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

Inheritance diagram for LAPACKFullMatrix< number >:

Public Types
typedef types::global_dof_index	size_type

Public Types inherited from TransposeTable< number >
typedef TableBase< 2, number >::size_type	size_type

Public Types inherited from TableBase< 2, number >
typedef AlignedVector< number >::size_type	size_type

Public Member Functions
	LAPACKFullMatrix (const size_type size=0)

	LAPACKFullMatrix (const size_type rows, const size_type cols)

	LAPACKFullMatrix (const LAPACKFullMatrix &)

LAPACKFullMatrix< number > &	operator= (const LAPACKFullMatrix< number > &)

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

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

LAPACKFullMatrix< number > &	operator= (const double d)

LAPACKFullMatrix< number > &	operator*= (const number factor)

LAPACKFullMatrix< number > &	operator/= (const number factor)

template<typename MatrixType >
void	copy_from (const MatrixType &)

void	reinit (const size_type size)

void	reinit (const size_type rows, const size_type cols)

unsigned int	m () const

unsigned int	n () const

template<typename MatrixType >
void	fill (const MatrixType &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, const number factor=1., const bool transpose=false)

template<typename number2 >
void	vmult (Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const

void	vmult (Vector< number > &w, const Vector< number > &v, const bool adding=false) const

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

void	vmult_add (Vector< number > &w, const Vector< number > &v) const

template<typename number2 >
void	Tvmult (Vector< number2 > &w, const Vector< number2 > &v, const bool adding=false) const

void	Tvmult (Vector< number > &w, const Vector< number > &v, const bool adding=false) const

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

void	Tvmult_add (Vector< number > &w, const Vector< number > &v) const

void	mmult (LAPACKFullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	mmult (FullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	Tmmult (LAPACKFullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	Tmmult (FullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	mTmult (LAPACKFullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	mTmult (FullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	TmTmult (LAPACKFullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	TmTmult (FullMatrix< number > &C, const LAPACKFullMatrix< number > &B, const bool adding=false) const

void	compute_lu_factorization ()

void	invert ()

void	apply_lu_factorization (Vector< number > &v, const bool transposed) const

void	apply_lu_factorization (LAPACKFullMatrix< number > &B, const bool transposed) const

void	compute_eigenvalues (const bool right_eigenvectors=false, const bool left_eigenvectors=false)

void	compute_eigenvalues_symmetric (const number lower_bound, const number upper_bound, const number abs_accuracy, Vector< number > &eigenvalues, FullMatrix< number > &eigenvectors)

void	compute_generalized_eigenvalues_symmetric (LAPACKFullMatrix< number > &B, const number lower_bound, const number upper_bound, const number abs_accuracy, Vector< number > &eigenvalues, std::vector< Vector< number > > &eigenvectors, const int itype=1)

void	compute_generalized_eigenvalues_symmetric (LAPACKFullMatrix< number > &B, std::vector< Vector< number > > &eigenvectors, const int itype=1)

void	compute_svd ()

void	compute_inverse_svd (const double threshold=0.)

std::complex< number >	eigenvalue (const size_type i) const

number	singular_value (const size_type i) 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

Public Member Functions inherited from TransposeTable< number >
	TransposeTable ()

	TransposeTable (const unsigned int size1, const unsigned int size2)

void	reinit (const unsigned int size1, const unsigned int size2, const bool omit_default_initialization=false)

AlignedVector< number >::const_reference	operator() (const unsigned int i, const unsigned int j) const

AlignedVector< number >::reference	operator() (const unsigned int i, const unsigned int j)

unsigned int	n_rows () const

unsigned int	n_cols () const

Public Member Functions inherited from TableBase< 2, number >
	TableBase ()

	TableBase (const TableIndices< N > &sizes)

	TableBase (const TableIndices< N > &sizes, InputIterator entries, const bool C_style_indexing=true)

	TableBase (const TableBase< N, number > &src)

	TableBase (const TableBase< N, T2 > &src)

	TableBase (TableBase< N, number > &&src)

	~TableBase ()

TableBase< N, number > &	operator= (const TableBase< N, number > &src)

TableBase< N, number > &	operator= (const TableBase< N, T2 > &src)

