Class of matrices containing double complex, and stored as a DenseMatrix<complex<double> >, but with solving functionality inherited from the abstract ComplexMatrix class. More...

#include <complex_matrices.h>

Inheritance diagram for oomph::DenseComplexMatrix:

Public Member Functions
	DenseComplexMatrix ()
	Empty constructor, simply assign the lengths N and M to 0. More...

	DenseComplexMatrix (const unsigned long &n)
	Constructor to build a square n by n matrix. More...

	DenseComplexMatrix (const unsigned long &n, const unsigned long &m)
	Constructor to build a matrix with n rows and m columns. More...

	DenseComplexMatrix (const unsigned long &n, const unsigned long &m, const std::complex< double > &initial_val)
	Constructor to build a matrix with n rows and m columns, with initial value initial_val. More...

	DenseComplexMatrix (const DiagonalComplexMatrix &diagonal_matrix)
	Constructor to build a dense matrix from a diagonal matrix. More...

	DenseComplexMatrix (const DenseComplexMatrix &matrix)
	Broken copy constructor. More...

void	operator= (const DenseComplexMatrix &)
	Broken assignment operator. More...

unsigned long	nrow () const
	Return the number of rows of the matrix. More...

unsigned long	ncol () const
	Return the number of columns of the matrix. More...

std::complex< double >	operator() (const unsigned long &i, const unsigned long &j) const
	Overload the const version of the round-bracket access operator for read-only access. More...

std::complex< double > &	operator() (const unsigned long &i, const unsigned long &j)
	Overload the non-const version of the round-bracket access operator for read-write access. More...

virtual	~DenseComplexMatrix ()
	Destructor, delete the storage for Index vector and LU storage (if any) More...

int	ludecompose ()
	Overload the LU decomposition. For this storage scheme the matrix storage will be over-writeen by its LU decomposition. More...

void	lubksub (Vector< std::complex< double > > &rhs)
	Overload the LU back substitution. Note that the rhs will be overwritten with the solution vector. More...

void	residual (const Vector< std::complex< double > > &x, const Vector< std::complex< double > > &rhs, Vector< std::complex< double > > &residual)
	Find the residual of Ax=b, ie r=b-Ax for the "solution" x. More...

void	multiply (const Vector< std::complex< double > > &x, Vector< std::complex< double > > &soln)
	Multiply the matrix by the vector x: soln=Ax. More...

void	multiply_transpose (const Vector< std::complex< double > > &x, Vector< std::complex< double > > &soln)
	Multiply the transposed matrix by the vector x: soln=A^T x. More...

void	multiply (const DenseComplexMatrix &matrix_in, DenseComplexMatrix &result)
	Multiply this matrix by the DenseComplexMatrix matrix_in. More...

void	scale (const double &c)
	Scale this matrix by a double c. More...

void	scale (const std::complex< double > &c)
	Scale this matrix by a complex number c. More...

Public Member Functions inherited from oomph::ComplexMatrixBase
	ComplexMatrixBase ()
	(Empty) constructor. More...

	ComplexMatrixBase (const ComplexMatrixBase &matrix)
	Broken copy constructor. More...

void	operator= (const ComplexMatrixBase &)
	Broken assignment operator. More...

virtual	~ComplexMatrixBase ()
	virtual (empty) destructor More...

virtual void	solve (Vector< std::complex< double > > &rhs)
	Complete LU solve (replaces matrix by its LU decomposition and overwrites RHS with solution). The default should not need to be over-written. More...

virtual void	solve (const Vector< std::complex< double > > &rhs, Vector< std::complex< double > > &soln)
	Complete LU solve (Nothing gets overwritten!). The default should not need to be overwritten. More...

virtual double	max_residual (const Vector< std::complex< double > > &x, const Vector< std::complex< double > > &rhs)
	Find the maximum residual r=b-Ax – generic version, can be overloaded for specific derived classes where the max. can be determined "on the fly". More...

Public Member Functions inherited from oomph::DenseMatrix< std::complex< double > >
	DenseMatrix ()
	Empty constructor, simply assign the lengths N and M to 0. More...

	DenseMatrix (const DenseMatrix &source_matrix)
	Copy constructor: Deep copy! More...

	DenseMatrix (const unsigned long &n)
	Constructor to build a square n by n matrix. More...

	DenseMatrix (const unsigned long &n, const unsigned long &m)
	Constructor to build a matrix with n rows and m columns. More...

	DenseMatrix (const unsigned long &n, const unsigned long &m, const std::complex< double > &initial_val)
	Constructor to build a matrix with n rows and m columns, with initial value initial_val. More...

