all entries with absolute value smaller than this are considered zero.
template<typename number>
std::size_t FullMatrix< number >::memory_consumption ( ) const

Determine an estimate for the memory consumption (in bytes) of this object.

template<typename number>
const_iterator FullMatrix< number >::begin ( ) const

Iterator starting at the first entry.

template<typename number>
const_iterator FullMatrix< number >::end ( ) const

Final iterator.

template<typename number>
const_iterator FullMatrix< number >::begin ( const size_type  r) const

Iterator starting at the first entry of row r.

template<typename number>
const_iterator FullMatrix< number >::end ( const size_type  r) const

Final iterator of row r.

template<typename number>
FullMatrix& FullMatrix< number >::operator*= ( const number  factor)

Scale the entire matrix by a fixed factor.

template<typename number>
FullMatrix& FullMatrix< number >::operator/= ( const number  factor)

Scale the entire matrix by the inverse of the given factor.

template<typename number>
template<typename number2 >
void FullMatrix< number >::add ( const number  a,
const FullMatrix< number2 > &  A 
)

Simple addition of a scaled matrix, i.e. *this += a*A.

The matrix A may be a full matrix over an arbitrary underlying scalar type, as long as its data type is convertible to the data type of this matrix.

template<typename number>
template<typename number2 >
void FullMatrix< number >::add ( const number  a,
const FullMatrix< number2 > &  A,
const number  b,
const FullMatrix< number2 > &  B 
)

Multiple addition of scaled matrices, i.e. *this += a*A + b*B.

The matrices A and B may be a full matrix over an arbitrary underlying scalar type, as long as its data type is convertible to the data type of this matrix.

template<typename number>
template<typename number2 >
void FullMatrix< number >::add ( const number  a,
const FullMatrix< number2 > &  A,
const number  b,
const FullMatrix< number2 > &  B,
const number  c,
const FullMatrix< number2 > &  C 
)

Multiple addition of scaled matrices, i.e. *this += a*A + b*B + c*C.

The matrices A, B and C may be a full matrix over an arbitrary underlying scalar type, as long as its data type is convertible to the data type of this matrix.

template<typename number>
template<typename number2 >
void FullMatrix< number >::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 
)

Add rectangular block.

A rectangular block of the matrix src is added to this. The upper left corner of the block being copied is (src_offset_i,src_offset_j). The upper left corner of the copied block is (dst_offset_i,dst_offset_j). The size of the rectangular block being copied is the maximum size possible, determined either by the size of this or src and the given offsets.

template<typename number>
template<typename number2 >
void FullMatrix< number >::Tadd ( const number  s,
const FullMatrix< number2 > &  B 
)

Weighted addition of the transpose of B to this.

A += s BT

template<typename number>
template<typename number2 >
void FullMatrix< number >::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 
)

Add transpose of a rectangular block.

A rectangular block of the matrix src is transposed and addedadded to this. The upper left corner of the block being copied is (src_offset_i,src_offset_j) in the coordinates of the non-transposed matrix. The upper left corner of the copied block is (dst_offset_i,dst_offset_j). The size of the rectangular block being copied is the maximum size possible, determined either by the size of this or src.

template<typename number>
void FullMatrix< number >::add ( const size_type  row,
const size_type  column,
const number  value 
)

Add a single element at the given position.

template<typename number>
template<typename number2 , typename index_type >
void FullMatrix< number >::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 
)

Add an array of values given by values in the given global matrix row at columns specified by col_indices in the full matrix. This function is present for compatibility with the various sparse matrices in deal.II. In particular, the two boolean fields elide_zero_values and col_indices_are_sorted do not impact the performance of this routine, as opposed to the sparse matrix case and are indeed ignored in the implementation.

template<typename number>
void FullMatrix< number >::add_row ( const size_type  i,
const number  s,
const size_type  j 
)

A(i,1...n) += s*A(j,1...n). Simple addition of rows of this

template<typename number>
void FullMatrix< number >::add_row ( const size_type  i,
const number  s,
const size_type  j,
const number  t,
const size_type  k 
)

A(i,1...n) += s*A(j,1...n) + t*A(k,1...n). Multiple addition of rows of this.

template<typename number>
void FullMatrix< number >::add_col ( const size_type  i,
const number  s,
const size_type  j 
)

A(1...n,i) += s*A(1...n,j). Simple addition of columns of this.