TableBase< N, number > &	operator= (TableBase< N, number > &&src)

bool	operator== (const TableBase< N, number > &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

void	fill (InputIterator entries, const bool C_style_indexing=true)

void	fill (const number &value)

AlignedVector< number >::reference	operator() (const TableIndices< N > &indices)

AlignedVector< number >::const_reference	operator() (const TableIndices< N > &indices) const

void	swap (TableBase< N, number > &v)

std::size_t	memory_consumption () const

void	serialize (Archive &ar, const unsigned int version)

Public 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)

Private Attributes
LAPACKSupport::State	state

LAPACKSupport::Properties	properties

std::vector< number >	work

std::vector< int >	ipiv

std::vector< number >	inv_work

std::vector< number >	wr

std::vector< number >	wi

std::vector< number >	vl

std::vector< number >	vr

std_cxx11::shared_ptr< LAPACKFullMatrix< number > >	svd_u

std_cxx11::shared_ptr< LAPACKFullMatrix< number > >	svd_vt

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

static ::ExceptionBase &	ExcNoSubscriber (char arg1, char arg2)

Protected Member Functions inherited from TransposeTable< number >
AlignedVector< number >::reference	el (const unsigned int i, const unsigned int j)

AlignedVector< number >::const_reference	el (const unsigned int i, const unsigned int j) const

Protected Member Functions inherited from TableBase< 2, number >
size_type	position (const TableIndices< N > &indices) const

AlignedVector< number >::reference	el (const TableIndices< N > &indices)

AlignedVector< number >::const_reference	el (const TableIndices< N > &indices) const

Protected Attributes inherited from TableBase< 2, number >
AlignedVector< number >	values

TableIndices< N >	table_size

Detailed Description

template<typename number>
class LAPACKFullMatrix< number >

A variant of FullMatrix using LAPACK functions wherever possible. In order to do this, the matrix is stored in transposed order. The element access functions hide this fact by reverting the transposition.

Note: In order to perform LAPACK functions, the class contains a lot of auxiliary data in the private section. The names of these data vectors are usually the names chosen for the arguments in the LAPACK documentation.

Author: Guido Kanschat, 2005

Definition at line 36 of file full_matrix.h.

Member Typedef Documentation

◆ size_type

template<typename number>

typedef types::global_dof_index LAPACKFullMatrix< number >::size_type

Declare type for container size.

Definition at line 59 of file lapack_full_matrix.h.

Constructor & Destructor Documentation

◆ LAPACKFullMatrix() [1/3]

template<typename number >

LAPACKFullMatrix< number >::LAPACKFullMatrix ( const size_type size = 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.

Definition at line 33 of file lapack_full_matrix.cc.

◆ LAPACKFullMatrix() [2/3]

template<typename number >

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

Constructor. Initialize the matrix as a rectangular matrix.

Definition at line 41 of file lapack_full_matrix.cc.

◆ LAPACKFullMatrix() [3/3]

template<typename number >

LAPACKFullMatrix< number >::LAPACKFullMatrix ( const LAPACKFullMatrix< number > & M )

Copy constructor. This constructor does a deep copy of the matrix. Therefore, it poses a possible efficiency problem, if for example, function arguments are passed by value rather than by reference. Unfortunately, we can't mark this copy constructor explicit, since that prevents the use of this class in containers, such as std::vector. The responsibility to check performance of programs must therefore remain with the user of this class.

Definition at line 50 of file lapack_full_matrix.cc.

Member Function Documentation

◆ operator=() [1/4]

template<typename number>

LAPACKFullMatrix< number > & LAPACKFullMatrix< number >::operator= ( const LAPACKFullMatrix< number > & M )

Assignment operator.

Definition at line 59 of file lapack_full_matrix.cc.

◆ operator=() [2/4]

template<typename number >

template<typename number2 >

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

Assignment operator from a regular FullMatrix.

Note: Since LAPACK expects matrices in transposed order, this transposition is included here.

Definition at line 89 of file lapack_full_matrix.cc.

◆ operator=() [3/4]

template<typename number >

template<typename number2 >

LAPACKFullMatrix< number > & LAPACKFullMatrix< number >::operator= ( const SparseMatrix< number2 > & M )

Assignment operator from a regular SparseMatrix.

