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

Inheritance diagram for FullMatrix< number >:

[legend]

Public Types
using	size_type = std::size_t

using	value_type = number

using	iterator = typename Table< 2, number >::iterator

using	const_iterator = typename Table< 2, number >::const_iterator

using	real_type = typename numbers::NumberTraits< number >::real_type

Public Member Functions
Constructors and initialization. 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 unsigned int src_r_i=0, const unsigned int src_r_j=dim - 1, const unsigned int src_c_i=0, const unsigned int 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 unsigned int dst_r=0, const unsigned int 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<typename 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 char separator=" ") const

std::size_t	memory_consumption () const

Iterator functions
iterator	begin (const size_type r)

iterator	end (const size_type r)

const_iterator	begin (const size_type r) const

const_iterator	end (const size_type r) const

Modifying operators
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 size_type 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

void	compress (VectorOperation::values)

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 ()

Detailed Description

template<typename number>
class FullMatrix< number >

This class implements a rectangular, dense ("full") matrix, that is, a matrix where we store every element whether it is zero or nonzero. This is in contrast to the SparseMatrix and related classes, which store a "sparse" representation in which memory is only allocated for those elements for which it is known that they are (or, more precisely, could be) nonzero.

The data type of the entries of the matrix is provided by the template argument number.

This class provides a number of operations that involve both the current matrix and either another matrix or one or more vectors. Each of these other objects may store their elements in a different data type than the current object does (again, as indicated by the corresponding template arguments of the other objects). In these cases, internal calculations are usually done with the accuracy of the vector argument, or with the more accurate of the data types.

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.

Definition at line 78 of file full_matrix.h.

Member Typedef Documentation

◆ size_type

template<typename number >

using FullMatrix< number >::size_type = std::size_t

This class only supports basic numeric types (i.e., we support double and float but not automatically differentiated numbers).

Note: we test real_type here to get the underlying scalar type when using std::complex. A type of used to index into this container.

Definition at line 97 of file full_matrix.h.

◆ value_type

template<typename number >

using FullMatrix< number >::value_type = number

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

Definition at line 103 of file full_matrix.h.

◆ iterator

template<typename number >

using FullMatrix< number >::iterator = typename Table<2, number>::iterator

Use the base class mutable iterator type.

Definition at line 108 of file full_matrix.h.

◆ const_iterator

template<typename number >

using FullMatrix< number >::const_iterator = typename Table<2, number>::const_iterator

Use the base class constant iterator type.

Definition at line 113 of file full_matrix.h.

◆ real_type

template<typename number >

using FullMatrix< number >::real_type = typename numbers::NumberTraits<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 alias is used to represent the return type of norms.

Definition at line 134 of file full_matrix.h.

Constructor & Destructor Documentation

◆ FullMatrix() [1/4]

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.

◆ FullMatrix() [2/4]

template<typename number >

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

Constructor. Initialize the matrix as a rectangular matrix.

◆ FullMatrix() [3/4]

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.

◆ FullMatrix() [4/4]

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

FullMatrix<double> M(IdentityMatrix(n));

FullMatrix

Definition full_matrix.h:79

FullMatrix::n

size_type n() const

IdentityMatrix

Definition identity_matrix.h:69

Member Function Documentation

◆ operator=() [1/4]

template<typename number >

template<typename number2 >

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

Variable assignment operator.

◆ operator=() [2/4]

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).

◆ operator=() [3/4]

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

M = IdentityMatrix(n);

◆ operator=() [4/4]

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.

◆ copy_from() [1/2]

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.

◆ copy_transposed()

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.

◆ copy_from() [2/2]

template<typename number >

template<int dim>

void FullMatrix< number >::copy_from	(	const Tensor< 2, dim > &	T,
		const unsigned int	src_r_i = `0`,
		const unsigned int	src_r_j = `dim - 1`,
		const unsigned int	src_c_i = `0`,
		const unsigned int	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.

◆ copy_to()

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 unsigned int	dst_r = `0`,
		const unsigned int	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.

◆ extract_submatrix_from()

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

matrix	The matrix from which a subset is to be taken from.
row_index_set	The set of rows of `matrix` from which to extract.
column_index_set	The 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.

◆ scatter_matrix_to()

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_set	The rows of `matrix` into which to write.
column_index_set	The columns of `matrix` into which to write.
matrix	The 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.

◆ fill() [1/2]

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.

◆ fill() [2/2]

template<typename number >

template<typename number2 >

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

Make function of base class available.

◆ fill_permutation()

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.

◆ set()

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

i	The row index of the element to be set.
j	The columns index of the element to be set.
value	The value to be written into the element.

◆ operator==()

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.

◆ m()

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.

◆ 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.

◆ all_zero()

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.

◆ matrix_norm_square()

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.

◆ matrix_scalar_product()

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 u^T 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.

◆ l1_norm()

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).

◆ linfty_norm()

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).

◆ frobenius_norm()

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.

◆ relative_symmetry_norm2()

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.

◆ determinant()

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.

◆ trace()

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.

◆ print()

template<typename number >

template<typename 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.

◆ print_formatted()

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 char *	separator = `" "`
	)		const

Print the matrix and allow formatting of entries.

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

Parameters

out	This specifies the stream to write to.
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.
separator	specifies a string printed to separate row entries.

◆ memory_consumption()

template<typename number >

std::size_t FullMatrix< number >::memory_consumption ( ) const

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

◆ begin() [1/2]

template<typename number >

iterator FullMatrix< number >::begin ( const size_type r )

Mutable iterator starting at the first entry of row r.