template<typename number>
void FullMatrix< number >::add_col ( const size_type  i,
const number  s,
const size_type  j,
const number  t,
const size_type  k 
)

A(1...n,i) += s*A(1...n,j) + t*A(1...n,k). Multiple addition of columns of this.

template<typename number>
void FullMatrix< number >::swap_row ( const size_type  i,
const size_type  j 
)

Swap A(i,1...n) <-> A(j,1...n). Swap rows i and j of this

template<typename number>
void FullMatrix< number >::swap_col ( const size_type  i,
const size_type  j 
)

Swap A(1...n,i) <-> A(1...n,j). Swap columns i and j of this

template<typename number>
void FullMatrix< number >::diagadd ( const number  s)

Add constant to diagonal elements of this, i.e. add a multiple of the identity matrix.

template<typename number>
template<typename number2 >
void FullMatrix< number >::equ ( const number  a,
const FullMatrix< number2 > &  A 
)

Assignment *this = a*A.

template<typename number>
template<typename number2 >
void FullMatrix< number >::equ ( const number  a,
const FullMatrix< number2 > &  A,
const number  b,
const FullMatrix< number2 > &  B 
)

Assignment *this = a*A + b*B.

template<typename number>
template<typename number2 >
void FullMatrix< number >::equ ( const number  a,
const FullMatrix< number2 > &  A,
const number  b,
const FullMatrix< number2 > &  B,
const number  c,
const FullMatrix< number2 > &  C 
)

Assignment *this = a*A + b*B + c*C.

template<typename number>
void FullMatrix< number >::symmetrize ( )

Symmetrize the matrix by forming the mean value between the existing matrix and its transpose, A = 1/2(A+AT).

Obviously the matrix must be quadratic for this operation.

template<typename number>
void FullMatrix< number >::gauss_jordan ( )

A=Inverse(A). A must be a square matrix. Inversion of this matrix by Gauss-Jordan algorithm with partial pivoting. This process is well- behaved for positive definite matrices, but be aware of round-off errors in the indefinite case.

In case deal.II was configured with LAPACK, the functions Xgetrf and Xgetri build an LU factorization and invert the matrix upon that factorization, providing best performance up to matrices with a few hundreds rows and columns.

The numerical effort to invert an n x n matrix is of the order n**3.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::invert< long double > ( const FullMatrix< number2 > &  M)

Assign the inverse of the given matrix to *this. This function is hardcoded for quadratic matrices of dimension one to four. However, since the amount of code needed grows quickly, the method gauss_jordan() is invoked implicitly if the dimension is larger.

template<typename number>
template<typename number2 >
void FullMatrix< number >::cholesky ( const FullMatrix< number2 > &  A)

Assign the Cholesky decomposition of the given matrix to *this. The given matrix must be symmetric positive definite.

ExcMatrixNotPositiveDefinite will be thrown in the case that the matrix is not positive definite.

template<typename number>
template<typename number2 >
void FullMatrix< number >::outer_product ( const Vector< number2 > &  V,
const Vector< number2 > &  W 
)

*this(i,j) = \(V(i) W(j)\) where \(V,W\) are vectors of the same length.

template<typename number>
template<typename number2 >
void FullMatrix< number >::left_invert ( const FullMatrix< number2 > &  M)

Assign the left_inverse of the given matrix to *this. The calculation being performed is (AT*A)-1 *AT.

template<typename number>
template<typename number2 >
void FullMatrix< number >::right_invert ( const FullMatrix< number2 > &  M)

Assign the right_inverse of the given matrix to *this. The calculation being performed is AT*(A*AT) -1.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::mmult< long double > ( FullMatrix< number2 > &  C,
const FullMatrix< number2 > &  B,
const bool  adding = false 
) const

Matrix-matrix-multiplication.

The optional parameter adding determines, whether the result is stored in C or added to C.

if (adding) C += A*B

if (!adding) C = A*B

Assumes that A and B have compatible sizes and that C already has the right size.

This function uses the BLAS function Xgemm if the product of the three matrix dimensions is larger than 300 and BLAS was detected during configuration. Using BLAS usually results in considerable performance gains.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::Tmmult< long double > ( FullMatrix< number2 > &  C,
const FullMatrix< number2 > &  B,
const bool  adding = false 
) const

Matrix-matrix-multiplication using transpose of this.