Note: Since LAPACK expects matrices in transposed order, this transposition is included here.

Definition at line 105 of file lapack_full_matrix.cc.

◆ operator=() [4/4]

template<typename number>

LAPACKFullMatrix< number > & LAPACKFullMatrix< number >::operator= ( const double d )

This operator assigns a scalar to a matrix. To avoid confusion with constructors, zero is the only value allowed for d

Definition at line 120 of file lapack_full_matrix.cc.

◆ operator*=()

template<typename number>

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

This operator multiplies all entries by a fixed factor.

Definition at line 135 of file lapack_full_matrix.cc.

◆ operator/=()

template<typename number>

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

This operator divides all entries by a fixed factor.

Definition at line 151 of file lapack_full_matrix.cc.

◆ copy_from()

template<typename number >

template<typename MatrixType >

void LAPACKFullMatrix< number >::copy_from ( const MatrixType & M )

inline

Assignment from different matrix classes, performing the usual conversion to the transposed format expected by LAPACK. This assignment operator uses iterators of the typename MatrixType. Therefore, sparse matrices are possible sources.

Definition at line 723 of file lapack_full_matrix.h.

◆ reinit() [1/2]

template<typename number >

void LAPACKFullMatrix< number >::reinit ( const size_type size )

Regenerate the current matrix by one that has the same properties as if it were created by the constructor of this class with the same argument list as this present function.

Definition at line 69 of file lapack_full_matrix.cc.

◆ reinit() [2/2]

template<typename number >

void LAPACKFullMatrix< number >::reinit	(	const size_type	rows,
		const size_type	cols
	)

Regenerate the current matrix by one that has the same properties as if it were created by the constructor of this class with the same argument list as this present function.

Definition at line 78 of file lapack_full_matrix.cc.

◆ m()

template<typename number >

unsigned int LAPACKFullMatrix< number >::m ( ) const

inline

Return the dimension of the codomain (or range) space.

Note: The matrix is of dimension \(m \times n\).

Definition at line 707 of file lapack_full_matrix.h.

◆ n()

template<typename number >

unsigned int LAPACKFullMatrix< number >::n ( ) const

inline

Return the dimension of the domain space.

Note: The matrix is of dimension \(m \times n\).

Definition at line 715 of file lapack_full_matrix.h.

◆ fill()

template<typename number>

template<typename MatrixType >

void LAPACKFullMatrix< number >::fill	(	const MatrixType &	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`,
		const number	factor = `1.`,
		const bool	transpose = `false`
	)

inline

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.

The final two arguments allow to enter a multiple of the source or its transpose.

Definition at line 746 of file lapack_full_matrix.h.

◆ vmult() [1/2]

template<typename number >

template<typename number2 >

void LAPACKFullMatrix< number >::vmult	(	Vector< number2 > &	w,
		const Vector< number2 > &	v,
		const bool	adding = `false`
	)		const

Matrix-vector-multiplication.

Depending on previous transformations recorded in state, the result of this function is one of

If state is LAPACKSupport::matrix or LAPACKSupport::inverse_matrix, this will be a regular matrix vector product using LAPACK gemv().
If state is LAPACKSupport::svd or LAPACKSupport::inverse_svd, this function first multiplies with the right transformation matrix, then with the diagonal matrix of singular values or their reciprocal values, and finally with the left transformation matrix.

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

Note: Source and destination must not be the same vector.; The template with number2 only exists for compile-time compatibility with FullMatrix. Only the case number2 = number is implemented due to limitations in the underlying LAPACK interface. All other variants throw an error upon invocation.

Definition at line 779 of file lapack_full_matrix.h.

◆ vmult() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::vmult	(	Vector< number > &	w,
		const Vector< number > &	v,
		const bool	adding = `false`
	)		const

Specialization of above function for compatible Vector::value_type.

Definition at line 170 of file lapack_full_matrix.cc.

◆ vmult_add() [1/2]

template<typename number >

template<typename number2 >

void LAPACKFullMatrix< number >::vmult_add	(	Vector< number2 > &	w,
		const Vector< number2 > &	v
	)		const

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

See the documentation of vmult() for details on the implementation.