DenseMatrix &	operator= (const DenseMatrix &source_matrix)
	Copy assignment. More...

std::complex< double > &	entry (const unsigned long &i, const unsigned long &j)
	The access function that will be called by the read-write round-bracket operator. More...

std::complex< double >	get_entry (const unsigned long &i, const unsigned long &j) const
	The access function the will be called by the read-only (const version) round-bracket operator. More...

virtual	~DenseMatrix ()
	Destructor, clean up the matrix data. More...

unsigned long	nrow () const
	Return the number of rows of the matrix. More...

unsigned long	ncol () const
	Return the number of columns of the matrix. More...

void	resize (const unsigned long &n)

void	resize (const unsigned long &n, const unsigned long &m)
	Resize to a non-square n x m matrix; any values already present will be transfered. More...

void	resize (const unsigned long &n, const unsigned long &m, const std::complex< double > &initial_value)
	Resize to a non-square n x m matrix and initialize the new values to initial_value. More...

void	initialise (const std::complex< double > &val)
	Initialize all values in the matrix to val. More...

void	output (std::ostream &outfile) const
	Output function to print a matrix row-by-row to the stream outfile. More...

void	output (std::string filename) const
	Output function to print a matrix row-by-row to a file. Specify filename. More...

void	indexed_output (std::ostream &outfile) const
	Indexed output function to print a matrix to the stream outfile as i,j,a(i,j) More...

void	indexed_output (std::string filename) const
	Indexed output function to print a matrix to a file as i,j,a(i,j). Specify filename. More...

void	output_bottom_right_zero_helper (std::ostream &outfile) const
	Output the "bottom right" entry regardless of it being zero or not (this allows automatic detection of matrix size in e.g. matlab, python). More...

void	sparse_indexed_output_helper (std::ostream &outfile) const
	Indexed output function to print a matrix to the stream outfile as i,j,a(i,j) for a(i,j)!=0 only. More...

Public Member Functions inherited from oomph::Matrix< T, MATRIX_TYPE >
	Matrix ()
	(Empty) constructor More...

	Matrix (const Matrix &matrix)
	Broken copy constructor. More...

void	operator= (const Matrix &)
	Broken assignment operator. More...

virtual	~Matrix ()
	Virtual (empty) destructor. More...

T	operator() (const unsigned long &i, const unsigned long &j) const
	Round brackets to give access as a(i,j) for read only (we're not providing a general interface for component-wise write access since not all matrix formats allow efficient direct access!) The function uses the MATRIX_TYPE template parameter to call the get_entry() function which must be defined in all derived classes that are to be fully instantiated. More...

T &	operator() (const unsigned long &i, const unsigned long &j)
	Round brackets to give access as a(i,j) for read-write access. The function uses the MATRIX_TYPE template parameter to call the entry() function which must be defined in all derived classes that are to be fully instantiated. If the particular Matrix does not allow write access, the function should break with an error message. More...

void	sparse_indexed_output (std::ostream &outfile, const unsigned &precision=0, const bool &output_bottom_right_zero=false) const
	Indexed output function to print a matrix to the stream outfile as i,j,a(i,j) for a(i,j)!=0 only with specified precision (if precision=0 then nothing is changed). If optional boolean flag is set to true we also output the "bottom right" entry regardless of it being zero or not (this allows automatic detection of matrix size in e.g. matlab, python). More...

void	sparse_indexed_output (std::string filename, const unsigned &precision=0, const bool &output_bottom_right_zero=false) const
	Indexed output function to print a matrix to the file named filename as i,j,a(i,j) for a(i,j)!=0 only with specified precision. If optional boolean flag is set to true we also output the "bottom right" entry regardless of it being zero or not (this allows automatic detection of matrix size in e.g. matlab, python). More...

Private Member Functions
void	delete_lu_factors ()

Private Attributes
Vector< long > *	Index
	Pointer to storage for the index of permutations in the LU solve. More...

std::complex< double > *	LU_factors
	Pointer to storage for the LU decomposition. More...

bool	Overwrite_matrix_storage

Additional Inherited Members
Protected Member Functions inherited from oomph::Matrix< T, MATRIX_TYPE >
void	range_check (const unsigned long &i, const unsigned long &j) const
	Range check to catch when an index is out of bounds, if so, it issues a warning message and dies by throwing an `OomphLibError`. More...

Protected Attributes inherited from oomph::DenseMatrix< std::complex< double > >
std::complex< double > *	Matrixdata
	Internal representation of matrix as a pointer to data. More...

unsigned long	N
	Number of rows. More...

unsigned long	M
	Number of columns. More...

Detailed Description

Class of matrices containing double complex, and stored as a DenseMatrix<complex<double> >, but with solving functionality inherited from the abstract ComplexMatrix class.

Definition at line 213 of file complex_matrices.h.

Constructor & Destructor Documentation

◆ DenseComplexMatrix() [1/6]

oomph::DenseComplexMatrix::DenseComplexMatrix ( )

inline

Empty constructor, simply assign the lengths N and M to 0.