The optional parameter adding determines, whether the result is stored in C or added to C.

if (adding) C += AT*B

if (!adding) C = AT*B

Assumes that A and B have compatible sizes and that C already has the right size.

This function uses the BLAS function Xgemm if the product of the three matrix dimensions is larger than 300 and BLAS was detected during configuration. Using BLAS usually results in considerable performance gains.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::mTmult< long double > ( FullMatrix< number2 > &  C,
const FullMatrix< number2 > &  B,
const bool  adding = false 
) const

Matrix-matrix-multiplication using transpose of B.

The optional parameter adding determines, whether the result is stored in C or added to C.

if (adding) C += A*BT

if (!adding) C = A*BT

Assumes that A and B have compatible sizes and that C already has the right size.

This function uses the BLAS function Xgemm if the product of the three matrix dimensions is larger than 300 and BLAS was detected during configuration. Using BLAS usually results in considerable performance gains.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::TmTmult< long double > ( FullMatrix< number2 > &  C,
const FullMatrix< number2 > &  B,
const bool  adding = false 
) const

Matrix-matrix-multiplication using transpose of this and B.

The optional parameter adding determines, whether the result is stored in C or added to C.

if (adding) C += AT*BT

if (!adding) C = AT*BT

Assumes that A and B have compatible sizes and that C already has the right size.

This function uses the BLAS function Xgemm if the product of the three matrix dimensions is larger than 300 and BLAS was detected during configuration. Using BLAS usually results in considerable performance gains.

template<typename number>
void FullMatrix< number >::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.) 
)

Add to the current matrix the triple product B A D. Optionally, use the transposes of the matrices B and D. The scaling factor scales the whole product, which is helpful when adding a multiple of the triple product to the matrix.

This product was written with the Schur complement BT A-1 D in mind. Note that in this case the argument for A must be the inverse of the matrix A.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::vmult< long double > ( Vector< number2 > &  w,
const Vector< number2 > &  v,
const bool  adding = false 
) const

Matrix-vector-multiplication.

The optional parameter adding determines, whether the result is stored in w or added to w.

if (adding) w += A*v

if (!adding) w = A*v

Source and destination must not be the same vector.

template<typename number>
template<typename number2 >
void FullMatrix< number >::vmult_add ( Vector< number2 > &  w,
const Vector< number2 > &  v 
) const

Adding Matrix-vector-multiplication. w += A*v

Source and destination must not be the same vector.

template<typename number>
template<typename number2 >
template void FullMatrix< number >::Tvmult< long double > ( Vector< number2 > &  w,
const Vector< number2 > &  v,
const bool  adding = false 
) const

Transpose matrix-vector-multiplication.

The optional parameter adding determines, whether the result is stored in w or added to w.

if (adding) w += AT*v

if (!adding) w = AT*v

Source and destination must not be the same vector.

template<typename number>
template<typename number2 >
void FullMatrix< number >::Tvmult_add ( Vector< number2 > &  w,
const Vector< number2 > &  v 
) const

Adding transpose matrix-vector-multiplication. w += AT*v

Source and destination must not be the same vector.

template<typename number>
template<typename somenumber >
void FullMatrix< number >::precondition_Jacobi ( Vector< somenumber > &  dst,
const Vector< somenumber > &  src,
const number  omega = 1. 
) const

Apply the Jacobi preconditioner, which multiplies every element of the src vector by the inverse of the respective diagonal element and multiplies the result with the damping factor omega.

template<typename number>
template<typename number2 , typename number3 >
number FullMatrix< number >::residual ( Vector< number2 > &  dst,
const Vector< number2 > &  x,
const Vector< number3 > &  b 
) const

dst=b-A*x. Residual calculation, returns the l2-norm |dst|.

Source x and destination dst must not be the same vector.

template<typename number>
template<typename number2 >
void FullMatrix< number >::forward ( Vector< number2 > &  dst,
const Vector< number2 > &  src 
) const

Forward elimination of lower triangle. Inverts the lower triangle of a rectangular matrix for a given right hand side.

If the matrix has more columns than rows, this function only operates on the left quadratic submatrix. If there are more rows, the upper quadratic part of the matrix is considered.

Note
It is safe to use the same object for dst and src.
template<typename number>
template<typename number2 >
void FullMatrix< number >::backward ( Vector< number2 > &  dst,
const Vector< number2 > &  src 
) const

Backward elimination of upper triangle.

See forward()

Note
It is safe to use the same object for dst and src.

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