Definition at line 792 of file lapack_full_matrix.h.

◆ vmult_add() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::vmult_add	(	Vector< number > &	w,
		const Vector< number > &	v
	)		const

Specialization of above function for compatible Vector::value_type.

Definition at line 288 of file lapack_full_matrix.cc.

◆ Tvmult() [1/2]

template<typename number >

template<typename number2 >

void LAPACKFullMatrix< 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

See the documentation of vmult() for details on the implementation.

Definition at line 804 of file lapack_full_matrix.h.

◆ Tvmult() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::Tvmult	(	Vector< number > &	w,
		const Vector< number > &	v,
		const bool	adding = `false`
	)		const

Specialization of above function for compatible Vector::value_type.

Definition at line 228 of file lapack_full_matrix.cc.

◆ Tvmult_add() [1/2]

template<typename number >

template<typename number2 >

void LAPACKFullMatrix< number >::Tvmult_add	(	Vector< number2 > &	w,
		const Vector< number2 > &	v
	)		const

Adding transpose matrix-vector-multiplication. w += A^T*v

See the documentation of vmult() for details on the implementation.

Definition at line 817 of file lapack_full_matrix.h.

◆ Tvmult_add() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::Tvmult_add	(	Vector< number > &	w,
		const Vector< number > &	v
	)		const

Specialization of above function for compatible Vector::value_type.

Definition at line 297 of file lapack_full_matrix.cc.

◆ mmult() [1/2]

template<typename number>

void LAPACKFullMatrix< number >::mmult	(	LAPACKFullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	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.

Definition at line 306 of file lapack_full_matrix.cc.

◆ mmult() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::mmult	(	FullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	B,
		const bool	adding = `false`
	)		const

Same as before, but stores the result in a FullMatrix, not in a LAPACKFullMatrix.

Definition at line 329 of file lapack_full_matrix.cc.

◆ Tmmult() [1/2]

template<typename number>

void LAPACKFullMatrix< number >::Tmmult	(	LAPACKFullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	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.

Definition at line 354 of file lapack_full_matrix.cc.

◆ Tmmult() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::Tmmult	(	FullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	B,
		const bool	adding = `false`
	)		const

Same as before, but stores the result in a FullMatrix, not in a LAPACKFullMatrix.

Definition at line 377 of file lapack_full_matrix.cc.

◆ mTmult() [1/2]

template<typename number>

void LAPACKFullMatrix< number >::mTmult	(	LAPACKFullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	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.

Definition at line 401 of file lapack_full_matrix.cc.

◆ mTmult() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::mTmult	(	FullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	B,
		const bool	adding = `false`
	)		const

Same as before, but stores the result in a FullMatrix, not in a LAPACKFullMatrix.

Definition at line 425 of file lapack_full_matrix.cc.

◆ TmTmult() [1/2]

template<typename number>

void LAPACKFullMatrix< number >::TmTmult	(	LAPACKFullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	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.

Definition at line 449 of file lapack_full_matrix.cc.

◆ TmTmult() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::TmTmult	(	FullMatrix< number > &	C,
		const LAPACKFullMatrix< number > &	B,
		const bool	adding = `false`
	)		const

Same as before, but stores the result in a FullMatrix, not in a LAPACKFullMatrix.

Definition at line 472 of file lapack_full_matrix.cc.

◆ compute_lu_factorization()

template<typename number >

void LAPACKFullMatrix< number >::compute_lu_factorization ( )

Compute the LU factorization of the matrix using LAPACK function Xgetrf.

Definition at line 496 of file lapack_full_matrix.cc.

◆ invert()

template<typename number >

void LAPACKFullMatrix< number >::invert ( )

Invert the matrix by first computing an LU factorization with the LAPACK function Xgetrf and then building the actual inverse using Xgetri.

Definition at line 585 of file lapack_full_matrix.cc.

◆ apply_lu_factorization() [1/2]

template<typename number>

void LAPACKFullMatrix< number >::apply_lu_factorization	(	Vector< number > &	v,
		const bool	transposed
	)		const

Solve the linear system with right hand side given by applying forward/backward substitution to the previously computed LU factorization. Uses LAPACK function Xgetrs.