Definition at line 235 of file complex_matrices.h.

◆ DenseComplexMatrix() [2/6]

oomph::DenseComplexMatrix::DenseComplexMatrix ( const unsigned long & n )

inline

Constructor to build a square n by n matrix.

Definition at line 240 of file complex_matrices.h.

◆ DenseComplexMatrix() [3/6]

oomph::DenseComplexMatrix::DenseComplexMatrix	(	const unsigned long &	n,
		const unsigned long &	m
	)

inline

Constructor to build a matrix with n rows and m columns.

Definition at line 245 of file complex_matrices.h.

◆ DenseComplexMatrix() [4/6]

oomph::DenseComplexMatrix::DenseComplexMatrix	(	const unsigned long &	n,
		const unsigned long &	m,
		const std::complex< double > &	initial_val
	)

inline

Constructor to build a matrix with n rows and m columns, with initial value initial_val.

Definition at line 251 of file complex_matrices.h.

◆ DenseComplexMatrix() [5/6]

oomph::DenseComplexMatrix::DenseComplexMatrix ( const DiagonalComplexMatrix & diagonal_matrix )

inline

Constructor to build a dense matrix from a diagonal matrix.

Definition at line 258 of file complex_matrices.h.

References i, and oomph::DiagonalComplexMatrix::nrow().

◆ DenseComplexMatrix() [6/6]

oomph::DenseComplexMatrix::DenseComplexMatrix ( const DenseComplexMatrix & matrix )

inline

Broken copy constructor.

Definition at line 271 of file complex_matrices.h.

References oomph::BrokenCopy::broken_copy().

◆ ~DenseComplexMatrix()

oomph::DenseComplexMatrix::~DenseComplexMatrix ( )

virtual

Destructor, delete the storage for Index vector and LU storage (if any)

Destructor clean up the LU factors that have been allocated.

Definition at line 190 of file complex_matrices.cc.

Member Function Documentation

◆ delete_lu_factors()

void oomph::DenseComplexMatrix::delete_lu_factors ( )

private

Function that deletes the storage for the LU_factors, if it is not the same as the matrix storage

Delete the storage that has been allocated for the LU factors, if the matrix data is not itself being overwritten.

Definition at line 172 of file complex_matrices.cc.

◆ lubksub()

void oomph::DenseComplexMatrix::lubksub ( Vector< std::complex< double > > & rhs )

virtual

Overload the LU back substitution. Note that the rhs will be overwritten with the solution vector.

Back substitute an LU decomposed matrix.

Reimplemented from oomph::ComplexMatrixBase.

Definition at line 450 of file complex_matrices.cc.

References i, and oomph::QuadTreeNames::N.

◆ ludecompose()

int oomph::DenseComplexMatrix::ludecompose ( )

virtual

Overload the LU decomposition. For this storage scheme the matrix storage will be over-writeen by its LU decomposition.

LU decompose a matrix, over-writing it and recording the pivots numbers in the Index vector. Returns the sign of the determinant.

Reimplemented from oomph::ComplexMatrixBase.

Definition at line 208 of file complex_matrices.cc.

References i, and oomph::QuadTreeNames::N.

◆ multiply() [1/2]

void oomph::DenseComplexMatrix::multiply	(	const Vector< std::complex< double > > &	x,
		Vector< std::complex< double > > &	soln
	)

virtual

Multiply the matrix by the vector x: soln=Ax.

Implements oomph::ComplexMatrixBase.

Definition at line 587 of file complex_matrices.cc.

References i, and oomph::QuadTreeNames::N.

Referenced by oomph::Conformal2DPMLElement::assemble_conformal_jacobian(), oomph::TangentiallyVaryingConformal2DPMLElement::assemble_conformal_jacobian(), and oomph::AnnularPMLElementBase::radial_to_cartesian_jacobian().

◆ multiply() [2/2]

void oomph::DenseComplexMatrix::multiply	(	const DenseComplexMatrix &	matrix_in,
		DenseComplexMatrix &	result
	)

Multiply this matrix by the DenseComplexMatrix matrix_in.

Function to multiply this matrix by the DenseComplexMatrix matrix_in.

Definition at line 675 of file complex_matrices.cc.

References i, oomph::ComplexMatrixBase::ncol(), ncol(), oomph::ComplexMatrixBase::nrow(), nrow(), and oomph::DenseMatrix< T >::resize().

◆ multiply_transpose()

void oomph::DenseComplexMatrix::multiply_transpose	(	const Vector< std::complex< double > > &	x,
		Vector< std::complex< double > > &	soln
	)

virtual

Multiply the transposed matrix by the vector x: soln=A^T x.

Implements oomph::ComplexMatrixBase.

Definition at line 628 of file complex_matrices.cc.