◆ end() [1/2]

template<typename number >

iterator FullMatrix< number >::end ( const size_type r )

One past the end mutable iterator of row r.

◆ begin() [2/2]

template<typename number >

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

Constant iterator starting at the first entry of row r.

◆ end() [2/2]

template<typename number >

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

One past the end constant iterator of row r.

◆ operator*=()

template<typename number >

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

Scale the entire matrix by a fixed factor.

◆ operator/=()

template<typename number >

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

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

◆ add() [1/6]

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.

◆ add() [2/6]

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.

◆ add() [3/6]

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.

◆ add() [4/6]

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.

◆ Tadd() [1/2]

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 B^T

◆ Tadd() [2/2]

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.

◆ add() [5/6]

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.

◆ add() [6/6]

template<typename number >

template<typename number2 , typename index_type >

void FullMatrix< number >::add	(	const size_type	row,
		const size_type	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.

◆ add_row() [1/2]

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

◆ add_row() [2/2]

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.

◆ add_col() [1/2]

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.

◆ add_col() [2/2]

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.

◆ swap_row()

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

◆ swap_col()

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

◆ diagadd()

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.

◆ equ() [1/3]

template<typename number >

template<typename number2 >

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

Assignment *this = a*A.

◆ equ() [2/3]

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.

◆ equ() [3/3]

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.

◆ symmetrize()

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+A^T).

Obviously the matrix must be quadratic for this operation.

◆ gauss_jordan()

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 \(n \times n\) matrix is of the order \(n^3\).

◆ invert()

template<typename number >

template<typename number2 >

void FullMatrix< number >::invert ( 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.

◆ cholesky()

template<typename number >

template<typename number2 >

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

Assign the Cholesky decomposition \(A=:L L^T\) of the given matrix \(A\) to *this, where \(L\) is lower triangular matrix. The given matrix must be symmetric positive definite.

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

◆ outer_product()

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.

◆ left_invert()

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 (A^T*A)^-1 *A^T.

◆ right_invert()

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 A^T*(A*A^T) ^-1.

◆ mmult()

template<typename number >

template<typename number2 >

void FullMatrix< number >::mmult	(	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.

◆ Tmmult()

template<typename number >

template<typename number2 >

void FullMatrix< number >::Tmmult	(	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 += A^T*B

if (!adding) C = A^T*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.

◆ mTmult()

template<typename number >

template<typename number2 >

void FullMatrix< number >::mTmult	(	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*B^T

if (!adding) C = A*B^T

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.

◆ TmTmult()

template<typename number >

template<typename number2 >

void FullMatrix< number >::TmTmult	(	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 += A^T*B^T

if (!adding) C = A^T*B^T

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.

◆ triple_product()

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 B^T A^-1 D in mind. Note that in this case the argument for A must be the inverse of the matrix A.

◆ vmult()

template<typename number >

template<typename number2 >

void FullMatrix< number >::vmult	(	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.

◆ vmult_add()

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.

◆ Tvmult()

template<typename number >

template<typename number2 >

void FullMatrix< number >::Tvmult	(	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 += A^T*v

if (!adding) w = A^T*v

Source and destination must not be the same vector.

◆ Tvmult_add()

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 += A^T*v

Source and destination must not be the same vector.

◆ precondition_Jacobi()

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.

◆ residual()

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.

◆ forward()

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.

◆ backward()

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.

◆ compress()

template<typename number >

void FullMatrix< number >::compress ( VectorOperation::values )

Dummy function for compatibility with distributed, parallel matrices.

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

include/deal.II/lac/full_matrix.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ size_type

◆ value_type

◆ iterator

◆ const_iterator

◆ real_type

Constructor & Destructor Documentation

◆ FullMatrix() [1/4]

◆ FullMatrix() [2/4]

◆ FullMatrix() [3/4]

◆ FullMatrix() [4/4]

Member Function Documentation

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ copy_from() [1/2]

◆ copy_transposed()

◆ copy_from() [2/2]

◆ copy_to()

◆ extract_submatrix_from()

◆ scatter_matrix_to()

◆ fill() [1/2]

◆ fill() [2/2]

◆ fill_permutation()

◆ set()

◆ operator==()

◆ m()

◆ n()

◆ all_zero()

◆ matrix_norm_square()

◆ matrix_scalar_product()

◆ l1_norm()

◆ linfty_norm()

◆ frobenius_norm()

◆ relative_symmetry_norm2()

◆ determinant()

◆ trace()

◆ print()

◆ print_formatted()

◆ memory_consumption()

◆ begin() [1/2]

◆ end() [1/2]

◆ begin() [2/2]

◆ end() [2/2]

◆ operator*=()

◆ operator/=()

◆ add() [1/6]

◆ add() [2/6]

◆ add() [3/6]

◆ add() [4/6]

◆ Tadd() [1/2]

◆ Tadd() [2/2]

◆ add() [5/6]

◆ add() [6/6]

◆ add_row() [1/2]

◆ add_row() [2/2]

◆ add_col() [1/2]

◆ add_col() [2/2]

◆ swap_row()

◆ swap_col()

◆ diagadd()

◆ equ() [1/3]

◆ equ() [2/3]

◆ equ() [3/3]

◆ symmetrize()

◆ gauss_jordan()

◆ invert()

◆ cholesky()

◆ outer_product()

◆ left_invert()

◆ right_invert()

◆ mmult()

◆ Tmmult()

◆ mTmult()

◆ TmTmult()