The flag transposed indicates whether the solution of the transposed system is to be performed.

Definition at line 617 of file lapack_full_matrix.cc.

◆ apply_lu_factorization() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::apply_lu_factorization	(	LAPACKFullMatrix< number > &	B,
		const bool	transposed
	)		const

Solve the linear system with multiple right hand sides (as many as there are columns in the matrix b) given by applying forward/backward substitution to the previously computed LU factorization. Uses LAPACK function Xgetrs.

The flag transposed indicates whether the solution of the transposed system is to be performed.

Definition at line 639 of file lapack_full_matrix.cc.

◆ compute_eigenvalues()

template<typename number >

void LAPACKFullMatrix< number >::compute_eigenvalues	(	const bool	right_eigenvectors = `false`,
		const bool	left_eigenvectors = `false`
	)

Compute eigenvalues of the matrix. After this routine has been called, eigenvalues can be retrieved using the eigenvalue() function. The matrix itself will be LAPACKSupport::unusable after this operation.

The optional arguments allow to compute left and right eigenvectors as well.

Note that the function does not return the computed eigenvalues right away since that involves copying data around between the output arrays of the LAPACK functions and any return array. This is often unnecessary since one may not be interested in all eigenvalues at once, but for example only the extreme ones. In that case, it is cheaper to just have this function compute the eigenvalues and have a separate function that returns whatever eigenvalue is requested.

Note: Calls the LAPACK function Xgeev.

Definition at line 661 of file lapack_full_matrix.cc.

◆ compute_eigenvalues_symmetric()

template<typename number>

void LAPACKFullMatrix< number >::compute_eigenvalues_symmetric	(	const number	lower_bound,
		const number	upper_bound,
		const number	abs_accuracy,
		Vector< number > &	eigenvalues,
		FullMatrix< number > &	eigenvectors
	)

Compute eigenvalues and eigenvectors of a real symmetric matrix. Only eigenvalues in the interval (lower_bound, upper_bound] are computed with the absolute tolerance abs_accuracy. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to abs_accuracy + eps * max( |a|,|b| ), where eps is the machine precision. If abs_accuracy is less than or equal to zero, then eps*|t| will be used in its place, where |t| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when abs_accuracy is set to twice the underflow threshold, not zero. After this routine has been called, all eigenvalues in (lower_bound, upper_bound] will be stored in eigenvalues and the corresponding eigenvectors will be stored in the columns of eigenvectors, whose dimension is set accordingly.

Note: Calls the LAPACK function Xsyevx. For this to work, deal.II must be configured to use LAPACK.

Definition at line 722 of file lapack_full_matrix.cc.

◆ compute_generalized_eigenvalues_symmetric() [1/2]

template<typename number>

void LAPACKFullMatrix< number >::compute_generalized_eigenvalues_symmetric	(	LAPACKFullMatrix< number > &	B,
		const number	lower_bound,
		const number	upper_bound,
		const number	abs_accuracy,
		Vector< number > &	eigenvalues,
		std::vector< Vector< number > > &	eigenvectors,
		const int	itype = `1`
	)

Compute generalized eigenvalues and eigenvectors of a real generalized symmetric eigenproblem of the form itype = 1: \(Ax=\lambda B x\) itype = 2: \(ABx=\lambda x\) itype = 3: \(BAx=\lambda x\), where A is this matrix. A and B are assumed to be symmetric, and B has to be positive definite. Only eigenvalues in the interval (lower_bound, upper_bound] are computed with the absolute tolerance abs_accuracy. An approximate eigenvalue is accepted as converged when it is determined to lie in an interval [a,b] of width less than or equal to abs_accuracy + eps * max( |a|,|b| ), where eps is the machine precision. If abs_accuracy is less than or equal to zero, then eps*|t| will be used in its place, where |t| is the 1-norm of the tridiagonal matrix obtained by reducing A to tridiagonal form. Eigenvalues will be computed most accurately when abs_accuracy is set to twice the underflow threshold, not zero. After this routine has been called, all eigenvalues in (lower_bound, upper_bound] will be stored in eigenvalues and the corresponding eigenvectors will be stored in eigenvectors, whose dimension is set accordingly.