References i, and oomph::QuadTreeNames::N.

◆ ncol()

unsigned long oomph::DenseComplexMatrix::ncol ( ) const

inlinevirtual

Return the number of columns of the matrix.

Implements oomph::ComplexMatrixBase.

Definition at line 288 of file complex_matrices.h.

References oomph::ComplexMatrixBase::ncol().

Referenced by oomph::PMLElementBase< 2 >::compute_laplace_matrix_and_det(), oomph::TangentiallyDiscontinuousConformal2DPMLElement::compute_transformed_normal_derivative(), and multiply().

◆ nrow()

unsigned long oomph::DenseComplexMatrix::nrow ( ) const

inlinevirtual

Return the number of rows of the matrix.

Implements oomph::ComplexMatrixBase.

Definition at line 284 of file complex_matrices.h.

References oomph::ComplexMatrixBase::nrow().

Referenced by oomph::PMLElementBase< 2 >::compute_laplace_matrix_and_det(), oomph::TangentiallyDiscontinuousConformal2DPMLElement::compute_transformed_normal_derivative(), and multiply().

◆ operator()() [1/2]

std::complex<double> oomph::DenseComplexMatrix::operator()	(	const unsigned long &	i,
		const unsigned long &	j
	)		const

inlinevirtual

Overload the const version of the round-bracket access operator for read-only access.

Implements oomph::ComplexMatrixBase.

Definition at line 293 of file complex_matrices.h.

◆ operator()() [2/2]

std::complex<double>& oomph::DenseComplexMatrix::operator()	(	const unsigned long &	i,
		const unsigned long &	j
	)

inline

Overload the non-const version of the round-bracket access operator for read-write access.

Definition at line 299 of file complex_matrices.h.

References oomph::ComplexMatrixBase::lubksub(), oomph::ComplexMatrixBase::ludecompose(), oomph::ComplexMatrixBase::multiply(), oomph::ComplexMatrixBase::multiply_transpose(), and oomph::ComplexMatrixBase::residual().

◆ operator=()

void oomph::DenseComplexMatrix::operator= ( const DenseComplexMatrix & )

inline

Broken assignment operator.

Definition at line 277 of file complex_matrices.h.

References oomph::BrokenCopy::broken_assign().

◆ residual()

void oomph::DenseComplexMatrix::residual	(	const Vector< std::complex< double > > &	x,
		const Vector< std::complex< double > > &	rhs,
		Vector< std::complex< double > > &	residual
	)

virtual

Find the residual of Ax=b, ie r=b-Ax for the "solution" x.

Find the residual of Ax=b, i.e. r=b-Ax.

Implements oomph::ComplexMatrixBase.

Definition at line 526 of file complex_matrices.cc.

References i, oomph::QuadTreeNames::N, and oomph::ComplexMatrixBase::residual().

◆ scale() [1/2]

void oomph::DenseComplexMatrix::scale ( const double & c )

Scale this matrix by a double c.

Scale the matrix by the real c.

Definition at line 719 of file complex_matrices.cc.

References i, and oomph::QuadTreeNames::N.

◆ scale() [2/2]

void oomph::DenseComplexMatrix::scale ( const std::complex< double > & c )

Scale this matrix by a complex number c.

Scale the matrix by the complex number c.

Definition at line 734 of file complex_matrices.cc.

References i, oomph::QuadTreeNames::N, and oomph::superlu_complex().

Member Data Documentation

◆ Index

Vector<long>* oomph::DenseComplexMatrix::Index

private

Pointer to storage for the index of permutations in the LU solve.

Definition at line 219 of file complex_matrices.h.

◆ LU_factors

std::complex<double>* oomph::DenseComplexMatrix::LU_factors

private

Pointer to storage for the LU decomposition.

Definition at line 222 of file complex_matrices.h.

◆ Overwrite_matrix_storage

bool oomph::DenseComplexMatrix::Overwrite_matrix_storage

private

Boolean flag used to decided whether the LU decomposition is stored separately, or not

Definition at line 226 of file complex_matrices.h.

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

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ DenseComplexMatrix() [1/6]

◆ DenseComplexMatrix() [2/6]

◆ DenseComplexMatrix() [3/6]

◆ DenseComplexMatrix() [4/6]

◆ DenseComplexMatrix() [5/6]

◆ DenseComplexMatrix() [6/6]

◆ ~DenseComplexMatrix()

Member Function Documentation

◆ delete_lu_factors()

◆ lubksub()

◆ ludecompose()

◆ multiply() [1/2]

◆ multiply() [2/2]

◆ multiply_transpose()

◆ ncol()

◆ nrow()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=()

◆ residual()

◆ scale() [1/2]

◆ scale() [2/2]

Member Data Documentation

◆ Index

◆ LU_factors

◆ Overwrite_matrix_storage