Note: Calls the LAPACK function Xsygvx. For this to work, deal.II must be configured to use LAPACK.

Definition at line 808 of file lapack_full_matrix.cc.

◆ compute_generalized_eigenvalues_symmetric() [2/2]

template<typename number>

void LAPACKFullMatrix< number >::compute_generalized_eigenvalues_symmetric	(	LAPACKFullMatrix< number > &	B,
		std::vector< Vector< number > > &	eigenvectors,
		const int	itype = `1`
	)

Same as the other compute_generalized_eigenvalues_symmetric function except that all eigenvalues are computed and the tolerance is set automatically. Note that this function does not return the computed eigenvalues right away since that involves copying data around between the output arrays of the LAPACK functions and any return array. This is often unnecessary since one may not be interested in all eigenvalues at once, but for example only the extreme ones. In that case, it is cheaper to just have this function compute the eigenvalues and have a separate function that returns whatever eigenvalue is requested. Eigenvalues can be retrieved using the eigenvalue() function. The number of computed eigenvectors is equal to eigenvectors.size()

Note: Calls the LAPACK function Xsygv. For this to work, deal.II must be configured to use LAPACK.

Definition at line 900 of file lapack_full_matrix.cc.

◆ compute_svd()

template<typename number >

void LAPACKFullMatrix< number >::compute_svd ( )

Compute the singular value decomposition of the matrix using LAPACK function Xgesdd.

Requires that the state is LAPACKSupport::matrix, fills the data members wr, svd_u, and svd_vt, and leaves the object in the state LAPACKSupport::svd.

Definition at line 519 of file lapack_full_matrix.cc.

◆ compute_inverse_svd()

template<typename number >

void LAPACKFullMatrix< number >::compute_inverse_svd ( const double threshold = 0. )

Compute the inverse of the matrix by singular value decomposition.

Requires that state is either LAPACKSupport::matrix or LAPACKSupport::svd. In the first case, this function calls compute_svd(). After this function, the object will have the state LAPACKSupport::inverse_svd.

For a singular value decomposition, the inverse is simply computed by replacing all singular values by their reciprocal values. If the matrix does not have maximal rank, singular values 0 are not touched, thus computing the minimal norm right inverse of the matrix.

The parameter threshold determines, when a singular value should be considered zero. It is the ratio of the smallest to the largest nonzero singular value s_max. Thus, the inverses of all singular values less than s_max/threshold will be set to zero.

Definition at line 564 of file lapack_full_matrix.cc.

◆ eigenvalue()

template<typename number >

std::complex< number > LAPACKFullMatrix< number >::eigenvalue ( const size_type i ) const

inline

Retrieve eigenvalue after compute_eigenvalues() was called.

Definition at line 828 of file lapack_full_matrix.h.

◆ singular_value()

template<typename number >

number LAPACKFullMatrix< number >::singular_value ( const size_type i ) const

inline

Retrieve singular values after compute_svd() or compute_inverse_svd() was called.

Definition at line 841 of file lapack_full_matrix.h.

◆ print_formatted()

template<typename number >

void LAPACKFullMatrix< 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.

Note: The entries stored resemble a matrix only if the state is either LAPACKSupport::matrix or LAPACK::inverse_matrix. Otherwise, calling this function is not allowed.

Definition at line 975 of file lapack_full_matrix.cc.

Member Data Documentation

◆ state

template<typename number>

LAPACKSupport::State LAPACKFullMatrix< number >::state

private

Since LAPACK operations notoriously change the meaning of the matrix entries, we record the current state after the last operation here.

Definition at line 614 of file lapack_full_matrix.h.

◆ properties

template<typename number>

LAPACKSupport::Properties LAPACKFullMatrix< number >::properties

private

Additional properties of the matrix which may help to select more efficient LAPACK functions.

Definition at line 620 of file lapack_full_matrix.h.

◆ work

template<typename number>

std::vector<number> LAPACKFullMatrix< number >::work

mutableprivate

The working array used for some LAPACK functions.

Definition at line 625 of file lapack_full_matrix.h.

◆ ipiv

template<typename number>

std::vector<int> LAPACKFullMatrix< number >::ipiv

private

The vector storing the permutations applied for pivoting in the LU- factorization.

Also used as the scratch array IWORK for LAPACK functions needing it.

Definition at line 633 of file lapack_full_matrix.h.

◆ inv_work

template<typename number>

std::vector<number> LAPACKFullMatrix< number >::inv_work

private

Workspace for calculating the inverse matrix from an LU factorization.

Definition at line 638 of file lapack_full_matrix.h.

◆ wr

template<typename number>

std::vector<number> LAPACKFullMatrix< number >::wr

private

Real parts of eigenvalues or the singular values. Filled by compute_eigenvalues() or compute_svd().

Definition at line 644 of file lapack_full_matrix.h.

◆ wi

template<typename number>

std::vector<number> LAPACKFullMatrix< number >::wi

private

Imaginary parts of eigenvalues. Filled by compute_eigenvalues.

Definition at line 649 of file lapack_full_matrix.h.

◆ vl

template<typename number>

std::vector<number> LAPACKFullMatrix< number >::vl

private

Space where left eigenvectors can be stored.

Definition at line 654 of file lapack_full_matrix.h.

◆ vr

template<typename number>

std::vector<number> LAPACKFullMatrix< number >::vr

private

Space where right eigenvectors can be stored.

Definition at line 659 of file lapack_full_matrix.h.

◆ svd_u

template<typename number>

std_cxx11::shared_ptr<LAPACKFullMatrix<number> > LAPACKFullMatrix< number >::svd_u

private

The matrix U in the singular value decomposition USV^T.

Definition at line 665 of file lapack_full_matrix.h.

◆ svd_vt

template<typename number>

std_cxx11::shared_ptr<LAPACKFullMatrix<number> > LAPACKFullMatrix< number >::svd_vt

private

The matrix V^T in the singular value decomposition USV^T.

Definition at line 671 of file lapack_full_matrix.h.

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

deal.II/lac/full_matrix.h
deal.II/lac/lapack_full_matrix.h
source/lac/lapack_full_matrix.cc

Public Types

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename number> class LAPACKFullMatrix< number >

Member Typedef Documentation

◆ size_type

Constructor & Destructor Documentation

◆ LAPACKFullMatrix() [1/3]

◆ LAPACKFullMatrix() [2/3]

◆ LAPACKFullMatrix() [3/3]

Member Function Documentation

◆ operator=() [1/4]

◆ operator=() [2/4]

◆ operator=() [3/4]

◆ operator=() [4/4]

◆ operator*=()

◆ operator/=()

◆ copy_from()

◆ reinit() [1/2]

◆ reinit() [2/2]

◆ m()

◆ n()

◆ fill()

◆ vmult() [1/2]

◆ vmult() [2/2]

◆ vmult_add() [1/2]

◆ vmult_add() [2/2]

◆ Tvmult() [1/2]

◆ Tvmult() [2/2]

◆ Tvmult_add() [1/2]

◆ Tvmult_add() [2/2]

◆ mmult() [1/2]

◆ mmult() [2/2]

◆ Tmmult() [1/2]

◆ Tmmult() [2/2]

◆ mTmult() [1/2]

◆ mTmult() [2/2]

◆ TmTmult() [1/2]

◆ TmTmult() [2/2]

◆ compute_lu_factorization()

◆ invert()

◆ apply_lu_factorization() [1/2]

◆ apply_lu_factorization() [2/2]

◆ compute_eigenvalues()

◆ compute_eigenvalues_symmetric()

◆ compute_generalized_eigenvalues_symmetric() [1/2]

◆ compute_generalized_eigenvalues_symmetric() [2/2]

◆ compute_svd()

◆ compute_inverse_svd()

◆ eigenvalue()

◆ singular_value()

◆ print_formatted()

Member Data Documentation

◆ state

◆ properties

◆ work

◆ ipiv

◆ inv_work

◆ wr

◆ wi

◆ vl

◆ vr

◆ svd_u

◆ svd_vt

template<typename number>
class LAPACKFullMatrix< number >